User:Moremajorthanmajor/2L 1s (perfect fourth-equivalent): Difference between revisions
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# | '''2L 1s<fourth>''', is a fourth-repeating MOS scale. The notation "<fourth>" means the period of the MOS is a fourth, disambiguating it from octave-repeating [[2L 1s]]. | ||
The generator range is 171.4 to 240 cents, placing it near the [[9/8|diatonic major second]], usually representing a major second of some type. The dark (chroma-negative) generator is, however, its fourth complement (240 to 342.9 cents). | |||
In the fourth-repeating version of the diatonic scale, each tone has a 4/3 perfect fourth above it. The scale has one major chord and two minor chords. | |||
[[Basic]] diatonic is in [[5ed4/3]], which is a very good fourth-based equal tuning similar to [[12edo]]. | |||
==Notation== | |||
There are 4 main ways to notate this scale. One method uses a simple fourth repeating notation consisting of 3 naturals (eg. Do Re Mi, Sol La Si). Given that 1-5/4-3/2 is fourth-equivalent to a tone cluster of 1-9/8-5/4, it may be more convenient to notate diatonic scales as repeating at the double, triple, quadruple or quintuple fourth (minor seventh, tenth, thirteenth or sixteenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 9/8. Notating this way produces a minor tenth which is the Dorian mode of Middletown[6L 3s], also known as the Mahur scale in Persian/Arabic music, a minor thirteenth which is the Aeolian mode of Bijou[8L 4s] or a minor sixteenth which is the Phrygian mode of Hyperionic. Since there are exactly 9 naturals in triple fourth notation, 12 in quadruple fourth and 15 in quintuple fourth notation, letters A-G plus J, Q or Q, S (GJABCQDEF or GABCQDSEF, flats written F molle) or dozenal or hex digits (0123456789XE0 or E1234567GABDE with flats written D molle or 123456789ABCDEF1 with flats written F molle) may be used. | |||
{| class="wikitable" | |||
|+Cents<ref name=":05">Fractions repeating more than 4 digits written as continued fractions</ref> | |||
! colspan="5" |Notation | |||
!Supersoft | |||
!Soft | |||
!Semisoft | |||
!Basic | |||
!Semihard | |||
!Hard | |||
!Superhard | |||
|- | |||
! colspan="2" |Diatonic | |||
! rowspan="2" |Mahur | |||
! rowspan="2" |Bijou | |||
! rowspan="2" |Hyperionic | |||
! rowspan="2" |~11ed4/3 | |||
! rowspan="2" |~8ed4/3 | |||
! rowspan="2" |~13ed4/3 | |||
! rowspan="2" |~5ed4/3 | |||
! rowspan="2" |~12ed4/3 | |||
! rowspan="2" |~7ed4\3 | |||
! rowspan="2" |~9ed4/3 | |||
|- | |||
!Fourth | |||
!Seventh | |||
|- | |||
|Do#, Sol# | |||
|Sol# | |||
|G# | |||
|0#, D# | |||
|1# | |||
|1\11 | |||
46; 6.5 | |||
|1\8 | |||
63; 6.{{Overline|3}} | |||
|2\13 | |||
77; 2, 2.6 | |||
| rowspan="2" |1\5 | |||
100 | |||
|3\12 | |||
124; 7.25 | |||
|2\7 | |||
141; 5.{{Overline|6}} | |||
|3\9 | |||
163.{{Overline|63}} | |||
|- | |||
|Reb, Lab | |||
|Lab | |||
|Jf, Af | |||
|1b, 1d | |||
|2f | |||
|3\11 | |||
138; 3.25 | |||
|2\8 | |||
126; 3.1{{Overline|6}} | |||
|3\13 | |||
116; 7.75 | |||
|2\12 | |||
82; 1.3{{Overline|18}} | |||
|1\7 | |||
70; 1.7 | |||
|1\9 | |||
54.{{Overline|54}} | |||
