-------------------------------------------- The Artemisia-10 Tuning in MET-24 Exploring Mohajira-7 Sets and Modes -------------------------------------------- [CAUTION: This is a first draft which needs proofreading, ideally not only by me but by others.] The tuning system called Artemisia-10, in honor of the famed Artemisia, Queen of Halicarnassus (fl. c. 480 BCE), grows out of two great musical traditions. The first is the ancient Greek tradition to which Artemisia herself belongs, and more specifically the Archytas Chromatic, whose disjunct form (see below) provides one element of this tuning. The second is the Near Eastern tradition, and especially its centrally important aspect exemplified by the `oudist Mansur Zalzal (?-791) who flourished in 8th-century Baghdad, and is credited for adding to the `oud a middle third fret, called the wusta Zalzal or middle finger fret of Zalzal. Various later theorists such as al-Farabi (c. 870-950), Ibn Sina (c. 980-1037), and Safi al-Din al-Urmawi (c. 1216-1294) discuss different possible locations for this fret of Zalzal, with al-Farabi's ratio of 27/22 (354.5 cents) the basis for his "Mode of Zalzal" which provides another element of Artemisia-10. More generally, the term Zalzalian refers to "middle intervals" somewhere between minor and major -- thus Zalzalian or middle seconds, thirds, sixths, and sevenths. Intervals of this type are vital both to Near Eastern music and theory of the classic era of around the 9th-15th centuries, as well as to later forms including those now prevailing. In an interesting offshoot of classic and modern Near Eastern traditions, a few Western musicians have sought to develop tunings that explore and in some instances "rediscover" a range of Zalzalian modes by alternating two Zalzalian or middle third generators. Thus Erv Wilson's "Rast/Bayyati matrix" alternates the two middle thirds found in al-Farabi's famous Mode of Zalzal, at 27/22 and 11/9 (347.4 cents); while Jacky Ligon alternates the middle thirds found in Ibn Sina's `oud tuning at 39/32 and 16/13 (342.5 and 359.5 cents). Jacques Dudon's Mohajira tunings grew out of his contemplation of the themes of "migration," exile, and the situation of refugees after the war between the USA and Iraq in 1991. These tunings in their most refined forms grow out of recurrent series of just intonation (JI) ratios and intervals, with an emphasis on Dudon's concept of differential coherence, or "-c" for short: the property of a tuning where the difference tones between its notes match the prime factors of the ratios in the tuning itself. However, the Mohajira concept can also be realized by chains of alternating middle third generators, in the manner of Erv Wilson and Jacky Ligon; or even by the use of a single size of middle third generator, which produces a simplified form of Mohajira tuning. Artemisia-10 implements the approach of Wilson and Ligon, two alternating middle third generators, in the context of a near-just tuning system called MET-24. In its ideal form, MET-24 is based on 2048-ed2, with two 12-note chains of fifths at 703.711 cents, and a spacing between chains at 57.422 cents. This permits, among other things, rather close approximations of two related and very beautiful differentially coherent Mohajira modes of Jacques Dudon: one form of a "Folk Rast" mode published by Dudon in _1/1_ (see Section 2.5 below); and his Ibina mode which would fit the 13th-15th century modal category of Nahaft (Section 3.2). It may be helpful to know that Dudon finds an optimal contrast for Mohajira between larger and smaller middle step and intervals to be around 12-17 cents. Drawing on classic tunings, he cites Ibn Sina's 'oud tuning with middle thirds at 39:32 and 16:13 (a difference of 512:507 or 16.990 cents); and a tuning of Safi al-Din with middle thirds at 72:59 and 59:48 (344.7 and 357.2 cents), a difference of 3481:3456, 12.478 cents) as exemplifying this optimal range. In MET-24, and more specifically in Artemisia-10, the generating middle thirds are at 357.422 cents and 346.289 cents, a difference of 11.133 cents, slightly smaller than Dudon's optimal range, but not too far from it. The Artemisia-10 system, in its tempered form in MET-24, is derived from the disjunct form of the Archytas Chromatic (28:27-243:224-32:27), with the upper interval of 32:27 divided into two middle seconds in the usual Near Eastern fashion. The tone of disjunction (4/3-3/2) is also divided into a smaller thirdtone and larger 2/3-tone. Thus in JI, using al-Farabi's Mode of Zalzal dividing 32:27 into steps of 12:11 and 88:81, we would have: |------ lower genus ---------|....tone...|------- upper genus--------| C----C+------D-------Ed------F----F+-----G----G+------A------Bd------C 1/1 28/27 9/8 27/22 4/3 112/81 3/2 14/9 27/16 81/44 2/1 0 63.0 203.9 354.5 498.0 561.0 702.0 764.9 905.9 1056.5 1200 28:27 243:224 12:11 88:81 28:27 243:224 28:27 243:224 12:11 88:81 63.0 140.9 150.6 143.5 63.0 140.9 63.0 140.9 150.6 143.5 The tempering in MET-24 makes the lower thirdtone step of the Archytas Chromatic (68.6 cents) closer to 27:26 (65.3 cents) than to 28:27 (63.0 cents); and also compresses the regular minor third from 32:27 to around 13:11 (tempered 288.9 cents, just 289.2 cents). Thus we have: |-------- lower genus --------|....tone...|------- upper genus -------| C----C+-------D-------Ed------F----F+-----G----G+------A------Bd------C 0 68.6 207.4 357.4 496.3 564.8 703.7 772.3 911.1 1061.1 1200 68.6 138.9 150.0 138.9 68.6 138.9 68.6 138.9 150.0 138.9 Note how this tempered scheme, with its two middle second step sizes at 138.9 cents (a near-just 13:12, 138.6 cents) and 150 cents (a near-just 12:11, 150.6 cents) closely approximates an 11:12:13 division. The division of the tone into thirdtone and 2/3-tone, e.g. C-C+-D at 68.6-138.9 cents, is not too far from 27:26:24 or 65.3-138.6 cents. Section 5 below shows a layout of this tuning plus two additional notes, Artemisia-12, for a standard 12-note keyboard. ----------------------------------------------------- 1. Chains of fifths and Rast/Bayyati or Mohajira sets ----------------------------------------------------- The structure of the Artemisia-10 decatonic system, although it is derived from the Chromatic of Archytas, can also be analyzed in terms of a kind of strategy addressed by Erv Wilson in his Rast/Bayyati Matrix, and by Jacques Dudon in some of his Mohajira tunings. The basic idea is to alternate two middle or neutral third generators which add up to some value of fifth (just or tempered), and to repeat the process until a set at a convenient size such as 7, 10, or 17, for example, results. From this perspective, Artemisia might be diagrammed as a lattice involving two chains of fifths: F--------C--------G---------D--------A 496.3 0 703.7 207.4 911.1 Ed--------Bd--------F+--------C+-------G+ 357.4 1061.1 564.8 68.6 772.3 This decatonic includes two heptatonic or 7-note Rast/Bayyati or Mohajira sets. The first begins from C on the upper chain of fifths, taken in the diagrams so far as the 1/1: 0 gen2 gen4 gen6 C--------G----------D---------A 0 703.7 207.4 911.1 \ / \ / \ / 1 2 3 4 5 6 \ / \ / \ / gen1 gen3 gen5 Ed--------Bd---------F+ 357.4 1061.1 564.8 This diagram shows how the seven notes of the set are produced by six successive generators, with the larger generator of 357.4 cents preceding and alternating with the smaller generator of 346.3 cents. The result is what Jacques Dudon has termed an "interlace" of two chains of fifths. Another 7-note Rast/Bayyati or Mohajira set results if we place the 1/1 or starting note at Ed on the lower chain of fifths, this time using the same generator sizes, but with the smaller generator (346.3 cents) preceding the larger (357.4 cents): gen1 gen3 gen5 G----------D----------A 346.3 1050.0 553,7 / \ / \ / \ 1 2 3 4 5 6 / \ / \ / \ 0 gen2 gen4 gen6 Ed-------Bd---------F+---------C+ 0 703.7 207.4 911.1 These two sets differ in that the first set features larger middle intervals with respect to our 1/1: thus C-Ed at 357.4 cents, C-Bd at 1061.1 cents, and C-F+ at 564.8 cents. These could represent, for example, 16/13 (359.5 cents), 24/13 (1061.4 cents), and 18/13 (563.4 cents). The second set features smaller middle intervals from the 1/1: Ed-G at 346.3 cent, Ed-D at 1050.0 cents, and Ed-A at 553.7 cents. These might represent, for example, 11/9 (347.4 cents), 11/6 (1049.4 cents), and 11/8 (551.3 cents). Each of these 7-note Rast/Bayyati or Mohajira sets features a set of seven modes or rotations. As we'll see, each set has some modes where larger middle intervals within a genus (Arab jins, plural ajnas) precede smaller ones; and other modes where the converse order applies. Further, the two sets "mirror" each other in the converse ordering of each mode, so that a mode which has smaller middle second steps precede larger ones in one set, while have the converse or "mirroring" order in the other set. --------------------------------------------------------------- 2. The seven modes of a Rast/Bayyati or Mohajira heptatonic set --------------------------------------------------------------- In surveying the modes or rotations of a Rast/Bayyati or Mohajira 7-note set, we may start for convenience with the mode starting on the 1/1, or the note from which the six middle or neutral third generators (alternating between larger and smaller sizes) give rise to the tuning. For our first Mohajira-7 set, where the larger middle third generator precedes the smaller, we have: 0 gen2 gen4 gen6 C--------G----------D---------A 0 703.7 207.4 911.1 \ / \ / \ / 1 2 3 4 5 6 \ / \ / \ / gen1 gen3 gen5 Ed--------Bd---------F+ 357.4 1061.1 564.8 Beginning from C, the 1/1, we have a mode which marks the first of seven modes or rotations. ------------------------------- 2.1. The First Mode of Mohajira ------------------------------- Uddal Mode (First Mode of Mohajira) |------------ uddal-5 ---------------|---------- rast-4 ----------| C4--------D4------Ed4-------F+4------G4--------A4-------Bd4------C5 0 207.4 357.4 564.8 703.7 911.1 1061.1 1200 207.4 150.0 207.4 138.9 207.4 150.0 138.9 T K T S T K S 78 88 96 108 117 132 144 156 1/1 44/39 16/13 18/13 3/2 22/13 24/13 2/1 0 288.8 359.5 563.4 702.0 910.8 1061.4 1200 44:39 12:11 9:8 13:12 44:39 12:11 13:12 208.8 150.6 203.9 138.6 208.8 150.6 138.6 Intervals are shown in cents, and adjacent intervals also using a Turkish notation where T(anini) indicates a regular tone, typically around 9:8 or 203.9 cents (here at 207.4 cents); K(abir) indicates a "greater" middle second step, here at 150.0 cents; and S(aghir) indicates a "lesser" middle second, here at 138.9 cents. Below these notations of MET-24 interval sizes in tempered cents, a possible JI interpretation is shown with ratios and cents. Additionally, above the approximate just ratios, there appear a set of numbers either in ascending order (e.g. here 78-156) to represent a harmonic series providing these ratios; or in descending order, to represent the string lengths of a monochord division for this purpose. While either representation is possible for any mode, I have tended to select the representation which seems easier to calculate, or which involves lower numbers. The upper rast tetrachord G4-A4-Bd4-C4, at 207.4-150.0-138.9 cents, has a T-K-S pattern: tone, followed by larger and then middle second. The notation "rast-4" identifies this pattern as rast, and shows that this rast jins or genus has a size of 4, i.e. a tetrachord. The lower pentachord, "uddal-5," has a pattern that is kindred to rast-4, but different. Like rast-4, it starts T-K, with a tone and larger middle second step, here 207.4-150.0 cents, and so has the same middle third size, 357.4 cents, as rast-4. However, instead of immediately closing with a smaller middle second, here at 138.9 cents, uddal-5 interposes another tone, so that we have T-K-T-S, or steps of 207.4-150.0-207.4-138.9 cents. In reference to the lowest note of the pentachord, we have 0-207.4-357.4-564.8-703.7 cents, with the fourth step at a kind of small tritone, here 564.8 cents, leading by a smaller middle second step to the perfect fifth that concludes the pentachord. Our rast-4 is close to 44:39-12:11-13:12 or 1/1-44/39-16/13-4/3, or 208.8-150.6-138.6 cents (0-208.8-359.5-498.0 cents). Our uddal-5 approximates 44:39-12:11-9:8-13:12 or 1/1-44/39-16/13-18/13-3/2, 208.8-150.6-203.9-138.6 cents or 0-208.8-359.5-563.4-702.0 cents. Note that in MET-24, the same size of 207.4 cents can represent either 44:39 or 9:8, for example, a difference of 352:351 (4.925 cents). The term Uddal, which the 15th-century theorist Mohammed al-Ladiqi uses for the pentachord T-J-T-J (with "J" meaning a middle second step of any size), may be the best name for this pentachord and its associated mode with an upper Rast tetrachord. The Turkish musician and theorist Ozan Yarman uses the term Penchgah for this T-K-T-S pattern, but in other Near Eastern usages it and related terms refer, for example, to an Iraqi Maqam Panjgah with a lower pentachord of T-T-K-S and an upper Rast tetrachord. When Uddal is capitalized, to describe a maqam or modal pattern (Arabic plural _maqamat_), it thus here implies a combination of ajnas or genera we may write as follows: Uddal = uddal-5|rast-4 Here the vertical bar | indicates conjunct ajnas or genera: that is, the highest note of uddal-5 (C4-G4) is also the lowest note of rast-4 (G4-C5). In Arab or Turkish music, both the rast-4 tetrachord and the related uddal-5 pentachord tend to follow an order where the larger middle second precedes the smaller: thus T-K-S or T-K-T-S. We may refer to this as a "KS" order. -------------------------------- 2.2. The Second Mode of Mohajira -------------------------------- The Second Mode of Mohajira has the same ordering of larger and smaller middle seconds as the First Mode or Uddal, but differs in some other respects: Nahaft Mode (Second Mode of Mohajira) |------- mohajira-4 -------|...tone...