Here are diagrams for one of the two principle "Mohajira in eventone" regions: the Meantone region (here at 695.6 to 698.0 cents). The other is the Gentle-Lower Archytan region (which might be placed at 703.4 to 708.0 cents). Within the Meantone region, the alternating generators for a Mohajira set are the middle thirds at +16 and -15 fifths. In the Gentle-Lower Archytan region, they are the middle thirds at -8 and +9 fifths. Also of interest in surveying the melodic possibilities and tetrachordal qualities of these regions are the sizes of smaller and larger middle second steps forming the various genera (Arabic ajnas, the plural of jins, "genus") of a Mohajira tuning or mode. In the Meantone region, these middle seconds are derived from +14 and -17 fifths. In the Gentle-Lower Archytan region, they are derived from +7 and -10 fifths. To obtain a basic 7-note Mohajira set within a tuning in the Meantone region, with its mappings for Mohajira generators of +16 and -15 fifths, we need at least a 19-MOS. Within the Gentle-Lower Archytan region, with its mappings of -8 and +9 fifths, a 12-MOS suffices for this basic Mohajira-7 set. These diagrams show Mohajira as found within regular meantone tunings; a companion survey will likewise address the Gentle-Lower Archytan region. -------- Mohajira in Meantone spectrum -- Wilson's Metameantone to 31-ed2 Contrast: _36.4___33.3___30.2___27.1___24.0___20.9___17.8___14.7___11.6____8.5____5.4____2.3____0 ............330.761..332.208.........336.130.............340.552.342.483...344.738.....347.408...> .............23/19....63/52...........17/14...............28/23...39/32.....72/49.......11/9..... +16 5ths: 329.6..331.2..332.8..334.4..336.0..337.6..339.2..340.8..342.4..344.0..345.6..347.2..348.4 5th.......695.6..695.7..695.8..695.9..696.0..696.1..696.2..696.3..696.4..696.5..696.6..696.7.....> -15 5ths: 366.0..364.5..363.0..361.5..360.0..358.5..357.0..355.5..354.0..352.5..351.0..349.5..348.4 ...........21/17................69/56....16/13.....59/48.......27/22.........49/40...60/49....... ..........365.825..............361.403..359.472...357.217.....354.547.......351.338.350.617...... Tuning.....metaMT........2/7-C........50-ed2.........Kornerup..................1/4-C..........31-ed2 5th........695.623......695.810.......696.0..........696.215..................696.578.........696.774 +16 5ths...329.968......332.996.......336.0..........339.440..................351.324.........348.387 -15 5ths...365.655......362.845.......360.0..........356.775..................345.255.........348.387 Contrast: __35.687_______29.879________24.0___________17.335____________________6.069____________0 Tuning.....metaMT........2/7-C........50-ed2.........Kornerup..................1/4-C..........31-ed2 5th........695.623......695.810.......696.0..........696.215..................696.578.........696.774 +14 5ths...138.722......141.345.......144.0..........147.010..................152.098.........154.839 -17 5ths...174.409......171.224.......168.0..........164.345..................158.167.........154.839 Contrast: __35.687_______29.879________24.0___________17.335____________________6.069____________0 ............138.573..140.949..143.498..........146.134...............150.637.........153.307.....> .............13/12...243/224...88/81..........4608/4235...............12/11...........59/54...... +14 5ths: 138.4..139.8..141.2..143.6..144.0..145.4..146.8..148.2..149.6..151.0..152.4..153.8..154.8 5th.......695.6..695.7..695.8..695.9..696.0..696.1..696.2..696.3..696.4..696.5..696.6..696.7.....> -17 5ths: 174.8..173.1..171.4..169.7..168.0..166.3..164.6..163.9..161.2..159.5..157.8..156.1..154.8 Contrast: _36.4___33.3___30.2___27.1___24.0___20.9___17.8___14.7___11.6____8.5____5.4____2.3_____0 ................21/19.....7-ed2.......54/49......11/10...........484/441..........23/21....128/117 ...............173.268..171.429......168.213....165.004..........161.074.........157.493...155.562 ------- Mohajira in Meantone spectrum -- 31-ed2 to 698.0 cents Contrast: __0.8____3.9____7.0___10.1___13.2___16.3___19.4___22.5___25.6___28.7___31.8___34.9___38.0 ......347.408..350.617.351.338.....354.547....357.217...359.472..361.403...........365.825.....368.914..> .......11/9.....60/49...49/40.......27/22......59/48.....16/13....69/56.............21/17.......99/80..... +16 5ths: 348.8..350.4..352.0..353.6..355.2..356.8..358.4..360.0..361.6..363.2..364.8..366.4..368.0 5th.......696.8..696.9..697.0..697.1..697.2..697.3..697.4..697.5..697.6..697.7..697.8..697.9..698.0 -15 5ths: 348.0..346.5..345.0..343.5..342.0..340.5..339.0..337.5..336.0..334.5..333.0..331.5..330.0 ............11/9.........72/59.......39/32...28/23................17/14.............63/52...23/19.... ...........347.408......344.738.....342.483.340.552..............336.130...........332.208.330.761..... Tuning....31-ed2........3/13-C.......2/9-C......3/14-C...........Tannic..43-ed2................1/6-PythC 5th......696.774.......696.992......697.176....697.347...........697.591.697.674................698.045 +16 5ths.348.387.......351.872......354.813....357.544...........361.462.362.791................368.720 -15 5ths.348.387.......345.120......342.363....339.802...........336.130.334.884................329.325 Contrast:...0 ___________6.752_______12.451_____17.742____________25.332__27.907_________________39.395 Tuning....31-ed2........3/13-C.......2/9-C......3/14-C...........Tannic..43-ed2................1/6-PythC 5th......696.774.......696.992......697.176....697.347...........697.591.697.674................698.045 +14 5ths.154.839.......157.888......160.462....162.851...........166.279.167.442................172.630 -17 5ths.154.839.......151.136......148.011....145.109...........140.947.139.535................133.235 Contrast:...0 ___________6.752_______12.451_____17.742____________25.332__27.907_________________39.395 ............155.562...157.493...........161.074...........165.004..........168.213.......171.429.....> ............128/117....23/21............484/441............11/10............54/49.........7-ed2 +14 5ths: 155.2..156.6..158.0..159.4..160.8..162.2..163.6..165.0..166.4..167.8..169.2..170.6..172.0 5th.......696.8..696.9..697.0..697.1..697.2..697.3..697.4..697.5..697.6..697.7..697.8..697.9..698.0 -17 5ths: 154.4..152.7..151.0..149.3..147.6..145.9..144.2..142.5..140.8..139.1..137.4..135.7..134.0 Contrast: __0.8____3.9____7.0___10.1___13.2___16.3___19.4___22.5___25.6___28.7___31.8___34.9___38.0 .............59/54.........12/11..........4608/4235....88/81......243/224....13/12..............27/25 ............153.307.......150.637..........146.134....143.498.....140.949...138.573............133.238 ------- Margo Schulter 1 March 2018