|- | |||
|'''Re, La''' | |||
|'''La''' | |||
|'''J, A''' | |||
|'''1''' | |||
|'''2''' | |||
|'''4\11''' | |||
'''184; 1.625''' | |||
|'''3\8''' | |||
'''189; 2.{{Overline|1}}''' | |||
|'''5\13''' | |||
'''193; 1, 1, 4.{{Overline|6}}''' | |||
|'''2\5''' | |||
'''200''' | |||
|'''5\12''' | |||
'''206; 1, 8.{{Overline|6}}''' | |||
|'''3\7''' | |||
'''211; 1, 3.25''' | |||
|'''4\9''' | |||
'''218.{{Overline|18}}''' | |||
|- | |||
|Re#, La# | |||
|La# | |||
|J#, A# | |||
|1# | |||
|2# | |||
|5\11 | |||
230; 1.3 | |||
|4\8 | |||
252; 1.58{{Overline|3}} | |||
|7\13 | |||
270; 1.0{{Overline|3}} | |||
| rowspan="2" |'''3\5''' | |||
'''300''' | |||
|8\12 | |||
331; 29 | |||
|5\7 | |||
352; 1.0625 | |||
|7\9 | |||
381.{{Overline|81}} | |||
|- | |||
|'''Mib, Sib''' | |||
|'''Sib''' | |||
|'''Af, Bf''' | |||
|'''2b, 2d''' | |||
|'''3f''' | |||
|'''7\11''' | |||
'''323; 13''' | |||
|'''5\8''' | |||
'''315; 1.2{{Overline|6}}''' | |||
|'''8\13''' | |||
'''309; 1, 2.1''' | |||
|'''7\12''' | |||
'''289; 1, 1.9''' | |||
|'''4\7''' | |||
'''282; 2.8{{Overline|3}}''' | |||
|'''5\9''' | |||
'''272.{{Overline|72}}''' | |||
|- | |||
|Mi, Si | |||
|Si | |||
|A, B | |||
|2 | |||
|3 | |||
|8\11 | |||
369; 4.{{Overline|3}} | |||
|6\8 | |||
378; 1.0{{Overline|5}} | |||
|10\13 | |||
387; 10.{{Overline|3}} | |||
|4\5 | |||
400 | |||
|10\12 | |||
413; 1, 3.8{{Overline|3}} | |||
|6\7 | |||
423; 1.{{Overline|8}} | |||
|8\9 | |||
436.{{Overline|36}} | |||
|- | |||
|Mi#, Si# | |||
|Si# | |||
|A#, B# | |||
|2# | |||
|3# | |||
|9\11 | |||
415; 2.6 | |||
| rowspan="2" |7\8 | |||
442; 9.5 | |||
|12\13 | |||
464; 1.9375 | |||
|5\5 | |||
500 | |||
|13\12 | |||
537; 14.5 | |||
|8\7 | |||
564; 1.41{{Overline|6}} | |||
|11\9 | |||
600 | |||
|- | |||
|Dob, Solb | |||
|Dob | |||
|Bb, Cf | |||
|3b, 3d | |||
|4f | |||
|10\11 | |||
461; 1, 1.1{{Overline|6}} | |||
|11\13 | |||
425; 1.24 | |||
|4\5 | |||
400 | |||
|9\12 | |||
372; 2.41{{Overline|6}} | |||
|5\7 | |||
352; 1.0625 | |||
|6\9 | |||
327.{{Overline|27}} | |||
|- | |||
!Do, Sol | |||
!Do | |||
!B, C | |||
!3 | |||
!4 | |||
!'''11\11''' | |||
'''507; 1.{{Overline|4}}''' | |||
!'''8\8''' | |||
'''505; 3.8''' | |||
!'''13\13''' | |||
'''503; 4, 2.{{Overline|3}}''' | |||
!'''5\5''' | |||
'''500''' | |||
!'''12\12''' | |||
'''496; 1.8125''' | |||
!'''7\7''' | |||
'''494; 8.5''' | |||
!'''9\9''' | |||
'''490.{{Overline|90}}''' | |||
|- | |||
|Do#, Sol# | |||
|Do# | |||
|B#, C# | |||
|3# | |||
|4# | |||
|12\11 | |||
553; 1.{{Overline|18}} | |||
|9\8 | |||
568; 2.375 | |||
|15\13 | |||
580; 1.55 | |||
| rowspan="2" |6\5 | |||
600 | |||
|15\12 | |||
620; 1.45 | |||
|9\7 | |||
635; 3.4 | |||
|12\9 | |||
654.{{Overline|54}} | |||
|- | |||
|Reb, Lab | |||
|Reb | |||
|Cf, Qf | |||
|4b, 4d | |||
|5f | |||
|14\11 | |||
646; 6.5 | |||
|10\8 | |||
631; 1.{{Overline|72}} | |||
|16\13 | |||
619; 2.{{Overline|81}} | |||
|14\12 | |||
579; 3.{{Overline|2}} | |||
|8\7 | |||
564; 1.41{{Overline|6}} | |||
|10\9 | |||
545.{{Overline|45}} | |||
|- | |||
|'''Re, La''' | |||
|'''Re''' | |||
|'''C, Q''' | |||
|'''4''' | |||
|'''5''' | |||
|'''15\11''' | |||