|------- bayyati-4 -------| D4------Ed4-------F+4------G4--------A4-------Bd4-----C5-------D5 0 150.0 357.4 496.3 703.7 853.7 992.6 1200 |---------- rast-4 ---------| 150.0 207.4 138.9 207.4 150.0 138.9 207.4 K T S T K S T 1872 1716 1521 1404 1248 1144 1056 936 1/1 12/11 16/13 4/3 3/2 18/11 39/22 2/1 0 150.6 359.5 498.0 702.0 852.6 991.2 1200 12:11 44:39 13:12 9:8 12:11 13:12 44:39 150.6 208.8 138.6 203.9 150.6 138.9 208.8 Nahaft may be analyzed as a mode with two disjunct tetrachords, with a tone intervening between them. The lower tetrachord D4-Ed4-F+4-G4 has a pattern K-T-S: larger middle second, tone, and smaller middle second, 150.0-207-4-138.9 cents. In classic 13th-14th century Near Eastern theory, this jins or genus is called `iraq, a term still used in some modern Arab theory. However, because the pattern is now less common in much of the Arab world as a distinct tetrachord, Jacques Dudon has proposed the name Mohajira both for the tetrachord itself, and for the set of modes which can be generated either by recurrent series in JI, or, as here, by alternating two just or tempered middle third generators (the method also used by Erv Wilson in his Rast/Bayyati Matrix, which he applies to al-Farabi's middle thirds at 27:22 and 11:9, 354.5 and 347.4 cents). After this lower mohajira-4 tetrachord and the tone of disjunction G4-A4, there is an upper tetrachord A4-Bd4-C5-D5 of a different pattern known in modern Arab theory as bayyati, here in the form of K-S-T or 150.0-138.9-207.4 cents. A JI interpretation might be 12:11-13:12-44:39 or 1/1-12/11-13/11-4/3, 150.6-138.6-208.8 cents or 0-150.6-289.2-498.0 cents. This would form a relatively simple harmonic series 33:36:39:44. In this analysis, we could notate the second mode of Mohajira, or Nahaft (a term from the era around 1300) in this fashion: Nahaft = mohajira-4 + bayyati-4 Here the connecting "+" sign marks two disjunct ajnas or genera with an intervening tone of disjunction. Another analysis is also possible, because in addition to the mohajira-4 jins at D4-G4 and the disjunct bayyati-4 at A4-D5 (with G4-A4 as the tone of disjunction), we have a conjunct rast-4 tetrachord (T-K-S) at G4-A4-Bd4-C4, 207.4-150.0-138.9 cents, whose lowest step G4 is the same as the highest step of the lower mohajira-4 jins. Thus an alternative notation: Nahaft = mohajira-4|rast-4|tone This notation expressly shows that with the two conjunct tetrachords, an upper tone serves to complete the octave, here C5-D5. Like our Uddal or First Mode, Nahaft in this version of Mohajira-7 follows the order KS, with the larger middle second preceding the smaller. This means, for example, that both Uddal and Nahaft have steps above the lowest note of the mode at 357.4 cents (207.4 + 150.0 cents, or T-K). This order also holds both for the upper rast-4 tetrachord of Uddal, T-K-S, and for the conjunct rast-4 of Nahaft. However, as we continue with our modal rotations, this KS ordering is subject to change, as our next mode illustrates. ------------------------------- 2.3. The Third Mode of Mohajira ------------------------------- Uddal|Mohajira Mode (Third Mode of Mohajira) |--------------- uddal-5 ---------------|----- mohajira-4 -------| Ed4-------F+4------G4---------A4-------Bd4-----C5--------D5------Ed5 0 207.4 346.3 553.7 703.7 842.6 1050.0 1200 207.4 138.9 207.4 150.0 138.9 207.4 150.0 T S T K S T K 1716 1521 1404 1248 1144 1056 936 858 1/1 44/39 11/9 11/8 3/2 13/8 11/6 2/1 0 208.8 347.4 551.3 702.0 840.5 1049.4 1200 44:39 13:12 9:8 12:11 13:12 44:39 12:11 208.8 138.6 203.9 150.6 138.9 208.8 150.6 Since I am not aware of a familiar name for this mode, I term it Uddal|Mohajira, to show that it has a lower uddal-5 jins (Ed-F+4-G4-A4-Bd4), somewhat as in the First Mode of Mohajira, and an upper mohajira-4 jins, Bd4-C5-D5-Ed5. However, both of these ajnas are a bit different, because of the ordering of the smaller and larger middle second steps. In the lower uddal-5, we here have T-S-T-K, with a tone, smaller middle second, tone, and then larger middle second -- 207.4-138.9-207.4-150.0 cents. This subtly contrasts with the uddal-5 of the First Mode, with T-K-T-S. Specifically, we have a lower third step at 346.3 cents, very close to a just 11/9 (347.4 cents), by contrast to 357.4 cents, close for example to 16/13 (359.5 cents). Also, the fourth or small tritone step of uddal-5 is here at 553.7 cents, quite close to a just 11/8 (551.3 cents), by contrast to the somewhat larger 564.8 cents of the First Mode, not far from 18/13 (563.4 cents). The upper mohajira-4 is also subtly different from the form we met in the Second Mode: S-T-K, or 138.9-207.4-150.0 cents. In the context of this Third Mode, steps above the lowest note of the mode result at 842.6 cents (a smaller middle sixth) and 1050.0 cents (a smaller middle seventh), close to the relatively simple ratios of 13/8 (840.5 cents) and 11/6 (1049.4 cents). While the Mohajira modes in MET-24 and other interpretations are captivating from a purely melodic view, someone seeking to build polyphony or counterpoint on this material might note, for example, the availability of a near-just 8:11:13 sonority on the lowest note of the mode (0-553.7-842.6 cents). Just as we have referred to the First and Second Modes of Mohajira based on this seven-note set as KS modes, where the larger middle second precedes the smaller, we may refer the the Third Mode as following a converse or SK order. More generally, the order of the Third Mode in a seven-note set will be the converse of that in the First and Second Modes. -------------------------------- 2.4. The Fourth Mode of Mohajira -------------------------------- Mohajirayn Mode (Fourth Mode of Mohajira) |--------- mohajira-4 --------|----- mohajira-4 --------|...tone..| F+4------G4---------A4-------Bd4-----C5--------D5------Ed5-------F+5 0 138.9 346.3 496.3 635.2 842.6 992.6 1200 138.9 207.4 150.0 138.9 207.4 150.0 207.4 S T K S T K T 792 858 968 1056 1144 1287 1404 1584 1/1 13/12 11/9 4/3 13/9 13/8 39/22 2/1 0 138.6 347.4 498.0 636.6 840.5 991.2 1200 13:12 44:39 12:11 13:12 9:8 12:11 44:39 138.6 208.8 150.6 138.6 203.9 150.6 208.8 The conventions of naming maqamat or modal patterns in Arab and Turkish music invite a beautiful way of describing this Fourth Mode: as Mohajirayn, or literally "Twin Mohajira," referring to the presence of two "twin" and specifically conjunct mohajira-4 tetrachords. This we have a lower "twin" at F+4-G4-A4-Bd4, S-T-K, and an identical conjunct "twin" at Bd4-C5-D5-Ed5, either at 138.9-207.4-150.0 cents. One JI interpretation would be 13:12-44:39-12:11 or 138.6-208.8-150.0 cents, with a harmonic series at 36:39:44:48, and a middle third at 11/9, closely approximated by the tempered 346.3 cents. As in other modes with two conjunct tetrachords, whether the same or different, an upper tone (here Ed5-F+5) completes the octave. For many Western musicians, the idea of a mode without a 3/2 or perfect fifth step may seem problematic (as reflected in the debates over the century on the validity or usefulness of the regular diatonic mode sometimes known as Locrian, B-C-D-E-F-G-A-B, which interestingly also consists of two "twin" tetrachords B-C-D-E and E-F-G-A plus an upper tone A-B. In both classic (9th-14th centuries or so) and modern Near Eastern theory, however, certain modes without a perfect fifth are routinely recognized and used. Melodically, if one explores the tetrachord boundaries, the mode takes shape, with a refreshingly different pattern than in modes with a perfect fifth. If one seeks out polyphonic applications, then focusing on parallel fourths rather than fifths is an attractive approach. World polyphonies may favor either fourths or fifths, or some combination; and it is interesting that in the earlier 11th century, both Ibn Sina and Guido d'Arezzo especially preferred the 4:3 fourth as a concord. Here, the twin and conjunct mohajira-4 tetrachords more specifically take the form S-T-K, with the smaller middle second preceding the larger, an SK order like that of the Third Mode, and converse to that of the First and Second Modes. ------------------------------------------------------------ 2.5. The Fifth Mode of Mohajira: Jacques Dudon's "Folk Rast" ------------------------------------------------------------ Folk Rast Mode (Fifth Mode of Mohajira) |--------- rast-4 ----------|...tone..|------- mohajira-4 ---------| G4---------A4-------Bd4-----C5--------D5-------Ed5--------F+5------G5 0 207.4 357.4 496.3 703.7 853.7 1061.1 1200 207.4 150.0 138.9 207.4 150.0 207.4 138.9 T K S T K T S 1584 1404 1287 1188 1056 968 858 792 1/1 44/39 16/13 4/3 3/2 18/11 24/13 2/1 0 208.8 359.5 498.0 702.0 852.6 1061.4 1200 44:39 12:11 13:12 9:8 12:11 44:39 13:12 208.8 150.6 138.6 203.9 150.6 208.8 138.6 The Fifth Mode has a lower rast-4 tetrachord in the T-K-S pattern (207.4-150.0-138.9 cents), and after a tone of disjunction, an upper mohajira-4 tetrachord in the K-T-S pattern (150.0-207.4-138.9 cents). In modern Arab theory, this mode with its lower rast-4 tetrachord belongs to the Rast family. Jacques Dudon has suggested the name "Folk Rast" for this form with disjunct rast-4 and mohajira-4 ajnas or genera. Such a pattern of T-K-S-T-K-T-S is also important, as Eric Ederer has noted, in some 20th-century Turkish theory. This mode shifts from the SK ordering of the Third and Fourth Modes back to the KS ordering of the First and Second Modes, with the larger middle second preceding the smaller, and with larger middle intervals above the lowest note of the mode (here approximating a larger middle third at 16/13, a middle sixth at 18/11, and a middle seventh at 24/13). We may notate the structure of this "Folk Rast" as follows Folk Rast = rast-4 + mohajira-4 Another possible interpretation would be a lower rast-4, and a conjunct upper uddal-5 pentachord -- the same ajnas as in the First Mode or Uddal, but with the rast-4 below the uddal-5 rather than above it: Folk Rast = rast-4|uddal-5 In the first interpretation of disjunct rast and mohajira tetrachords, there is often a tendency to emphasize the fifth degree, and we may borrow an element of modern Turkish theory by sometimes conceiving of the mode as having a lower "rast-5" pentachord and upper mohajira-4. Folk Rast = rast-5|mohajira-4 All of these interpretations are possible, and may inspire different patterns of melodic emphasis and development. Our realization of this "Folk Rast" mode in MET-24 generally provides a close approximation of Jacques Dudon's JI Mohajira series published in "Differential Coherence: Experimenting with New Areas of Consonance," _1/1_ (Vol. 11, No. 2, Winter 2003), in a version with a 3/2 fifth: The property of differential coherence arises when difference tones between the steps of a tuning match the ratios of the tuning. For example, the differences between steps at 104 and 117, or 117 and 128, at 13 and 11 respectively, match the tuning's ratios with prime factors of 11 and/or 13. |--------- rast-4 ----------|...tone..|------- mohajira-4 ---------| G4---------A4-------Bd4-----C5--------D5-------Ed5--------F+5------G5 0 207.4 357.4 496.3 703.7 853.7 1061.1 1200 207.4 150.0 138.9 207.4 150.0 207.4 138.9 T K S T K T S 78 88 96 104 117 128 144 156 1/1 44/39 16/13 4/3 3/2 64/39 24/13 2/1 0 208.8 359.5 498.0 702.0 857.5 1061.4 1200 44:39 12:11 13:12 9:8 128:117 9:8 13:12 208.8 150.6 138.6 203.9 155.6 203.9 138.6 The most notable divergences between the just and tempered versions of Dudon's differentially coherent (-c) Folk Rast mode involve the sixth degree at a just ratio of 64/39 (857.5 cents), realized in MET-24 at 853.7 cents, much closer to 18/11; and the melodic step from the fifth to this note, 3/2-64/39, at 128:117 (155.6 cents), realized at a tempered 150.0 cents, an approximation of 12:11 (150.6 cents) which differs from Dudon's 128:117 by 352:351 (4.925 cents). Dudon's upper tetrachord is a permutation of Ibn Sina's tetrachords 9:8-13:12-128:117 (used in his `oud tuning and his Mustaqim mode, see Sections 3.1 and 4.2 below) and 13:12-9:8-128:117, precisely mirroring the latter, which could be expressed as STK (smaller middle second, tone, larger middle second), and Dudon's permutation as KTS. Here the MET-24 placement of the middle sixth step at 853.7 cents is about 1.1 cents wide of 18/11, and 3.8 cents narrow of Dudon's 64/39. A greater discrepancy occurs in the representation of Dudon's classic 128:117 step (155.6 cents) as a tempered 150.0 cents, about 5.6 cents narrow of this ratio, and 0.6 cents narrow of 12:11. ------------------------------- 2.6. The Sixth Mode of Mohajira ------------------------------- Bayyati-4|Mohajira-4 Mode (Sixth Mode of Mohajira) |-------- bayyati-4 ---------|------- mohajira-4 ---------|..tone..| A4-------Bd4------C5--------D5-------Ed5--------F+5------G5-------A5 0 150.0 288.9 496.3 646.3 853.7 992.6 1200 150.0 138.9 207.4 150.0 207.4 138.9 207.4 K S T K T S T 66 72 78 88 96 108 117 132 1/1 12/11 13/11 4/3 16/11 18/11 39/22 2/1 0 150.6 289.2 498.0 648.7 852.6 991.4 1200 12:11 13:12 44:39 12:11 9:8 13:12 44:39 150.6 138.6 208.8 150.6 203.9 138.6 208.8 This beautiful mode has a lower bayyati-4 tetrachord in the K-S-T pattern (150.0-138.9-207.4 cents) and a conjunct mohajira-4 tetrachord in the K-T-S pattern (150.0-207.4-138.9 cents), with the affinities and contrasts between these tetrachords lending enchantment. Like the Fourth Mode or Mohajirayn, there is no perfect fifth or 3/2 step, with the fourth step as pivotal, the note where the two tetrachords meet; an upper tone (G5-A5) completes the octave. The bayyati-4 and mohajira-4 patterns of K-S-T and K-T-S show a KS order, with the larger middle second step preceding the smaller. Larger middle intervals resulting above the lowest note include approximate ratios for the middle second of 12/11, a diminished fifth at around 16/11, and a middle sixth at around 18/11. In the 13th century, the musician and theorist Safi al-Din al-Urmawi described this variety of mode as Hijaz, a name which at the time had a number of different understandings. However, another interpretation by Qutb al-Din al-Shirazi around 1300 in which Hijaz has a middle step appreciably larger than a standard 9:8 tone has won general acceptance. More specifically, Qutb al-Din described Hijaz at 12:11-7:6-22:21 or 1/1-12/11-14/11-4/3, 150.6-266.9-80.5 cents or 0-150.6-417.5-498.0 cents, a permutation of Ptolemy's Intense Chromatic (22:21-12:11-7:6). More generally, while the tuning of Hijaz is highly variable, the term tends to imply a tetrachord with the second or middle interval somewhere between around 8:7 (231.2 cents) and 32:27 (294.1 cents). For the moment, the name of "Bayyati|Mohajira" Mode, or more pedantically "Bayyati|Mohajira|Tone" Mode to make explicit that both conjunct ajnas are tetrachords and that an upper tone completes the octave, may be a solution. Using a shorthand that appears in the scale archive for Manuel Op de Coul's excellent Scala generation and analysis program Scala freely available on the World Wide Web, one could also nickname this mode "Baya|Moha," i.e. "Bayyati|Mohajira." The analysis would be: bayyati-4|mohajira-4|tone My intuition is that in the 13th-14th centuries, the shifting between conjunct tetrachord patterns such as KST and KTS was much relished, and exploration of this mode will often cultivate such an effect. At the same time, a more "modern" possibility is also open to provide an interesting contrast. One may focus on the lower bayyati-4 jins, for example, plus the notes immediately below the final or resting note (here A4) that provide a kind of cadential figure: |------- bayyati-4 ---------| F+4------G4---------A4------Bd4-----C5---------D5 853.7 992.6 0 150.0 288.9 496.3 138.9 207.4 150.0 138.9 207.4 S T K S T 18/11 39/22 1/1 12/11 13/11 4/3 852.6 991.2 0 150.6 289.2 498.0 Here the lower melodic pattern of melodic steps S-T (138.9-207.4 cents) leading up to the final reinforce a focus on A4. The Arab theorist Sami Abu Shumays speaks of "jins baggage," notes that attach to a given tetrachord or other jins, as here with these steps below bayyati-4. One can center one's exploration of the mode on this region of F+4-D5, bayyati-4 and its attached lower notes or "baggage," for a while, and then shift the focus by ascending into the upper mohajira-4 jins (D5-Ed5-F+4-G5) and eventually to the octave of the final, A5; or by descending further than the F+4-G4-A4 cadential figure, so that a lower mohajira tetrachord emerges: D4-Ed4-F+4-G4. Here the note Ed4, a "superfourth" at around 11/8 below the final A4 rather than a perfect fourth, can be pivotal in marking a shift from the bayyati-4 tetrachord and the cadential steps immediately below it, to the realm of this mohajira-4 jins. --------------------------------- 2.7. The Seventh Mode of Mohajira --------------------------------- `Awj Mode (Seventh Mode of Mohajira) |-------- mohajira-4 ---------|...tone...