'''692; 3.25''' | |||
|'''11\8''' | |||
'''694; 1, 2.8''' | |||
|'''18\13''' | |||
'''696; 1.291{{Overline|6}}''' | |||
|'''7\5''' | |||
'''700''' | |||
|'''17\12''' | |||
'''703; 2, 2.1{{Overline|6}}''' | |||
|'''10\7''' | |||
'''705; 1.1{{Overline|3}}''' | |||
|'''13\9''' | |||
'''709.{{Overline|09}}''' | |||
|- | |||
|Re#, La# | |||
|Re# | |||
|C#, Q# | |||
|4# | |||
|5# | |||
|16\11 | |||
738; 2.1{{Overline|6}} | |||
|12\8 | |||
757; 1, 8.5 | |||
|20\13 | |||
774; 5.1{{Overline|6}} | |||
| rowspan="2" |'''8\5''' | |||
'''800''' | |||
|20\12 | |||
827; 1, 1.41{{Overline|6}} | |||
|12\7 | |||
847; 17 | |||
|16\9 | |||
872.{{Overline|72}} | |||
|- | |||
|'''Mib, Sib''' | |||
|'''Mib''' | |||
|'''Qf, Df''' | |||
|'''5b, 5d''' | |||
|'''6f''' | |||
|'''18\11''' | |||
'''830; 1.3''' | |||
|'''13\8''' | |||
'''821; 19''' | |||
|'''21\13''' | |||
'''812; 1, 9.{{Overline|3}}''' | |||
|'''19\12''' | |||
'''786; 4.8{{Overline|3}}''' | |||
|'''11\7''' | |||
'''776; 2.125''' | |||
|'''14\9''' | |||
'''763.{{Overline|63}}''' | |||
|- | |||
|Mi, Si | |||
|Mi | |||
|Q, D | |||
|5 | |||
|6 | |||
|19\11 | |||
876; 1.08{{Overline|3}} | |||
|14\8 | |||
884; 4.75 | |||
|23\13 | |||
890; 3.1 | |||
|9\5 | |||
900 | |||
|22\12 | |||
910; 2.9 | |||
|13\7 | |||
917; 1.{{Overline|54}} | |||
|17\9 | |||
927.{{Overline|27}} | |||
|- | |||
|Mi#, Si# | |||
|Mi# | |||
|Q#, D# | |||
|5# | |||
|6# | |||
|20\11 | |||
923: 13 | |||
| rowspan="2" |15\8 | |||
947; 2, 1.4 | |||
|25\13 | |||
967; 1, 2.875 | |||
|10\5 | |||
1000 | |||
|25\12 | |||
1034; 2, 14 | |||
|15\7 | |||
1058; 1, 4.{{Overline|6}} | |||
|20\9 | |||
1090.{{Overline|90}} | |||
|- | |||
|Dob, Solb | |||
|Solb | |||
|Df, Sf | |||
|6b, 6d | |||
|7f | |||
|21\11 | |||
969; 4.{{Overline|3}} | |||
|24\13 | |||
929; 31 | |||
|9\5 | |||
900 | |||
|21\12 | |||
868; 1, 28 | |||
|11\7 | |||
776; 2.125 | |||
|15\9 | |||
818.{{Overline|18}} | |||
|- | |||
!Do, Sol | |||
!Sol | |||
!D, S | |||
!6 | |||
!7 | |||
!22\11 | |||
1015; 2.6 | |||
!16\8 | |||
1010; 1.9 | |||
!26\13 | |||
1006; 2, 4.{{Overline|6}} | |||
!10\5 | |||
1000 | |||
!24\12 | |||
993; 9.{{Overline|6}} | |||
!14\7 | |||
988; 4.25 | |||
!18\9 | |||
981.{{Overline|81}} | |||
|- | |||
|Do#, Sol# | |||
|Sol# | |||
|D#, S# | |||
|6# | |||
|7# | |||
|23\11 | |||
1061; 1, 1.1{{Overline|6}} | |||
|17\8 | |||
1073; 1, 2.1{{Overline|6}} | |||
|28\13 | |||
1083; 1.{{Overline|148}} | |||
| rowspan="2" |11\5 | |||
1100 | |||
|27\12 | |||
1117; 4, 7 | |||
|16\7 | |||
1129; 2, 2.{{Overline|3}} | |||
|24\9 | |||
1309.{{Overline|09}} | |||
|- | |||
|Reb, Lab | |||
|Lab | |||
|Ef | |||
|7b, 7d | |||
|8f | |||
|25\11 | |||
1153; 1.{{Overline|18}} | |||
|18\8 | |||
1136; 1.1875 | |||
|29\13 | |||
1122; 1.7{{Overline|2}} | |||
|26\12 | |||
1075; 1.16 | |||
|15\7 | |||
1058; 1, 4.{{Overline|6}} | |||
|19\9 | |||
1036.{{Overline|36}} | |||
|- | |||
|'''Re, La''' | |||
|'''La''' | |||
|'''E''' | |||
|'''7''' | |||
|'''8''' | |||
|'''26\11''' | |||
'''1200''' | |||
|'''19\8''' | |||
'''1200''' | |||
|'''31\13''' | |||
'''1200''' | |||
|'''12\5''' | |||
'''1200''' | |||
|'''29\12''' | |||
'''1200''' | |||