|------- mohajira-4 --------| Bd4------C5---------D5-------Ed5--------F+5-----G5---------A5-------Bd5 0 138.9 346.3 496.3 703.7 842.6 1050.0 1200 138.9 207.4 150.0 207.4 138.9 207.4 150.0 S T K T S T K 72 78 88 96 108 117 132 144 1/1 13/12 11/9 4/3 3/2 13/8 11/6 2/1 0 138.6 347.4 498.0 702.0 840.5 1049.4 1200 13:12 44:39 12:11 9:8 13:12 44:39 12:11 138.6 208.8 150.6 203.9 138.6 208.8 150.6 The Seventh Mode of Mohajira, and the last rotation before returning to the starting point of the First Mode of Uddal, is known in Near Eastern theory around 1300 as `Awj, as Jacques Dudon notes. There are two disjunct mohajira-4 tetrachords, Bd4-C5-D5-Ed5, and after a tone of disjunction (Ed5-F+5), F+5-G5-A5-Bd5, each here in the pattern S-T-K, with the smaller middle second preceding the larger (138.6-207.4-150.0 cents). This is an SK order, in contrast to the KS order of the Fifth and Sixth Modes, for example. Thus we have smaller middle intervals above the lowest note of the mode, here approximating 13/12, 11/9, 13/8, and 11/6, for example. The classic name `Awj also refers, at least in current usage, to the step `awj in the Arab gamut, at a larger middle seventh above the step rast, deemed the 1/1 of the gamut. Whatever evolutionary connection may or may not hold between the 13th-14th century modal type `Awj and the step in the modern Arab gamut, here our mode with two disjunct mohajira-4 ajnas, fitting the modal type, happens to occur on the large middle seventh step (~24/13) of the First Mode of Mohajira, Uddal, so that the name seems apropos in the context of Jacques Dudon's Mohajira-7 sets. This mode with its two disjunct mohajira tetrachords has great symmetry, and might also be called Mohajira, as in modern Arab or Turkish music, two disjunct Rast tetrachords (T-K-S-T-T-K-S) are known as Maqam Rast (and also as the "Arab Fundamental Scale"). However, the classic name `Awj is very attractive, and accurately locates the final of this modal rotation as the middle seventh step of Uddal, the First Mode of Mohajira. The structure of `Awj can be summed up: mohajira-4 + mohajira-4 One way of getting contrast and variety is to explore the symmetry of the two mohajira-4 tetrachords, and then, for example, take the fourth and highest step of the first tetrachord as a pivot from which to shift to a focus on the pentachord above this note, Ed5-F+5-G5-A5-Bd5, a uddal-5 with smaller middle intervals (~1/1-9/8-11/9-11/8-3/2). In this interpretation, what was the tone of disjunction (Ed-F+) between two identical mohajira-4 ajnas becomes the lower tone of an upper uddal-5 jins. We thus have: mohajira-4|uddal-5 This alternative structure for Mode 7 gives the same ajnas as in Mode 3, but with mohajira-4 below rather than above uddal-5: |-------- uddal-5 ---------|----- mohajira-4 ----| Mode 3: Ed4 F+4 G4 A4 Bd4 C5 D4 Ed5 0 207.4 346.3 553.7 703.7 842.6 1050.0 1200 207.4 138.6 207.4 150.0 138.6 207.4 150.0 T S T K S T K |---- mohajira-4 -----|-------- uddal-5 ---------| Mode 7: Bd4 C4 D4 Ed4 F+5 G5 A5 Bd5 0 138.6 346.3 496.3 703.7 842.6 1050.0 1200 138.6 207.4 150.0 207.4 138.6 207.4 150.0 S T K T S T K ------------------------------ 2,8. Summary of Mohajira Modes ------------------------------ In this survey of the seven modes of Mohajira, or more specifically of a Mohajira-7 set, we have used such a set arising from a process where the larger middle third generator (357.4 cents) preceded the smaller (346.3 cents). When modes such as the First Mode or Uddal have a corresponding order with larger middle second steps preceding smaller ones (KS order), we may refer to them as following a "generating" order, that is the same order as the sequence of larger and smaller generators. When the order is the converse (SK order), we may speak of a "converse" order. There is a connection between the ordering or larger and smaller middle third generators in building a Mohajira-7 set, and the ordering of larger and smaller middle second steps in a given mode of Mohajira-7, since modes with a "generating" order (here KS) will have similar sizes of middle intervals above the lowest note as the First Mode or Uddal (which has its final on the starting step for generating process). Modes with a "converse" order (here SK) add contrast not only by their different orderings of melodic steps, but by the different (here smaller) middle intervals above the lowest note of the mode. What follows is a quick overview of which modes have a generating or converse order, here for our present Mohajira-7 set where the larger middle third generator preceded the smaller in the generating process. Mode 1: Uddal (generating order -- KS) |------------ uddal-5 ---------------|---------- rast-4 ----------| C4--------D4------Ed4-------F+4------G4--------A4-------Bd4------C5 0 207.4 357.4 564.8 703.7 911.1 1061.1 1200 207.4 150.0 207.4 138.9 207.4 150.0 138.9 T K T S T K S Mode 2: Nahaft (generating order -- KS) |------- mohajira-4 -------|...tone...|------- bayyati-4 -------| D4------Ed4-------F+4------G4--------A4-------Bd4-----C5-------D5 0 150.0 357.4 496.3 703.7 853.7 992.6 1200 150.0 207.4 138.9 207.4 150.0 138.9 207.4 K T S T K S T Mode 3: Uddal-5|Mohajira-4 (converse order -- SK) |--------------- uddal-5 ---------------|----- mohajira-4 -------| Ed4-------F+4------G4---------A4-------Bd4-----C5--------D5------Ed5 0 207.4 346.3 553.7 703.7 842.6 1050.0 1200 207.4 138.9 207.4 150.0 138.9 207.4 150.0 T S T K S T K Mode 4: Mohajirayn (converse order -- SK) |--------- mohajira-4 --------|----- mohajira-4 --------|...tone..| F+4------G4---------A4-------Bd4-----C5--------D5------Ed5-------F+5 0 138.9 346.3 496.3 635.2 842.6 992.6 1200 138.9 207.4 150.0 138.9 207.4 150.0 207.4 S T K S T K T Mode 5: Folk Rast (generating order -- KS) |--------- rast-4 ----------|...tone..|------- mohajira-4 ---------| G4---------A4-------Bd4-----C5--------D5-------Ed5--------F+5------G5 0 207.4 357.4 496.3 703.7 853.7 1061.1 1200 207.4 150.0 138.9 207.4 150.0 207.4 138.9 T K S T K T S Mode 6: Bayyati-4|Mohajira-4 (generating order -- KS) |-------- bayyati-4 ---------|------- mohajira-4 ---------|..tone..| A4-------Bd4------C5--------D5-------Ed5--------F+5------G5-------A5 0 150.0 288.9 496.3 646.3 853.7 992.6 1200 150.0 138.9 207.4 150.0 207.4 138.9 207.4 K S T K T S T Mode 7: `Awj (converse order -- SK) |-------- mohajira-4 ---------|...tone...|------- mohajira-4 --------| Bd4------C5---------D5-------Ed5--------F+5-----G5---------A5-------Bd5 0 138.9 346.3 496.3 703.7 842.6 1050.0 1200 138.9 207.4 150.0 207.4 138.9 207.4 150.0 S T K T S T K -------------------------------------------------------------------- 3. Symmetries and Reflections: A second Mohajira-7 set and its modes -------------------------------------------------------------------- As explained in Section 1, the Artemisia-10 decatonic tuning actually includes two Mohajira-7 sets. In Section 2, we explored the set that results from a series of generators starting with the larger middle third at 357.422 cents, alternating with the smaller middle third at 346.289 cents. We now compare the modes of the Mohajira-7 set using the same generators, but in reverse order, starting with the smaller middle third: gen1 gen3 gen5 G----------D----------A 346.3 1050.0 553,7 / \ / \ / \ 1 2 3 4 5 6 / \ / \ / \ 0 gen2 gen4 gen6 Ed-------Bd---------F+---------C+ 0 703.7 207.4 911.1 This Mohajira-7 set generates modal patterns similar to that of the first set, with similar ajnas, but in different permutations -- more specifically, with the ordering of larger and smaller middle second steps reversed. Allowing for this change, we will find that the same musical logic applies, producing the same sequence of modes showing a generating order or converse order (see Section 2.8 above). ------------------------------------------------ 3.1. The First Mode of Mohajira: Uddal Revisited ------------------------------------------------ Uddal Mode (First Mode of Mohajira) |-------------- uddal-5 -------------|--------- mustaqim-4 -------| Ed4------F+4-------G4--------A4------Bd4-------C+5------D5--------Ed5 0 207.4 346.3 553.7 703.7 911.1 1050.0 1200 207.4 138.9 207.4 150.0 207.4 138.9 150.0 T S T K T S K 132 117 108 96 88 78 72 66 1/1 44/39 11/9 11/8 3/2 22/13 11/6 2/1 0 288.8 346.3 553.7 702.0 910.8 1049.4 1200 44:39 13:12 9:8 12:11 44:39 13:12 12:11 208.8 138.9 203.9 150.0 208.8 138.9 150.6 As with our first Mohajira-7 set, the First Mode is Uddal. However, following the order of middle third generators in our second set with the smaller generator preceding the larger, we find that the lower Uddal pentachord has its steps arranged T-S-T-K, with the smaller middle second at 138.9 cents (a near-just 13:12) preceding the larger middle second at 150.0 cents (a near-just 12:11). This is in contrast to the T-K-T-S arrangement in the first set (Section 2.1). Likewise, the upper tetrachord shifts from T-K-S in the first set to the present arrangement of T-S-K. While either arrangement would in classic 13th-14th century Near Eastern theory be called "Rast" (generically any T-J-J), Ibn Sina's earlier name of Mustaqim may nicely fit the T-S-K arrangement, and distinguish it from the T-K-S arrangement typical of a modern Arab or Turkish Rast. Ibn Sina, for his `oud tuning, favored a tuning for this tetrachord with steps of 9:8-13:12-128:117 (203.9-138.6-155.6 cents), and described a mode he called Mustaqim with two such conjunct tetrachords plus an upper 9:8 tone. (As we will see in Section 4.2, a rather close approximation of Ibn Sina's Mustaqim mode is available in Artemisia-10, although it is not a mode found in any single Mohajira-7 set.) An interesting ramification of this SK order for our new Mohajira-7 set is that the First or Uddal Mode yields some near-just approximations of rather simple ratios above the lowest note: thus a middle third near 11/9, a "superfourth" near 11/8, and a middle seventh near 11/6. As with the first Mohajira-7 set, so here, the First Mode follows the same order of smaller and larger middle steps and intervals as the generating sequence. Thus with the first set, this mode follows a KS order; here, it follows an SK order. ---------------------------------------------------------- 3.2. The Second Mode of Mohajira and Jacques Dudon's Ibina ---------------------------------------------------------- Nahaft Mode (Second Mode of Mohajira) |--------- mohajira-4 ------|...tone..|------ bayyati-4 ------| F+4-------G4--------A4------Bd4-------C+5-----D5-----Ed5------F+5 0 138.9 346.3 496.3 703.7 842.6 992.6 1200 |------- mustaqim-4 -----| 138.9 207.4 150.0 207.4 138.9 150.0 207.4 S T K T S K T 792 858 968 1056 1188 1287 1404 1584 1/1 13/12 11/9 4/3 3/2 13/8 39/22 2/1 0 138.6 346.3 498.0 702.0 840.5 991.2 1200 13:12 44:39 12:11 9:8 13:12 12:11 44:39 138.6 203.9 150.0 207.4 138.6 150.6 208.8 As with the first Mohajira-7 set, so with this, our Second Mode is Nahaft, which can be interpreted either as a lower mohajira-4 tetrachord and a disjunct upper bayyati-4 tetrachord; or as conjunct tetrachords of mohajira-4 and rast-4. Note that here the rast-4 tetrachord has the order T-S-K, and so is called mustaqim-4, after Ibn Sina's Mustaqim mode (Section 3.1). This tempering of Nahaft is generally very close to Jacques Dudon's beautiful Ibina series, related to his Folk Rast mode (Section 2.5). The just Ibina series has ratios of 72:78:88:96:108:117:128:144, and like Dudon's Folk Rast is differentially coherent: |--------- mohajira-4 ------|...tone..|------ bayyati-4 ------| F+4------G4--------A4------Bd4-------C+5-----D5-----Ed5------F+5 0 138.9 346.3 496.3 703.7 842.6 992.6 1200 138.9 207.4 150.0 207.4 138.9 150.0 207.4 S T K T S K T |------- mustaqim-4 -----| 72 78 88 96 108 117 128 144 1/1 13/12 11/9 4/3 3/2 13/8 16/9 2/1 0 138.6 346.3 498.0 702.0 840.5 996.1 1200 13:12 9:8 12:11 9:8 13:12 128:117 9:8 138.9 203.9 150.0 207.4 138.6 155.6 203.9 Dudon's Ibina tuning of Maqam Nahaft includes, on the 4/3 step, Ibn Sina's tetrachord associated with his Mustaqim mode in its just form: 9:8-13:12-128:117 (203.9-138.6-128:117), or in terms of the 4/3 step, 1/1-9/8-39/32-4/3 (0-203.9-342.5-498.0 cents). While MET-24 nicely approximates the note in the Ibina tuning above the 1/1, with the greatest divergence at 16/9, a just 996.1 cents, realized as 992.6 cents (3.5 cents narrow), within the Mustaqim tetrachord we find that Ibn Sina's and Dudon's 39:32 (342.5 cents) is realized at 346.3 cents, 3.8 cents wide (and about 1.1 cents narrow of 11:9). As with Dudon's related Folk Rast mode, the greatest discrepancy in a MET-24 realization is that between Ibn Sina's or Dudon's step of 128:117 and the tempered step of 150.0 cents, almost 5.6 cents narrow. The second mode of Nahaft follows the generating order of a Mohajira-7 set: thus here SK, and in the first set (Section 2.2) KS. ------------------------------- 3.3. The Third Mode of Mohajira ------------------------------- Uddal|Mohajira Mode (Third Mode of Mohajira) |------------- uddal-5 --------------|----- mohajira-4 ------| G4--------A4------Bd4-------C+5------D5-----Ed5------F+5-----G5 0 207.4 357.4 564.8 703.7 853.7 1061.1 1200 207.4 150.0 207.4 138.9 150.0 207.4 138.9 T K T S K T S 1584 1404 1287 1144 1056 968 858 792 1/1 44/39 16/13 18/13 3/2 18/11 24/13 2/1 0 288.8 359.5 563.4 702.0 852.5 1061.4 1200 9:8 12:11 9:8 13:12 12:11 44:39 13:12 203.9 150.0 207.4 138.6 150.6 208.8 138.6 As with our first Mohajira-7 set, so with this, the third mode yields a lower uddal-5 pentachord and an upper mohajira-4 tetrachord. This Third Mode follows a converse order to the order of the generating middle thirds: that is, with the smaller middle third preceding the larger as in this this, we find that this mode has larger middle intervals above the lowest note: here the larger middle third at 357.4 cents, middle sixth at 853.7 cents, and middle seventh at 1061.1 cents, approximating 16/13, 18/11, and 24/13. In Doug Leedy's view, the fourth step, at a tone above the middle third step, could be deemed likewise a "mid-fourth," here at 564.8 cents, close to 18/13. Comparing this version of the Third Mode to that in the first set (Section 2.3) will show that there, with the larger middle third generator preceding the smaller, smaller middle intervals prevail, approximating for example 11/9, 13/8, and 11/6, with Leedy's "mid-fourth" at likewise at a near-just 11/8. In either set, the lower uddal-5 jins of this mode contrasts subtly with that of the First Mode, which follows the generating order of the set, as compared to the converse order of the Third Mode. -------------------------------- 3.4. The Fourth Mode of Mohajira -------------------------------- Mohajirayn Mode (Fourth Mode of Mohajira) |------ mohajira-4 ------|------- mohajira-4 -------|...tone..| A4------Bd4-------C+5-----D5------Ed5-------F+5-----G5---------A5 0 150.0 357.4 496.4 646.3 853.7 992.6 1200 150.0 207.4 138.9 150.0 207.4 138.9 207.4 K T S K T S T 1872 1716 1521 1404 1248 1144 1056 936 1/1 12/11 16/13 4/3 16/11 18/11 39/22 2/1 0 150.6 359.5 498.0 648.7 852.5 991.2 1200 12:11 44:39 13:12 12:11 9:8 13:12 44:39 150.6 208.8 138.6 150.6 203.9 138.6 208.8 The Fourth Mode of Mohajirayn or "Twin Mohajira," with its two conjunct mohajira-4 ajnas, again features a converse order. With the smaller middle third generator preceding the larger, we here have larger middle second steps preceding smaller ones (here K-T-S), and larger middle second steps above the lowest note of the mode -- here, approximations of 12/11, 16/13, and 18/11. The fifth step, at a tone below the middle sixth step, likewise approximates 16/11. ------------------------------- 3.5. The Fifth Mode of Mohajira ------------------------------- Folk Rast or Folk Mustaqim Mode (Fifth Mode of Mohajira) |-------- rast-4 ----------|...tone..|------- mohajira-4 -------| Bd4-------C+5------D5------Ed5-------F+5------G5--------A5-------B5 0 207.4 346.3 496.3 703.7 842.6 1050.0 1200 207.4 138,9 150.0 207.4 138.9 207.4 150.0 T S K T S T K 1716 1521 1404 1287 1144 1056 936 858 1/1 44/39 11/9 4/3 3/2 13/8 11/6 2/1 0 208.8 347.4 498.0 702.0 840.5 1049.4 1200 44:39 13:12 12:11 9:8 13:12 44:39 12:11 208.8 138.6 150.6 203.9 138.6 208.8 138.6 Like the Fifth Mode of our first Mohajira-7 set, this version of the Fifth Mode could be described generically as Dudon's Folk Rast, since in classic 13th-14th century Near Eastern theory, Rast relates generally to the tetrachord T-J-J or a tone followed by two middle second steps (J). Since in modern Arab or Turkish music, the term Rast tends to imply more specifically an ordering of T-K-S, we may use Ibn Sina's name Mustaqim for the T-S-K order that prevails here. Interestingly, Ibn Sina's Arabic name _mustaqim_ and the later Persian name _rast_ can both mean "right, correct, proper, standard." Thus we might speak of this version of the Fifth Mode as "Folk Mustaqim." With either set, this mode of Folk Rast (or Folk Mustaqim) follows the generating order of the set: thus larger middle seconds preceding smaller ones in the first set (T-K-S, K-T-S), and smaller middle second preceding larger ones in this set (T-S-K, S-T-K) in this one, in accordance with the ordering of larger and smaller and smaller middle third generators. ------------------------------- 3.6. The Sixth Mode of Mohajira ------------------------------- Bayyati-4|Mohajira-4 Mode (Sixth Mode of Mohajira) |-------- bayyati-4 ----------|------- mohajira-4 -------|...tone..| C+5------D5-------Ed5---------F+5------G5--------A5------Bd5-------C+6 0 138.9 288.9 496.3 635.2 842.6 992.6 1200 138.9 150.0 207.4 138.9 207.4 150.0 207.4 S K T S T K T 156 144 132 117 108 96 88 78 1/1 13/12 13/11 4/3 13/9 13/8 39/22 2/1 0 138.6 289.2 498.0 636.6 840.5 991.4 1200 13:12 12:11 44:39 13:12 9:8 12:11 44:39 138.6 138.6 208.8 138.6 203.9 150.6 208.8 The intriguing Sixth Mode again has a lower bayyati-4 and a conjunct mohajira-4 tetrachord, this time with smaller middle intervals above the lowest note. As with the last set, so with this, the Sixth Mode follows the order of middle third generators, here with the smaller generator first, and so smaller middle second steps first within the ajnas of this mode (S-K-T, S-T-K). In this version of the Sixth Mode, Zalzalian ratios approximated include 13/12 and 13/8 -- and also the fifth step at 13/9, a tone below the middle sixth step at 13/8. In Persian music, around 13/9 is one common tuning for what is termed a koron fifth step, that is, a fifth lowered by about a third of a tone from a perfect fifth at around 3/2. As we'll see (Section 4.3), the Artemisia-10 tuning includes a characteristic variation on the Persian modal family or dastgah of Shur in which this koron fifth plays a prominent role, with two conjunct shur-4 tetrachords (synonymous with Arab bayyati-4), as contrasted with the Sixth Mode of Mohajira with conjunct bayyati-4 and mohajira-4. --------------------------------- 3.7. The Seventh Mode of Mohajira --------------------------------- `Awj Mode (Seventh Mode of Mohajira) |-------- mohajira-4 ---------|...tone...|------- mohajira-4 ---------| Bd4-------C5---------D5------Ed5--------F+5-------G5---------A5------Bd5 0 150.0 357.4 496.3 703.7 853.7 1061.1 1200 150.0 207.4 138.9 207.4 150.0 207.4 138.9 K T S T K T S 1872 1716 1521 1404 1248 1144 1014 936 1/1 12/11 16/13 4/3 3/2 18/11 24/13 2/1 0 150.6 359.5 498.0 702.0 852.5 1061.4 1200 12:11 44:39 13:12 9:8 12:11 44:39 13:12 150.6 208.8 138.6 203.9 150.6 208.8 138.6 The Seventh Mode is again `Awj, with two disjunct mohajira-4 tetrachords, which to some musicians interested in Jacques Dudon's Mohajira-7 set may be the most familiar mode because of its symmetry: in generic terms, J-T-J-T-J-T-J. Here, while two tetrachords are indeed identical (K-T-S), the subtle distinction between larger and smaller middle seconds provides some variety. In either the first Mohajira-7 set or this one, the Seventh Mode has a converse order. Here, with the smaller middle third generator preceding the larger, we have the `Awj mode with larger middle intervals above the lowest voice, approximating 12/11, 16/13, 18/11, and 24/13. In the first set, with the larger middle third generator preceding the smaller, we had smaller middle intervals approximating 13/12, 11/9, 13/8, and 11/6, and an S-T-K order in each mohajira-4 jins (smaller middle second step before larger). ----------------------------------------------------- 3.8. Summary of Mohajira Modes: Second Mohajira-7 Set ----------------------------------------------------- As with Section 2.8 for the first set, this section provides an overview of Mohajira modes for the second set, with each mode indicated as following either a generating order or converse order. Mode 1: Uddal (generating order -- SK) |-------------- uddal-5 -------------|--------- mustaqim-4 -------| Ed4------F+4-------G4--------A4------Bd4-------C+5------D5--------Ed5 0 207.4 346.3 553.7 703.7 911.1 1050.0 1200 207.4 138.9 207.4 150.0 207.4 138.9 150.0 T S T K T S K Mode 2: Nahaft (generating order -- SK) |--------- mohajira-4 ------|...tone..|------ bayyati-4 ------| F+4-------G4--------A4------Bd4-------C+5-----D5-----Ed5------F+5 0 138.9 346.3 496.3 703.7 842.6 992.6 1200 138.9 207.4 150.0 207.4 138.9 150.0 207.4 S T K T S K T Mode 3: Uddal-5|Mohajira-4 (converse order -- KS) |------------- uddal-5 --------------|----- mohajira-4 ------| G4--------A4------Bd4-------C+5------D5-----Ed5------F+5-----G5 0 207.4 357.4 564.8 703.7 853.7 1061.1 1200 207.4 150.0 207.4 138.9 150.0 207.4 138.9 T K T S K T S Mode 4: Mohajirayn (converse order -- KS) |------ mohajira-4 ------|------- mohajira-4 -------|...tone..| A4------Bd4-------C+5-----D5------Ed5-------F+5-----G5---------A5 0 150.0 357.4 496.4 646.3 853.7 992.6 1200 150.0 207.4 138.9 150.0 207.4 138.9 207.4 K T S K T S T Mode 5: Folk Rast or Folk Mustaqim (generating order -- SK) |-------- mustaqim-4 ------|...tone..|------- mohajira-4 -------| Bd4-------C+5------D5------Ed5-------F+5------G5--------A5-------B5 0 207.4 346.3 496.3 703.7 842.6 1050.0 1200 207.4 138,9 150.0 207.4 138.9 207.4 150.0 T S K T S T K Mode 6: Bayyati-4|Mohajira-4 (generating order -- SK) |-------- bayyati-4 ----------|------- mohajira-4 -------|...tone..| C+5------D5-------Ed5---------F+5------G5-------A5-------Bd5-------C+6 0 138.9 288.9 496.3 635.2 842.6 992.6 1200 138.9 150.0 207.4 138.9 207.4 150.0 207.4 S K T S T K T Mode 7: `Awj (converse order -- KS) |-------- mohajira-4 ---------|...tone...|------- mohajira-4 ---------| Bd4-------C5---------D5------Ed5--------F+5-------G5---------A5------Bd5 0 150.0 357.4 496.3 703.7 853.7 1061.1 1200 150.0 207.4 138.9 207.4 150.0 207.4 138.9 K T S T K T S ------------------------------------------------------- 4. Some Other Near Eastern Modes in Artemisia-10 Tuning ------------------------------------------------------- In addition to the two Mohajira-7 sets we've explored, there are some other Near Eastern modes available in Artemisia-10. We look first at two classic tunings, one described by al-Farabi (c. 870-950) and the other by Ibn Sina (c. 980-1037), each expanding by rotation into a family of modes analogous to that of a Mohajira-7 set. These families are of current as well as historical interest for Arab and Persian music. There are also two modes which may be of special interest. The first, a rotation of Ibn Sina's Mustaqim, is in terms of modern Persian music a form of the Dastgah-e Shur, or modal family of Shur, with two conjunct Shur tetrachords (like the Arab Bayyati tetrachords we have met in the Mohajira-7 sets) forming a kind of "twin Shur" that is a beautiful counterpart to the Mohajirayn or "Twin Mohajira" modes (Sections 2.4, 3.4). The second, a form of Arab Hijazkar, nicely complements the modern or disjunct form of Maqam Rast available at the same location of C. In Greek terms, Hijazkar involves chromatic tetrachords, in contrast to the various forms of diatonic tetrachords found in the rotations of Mohajira-7, and also Rast and Mustaqim. ---------------------------------------------------- 4.1. Conjunct and Disjunct Rast, and Other Rotations ---------------------------------------------------- Al-Farabi's "Mode of Zalzal" is a fine example of the Near Eastern modality that by the 13th century would be known as Rast. Starting from the note G in Artemisia-10, we have available this approximation: |--------- rast-4 ----------|---------- rast-4 ---------|...tone..| G4---------A4-------Bd4-----C5--------D5-------Ed5------F---------G5 0 207.4 357.4 496.3 703.7 853.7 992.6 1200 207.4 150.0 138.9 207.4 150.0 138.9 207.4 T K S T K S T 432 384 352 324 288 264 243 216 1/1 9/8 27/22 4/3 3/2 18/11 16/9 2/1 0 203.9 354.5 498.0 702.0 852.6 996.1 1200 9:8 12:11 88:81 9:8 12:11 88:81 9:8 203.9 150.6 143.5 203.9 150.6 143.5 203.9 This diagram shows al-Farabi's just ratios, and a monochord tuning to realize them, based on tetrachords of 108:96:88:81 (9:8-12:11-88:81). The greatest differences from JI values above the lowest note or 1/1 step in the MET-24 version interestingly involve not the Zalzalian or middle intervals (27/22 and 18/11), but the 9/8 tone and 16/9 minor seventh, respectively wide and narrow by some 3.5 cents. Melodically, however, al-Farabi's smaller middle second step of 88:81 (143.5 cents) is compressed to 138.9 cents (a near-just 13:12), a difference of some 4.6 cents. A closer JI model for the MET-24 realization of Rast, and especially the melodic steps, follows the lower tetrachord of Jacques Dudon's "Folk Rast" mode of Mohajira (see Section 2.5): |--------- rast-4 ----------|---------- rast-4 ---------|...tone..| G4---------A4-------Bd4-----C5--------D5-------Ed5------F---------G5 |-------- bayyati-4 --------| 0 207.4 357.4 496.3 703.7 853.7 992.6 1200 207.4 150.0 138.9 207.4 150.0 138.9 207.4 T K S T K S T 1872 1521 1521 1404 1248 1144 1056 936 1/1 44/39 16/13 4/3 3/2 18/11 39/22 2/1 0 208.8 359.5 498.0 702.0 852.6 991.2 1200 44:39 12:11 13:12 9:8 12:11 13:12 44:39 208.8 150.6 138.5 203.9 150.6 138.6 208.8 This JI mode is based on Dudon's tetrachord of 39:44:48:52, which the MET-24 tuning approximates quite closely. This version also shows how, in addition to the two conjunct Rast tetrachords, there is an upper bayyati-4 tetrachord on the fifth step. This choice between a focus on rast-4 on the fourth step, or bayyati-4 on the fifth step, is also a feature of Nahaft (Sections 2.2, 3.2), where the lower or "root" tetrachord is mohajira-4 rather than, as here, rast-4. At some point after the 14th century, this original or conjunct form of Rast became a less common form than the rotation on its fourth step, already known to Safi al-Din in the 13th century as one form carrying the name of Kardaniya, with two disjunct rast-4 tetrachords. Eventually the term Rast came mainly to designate this disjunct form, with the conjunct form as a variation known in modern Arab theory, for example, as Nairuz Rast or Nirz Rast. This disjunct or modern form of Rast is available in Artemisia-10 on the note C: |--------- rast-4 ----------|...tone..|--------- rast-4 ----------| C4---------D4-------Ed4-----F4--------G4---------A4------Bd4------C5 0 207.4 357.4 496.3 703.7 911.1 1061.1 1200 207.4 150.0 138.9 207.4 207.4 150.0 138.9 T K S T T K S 78 88 96 104 117 132 144 156 1/1 44/39 16/13 4/3 3/2 22/13 24/13 2/1 0 208.8 359.5 498.0 702.0 910.7 1061.4 1200 44:39 12:11 13:12 9:8 44:39 12:11 13:12 208.8 150.6 138.6 203.9 207.4 150.6 138.6 A characteristic both of al-Farabi's conjunct Rast, and of modern disjunct Rast as realized in Arab and Turkish practices, is that the larger middle second step precedes the smaller -- that is, a KS order. In MET-24, these steps are at 150.0 and 138.9 cents, closely approximating the superparticular ratios of 12:11 and 13:12 at 150.6 and 138.6 cents. Starting with either conjunct or disjunct Rast, we can derive a set of seven modes by rotation. Here I start with disjunct Rast, since this is the order used in modern Arab theory. Mode 1: Disjunct Rast (rast4-rast4) |--------- rast-4 ----------|...tone..|--------- rast-4 ----------| C4---------D4-------Ed4-----F4--------G4---------A4------Bd4------C5 0 207.4 357.4 496.3 703.7 911.1 1061.1 1200 207.4 150.0 138.9 207.4 207.4 150.0 138.9 T K S T T K S 78 88 96 104 117 132 144 156 1/1 44/39 16/13 4/3 3/2 22/13 24/13 2/1 0 208.8 359.5 498.0 702.0 910.7 1061.4 1200 44:39 12:11 13:12 9:8 44:39 12:11 13:12 208.8 150.6 138.6 203.9 207.4 150.6 138.6 Mode 2: Huseyni (bayyati4-bayyati4) |------ bayyati-4 ----------|...tone..