|'''17\7''' | |||
'''1200''' | |||
|'''22\9''' | |||
'''1200''' | |||
|- | |||
|Re#, La# | |||
|La# | |||
|E# | |||
|7# | |||
|8# | |||
|27\11 | |||
1246; 6,5 | |||
|20\8 | |||
1263; 6.{{Overline|3}} | |||
|33\13 | |||
1277; 2, 2.6 | |||
| rowspan="2" |'''13\5''' | |||
'''1300''' | |||
|32\12 | |||
1324; 7.25 | |||
|19\7 | |||
1341; 5.{{Overline|6}} | |||
|25\9 | |||
1363.{{Overline|63}} | |||
|- | |||
|'''Mib, Sib''' | |||
|'''Sib''' | |||
|'''Ff''' | |||
|'''8b, Fd''' | |||
|'''9f''' | |||
|'''29\11''' | |||
'''1338; 3.25''' | |||
|'''21\8''' | |||
'''1326; 3.16̄''' | |||
|'''34\13''' | |||
'''1316; 7.75''' | |||
|'''31\12''' | |||
'''1282; 1.3{{Overline|18}}''' | |||
|'''18\7''' | |||
'''1270; 1.7''' | |||
|'''23\9''' | |||
'''1254.{{Overline|54}}''' | |||
|- | |||
|Mi, Si | |||
|Si | |||
|F | |||
|8, F | |||
|9 | |||
|30\11 | |||
1384; 1.625 | |||
|22\8 | |||
1389; 2.1̄ | |||
|36\13 | |||
1393; 1, 1, 4.{{Overline|6}} | |||
|14\5 | |||
1400 | |||
|34\12 | |||
1406; 1, 8.{{Overline|6}} | |||
|20\7 | |||
1411; 1, 3.25 | |||
|26\9 | |||
1418.{{Overline|18}} | |||
|- | |||
|Mi#, Si# | |||
|Si# | |||
|F# | |||
|8#, F# | |||
|9# | |||
|31\11 | |||
1430; 1.3 | |||
| rowspan="2" |23\8 | |||
1452; 1.58{{Overline|3}} | |||
|38\13 | |||
1470; 1.0{{Overline|3}} | |||
|15\5 | |||
1500 | |||
|37\12 | |||
1531; 29 | |||
|22\7 | |||
1552; 1.0625 | |||
|29\9 | |||
1581.{{Overline|81}} | |||
|- | |||
|Dob, Solb | |||
|Dob | |||
|Gf | |||
|9b, Gd | |||
|Af | |||
|32\11 | |||
1476; 1.08{{Overline|3}} | |||
|37\13 | |||
1432: 3.875 | |||
|14\5 | |||
1400 | |||
|33\12 | |||
1365; 1.9{{Overline|3}} | |||
|19\7 | |||
1341; 5.{{Overline|3}} | |||
|24\9 | |||
1309.{{Overline|09}} | |||
|- | |||
!Do, Sol | |||
!Do | |||
!G | |||
!'''9, G''' | |||
!A | |||
!33\11 | |||
1523; 13 | |||
!24\8 | |||
1515; 1.2{{Overline|6}} | |||
!39\13 | |||
1509; 1, 2.1 | |||
!15\5 | |||
1500 | |||
!36\12 | |||
1489; 1, 1.9 | |||
!21\7 | |||
1482; 2.8{{Overline|3}} | |||
!27\9 | |||
1472.{{Overline|72}} | |||
|- | |||
|Do#, Sol# | |||
|Do# | |||
|G# | |||
|9#, G# | |||
|A# | |||
|34\11 | |||
1569; 4.{{Overline|3}} | |||
|25\8 | |||
1578; 1.05̄ | |||
|41\13 | |||
1587; 10.{{Overline|3}} | |||
| rowspan="2" |16\5 | |||
1600 | |||
|39\12 | |||
1613; 1, 3.8{{Overline|3}} | |||
|23\7 | |||
1623; 1.{{Overline|8}} | |||
|30\9 | |||
1636.{{Overline|36}} | |||
|- | |||
|Reb, Lab | |||
|Reb | |||
|Jf, Af | |||
|Xb, Ad | |||
|Bf | |||
|36\11 | |||
1661; 1, 1.1{{Overline|6}} | |||
|26\8 | |||
1642; 9.5 | |||
|42\13 | |||
1625; 1.24 | |||
|38\12 | |||
1572; 29 | |||
|22\7 | |||
1552; 1.0625 | |||
|28\9 | |||
1527.{{Overline|27}} | |||
|- | |||
|'''Re, La''' | |||
|'''Re''' | |||
|'''J, A''' | |||
|'''X, A''' | |||
|'''B''' | |||
|'''37\11''' | |||
'''1707; 1.{{Overline|4}}''' | |||
|'''27\8''' | |||
'''1705; 3.8''' | |||
|'''44\13''' | |||
'''1703; 4, 2.3̄''' | |||
|'''17\5''' | |||
'''1700''' | |||
|'''41\12''' | |||
'''1696; 1.8125''' | |||
|'''24\7''' | |||
'''1694; 8.5''' | |||
|'''31\9''' | |||
'''1690.{{Overline|90}}''' | |||
|- | |||
|Re#, La# | |||
|Re# | |||
|J#, A# | |||
|X#, A# | |||
|B# | |||
|38\11 | |||