|------- bayyati-4 --------| D4-------Ed4------F5--------G5--------A5-------Bd4------C5-------D5 0 150.0 288.9 496.3 703.7 853.7 992.6 1200 150.0 138.9 207.4 207.4 150.0 138.9 207.4 K S T T K S T 66 72 78 88 99 108 117 132 1/1 12/11 13/11 4/3 3/2 18/11 39/22 2/1 0 150.6 289.2 498.0 702.0 852.5 991.2 1200 12:11 13:12 9:8 9:8 12:11 13:12 44:39 150.6 138.6 203.9 203.9 150.6 138.6 208.8 Maqam Huseyni places an emphasis on the fifth step A, the lowest note of the upper bayyati-4 tetrachord. This JI model for the MET-24 realization, based on tetrachords of 33:36:39:44 (12:11-13:12-44:39), is identical to William Lyman Young's "exquisite 3/4 tone Hellenic lyre" tuning included in the scale archive for Manuel Op de Coul's Scala as young-wt.scl. While the description of Young's scale quoted in the note to the Scale file suggests that it was inspired by ancient Greek music, this tuning happens also to be a fine realization of Maqam Huseyni. Mode 3: Sika (sika-3|rast-4|rast-3) |----- sika-3 ----|--------- rast-4 ----------|------ rast-3 ----| Ed4------F5--------G5--------A5-------Bd4------C5--------D5------Ed5... 0 138.9 346.3 553.7 703.7 842.6 1050.0 1200 138.9 207.4 207.4 150.0 138.9 207.4 150.0 S T T K S T K 72 78 88 99 108 117 132 144 1/1 13/12 11/9 11/8 3/2 13/8 11/6 2/1... 0 138.9 347,4 551.3 702.0 840.5 1049.4 1200 13:12 44:39 9:8 12:11 13:12 44:39 12:11 138.6 203.9 203.9 150.6 138.6 208.8 150.6 Maqam Sika, which gets its name from the Arabic form of Persian Segah (the "third" note or position), has a structure featuring a lower or root jins of a trichord (S-T) rather than a tetrachord, with an emphasis on the third step of the mode. There follows a middle tetrachord of rast-4, and, if we view Sika for the moment as though it were an octave mode, an upper rast-3 trichord (T-K). In practice, however, Sika freely crosses octave boundaries with its ajnas, so that the upper rast jins typically expands into a full rast-4 pulling up to the step F5 (C5-D5-Ed5-F5 or T-K-S). The sika-3 trichord is a modern manifestation of the same sensibility as the classic tetrachord known as `iraq, either K-T-S or, as here, S-T-K. As we shall see in Mode 7, fittingly named Maqam `Iraq, it is possible to find this `iraq tetrachord in modern Arab theory; but, in practice, it is the sika-3 trichord that serves as a division between the ajnas or genera as sung or played. Certain modern Near Eastern styles do feature the `iraq-4 tetrachord or an equivalent: for example, the Persian Dastgah-e Segah, which has a lower tetrachord of this variety. However, given the less common use of this type of tetrachord in Arab practice as a distinct jins or genus -- in contrast to the very common use of the sika-3 trichord -- Dudon's Mohajira may be seen as the revival of classic Near Eastern modalities such as `Awj and Nahaft featuring this tetrachord. Mode 4: Najdi (najdi-5|rast-4) |------------ najdi-5 ----------------|---------- rast-4 ----------| F4--------G4---------A4-------Bd4-----C5--------D5-------Ed5------F5 0 207.4 414.8 564.8 703.7 911.1 1061.1 1200 207.4 207.4 150.0 138.9 207.4 150.0 138.9 T T K S T K S 792 702 624 572 528 468 429 396 1/1 44/39 33/26 18/13 3/2 22/13 24/13 2/1 0 288.8 412.7 563.4 702.0 910.8 1061.4 1200 44:39 9:8 12:11 13:12 44:39 12:11 13:12 208.8 203.9 150.6 208.8 208.8 150.6 138.6 Najdi, the fourth rotation of disjunct or modern Rast, has a structure rather like Uddal as the First Mode of Mohajira-7 (Sections 2.1, 3.1), but with a major third rather than the middle third of Uddal. Here the pattern for the lower pentachord is T-T-K-S, with two tones, followed by a larger and then a smaller middle second step; with Uddal, the pattern is T-K-T-S, that is: tone, larger middle second, tone, smaller middle second. Both modes share the raised fourth step, here at around 18/13 (as also in the Uddal in Section 1.1) and the upper Rast tetrachord on the fifth step. In 21st-century derivative polyphony representing a "fusion" of Near Eastern and medieval European styles, both Uddal and Najdi feature a three-voice cadence where a middle third and sixth above the lowest note expand stepwise to a fifth and octave on the final. Thus in this version of Najdi, or also the Uddal of Section 1.1: Ed5----F5 Bd4----C4 G4-----F4 This is from a (neo)medieval European perspective a variation on standard 13th-14th century cadences like this, with either a minor or major third and sixth (the latter preferred by the early 14th century) expanding to fifth and octave respectively, with characteristic motion of the two upper voices in fourths: E5-----F5 B4-----C5 G4-----F4 In a Near Eastern context, Najdi is beautiful in purely melodic terms, although it appears to be one of the less common rotations or variations on Rast. A more common form is Maqam Jaharka on the fourth step of Rast (jaharkah being the Arabic form of Persian chahargah, the "fourth" step or position). Maqam Jaharka differs from Najdi in having a perfect rather than raised fourth step, so that there are two disjunct tetrachords. The lower tetrachord is called `ajam, with two tones (as in Najdi) and a regular semitone to complete the 4:3 fourth, thus F3-G3-A3-Bb4, then a tone of disjunction Bb4-C5, and then, as in Najdi, an upper Rast tetrachord, C5-D5-Ed5-F5. In classic Near Eastern theory, a regular diatonic semitone is called a bakkiya, shown by the letter B, so an `ajam tetrachord would be notated T-T-B, and Maqam Jaharka as T-T-B-T-T-K-S. Maqam Jaharka is available in Artemisia-12, an expansion of the Artemisia-10 set (see Section 5). However, one advantage of focusing on the decatonic set is that it may highlight some modal forms such as Maqam Najdi which are less well known and appreciated. Mode 5: Conjunct or Classic Rast (rast-4|rast=4 or rast-5|bayyati-4) |--------- rast-4 ----------|---------- rast-4 ---------|...tone..| G4---------A4-------Bd4-----C5--------D5-------Ed5------F---------G5 |-------- bayyati-4 --------| 0 207.4 357.4 496.3 703.7 853.7 992.6 1200 207.4 150.0 138.9 207.4 150.0 138.9 207.4 T K S T K S T 1872 1716 1521 1404 1248 1144 1056 936 1/1 44/39 16/13 4/3 3/2 18/11 39/22 2/1 0 208.8 359.5 498.0 702.0 852.6 991.2 1200 44:39 12:11 13:12 9:8 12:11 13:12 44:39 208.8 150.6 138.5 203.9 150.6 138.6 208.8 This conjunct version of Maqam Rast was discussed at the beginning of this section. One attractive option is to take the upper bayyati-4 jins on the fifth step of D as the basis for a modulation to Maqam Huseyni, the second rotation of disjunct Rast, on this step, eventually returning to a focus on the lower tetrachord (or pentachord) of Rast. There is an invitation to contrasts between a focus on the two conjunct rast tetrachords, an approach which tends to highlight the fourth step C5 common to both tetrachords; and a focus on the lower pentachord of Rast (in Turkey theory, rast-5) and the upper bayyati-4, and approach which tends to highlight the fifth step of D5 and also opens the way to a possible modulation to Huseyni on D. Mode 6: Bayyatayn or "Twin Bayyati" (bayyati-4|bayyati-4|tone) |------- bayyati-4 --------|-------- bayyati-4 --------|...tone...| A4-------Bd4-----C5--------D5------Ed5-----F5---------G5---------A5 0 150.0 288.9 496.3 646.3 785.2 992.6 1200 150.0 138.9 207.4 150.0 138.9 207.4 207.4 K S T K S T T 66 72 78 88 96 104 117 132 1/1 12:11 13/11 4/3 16/11 52/33 39/22 2/1 0 150.6 289.2 498.0 648.7 787.3 991.2 1200 12:11 13:12 44:39 12:11 13:12 9:8 44:39 150.6 138.5 208.8 150.6 138.6 203.4 208.8 This version of Bayyatayn or "Twin Bayyati" with its two conjunct bayyati-4 tetrachords follows the same order as Rast in placing larger before smaller middle second steps (K-S-T). Near Eastern writers of the 9th-11th century, including Ibn Sina, discuss a technique of ornamentation by playing more than one note at the same time (e.g. on the `oud), and Ibn Sina especially likes fourths. Bayyatayn, for musicians interested in this kind of simple polyphony, invites passages in parallel fourths, an approach underscored by the absence of a perfect fifth step in this mode. As we shall see in the next section (4.2), a form of "Twin Shur" with the same basic tetrachords but a converse order of middle second steps in the shur tetrachords (equivalent to Arab bayyati-4), S-K-T, is one characteristic configuration used in Dastgah-e Shur. Mode 7: `Iraq (sika3|bayyati4-rast-3) |----- sika-3 ----|--------- bayyati-4 --------|------ rast-3 ----| Bd4------C5--------D5-------Ed5------F5--------C5--------D5-0-----Ed5... 0 138.9 346.3 496.3 635.2 842.6 1050.0 1200 138.9 207.4 150.0 138.9 207.4 207.4 150.0 S T K S T T K 72 78 88 96 104 117 132 144 1/1 13/12 11/9 4/3 13/9 13/8 11/6 2/1... 0 138.9 347,4 496.3 636.6 840.5 1049.4 1200 13:12 44:39 12:11 13:12 9:8 44:39 12:11 138.6 208.8 150.6 138.6 203.9 208.8 150.6 |-------- `iraq-4 ---------|--------------- sika-5 ---------------| Maqam `Iraq, the seventh rotation of disjunct Rast, has a structure rather like Maqam Sika (the third rotation), with lower sika-3, a middle bayyati-4 (as compared to the rast-4 of Sika), and an upper rast-3 that typically expands into a full rast-4 going beyond the octave and leading up to F5 to complete the fourth C5-F5. Like Maqam Sika, Maqam `Iraq as a rotation of Rast has a converse ordering of middle second steps, with the smaller step first, and smaller middle intervals above the lowest voice, here approximating 13/12, 11/9, 13/8, and 11/6 -- and also 13/9 as the lowered fifth step. As shown at the bottom of the diagram, in some modern Arab theory as surveyed by Scott Marcus, Maqam `Iraq can be analyzed as a lower iraq-4 tetrachord (here S-T-K) plus an upper sika-5 pentachord (S-T-T-K). This approach harkens back to the Systematist school of Safi al-Din in the 13th century, and his followers and commentators through the following generators, who often build modes by joining a lower tetrachord to an upper pentachord. Safi al-Din in his _Kitab al-Adwar_ or "Book of Cycles" defines seven types of lower tetrachords and 12 types of upper pentachords, cataloguing each possible combination to arrive at a set of 84 modes. There is no reason that the interpretation of a lower `iraq-4 jins and upper sika-5 might not be translated into musical practice; it would produce different musical patterns than the prevailing Arab interpretation of a lower sika-3 trichord and conjunct bayyati-4 tetrachord, for example inviting a greater emphasis on the fourth step of the mode, as compared with the focus on the third step in the standard Arab interpretation. Eric Ederer, in studying modern Turkish theory and practice, concludes that although maqamat are often analyzed in terms of tetrachords or pentachords only, performers understand maqamat such as Segah (corresponding to Arab Sika) and related forms to involve a lower trichord (like the Arab sika-3) plus a conjunct tetrachord, etc. However, the understanding in practice as well as theory of a lower tetrachord of the `iraq-4 variety (or Jacques Dudon's mohajira-4) in the Persian Dastgah-e Segah, for example, shows how alternative interpretations of the same set of notes and intervals are possible. In performances based on modern Near Eastern styles, the sika-3 interpretation is appropriate and beautiful. In the context of a performance focusing on classic 11th-15th century modes, or modern counterparts in a Mohajira-7 set, experimenting with alternative understandings of the ajnas or genera in rotations of Rast such as Sika and `Iraq is an added possibility. -------------------------------------- 4.2. Ibn Sina's Mustaqim and Rotations -------------------------------------- Ibn Sina's Mustaqim is another form of what 13th-century Near Eastern theory would call Rast, meaning the classic form of conjunct Rast. Indeed Ibn Sina places the middle third of Zalzal in his `oud tuning, featured in this mode, at 39/32 (342.5 cents), very close to the slightly higher placement reported as common by Safi al-Din at 72/59 (344.7 cents). Thus in the 13th century, Ibn Sina's Mustaqim and the mode known to Safi al-Din as Rast would be essentially synonymous, even as the names of Mustaqim and Rast are simply Arabic and Persian words for the same concepts of "right, correct, proper, standard, orthodox." From a 21st-century perspective, however, Maqam Rast is widely understood in Arab and Turkish music to mean a form of this mode (or the closely related modern form with disjunct tetrachords) where the larger middle second precedes the smaller: that is, with tetrachords of T-K-S. Thus Ibn Sina's term Mustaqim is a handy way to describe the same basic modal forms with tetrachords where the smaller middle second precedes the larger, T-S-K. In other words, from a current perspective, Rast would be a generic term for a mode featuring conjunct or disjunct tetrachords of T-J-J (with the Systematist notation "J" simply meaning a mujannab or middle second step, whether larger or smaller); while Mustaqim or T-S-K is a species of Rast. When the term Rast is used without qualification, however, it often tends to imply the prevailing Arab and Turkish arrangement of T-K-S. There are actually three classic models for Mustaqim, two of them relating to practical tunings. Thus Ibn Sina recommends a tuning of 1/1-9/8-39/32-4/3 (0-203.9-342.5-498.0 cents), or 9:8-13:12-128:117 (203.9-138.6-155.6 cents). Safi al-Din's account of a common practical tuning, which he makes the basis of one of his principal tetrachords, is as mentioned very similar: 1/1-9/8-72/59-4/3 (0-203.9-344.7-498.0 cents) or 9:8-64:59-59:54 (203.9-140.8-153.3 cents). In fact, Ibn Sina reports as one practice of his time the fretting that Safi al-Din expresses in mathematical terms, by saying that some people place the wusta Zalzal or middle third fret at midway between the usual frets for a tone (9/8) and fourth (4/3). If we take the overall length of a string at 72, then the 9/8 fret would be at a length of 64, and the 4/3 fret at a length of 54. The midpoint of these two frets would be 59, thus producing the tetrachord which Safi al-Din adopts as an integral part of his system. The tempered MET-24 version of Mustaqim is generally closer to Safi al-Din's tuning, with the middle third at 346.3 cents being nearer to 72/59 than to 39/32: Comparison with Ibn Sina's tuning |------- mustaqim-4 -------|------- mustaqim-4 ------|...tone...| F+4-------G+4------A4------Bd4-------C+5------D5-----Ed5--------F+5 0 207.4 346.3 496.3 703.7 842.6 992.6 1200 |--------- shur-4 ---------| 207.4 138,9 150.0 207.4 138.9 150.0 207.4 T S K T S K T 1872 1664 1536 1404 1248 1152 1053 936 1/1 9/8 39/32 4/3 3/2 13/8 16/9 2/1 0 203.9 342.5 498.0 702.0 840.5 996.1 1200 9:8 13:12 128:117 9:8 13:12 128:117 9:8 203.9 138.6 155.6 203.9 138.6 155.6 203.9 Comparison with Safi al-Din's tuning |------- mustaqim-4 -------|------- mustaqim-4 ------|...tone...