1753; 1.{{Overline|18}} | |||
|28\8 | |||
1768; 2.375 | |||
|46\13 | |||
1780; 1.55 | |||
| rowspan="2" |'''18\5''' | |||
'''1800''' | |||
|44\12 | |||
1820; 1.45 | |||
|26\7 | |||
1835; 3,4 | |||
|34\9 | |||
1854.{{Overline|54}} | |||
|- | |||
|'''Mib, Sib''' | |||
|'''Mib''' | |||
|'''Af, Bf''' | |||
|'''Eb, Bd''' | |||
|'''Cf''' | |||
|'''40\11''' | |||
'''1846; 6.5''' | |||
|'''29\8''' | |||
'''1831; 1.{{Overline|72}}''' | |||
|'''47\13''' | |||
'''1819; 2.{{Overline|81}}''' | |||
|'''43\12''' | |||
'''1779; 3.{{Overline|2}}''' | |||
|'''25\7''' | |||
'''1764; 1, 3.25''' | |||
|'''32\9''' | |||
'''1745.{{Overline|45}}''' | |||
|- | |||
|Mi, Si | |||
|Mi | |||
|A, B | |||
|E, B | |||
|C | |||
|41\11 | |||
1892; 3.25 | |||
|30\8 | |||
1894; 1, 2.8 | |||
|49\13 | |||
1896; 1.291{{Overline|6}} | |||
|19\5 | |||
1900 | |||
|46\12 | |||
1903; 2, 2.1{{Overline|6}} | |||
|27\7 | |||
1905; 1, 7.5 | |||
|35\9 | |||
1909.{{Overline|09}} | |||
|- | |||
|Mi#, Si# | |||
|Mi# | |||
|A#, B# | |||
|E#, B# | |||
|C# | |||
|42\11 | |||
1938; 2.1{{Overline|6}} | |||
| rowspan="2" |31\8 | |||
1957; 1, 8.5 | |||
|51\13 | |||
1974; 5.1{{Overline|6}} | |||
|20\5 | |||
2000 | |||
|49\12 | |||
2027; 1, 1.41{{Overline|6}} | |||
|29\7 | |||
2047; 17 | |||
|38\9 | |||
2072.{{Overline|72}} | |||
|- | |||
|Dob, Solb | |||
|Solb | |||
|Bb, Cf | |||
|0b, Dd | |||
|Df | |||
|43\15 | |||
1984; 1.625 | |||
|50\13 | |||
1935; 2.0{{Overline|6}} | |||
|19\5 | |||
1900 | |||
|45\12 | |||
1862; 14.5 | |||
|26\7 | |||
1835; 3,4 | |||
|33\9 | |||
1800 | |||
|- | |||
!Do, Sol | |||
!Sol | |||
!B, C | |||
!0, D | |||
!D | |||
!44\11 | |||
2030; 1.3 | |||
!32\8 | |||
2021; 19 | |||
!52\13 | |||
2012; 1, 9.{{Overline|3}} | |||
!20\5 | |||
2000 | |||
!48\12 | |||
1986; 4.8{{Overline|3}} | |||
!28\7 | |||
1976; 2.125 | |||
!36\9 | |||
1963.{{Overline|63}} | |||
|- | |||
|Do#, Sol# | |||
|Sol# | |||
|B#, C# | |||
|0#, D# | |||
|D# | |||
|45\11 | |||
2076; 1.08{{Overline|3}} | |||
|33\8 | |||
2084; 4.75 | |||
|54\13 | |||
2090; 3.1 | |||
| rowspan="2" |21\5 | |||
2100 | |||
|51\12 | |||
2110; 2.9 | |||
|30\7 | |||
2117; 1.{{Overline|54}} | |||
|39\9 | |||
2127.{{Overline|27}} | |||
|- | |||
|Reb, Lab | |||
|Lab | |||
|Cf, Qf | |||
|1b, 1d | |||
|Ef | |||
|47\11 | |||
2169; 4.{{Overline|3}} | |||
|34\8 | |||
2147; 2, 1.4 | |||
|55\13 | |||
2129; 31 | |||
|50\12 | |||
2068; 1, 28 | |||
|29\7 | |||
2047; 17 | |||
|37\9 | |||
2018.{{Overline|18}} | |||
|- | |||
|'''Re, La''' | |||
|'''La''' | |||
|'''C, Q''' | |||
|'''1''' | |||
|'''E''' | |||
|'''48\11''' | |||
'''2215; 2.6''' | |||
|'''35\8''' | |||
'''2210; 1.9''' | |||
|'''57\13''' | |||
'''2206; 2, 4.{{Overline|6}}''' | |||
|'''22\5''' | |||
'''2200''' | |||
|'''53\12''' | |||
'''2193; 9.{{Overline|6}}''' | |||
|'''31\7''' | |||
'''2188; 4.25''' | |||
|'''40\9''' | |||
'''2181.{{Overline|81}}''' | |||
|- | |||
|Re#, La# | |||
|La# | |||
|C#, Q# | |||
|1# | |||
|E# | |||
|49\11 | |||
2261; 1, 1.1{{Overline|6}} | |||
|36\8 | |||
2273; 1, 2.1{{Overline|6}} | |||
|59\13 | |||
2083; 1.{{Overline|148}} | |||
| rowspan="2" |'''23\5''' | |||
'''2300''' | |||
|56\12 | |||
2327; 4, 7 | |||
|33\7 | |||
2329; 2, 2.{{Overline|3}} | |||
|43\9 | |||
2345.{{Overline|45}} | |||
|- | |||
|'''Mib, Sib''' | |||
|'''Sib''' | |||
|'''Qf, Df''' | |||
|'''2b, 2d''' | |||
|'''Ff''' | |||
|'''51\11''' | |||
'''2353; 1.{{Overline|18}}''' | |||
|'''37\8''' | |||
'''2336; 1.1875''' | |||
|'''61\13''' | |||
'''2322; 1.7{{Overline|2}}''' | |||
|'''55\12''' | |||
'''2275; 1.16''' | |||
|'''32\7''' | |||
'''2258; 1, 4.{{Overline|6}}''' | |||
|'''41\9''' | |||
'''2236.{{Overline|36}}''' | |||
|- | |||
|Mi, Si | |||
|Si | |||
|Q, D | |||
|2 | |||
|F | |||
|52\11 | |||
2400 | |||
|38\8 | |||
2400 | |||
|62\13 | |||
2400 | |||
|24\5 | |||
2400 | |||
|58\12 | |||
2400 | |||
|34\7 | |||
2400 | |||
|44\9 | |||
2400 | |||
|- | |||
|Mi#, Si# | |||
|Si# | |||
|Q#, D# | |||
|2# | |||
|F# | |||
|53\11 | |||
2446; 6.5 | |||
| rowspan="2" |39\8 | |||
2463; 6.{{Overline|3}} | |||
|64\13 | |||
2477; 2, 2.6 | |||
|25\5 | |||
2500 | |||
|61\12 | |||
2524; 7.25 | |||
|36\7 | |||
2541; 5.{{Overline|6}} | |||
|47/9 | |||
2563.{{Overline|63}} | |||
|- | |||
|Dob, Solb | |||
|Dob | |||
|Df, Sf | |||
|3b, 3d | |||
|1f | |||
|54\11 | |||
2492; 3.25 | |||
|63\13 | |||
2438; 1.1{{Overline|36}} | |||
|24\5 | |||
2400 | |||
|57\12 | |||
2358; 1.61̄ | |||
|33\7 | |||
2329; 2, 2.{{Overline|3}} | |||
|42\9 | |||
2390.{{Overline|90}} | |||
|- | |||
!Do, Sol | |||
!Do | |||
!D, S | |||
!3 | |||
!1 | |||
!55\11 | |||
2538; 2.1{{Overline|6}} | |||
!40\8 | |||
2526; 3.1{{Overline|6}} | |||
!65\13 | |||
2516; 7.75 | |||
!25\5 | |||
2500 | |||
!60\12 | |||
2482; '''1.3{{Overline|18}}''' | |||
!35\7 | |||
2470; 1.7 | |||
!45\9 | |||
2454.{{Overline|54}} | |||
|} | |||
{| class="wikitable" | |||
|+Relative cents<ref name=":05" /> | |||
! colspan="5" |Notation | |||
!Supersoft | |||
!Soft | |||
!Semisoft | |||
!Basic | |||
!Semihard | |||
!Hard | |||
!Superhard | |||
|- | |||
! colspan="2" |Diatonic | |||
! rowspan="2" |Mahur | |||
! rowspan="2" |Bijou | |||
! rowspan="2" |Hyperionic | |||
! rowspan="2" |~11ed4/3 | |||
! rowspan="2" |~8ed4/3 | |||
! rowspan="2" |~13ed4/3 | |||
! rowspan="2" |~5ed4/3 | |||
! rowspan="2" |~12ed4/3 | |||
! rowspan="2" |~7ed4\3 | |||
! rowspan="2" |~9ed4/3 | |||
|- | |||
!Fourth | |||
!Seventh | |||
|- | |||
|Do#, Sol# | |||
|Sol# | |||
|G# | |||
|0#, D# | |||
|1# | |||
|1\11 | |||
''45.{{Overline|45}}'' | |||
|1\8 | |||
''62.5'' | |||
|2\13 | |||
''76; 1.08{{Overline|3}}'' | |||
| rowspan="2" |1\5 | |||
''100'' | |||
|3\12 | |||
''125'' | |||
|2\7 | |||
''142; 1.1{{Overline|6}}'' | |||
|3\9 | |||
''166.{{Overline|6}}'' | |||
|- | |||
|Reb, Lab | |||
|Lab | |||
|Jf, Af | |||
|1b, 1d | |||
|2f | |||
|3\11 | |||
''136.{{Overline|36}}'' | |||
|2\8 | |||
''125'' | |||
|3\13 | |||
''115; 2.6'' | |||
|2\12 | |||
''83.{{Overline|3}}'' | |||
|1\7 | |||
''71; 2.{{Overline|3}}'' | |||
|1\9 | |||
''55.5̄'' | |||
|- | |||
|'''Re, La''' | |||
|'''La''' | |||
|'''J, A''' | |||
|'''1''' | |||
|'''2''' | |||
|'''4\11''' | |||
'''''181.{{Overline|81}}''''' | |||
|'''3\8''' | |||
'''''187.5''''' | |||
|'''5\13''' | |||
'''''192; 3.25''''' | |||
|'''2\5''' | |||