| F+4-------G+4------A4------Bd4-------C+5------D5-----Ed5--------F+5 0 207.4 346.3 496.3 703.7 842.6 992.6 1200 |--------- shur-4 ---------| 207.4 138.9 150.0 207.4 138.9 150.0 207.4 T S K T S K T 288 256 236 216 192 177 162 144 1/1 9/8 72/59 4/3 3/2 96/59 16/9 2/1 0 203.9 344.7 498.0 702.0 842.8 996.1 1200 9:8 64:59 59:54 9:8 64:59 59:54 9:8 203.9 140.8 153.3 203.9 140.8 153.3 203.9 Ibn Sina additionally provides a simplified mathematical model for his tetrachord of 9:8-13:12-128:117, evidently not meant as a practical implementation. Following his earlier observation that the large middle second step of 128:117 in his tuning "resembles" the simpler and superparticular ratio of 12:11, he remarks that the two middle second steps are thus 13:12 and approximately 12:11. If one attempted literally to implement a tetrachord with just steps of 13:12 and 12:11, for example starting from the 4/3 fret, and subtracting first 1/12 of this length, and then 1/13 of the remaining length to place the fret for the tone, then the tone would be at 44/39 (208.8 cents) instead of the standard 9/8 (203.9 cents). Ibn Sina need not be concerned with this complication, since he is apparently offering a theoretical superparticular approximation for his upper interval or 128:117 rather than defining a practical tuning. It would seem unlikely that he was intent on changing the traditional placement of the 9/8 fret, for example. However, in the tempered tuning of MET-24, Ibn Sina's theoretical model of a tetrachord at 44:39:36:33 or 44:39-13:12-12:11 (208.8-138.6-150.6 cents) serves as a close approximation. While the ratios for a single tetrachord at 44:39:36:33 are strikingly simple. a JI tuning Mustaqim reflecting some of the fine points of the MET-24 realization requires much higher numbers for a monochord division, comparable to those for Ibn Sina's Mustaqim (9:8-13:12-128:117): |------- mustaqim-4 -------|------- mustaqim-4 ------|...tone...| F+4-------G+4------A4------Bd4-------C+5------D5-----Ed5--------F+5 0 207.4 346.3 496.3 703.7 842.6 992.6 1200 |--------- shur-4 ---------| 207.4 138,9 150.0 207.4 138.9 150.0 207.4 T S K T S K T 1716 1521 1404 1287 1144 1056 968 858 1/1 44/39 11/9 4/3 3/2 13/8 39/22 2/1 0 208.8 347.4 498.0 702.0 840.5 991.2 1200 44:39 13:12 12:11 9:8 13:12 12:11 44:39 208.8 138.6 150.6 203.9 138.6 150.6 208.8 For example, the tempered tone at 207.4 cents represents both 44:39 (208.8 cents) and 9:8 (203.9 cents). In JI, the fourth between the 11/9 and 13/8 steps would be at 117:88 (493.1 cents), narrower than a pure 4:3 (498.0 cents) by 352:351 or 4.925 cents). In the tempered version, however, all fourths are slightly narrow by 1.756 cents, and all fifths wide by the same amount. Having noted these fine points about the classic practical tunings for Mustaqim, and Ibn Sina's theoretical model, we may consider the rotations of Mustaqim, which are the same as for Rast apart from the different ordering of larger and smaller middle second steps, and thus the sizes of other middle intervals. Mode 1: Mustaqim (mustaqim-4|mustaqim-4|tone) |------- mustaqim-4 -------|------- mustaqim-4 ------|...tone...| F+4-------G+4------A4------Bd4-------C+5------D5-----Ed5--------F+5 0 207.4 346.3 496.3 703.7 842.6 992.6 1200 |--------- shur-4 ---------| 207.4 138,9 150.0 207.4 138.9 150.0 207.4 T S K T S K T 1716 1521 1404 1287 1144 1056 968 858 1/1 44/39 11/9 4/3 3/2 13/8 39/22 2/1 0 208.8 347.4 498.0 702.0 840.5 991.2 1200 44:39 13:12 12:11 9:8 13:12 12:11 44:39 208.8 138.6 150.6 203.9 138.6 150.6 208.8 If one is considering Mustaqim as a form or variation of Maqam Rast, then the upper tetrachord on the fifth step, representing in Arab terms bayyati-4, but which in a Persian context might be called shur-4, offers an alternative focus for emphasis to the twin mustaqim-4 tetrachords on the first and fourth steps. While the maqam tradition prevailed in Persia along with the Arab world in the era of Ibn Sina and Safi al-Din al-Urmawi, around the 16th-18th centuries this tradition developed into the modern Persian or more generally Iranian dastgah system. While the maqam tradition often involves extended performances in which a performer focuses on a given maqam while modulating into many other maqamat, the dastgah system in effect condenses this approach into a more structured performance within a given dastgah family of modes, moving through a suite of gushe-ha (Persian plural of gushe) or melodic themes, some of them independent modes in their own right. Some of the dastgah-ha are rather closely related to maqamat found in Arab or Turkish practice: thus Dastgah-e Shur (the "Dastgah of Shur") resembles Arab Maqam Bayyati or Turkish Maqam Ushshak. However, as it happens, there is no Dastgah-e Mustaqim in modern Persian classical music, although certain gushe-ha may resemble Mustaqim. Thus this discussion generally takes a more "maqamistic" perspective, although Mustaqim does contain much of the material for the modern Iranian dastgah system. However, I will use some Persian terms for ajnas or genera, for example "shur-4" for the tetrachord on the fifth step of Mustaqim. This usage focuses on intervallic patterns relevant to the dastgah system, although not on the specific features of that system. Within the context of Artemisia-10, Mustaqim differs from classic Nahaft, and more particularly the exquisite shading of Jacques Dudon's Ibina (see Section 3.2), only in that the second step is a tone rather than a middle second (here, G+4 rather than G4). Mode 2: Twin Shur (shur-4|shur-4|tone) |-------- bayyati-4 ----------|------- mohajira-4 -------|...tone..| G+4------A4-------Bd4---------C+5------D5------Ed5-------Bd5-------C+6 0 138.9 288.9 496.3 635.2 785.2 992.6 1200 138.9 150.0 207.4 138.9 150.0 207.4 207.4 S K T S K T T 156 144 132 117 108 99 88 78 1/1 13/12 13/11 4/3 13/9 52/33 39/22 2/1 0 138.6 289.2 498.0 636.6 787.3 991.4 1200 13:12 12:11 44:39 13:12 12:11 9:8 44:39 138.6 138.6 208.8 138.6 150.6 203.9 208.8 This mode evokes one aspect of the Iranian Dastgah-e Shur in ways that will be addressed in Section 4.3. It is also a possible realization of the Arab Maqam Bayyatayn or "Twin Bayyati" using tetrachords of S-K-T rather than K-S-T. Both of these arrangements are more generally used in the Bayyati family of maqamat. For many Arab musicians, Maqam Bayyati and related forms call for an order of S-K-T (smaller middle second first), in contrast to the order of K-S-T that would result from starting these maqamat on the second step of Rast (with the lower pentachord of Maqam Rast as T-K-S-T, producing a tetrachord of K-S-T from its second degree). Scott Marcus and Jacques Dudon report a widespread understanding that an idiomatic Bayyati should be S-K-T. The 20th-century Syrian theorist Tawfiq al-Sabbagh, however, known for his attentiveness to fine nuances of intonation, describes the lower tetrachord of Bayyati in terms of the 53-comma system of Turkey and Syria as 7-6-9 commas, or in our terms as K-T-S. Amine Beyhom notes two different tastes and practices in Lebanon: a learned or classical style setting the first step of Bayyati at around 155 cents, similar to the first middle second of Rast; and a popular style setting it appreciably lower, around 130 cents. Thus the above tuning of the Twin Shur or also Bayyatayn mode might be highly idiomatic to many Arab musicians, although tastes vary. Mode 3: `Iraq of Mustaqim (`iraq-4|sika-5) |--------- `iraq-4 -----------|-------------- sika-5 ---------------| A4--------Bd4---------C+5------D5--------Ed5------F+5-------G+5------A5 0 150.0 357.4 496.3 646.3 853.7 1061.1 1200 |----- muye-3 -----| 150.0 207.4 138.9 150.0 207.4 207.4 138.9 K T S K T T S 144 132 117 108 99 88 78 72 1/1 12/11 16/13 4/3 16/11 18/11 24/13 2/1 0 150.6 359.5 498.0 648.7 852.5 1061.4 1200 12:11 44:39 13:12 12:11 9:8 44:39 13:12 150.6 208.8 138.6 150.6 203.9 208.8 138.6 Here the lower tetrachord is characteristic of the modern Iranian Dastgah-e Segah, where Hormoz Farhat identifies the intervals as a larger middle second, a tone, and a smaller middle second (in our terms, K-T-S). However, there are various intricacies and inflections in this dastgah which go beyond the scope of this discussion. One touch which is available within this mode is focusing on a trichord from the third to the fifth step (C+5-D5-Ed5) whose S-K order is identical to that of Shur, and might be described as a "shur-3" trichord. Hormoz Farhat identifies this focus as Gushe-ye Muye (the Gushe or melodic theme of Muye), and in the Dastgah-e Shur it occurs after first exploring the lower tetrachord, which could be described in classic terms as `iraq-4, or in this context as a segah-4 because of its central role in the Daramad or opening of Shur which sets the tone for the dastgah. This tetrachord is synonymous with Jacques Dudon's mohajira-4. Following a classic Systematist approach noted by some modern Arab theorists, it is possible to regard this mode as a lower `iraq=4 and upper sika-5, using the Arabic name sika (equivalent to Persian segah), since it is identical to the first five notes of Maqam Sika (although there the division is into a lower trichord and middle tetrachord, etc., see Section 4.1). One could also treat this mode as an intonational variation on Arab Maqam `Iraq, with the same basic structure but a converse order of larger and smaller middle seconds. This approach would invite a prominent focus on the bayyati-4 tetrachord on the third step (C+5-D5-Ed5-F+5), a focus somewhat resembling that of Gushe-ye Muye in Iranian Segah with its similar trichord (C+5-D5-Ed5) on this step. In the spirit of Jacques Dudon's Mohajira, which seeks to bring back into more common use classic modal forms or intonation where these is little modern practice to serve as a guide. one might also approach this mode experimentally, seeking out various divisions and ajnas and seeing which seem most pleasing. Mode 4: Disjunct Mustaqim (Mustaqim4-Mustaqim4) |------- mustaqim-4 -------|...tone..|-------- mustaqim-4 --------| Bd4-------C+5------D5------Ed5-------F+5--------G+5-------A5-------Bd5 0 207.4 346.3 496.3 703.7 911.1 1050.0 1200 207.4 138,9 150.0 207.4 207.4 138.9 150.0 T S K T T S K 132 117 108 99 88 78 72 66 1/1 44/39 11/9 4/3 3/2 22/13 11/6 2/1 0 208.8 347.4 498.0 702.0 910.8 1049.4 1200 44:39 13:12 12:11 9:8 44:39 13:12 12:11 208.8 138.6 150.6 203.9 208.8 138.6 150.6 Disjunct Mustaqim could be treated like a low version of modern Arab or Turkish Rast, since it follows the same pattern, apart from the converse order of middle second steps (T-S-K rather than T-K-S) and thus the smaller sizes of middle intervals. Scott Marcus reports that at least one 20th-century Arab theorist associates this T-S-K variation on Rast with a Maqam Rast Jadid ("New Rast"), which may have a _sayir_ (melodic procedure or development) differing from that of usual Arab Rast with a T-K-S pattern. Mode 5: Disjunct Shur (shur4-shur4) |-------- shur-4 ----------|...tone..|---------- shur-4 --------| C+5------D5------Ed5-------F+5-------G+5-----A5------Bd5--------C+6 0 138.9 288.9 496.3 703.7 842.6 992.6 1200 138.9 150.0 207.4 207.4 138.9 150.0 207.4 S K T T S K T 156 144 132 117 104 96 88 78 1/1 13/12 13/11 4/3 3/2 13/8 39/22 2/1 0 138.6 289.2 498.0 702.0 840.5 991.2 1200 13:12 12:11 9:8 9:8 13:12 12:11 44:39 138.6 150.6 203.9 203.9 139.5 150.6 208.8 This beautiful mode is one aspect of the Iranian Dastgah-e Shur, with at least some performances of the national song _Ay, Iran_ giving prominence to the middle sixth step, here tuned at a near-just 13/8 (and almost precisely at the 96/59 ratio, 842.8 cents, which would result from Safi al-Din's middle third at 72/59 plus a pure 4:3 fourth). The pattern is similar to Arab or Turkish Maqam Huseyni as the second rotation of Rast, but with smaller middle intervals, and tetrachords of S-K-T rather than K-S-T. Mode 6: Sika of Mustaqim (sika-5|`iraq-4) |------------- sika-5 ----------------|--------- `iraq-4 --------| D5------Ed5--------F+5-------G+5------A5------Bd5-------C+6------D6 0 150.0 357.4 564.8 703.7 853.7 1061.1 1200 150.0 207.4 207.4 138.9 150.0 207.4 138.9 K T T S K T S 144 132 117 104 96 88 78 72 1/1 12/11 16/13 18/13 3/2 18/11 24/13 2/1 0 150.6 359.5 563.4 702.0 852.6 1061.4 1200 12:11 44:39 9:8 13:12 12:11 44:39 13:12 150.6 208.8 203.9 139.5 150.6 208.8 138.6 This mode is like Maqam Sika, but with a converse order of larger and middle second step. In a Systematist-like view, it could be analyzed as a lower sika-5 pentachord and upper `iraq-4 (or mohajira-4) tetrachord. If taken as a variation on Maqam Sika, the scheme of that maqam might apply: lower sika-3 (here K-T), middle mustaqim-4 (T-S-K), and upper mustaqim-3/4, which might pull up beyond the octave to the step Ed6 to complete a mustaqim tetrachord (Bd5-C+6-D6-Ed6). A subtle and interesting difference from Sika of a usual Arab Rast is that the step below the final of the mode D5, or its octave, D6, is a smaller middle second below it, here 138.9 cents (a virtually just 13:12), allowing for a more economic cadential motion (C+5-D5 or C+6-D6). In a usual Arab Sika, where the usual step below the final (e.g. D5-Ed5 or D6-Ed6 in Artemisia-10 at 150.0 cents, a virtually just 12:11) is a larger middle second, performers sometimes make small adjustments at cadences to raise the note below the final and so obtain a smaller cadential step. This kind of nuance is available in the full MET-24 tuning. Mode 7: Najdi of Mustaqim (najdi-5|mustaqim-4) |-------------- najdi-5 ---------------|------ mustaqim-4 ---------| Ed5--------F+5--------G+5------A5------Bd5-------C+6------D6-------Ed5 0 207.4 414.8 553.7 703.7 911.1 1050.0 1200 207.4 207.4 138.9 150.0 207.4 138.9 150.0 T T S K T S K 132 117 104 96 88 78 72 66 1/1 44/39 33/26 11/8 3/2 22/13 11/6 2/1 0 150.6 412.7 553.3 702.0 910.7 1049.4 1200 44:39 9:8 13:12 12:11 44:39 13:12 12:11 208.8 203.9 139.5 150.6 208.8 138.6 150.6 This rotation of Mustaqim is a variation of Maqam Najdi with a converse order of smaller and larger middle second steps. Like a usual Najdi, it might be viewed as a lower tone plus two conjunct tetrachords of rast-4, here in its mustaqim-4 shading (T-S-K rather than T-K-S). In experimental settings, there are some interesting possibility for polyphony involving this mode. Here the Najdi (and Uddal) cadence discussed in Section 4.1 takes on a different shading with its smaller middle third and sixth: D6-----Ed6 A5-----Bd5 F+5----Ed5 Here the third at 346.3 cents and sixth at 842.6 cents are at a near-just 11/9 and 13/8, with each upper voice ascending by 150.0 cents (a near-just 12:11) while the lowest voice descends by a tone. Adapting a 13th-century European idiom to this mode, we might arrive at progressions like the following: Ed6---D6--C+6---D6--Ed6 Bd5-------C+6-------Bd5 Ed5-------F+5-------Ed5 The three voices start at a richly stable 2:3:4 sonority, Ed5-Bd5-Ed6 (with the fifth and fourth respectively wide and narrow by 1.756 cents), and the highest voice descends through D6, creating a momentary sonority of Ed5-Bd-D6 (0-703.7-1050.0 cents) at a near-just 6:9:11, which resolves to the stable fifth F+5-C+6, with the outer 11:6 middle seventh contracting to a fifth, and the 11:9 middle third between the two upper voices contracting to a unison. Then the highest voice ascends through D6, creating a momentary sonority of F+6-C+6-D6 or 0-703.7-842.6 cents or a near-just 8:12:13, which resolves back to the stable 2:3:4 sonority Ed5-Bd5-Ed6, with the outer 13:8 middle sixth expanding to an octave, and the upper 13:12 middle second expanding to a fourth. It is characteristic of this procedure that the lower two voices move together in fifths, while the upper voice moves in contrary motion, giving rise to momentary unstable sonorities which resolve by directed stepwise contrary motion. From a purely melodic standpoint, which is the usual focus of maqam and dastgah music, there is the possibility of seeking out various ajnas or genera potentially present within a mode such as this. For example, at the fourth to seventh steps of Najdi we have an `iraq-4 or mohajira-4 tetrachord A5-Bd5-C+6-D6. Focusing at some point upon this tetrachord, one might modulate into the Mohajirayn or Twin Mohajira discussed in Section 3.4, the mode of A5-Bd5-C+6-D6-Ed6-F+6-G6-A6. Another possibility would be an engaging mode of the Systematist era (13th-15th centuries) known as Rahawi, with conjunct tetrachords of lower `iraq-4 or mohajira-4, and upper bayyati-4 (or shur-4). Rahawi Mode (`iraq-4|bayyati-4|tone) |-------- `iraq-4 -------|------- bayyati-4 --------|...tone..