'''''200''''' | |||
|'''5\12''' | |||
'''''208.{{Overline|3}}''''' | |||
|'''3\7''' | |||
'''''214; 3.5''''' | |||
|'''4\9''' | |||
'''''222.{{Overline|2}}''''' | |||
|- | |||
|Re#, La# | |||
|La# | |||
|J#, A# | |||
|1# | |||
|2# | |||
|5\11 | |||
''227.{{Overline|27}}'' | |||
|4\8 | |||
''250'' | |||
|7\13 | |||
''269; 4.{{Overline|3}}'' | |||
| rowspan="2" |'''3\5''' | |||
'''''300''''' | |||
|8\12 | |||
''333.{{Overline|3}}'' | |||
|5\7 | |||
''357; 7'' | |||
|7\9 | |||
''388.{{Overline|8}}'' | |||
|- | |||
|'''Mib, Sib''' | |||
|'''Sib''' | |||
|'''Af, Bf''' | |||
|'''2b, 2d''' | |||
|'''3f''' | |||
|'''7\11''' | |||
'''''318.{{Overline|18}}''''' | |||
|'''5\8''' | |||
'''''312.5''''' | |||
|'''8\13''' | |||
'''''307; 1.{{Overline|4}}''''' | |||
|'''7\12''' | |||
'''''291.6̄''''' | |||
|'''4\7''' | |||
'''''285; 1.4''''' | |||
|'''5\9''' | |||
'''''277.{{Overline|7}}''''' | |||
|- | |||
|Mi, Si | |||
|Si | |||
|A, B | |||
|2 | |||
|3 | |||
|8\11 | |||
''363.{{Overline|63}}'' | |||
|6\8 | |||
''375'' | |||
|10\13 | |||
''384; 1.625'' | |||
|4\5 | |||
''400'' | |||
|10\12 | |||
''416.{{Overline|6}}'' | |||
|6\7 | |||
''428; 1.75'' | |||
|8\9 | |||
''444.{{Overline|4}}'' | |||
|- | |||
|Mi#, Si# | |||
|Si# | |||
|A#, B# | |||
|2# | |||
|3# | |||
|9\11 | |||
''409.{{Overline|09}}'' | |||
| rowspan="2" |7\8 | |||
''437.5'' | |||
|12\13 | |||
''461; 1, 1.1{{Overline|6}}'' | |||
|5\5 | |||
''500'' | |||
|13\12 | |||
''541.{{Overline|6}}'' | |||
|8\7 | |||
''571; 2.{{Overline|3}}'' | |||
|11\9 | |||
''611.1̄'' | |||
|- | |||
|Dob, Solb | |||
|Dob | |||
|Bb, Cf | |||
|3b, 3d | |||
|4f | |||
|10\11 | |||
''454.{{Overline|54}}'' | |||
|11\13 | |||
''423; 13'' | |||
|4\5 | |||
''400'' | |||
|9\12 | |||
''375'' | |||
|5\7 | |||
''357; 7'' | |||
|6\9 | |||
''333.{{Overline|3}}'' | |||
|- | |||
!Do, Sol | |||
!Do | |||
!B, C | |||
!3 | |||
!4 | |||
! colspan="7" |''500'' | |||
|- | |||
|Do#, Sol# | |||
|Do# | |||
|B#, C# | |||
|3# | |||
|4# | |||
|12\11 | |||
''545.{{Overline|45}}'' | |||
|9\8 | |||
''562.5'' | |||
|15\13 | |||
''576; 1.08{{Overline|3}}'' | |||
| rowspan="2" |6\5 | |||
''600'' | |||
|15\12 | |||
''625'' | |||
|9\7 | |||
''642; 1.1{{Overline|6}}'' | |||
|12\9 | |||
''666.{{Overline|6}}'' | |||
|- | |||
|Reb, Lab | |||
|Reb | |||
|Cf, Qf | |||
|4b, 4d | |||
|5f | |||
|14\11 | |||
''636.{{Overline|36}}'' | |||
|10\8 | |||
''625'' | |||
|16\13 | |||
''615; 2.6'' | |||
|14\12 | |||
''583.{{Overline|3}}'' | |||
|8\7 | |||
''571; 2.{{Overline|3}}'' | |||
|10\9 | |||
''555.5̄'' | |||
|- | |||
|'''Re, La''' | |||
|'''Re''' | |||
|'''C, Q''' | |||
|'''4''' | |||
|'''5''' | |||
|'''15\11''' | |||
'''''681.{{Overline|81}}''''' | |||
|'''11\8''' | |||
'''''687.5''''' | |||
|'''18\13''' | |||
'''''692; 3.25''''' | |||
|'''7\5''' | |||
'''''700''''' | |||
|'''17\12''' | |||
'''''708.{{Overline|3}}''''' | |||
|'''10\7''' | |||
'''''714; 3.5''''' | |||
|'''13\9''' | |||
'''''722.{{Overline|2}}''''' | |||
|- | |||
|Re#, La# | |||
|Re# | |||
|C#, Q# | |||
|4# | |||
|5# | |||
|16\11 | |||
''727.{{Overline|27}}'' | |||
|12\8 | |||
''750'' | |||
|20\13 | |||
''769; 4.{{Overline|3}}'' | |||