| A4------Bd4-------C+5-----D5------Ed5-----F5--------G5---------A5 0 150.0 357.4 496.4 646.3 785.2 992.6 1200 150.0 207.4 138.9 150.0 138.9 207.4 207.4 K T S K S T T 624 572 507 468 429 396 352 312 1/1 12/11 16/13 4/3 16/11 52/33 39/22 2/1 0 150.6 359.5 498.0 648.7 787.3 991.2 1200 12:11 44:39 13:12 12:11 13:12 9:8 44:39 150.6 208.8 138.6 150.6 138.6 203.9 208.8 The shift between the iraq-4 (or mohajira-4) and bayyati-4 tetrachords has a captivating and enchanting quality that fits well with Jacques Dudon's Mohajira-7 set of modes, although it does not itself occur within that set. With Systematist modes like Rahawi where details on the original sayir or melodic pathway and development may be largely unknown, musical intuition and inspiration from known practices in the classic and later eras are the best available guides. This process of creativity is also one important aspect of Dudon's Mohajira tunings and related forms. --------------------------------------------- 4.3. Twin Shur and the Iranian Dastgah-e Shur --------------------------------------------- One of the rotations of Mustaqim addressed in the last section is of special interest as it represents one facet of the Persian, or more generally Iranian, Dastgah-e Shur: Mode 2: Twin Shur (shur-4|shur-4|tone) |-------- bayyati-4 ----------|------- mohajira-4 -------|...tone..| G+4------A4-------Bd4---------C+5------D5------Ed5-------Bd5-------C+6 0 138.9 288.9 496.3 635.2 785.2 992.6 1200 138.9 150.0 207.4 138.9 150.0 207.4 207.4 S K T S K T T 156 144 132 117 108 99 88 78 1/1 13/12 13/11 4/3 13/9 52/33 39/22 2/1 0 138.6 289.2 498.0 636.6 787.3 991.4 1200 13:12 12:11 44:39 13:12 12:11 9:8 44:39 138.6 138.6 208.8 138.6 150.6 203.9 208.8 In modern Persian classical music, Shur is the premier dastgah or modal family, as exemplified by its signature tetrachord of S-K-T, that is, smaller and larger middle second steps followed by a tone. The tuning here of approximately 52:48:44:39 or 13:12-12:11-44:39 (in JI, 138.6-150.6-208.8 cents) may by typical of one common practice, but there is great variety. Thus Hormoz Farhat prefers a tuning of around 135-160-205 cents (comparable to a permutation of Ibn Sina's Mustaqim, 13:12-128:117-9:8 at 138.6-155.6-203.9 cents), while Dariush Safvate in 1966 used a tuning of 136-140-224 cents, with a minor third at 276 cents, in contrast to Farhat's 295 cents or so. Here the minor third at 288.9 cents is a virtually just 13:11 (289.2 cents). In a performance in Dastgah-e Shur, the modal family of Shur, the music opens in the Daramad, focusing mainly on the lower tetrachord above the final, and then moves through an assortment of melodic themes and modal configurations. One of these configurations features two conjunct Shur tetrachords, one on the final or resting note (Here G+4), and the other on the fourth step (here C+5). Thus this Twin Shur mode is a kind of snapshot or vignette from the larger scenario of a performance in Shur. This set of notes alone cannot realize the full scope of a Shur performance, in part because there is no 3/2 or perfect fifth step above the final, which does play an important role in the larger structure of Shur. However, the step D5 at around 13/9, known as a "koron fifth" after the koron, a Persian accidental (shown in ASCII as "p") that lowers a note often by about a third of a tone, plays a role frequently as important as that of the 3/2. Here the koron fifth is at 635.2 cents, around 13/9 (636.6 cents), or about a third of a tone below 3/2 (which is not present in Artemisia-10). A very characteristic idiom in Shur is to descend from the minor sixth (here 785.2 cents, which can represent either 52/33 at 787.3 cents or the slightly smaller 11/7 at 782.5 cents) through the koron fifth to the fourth, on the way down toward the final. In a fuller realization of Shur, the contrast between the regular fifth at around 3/2 and this koron fifth at somewhere not too far generally from 13/9 (Farhat places it at an even 630 cents), with the koron fifth especially expressive in descending passages, is one of the cardinal features of this dastgah. In the more limited setting of Artemisia-10, this vignette from Dastgah-e Shur with two conjunct Shur tetrachord could be used either to explore some of the Iranian gushe-ha or melodic themes which relate to this configuration; or to improvise in a more experimental way. The tuning would also fit the Arab Maqam Bayyatayn or "Twin Bayyati." I should add that in the full MET-24, there are other locations where a full realization of the Dastgah-e Shur is possible. Artemisia-10 is only a kind of modal sampler, but one which may encourage a focus on some less well-known modes -- less well-known especially in the West, where there is a widespread assumption (challenged by much Near Eastern practice) that any valid mode must have a perfect fifth or 3/2 step. -------------------------------------------- 4.4. Maqam Hijazkar and its Relation to Rast -------------------------------------------- A popular maqam available on C, also the final for a modern or disjunct Rast, is Maqam Hijazkar. Unlike the various modes we have considered so far all fitting the Greek concept of a diatonic genus, Hijazkar has two disjunct Hijaz tetrachords which are a characteristic Near Eastern manifestation of the Greek chromatic. In a diatonic tetrachord, no adjacent interval is larger than about half of a perfect fourth, or roughly 250 cents (if we take the fourth to be at a just 4:3, or 498.045 cents, then precisely half of this would be around 249.0225 cents). We might apply this concept to trichords and pentachords also, which may be termed diatonic if no step is larger than around 250 cents. For the most part we have more specifically focused on what may be termed the Zalzalian diatonic, where a diatonic tetrachord has one or more Zalzalian or middle steps: typically, in our examples, a smaller middle step (here at 138.9 cents, around 13:12) plus a larger middle step (here at 150.0 cents, around 12:11) plus a regular tone at or close to 9:8 (here 207.4 cents). Hijazkar, however, has a different form, and one supported by the basic structure of Artemisia-10. While there are various intonational understandings and shadings of Hijazkar, here we focus on a general type referred to by Amine Beyhom, a Lebanese musician and theorist, as Zirkula. Rast and Zirkula are closely related because both feature disjunct tetrachords with a larger middle third, here at 357.4 cents, close to the classic sizes of al-Farabi's 27/22 (354.5 cents) or Ibn Sina's 16/13 (359.5 cents). What changes between Rast and Hijazkar in its Zirkula form is shown by comparing a rast-4 tetrachord with hijaz-4: rast-4 C4---------D4--------Ed4------F4 0 207.4 357.4 496.3 207.4 150.0 138.9 T K S hijaz-4 C4----C+4------------Ed4------F4 0 68.6 357.4 496.3 68.6 288.9 138.9 B A S In Rast, the second note of the tetrachord is a tone around 9:8 (here 207.4 cents); the third note the Rast third at 357.4 cents; and the fourth note the usual 4:3 fourth to complete the tetrachord. The intervals follow the T-K-S pattern: tone, larger middle second, and smaller middle second (here around 9:8 or 44:39; 12:11; and 13:12). In this version of Hijazkar, only one of these notes changes: the second note, lowered from a regular tone at D4 (207.4 cents) to C+4 at 68.6 cents, almost exactly a third of a tone. Between this second note and the usual Rast third at 357.4 cents is a large or chromatic step Cx4-Ed4 at 288.9 cents, a virtually just 13:11. The small middle second step Ed4-F4 from this Rast third to the perfect fourth completing the tetrachord remains the same. To notate this chromatic pattern, we may use the Systematist symbol B for Bakkiya for the lower semitone or thirdtone, and the modern Turkish symbol A for the large or chromatic step, which stands essentially for what in the West is called an "augmented" step; the letter S, as usual, stands for Saghir, a "lesser" or smaller middle second. Thus the pattern of Hijazkar in its Zirkula form is B-A-S. The following diagram shows both tetrachords of our Hijazkar, and also one JI interpretation for this tempered version: |-------- hijaz-4 ---------|...tone..|--------- hijaz-4 ----------| C4----C+4---------Ed4------F4--------G4----G+4-----------Bd4------C5 0 68.6 357.4 496.3 703.7 772.3 1061.1 1200 68.6 288.9 138.9 207.4 68.6 288.9 138.9 B A S T B A S 528 507 429 396 352 338 286 264 1/1 176/169 16/13 4/3 3/2 264/169 24/13 2/1 0 70.3 359.5 498.0 702.0 772.2 1061.4 1200 176:169 13:11 13:12 9:8 176:169 13:11 13:12 70.3 289.2 138.6 203.9 70.3 289.2 138.6 The middle and upper intervals of the hijaz-4 tetrachord are very close to a just 13:11 and 13:12. If we assume a pure 4:3 fourth, and subtract these steps, this leaves a ratio for the first thirdtone step of 176:169 or 70.3 cents. The tempered thirdtone step C4-C+4 is not far from this, at 68.6 cents, about as narrow of a theoretical 176:169 (1.708 cents) as the tempered fourth is from a just 4:3 (1.756 cents). Typically, the first step of hijaz-4 in this Zirkula variety would be a regular diatonic semitone, which in MET-24 is 81.4 cents (e.g. E-F or B-C), close to 22:21 (80.5 cents) -- an interval not present in Artemisia-10, with the smaller 68.6-cent step as the nearest equivalent. The large middle or chromatic step of the tetrachord at 288.9 cents is identical to the regular minor third of MET-24, which can be found in Artemisia-10 at such locations as D-F and A-C; in this mode it occurs as an augmented step at C+4-Ed4 and G+3-Bd4. There is a widespread view among Near Eastern musicians that Hijaz at least ideally has this middle step as a "plus-tone," or as Amine Beyhom puts it as a "slightly augmented second," somewhat smaller than a regular minor third often at or near the Pythagorean 32/27 (294.1 cents) from three pure 4:3 fourths, and at 288.9 cents or a near-just 13/11 in Artemisia-10. One favored region is around 7:6 (266.9 cents), including what might be called the upper suburbs of the region around 270-275 cents. The MET-24 tuning includes intervals of 264.8 and 276.0 cents often used for this chromatic step in modes like Hijazkar, but Artemisia-10 does not include them. However, larger chromatic steps in hijaz tetrachords at or around the same size as the regular minor third are also in widespread use in Turkish music, for example. Even within the limited scope of Artemisia-10, the modulation between Rast and Hijazkar on the shared final of C is an idiom of modern Arab music available for use. At the same time, the wealth of rotations of Jacques Dudon's Mohajira-7 set, and of Rast and Mustaqim, provides a kind of Near Eastern modal sampler. To get more of a sense of maqam music as a richly populated network of maqamat where the identity of each maqam is shaped in part by its modulatory connections within the network, and where various inflections are often a part of its character, a larger tuning set is necessary. The Artemisia-12 tuning has more of these possibilities, with the full MET-24 tuning still more. However, any fixed-pitched tuning of moderate size can only be in the end a sampler of the fast possibilities of maqam. With Persian dastgah music, another approach is possible for instruments with a limited number of notes. Because the dastgah or modal family concept focuses a given performance on a specific dastgah or family, with a suite-like structure flowing through a set of gushe-ha or melodic themes, instruments like the santur can satisfactorily cover the material of a given dastgah with only about ten notes per octave -- often not all tuned within a single octave. For example, Dastgah-e Shur, taking D4 as the final (this placement varies), often calls for Bp3 (that is, B3 lowered by a koron or about a third of a tone, forming a smaller middle third below D4) but Bb4 (a minor sixth above the final). Likewise, it often calls for the middle second Ep4 (as part of the signature Shur tetrachord, D4-Ep4-F4-G4) but a minor ninth step at Eb5. Tuning different octaves on the santur differently is an effective strategy on an instrument traditionally supporting only about eight or nine notes in any one octave. By comparison, Artemisia-10 seeks mostly to offer a diverse set of modes which may sometimes invite experimental pathways and connections not necessarily known to any established Near Eastern practice, either in the 13th century or today. At the same time, it can be used as a subset of the larger MET-24 tuning which does support also such known patterns and connections, as best documented in 19th-21st century practice, plus some notated music as well as a wealth of theory from earlier centuries. ------------------------------------------------ 4.5. A Note on Rast and `Awj (Disjunct Mohajira) ------------------------------------------------ In Systematist sources, as Jacques Dudon has pointed out, the mode with disjunct `iraq or mohajira tetrachords, J-T-J-T-J-T-J, is called `Awj. Whatever the origins of this name, interestingly it fits a relationship between disjunct or modern Rast and this mode of Mohajira in Artemisia-10. Modern Arab theory takes disjunct Rast as the "Arab Fundamental Scale," and assigns these names to its step, with rast as the name for the final and the also a cardinal reference point or 1/1 for the gamut as a whole. |--------- rast-4 ----------|...tone..|--------- rast-4 ----------| rast duka sika jaharka nawa huseyni `awj kirdan C4---------D4-------Ed4-----F4--------G4---------A4------Bd4------C5 0 207.4 357.4 496.3 703.7 911.1 1061.1 1200 207.4 150.0 138.9 207.4 207.4 150.0 138.9 T K S T T K S We find that the middle seventh step of Rast Bd4, called `awj, is the final for Maqam `Awj or disjunct Mohajira: |-------- mohajira-4 ---------|...tone...|------- mohajira-4 --------| Bd4------C5---------D5-------Ed5--------F+5-----G5---------A5-------Bd5 0 138.9 346.3 496.3 703.7 842.6 1050.0 1200 138.9 207.4 150.0 207.4 138.9 207.4 150.0 S T K T S T K The one note of `awj which cannot be derived from a rotation of Rast is the perfect fifth F+5 -- which, however, occurs an octave lower (F+4) in the First Mode of Mohajira, Maqam Uddal (see Section 2.1), with `Awj as the Seventh Mode of Mohajira: |------------ uddal-5 ---------------|---------- rast-4 ----------| C4--------D4------Ed4-------F+4------G4--------A4-------Bd4------C5 0 207.4 357.4 564.8 703.7 911.1 1061.1 1200 207.4 150.0 207.4 138.9 207.4 150.0 138.9 T K T S T K S Thus the Systematist name `Awj for Dudon's disjunct Mohajira offers a helpful cue on where to find this mode in Artemisia-10: on the seventh step of modern or disjunct Rast, Bd4, called `awj. --------------------------------------------------- 5. Mapping Artemisia-10 to a Usual 12-note Keyboard --------------------------------------------------- While Artemisia-10 is a decatonic scale, standard keyboards have 12 notes per octave. This invites an expanded tuning set using all 12 of these notes which I term Artemisia-12. The additional notes are the regular minor third and minor seventh above C, the note serving as the 1/1 or final for the Mohajira-7 series with the larger middle third generator preceding the smaller (Section 2), and also for a modern or disjunct Rast, the Arab Fundamental Scale (Section 4.1). These additional notes are mapped to Eb and Bb, with the seven natural keys presenting modern Rast (C-C) and its rotations: 68.6 288.9 564.8 772.3 992.6 C+4 Eb4 F+4 G+4 Bb4 68.6|138.9 81.4|68.6 68.6|138.9 68.6|138.9 81.4|68.6 C4 D4 Ed4 F4 G4 A4 Bd4 C5 0 207.4 357.4 496.3 703.7 911.1 1061.1 1200 207.4 150.0 138.9 207.4 207.4 150.0 138.9 T K S T T K S Among the naturals, C4-D4, F4-G4, and G4-A4 are steps of a regular tone at 207.4 cents; D4-Ed4 and A4-Bd4 are larger middle second steps at 150.0 cents; and Ed4-F4 and Bd4-C5 are smaller middle second steps at 138.9 cents. These ratios correspond, for example, to 9:8 or 44:39; 12:11; and 13:12. In the likely widespread Pythagorean tuning for 14th-century European keyboards of Eb-G#, or meantone tunings with these range of accidentals evidently very common in the 16th century, there are two flats (Eb and Bb) and three sharps (C#, F#, G#). Those familiar with such arrangements may find them helpful in distinguishing between the two kinds of accidentals that occur in Artemisia-12. The two notes added to Artemisia-10, Eb and Bb, serve as regular flats at a regular diatonic semitone or 81.4 cents above D and A, close to the just ratio of 22:21 (80.5 cents). In contrast, the notes at the locations associated with sharps in an historical European Eb-G# tuning here are noted C+, F+, and G+, located at a small semitone or thirdtone above C, F, and G, 68.6 cents. In modern Persian music and notation, these notes would be called sori steps, with a sori (ASCII ">") raising a note often by about a third of a tone: thus C>, F>, and G>. Instead of flats and sharps, we thus have flats and soris. The Persian sori is more or less equivalent to an Arab half-flat or ASCII "+" so that C> and C+ may be deemed synonymous, with either subject to many variations in actual tuning. Ten of the 12 steps have perfect fifths at 703.7 cents. The two exceptions are A-Ed at 646.3 cents, a near-just 16:11 (648.7 cents); and G+-Eb at 716.6 cents, at the same keyboard location as the Pythagorean or meantone diminished sixth or "wolf fifth" G#-Eb. In short, the original Artemisia-10 set is available in this keyboard mapping by disregarding Eb and Bb; including these notes produces Artemisia-12. While the main focus of this paper is on the Mohajira, Rast, and Mustaqim rotations, using the full Artemisia-12 set can substantially expand both the range of modal forms and inflections available and the modulatory possibilities in accord with modern Arab practice, thus offering at least a taste of this practice. Let us quickly sample a few inflections and modulations that the Artemisia-12 set makes possible. The textbook form of modern Rast has two disjunct Rast tetrachords, here starting from C, but this is more specifically the typical ascending form of Maqam Rast: |--------- rast-4 ----------|...tone..|--------- rast-4 ----------| rast duka sika jaharka nawa huseyni `awj kirdan C4---------D4-------Ed4-----F4--------G4---------A4------Bd4------C5 0 207.4 357.4 496.3 703.7 911.1 1061.1 1200 207.4 150.0 138.9 207.4 207.4 150.0 138.9 T K S T T K S In descending, however, the seventh step Bd4 is often lowered to a minor seventh Bb4, giving rise to some new tetrachordal possibilities: |--------- rast-4 ----------|...tone..|-------- nahawand-4 -------| rast duka sika jaharka nawa huseyni `ajam kirdan |---------- `ajam-4 --------| C4---------D4-------Ed4-----F4--------G4---------A4----Bb4--------C5 0 207.4 357.4 496.3 703.7 911.1 992.6 1200 207.4 150.0 138.9 207.4 207.4 81.4 207.4 T K S T T B T This form of Rast is sometimes known in the Arab world as Suzdilar, since it is associated with one aspect of a much more complex maqam, Suz-i Dilara ("Fire of the Heart"). The middle seventh step `awj above rast is replaced by the minor seventh step `ajam, which leads to a Turkish name for this mode: Ajamli Rast. New choices for an upper jins include a disjunct nahawand-4, T-B-T, like Western Dorian or Aeolian; or a conjunct `ajam-4, T-T-B, like Western Mixolydian or Ionian. These ajnas bring into play a pleasant contrast between the lower rast-4 as a Zalzalian diatonic, and nahawand-4 or `ajam-4 as a regular diatonic much like the classic Pythagorean variety. This fluidity in Rast of the seventh degree, Bd4/Bb4, reflects a tendency found also in the medieval and Renaissance European modes of B/Bb. The note Bd4 pulls up toward C5, the octave of the final C4, while Bb4 pulls down in a descent back toward the final. Likewise a number of European modes feature the frequent use of B-natural in ascending, but Bb in descending, with this contrast especially typical of Dorian on D and Lydian on F. Using the full Artemisia-12 set also makes it possible to explore Maqam Bayyati, which has its usual untransposed location on D, the second step of Rast. The added Bb4 at once supplies the essential minor sixth step which is part of a "textbook" Bayyati, and enables the different forms of Bayyati often associated with ascending or descending motion: |------ bayyati-4 ----------|-------- nahawand-4 -------|...tone..| D4-------Ed4------F5--------G5---------A5----Bb4--------C5-------D5 0 150.0 288.9 496.3 703.7 785.2 992.6 1200 150.0 138.9 207.4 207.4 81.4 207.4 207.4 K S T T B T T This conjunct bayyati-4|nahawand-4 is very common, but in ascending contexts this constellation is also characteristic: |------ bayyati-4 ----------|---------- rast-4 ---------|...tone..| D4-------Ed4------F5--------G5--------A5-------Bd4------C5-------D5 0 150.0 288.9 496.3 703.7 853.7 992.6 1200 150.0 138.9 207.4 207.4 150.0 138.9 207.4 K S T T K S T Still a third variation within Bayyati is a conjunct upper tetrachord of hijaz-4, which the Lebanese musician and scholar Ali Jihad Racy describes as a "pre-cadential" idiom, and receives more emphasis in the related maqamat of Bayyati Shuri and Turkish Beyati: |------ bayyati-4 ----------|--------- hijaz-4 ---------|...tone..| D4-------Ed4------F5--------G5----G+5----------Bd4------C5-------D5 0 150.0 288.9 496.3 564.8 853.7 992.6 1200 150.0 138.9 207.4 68.6 288.9 138.9 207.4 K S T B A S T Another situation where Bb comes into play is in the very popular Maqam Hijaz with its untransposed final on D, the same step as Maqam Bayyati (and also Maqam Huseyni, see Section 4.1). Here the ascending form has a lower hijaz-4 and a conjunct rast-4: |------ bayyati-4 ----------|---------- rast-4 ---------|...tone..| D4-----Eb4---------F+5------G5--------A5-------Bd4------C5-------D5 0 81.4 357.4 496.3 703.7 853.7 992.6 1200 81.4 276.0 138.9 207.4 150.0 138.9 207.4 B A S T K S T In descending, however, the upper rast-4 tends to become a nahawand-4 with Bb4: |--------- hijaz-4 ---------|-------- nahawand-4 -------|...tone..| D4-----Eb4---------F+5------G5--------A5-----Bb4--------C5-------D5 0 81.4 357.4 496.3 703.7 785.2 992.6 1200 81.4 276.0 138.9 207.4 81.4 207.4 207.4 B A S T B T T Note that in this Hijaz, the lower step of the hijaz-4 tetrachord is the regular minor second at 81.4 cents, with a middle step at 276.0 cents, not too far from 7:6, and in the stylish range of around 260-280 cents often preferred for a small chromatic interval. This also leads to the topic of modulations. While Artemisia-12 does not have enough notes in the right places to approximate a full modulatory network of maqamat, it does permit some common scenarios. For example, suppose we are playing in Rast on C. The usual location for Maqam Hijaz is on D, but, as Scott Marcus explains, it is generally considered unstylish (at least in the classic Egyptian practice he studied) to move directly from a maqam on C to one on D. Rather, one normally plays a desired maqam based on D by transposing it up a fourth to G, the fifth step of Rast, and making the modulation from that step. Happily we find that for Hijaz on G, both the ascending and descending forms addressed above are available, with a nuance of difference: |-------- hijaz-4 ----------|---------- rast-4 ---------|...tone..| G4----G+4---------Bd4------C5--------D5-------Ed5------F5---------G5 0 68.6 357.4 496.3 703.7 853.7 992.6 1200 68.6 288.9 138.9 207.4 150.0 138.9 207.4 B A S T K S T |-------- hijaz-4 ----------|------- nahawand-5 --------|...tone..| G4----G+4---------Bd4------C5--------D5-----Eb5--------F5---------G5 0 68.6 357.4 496.3 703.7 785.2 992.6 1200 68.6 288.9 138.9 207.4 81.4 207.4 207.4 B A S T B T T The nuance involves the lowest step of the hijaz-4 tetrachord, here at a thirdtone G4-G+4 of 68.6 cents rather than a regular diatonic semitone or minor second like the step between fifth and minor sixth, D5-Eb5, at 81.4 cents. In some styles of polyphony, the resulting wolf or semiwolf fifth, as judged by Western standards, at G+4-Eb4 (716.6 cents) might cause complications; but in the art of maqam, oriented mainly to pure melody, such intervals generally cause no problems, since these two notes are unlikely to be played simultaneously. If one did wish to improvise simple polyphony, a solution with the larger MET-24 gamut might be, for example, accompany G+4 with the lower fifth or upper fourth (C+4 or C+5), and Eb5 with the lower fourth or upper fifth (Bb4 or Bb5). A different modulatory scenario might arise if we were playing Maqam Bayyati on D as discussed in some of the illustrations above. Rather than move directly to a maqam like Rast typically based on C (the step below), the idiomatic solution is instead to modulate to such a maqam on G, the fourth step of Bayyati, thus transposing the C-based maqam up a fifth. Here we shall consider Maqam Nahawand, which shares with Rast the final of C, and so from Bayyati on D would be played on G: |------ nahawand-4 ---------|...tone..|-------- hijaz-4 --------| G4--------A4-----Bb4--------C5--------D5-----Eb5-------F+5------G5 0 207.4 288.9 496.3 703.7 785.2 1061.1 1200 207.4 81.4 207.4 207.4 81.4 276.0 138.6 T B T T B A S This is more specifically the ascending form of Nahawand, with a lower nahawand-4 and disjunct hijaz-4. Here both regular semitones come into use: A4-Bb4 in the regular diatonic tetrachord of nahawand; and D5-Eb5 as the lower step of a chromatic hijaz-4 tetrachord, here with a middle step at 276.0 cents. It may be noteworthy that these 276-cent or "plus-tone" steps are available at Eb-F+, F-G+, and Bb-C+, with the last of these in use in this version of Nahawand. One descending form of Nahawand substitutes the minor seventh F5 for the middle seventh F+5, another example of a common theme of fluid or inflected degrees shifting to fit a given melodic context. In Turkish music this tendency as discussed by Eric Ederer is called _cazibe_ (with the "c" in the modern Turkish alphabet pronounced like English "j" -- and thus the Turkish spelling of Hicaz for Arabic Hijaz). Ederer translates _jazibe_ as "gravity," although some prefer "attraction," and indeed in Byzantine music one speaks of "the law of attraction" to explain similar inflections. |------ nahawand-4 ---------|----- nahawand-4 ---------|...tone..| G4--------A4-----Bb4--------C5--------D5-----Eb5-------F5-------G5 |--------- kurdi-4 --------| 0 207.4 288.9 496.3 703.7 785.2 992.6 1200 207.4 81.4 207.4 207.4 81.4 207.4 207.4 T B T T B T T The lowered seventh step gives rise to a conjunct nahawand-4 tetrachord on C5, the fourth step of Nahawand; and also a disjunct tetrachord on D5, the fifth step, called Kurdi (B-T-T), which resembles European Phrygian. While Artemisia-12 does not provide anything like a full modulatory network of maqamat, it does invite some creative solutions. For example, suppose we are now in Nahawand on G, and want to modulate to Rast on this same step (just as it is common to move between Rast and Nahawand on C, the untransposed final for both maqamat). A problem is that we do not have the major sixth E5 that is a part of disjunct Rast on G4. However, there is an alternative that shares with Nahawand the element of a fluid seventh degree that often tends toward the middle seventh step F+5 in ascending but the minor seventh F5 in descending. For a disjunct Rast, we substitute Jacques Dudon's Folk Rast (the Fifth Mode of Mohajira, see Section 2.5) on this same final of G: |--------- rast-4 ----------|...tone..|------- mohajira-4 ---------| G4---------A4-------Bd4-----C5--------D5-------Ed5--------F+5------G5 0 207.4 357.4 496.3 703.7 853.7 1061.1 1200 207.4 150.0 138.9 207.4 150.0 207.4 138.9 T K S T K T S For the descending form, we can use a conjunct Rast, the original Rast described by al-Farabi as his Mode of Zalzal, and codified by Safi al-Din and other Systematists under the name Rast: |--------- rast-4 ----------|---------- rast-4 ---------|...tone..| G4---------A4-------Bd4-----C5--------D5-------Ed5------F---------G5 |-------- bayyati-4 --------| 0 207.4 357.4 496.3 703.7 853.7 992.6 1200 207.4 150.0 138.9 207.4 150.0 138.9 207.4 T K S T K S T In sum, the Artemisia-10 and Artemisia-12 sets of MET-24 may serve at once as a sampler of some intriguing Near Eastern modes and rotations, including the Mohajira-7 set of Jacques Dudon; and an invitation to participate in Dudon's project of revisiting some classic modal forms and exploring new patterns, especially where the old ones may not be well-documented. In Artemisia-12 at least to a degree, and more fully in a larger tuning system like the complete MET-24, one can use these patterns to supplement those of more familiar modern practices in the realm of maqam music and the related Iranian dastgah system. Also, while these tunings focus on a traditional art of pure melody, they also provide opportunities to explore techniques of Zalzalian polyphony which can respect and realize in the vertical and horizontal dimensions alike the intonational diversity and flexibility of this art. Margo Schulter 30 December 2018