| rowspan="2" |'''8\5''' | |||
'''''800''''' | |||
|20\12 | |||
''833.{{Overline|3}}'' | |||
|12\7 | |||
''857; 7'' | |||
|16\9 | |||
''888.{{Overline|8}}'' | |||
|- | |||
|'''Mib, Sib''' | |||
|'''Sib''' | |||
|'''Qf, Df''' | |||
|'''5b, 5d''' | |||
|'''6f''' | |||
|'''18\11''' | |||
'''''818.{{Overline|18}}''''' | |||
|'''13\8''' | |||
'''''812.5''''' | |||
|'''21\13''' | |||
'''''807; 1.{{Overline|4}}''''' | |||
|'''19\12''' | |||
'''''791.{{Overline|6}}''''' | |||
|'''11\7''' | |||
'''''785; 1.4''''' | |||
|'''14\9''' | |||
'''''777.{{Overline|7}}''''' | |||
|- | |||
|Mi, Si | |||
|Si | |||
|Q, D | |||
|5 | |||
|6 | |||
|19\11 | |||
''863.{{Overline|63}}'' | |||
|14\8 | |||
''875'' | |||
|23\13 | |||
''884; 1.625'' | |||
|9\5 | |||
''900'' | |||
|22\12 | |||
''916.{{Overline|6}}'' | |||
|13\7 | |||
''928; 1.75'' | |||
|17\9 | |||
''944.{{Overline|4}}'' | |||
|- | |||
|Mi#, Si# | |||
|Si# | |||
|Q#, D# | |||
|5# | |||
|6# | |||
|20\11 | |||
''909.{{Overline|09}}'' | |||
| rowspan="2" |15\8 | |||
''937.5'' | |||
|25\13 | |||
''961; 1, 1.1{{Overline|6}}'' | |||
|10\5 | |||
''1000'' | |||
|25\12 | |||
''1041.{{Overline|6}}'' | |||
|15\7 | |||
''1071; 2.{{Overline|3}}'' | |||
|20\9 | |||
''1111.1̄'' | |||
|- | |||
|Dob, Solb | |||
|Solb | |||
|Df, Sf | |||
|6b, 6d | |||
|7f | |||
|21\11 | |||
''954.{{Overline|54}}'' | |||
|24\13 | |||
''923; 13'' | |||
|9\5 | |||
''900'' | |||
|21\12 | |||
''875'' | |||
|12\7 | |||
''857; 7'' | |||
|15\9 | |||
''833.{{Overline|3}}'' | |||
|- | |||
!Do, Sol | |||
!Sol | |||
!D, S | |||
!6 | |||
!7 | |||
! colspan="7" |''1000'' | |||
|- | |||
|Do#, Sol# | |||
|Sol# | |||
|D#, S# | |||
|6# | |||
|7# | |||
|23\11 | |||
''1045.{{Overline|45}}'' | |||
|17\8 | |||
''1062.5'' | |||
|28\13 | |||
''1076; 1.08{{Overline|3}}'' | |||
| rowspan="2" |11\5 | |||
''1100'' | |||
|27\12 | |||
''1125'' | |||
|16\7 | |||
''1142; 1.1{{Overline|6}}'' | |||
|21\9 | |||
''1166.{{Overline|6}}'' | |||
|- | |||
|Reb, Lab | |||
|Lab | |||
|Ef | |||
|7b, 7d | |||
|8f | |||
|25\11 | |||
''1136.{{Overline|36}}'' | |||
|18\8 | |||
''1125'' | |||
|29\13 | |||
''1115; 2.6'' | |||
|26\12 | |||
''1083.{{Overline|3}}'' | |||
|22\7 | |||
''1571; 2.{{Overline|3}}'' | |||
|19\9 | |||
''1055.5̄'' | |||
|- | |||
|'''Re, La''' | |||
|'''La''' | |||
|'''E''' | |||
|'''7''' | |||
|'''8''' | |||
|'''26\11''' | |||
'''''1181.{{Overline|81}}''''' | |||
|'''19\8''' | |||
'''''1187.5''''' | |||
|'''31\13''' | |||
'''''1192; 3.25''''' | |||
|'''12\5''' | |||
'''''1200''''' | |||
|'''29\12''' | |||
'''''1208.{{Overline|3}}''''' | |||
|'''17\7''' | |||
'''''1214; 3.5''''' | |||
|'''22\9''' | |||
'''''1222.{{Overline|2}}''''' | |||
|- | |||
|Re#, La# | |||
|La# | |||
|E# | |||
|7# | |||
|8# | |||
|27\11 | |||
''1227.{{Overline|27}}'' | |||
|20\8 | |||
''1250'' | |||
|33\13 | |||
''1269; 4.{{Overline|3}}'' | |||
| rowspan="2" |'''13\5''' | |||
'''''1300''''' | |||
|32\12 | |||
''1333.{{Overline|3}}'' | |||
|19\7 | |||
''1357; 7'' | |||
|25\9 | |||
''1388.{{Overline|8}}'' | |||
|- | |||
|'''Mib, Sib''' | |||
|'''Sib''' | |||
|'''Ff''' | |||
|'''8b, Fd''' | |||
|'''9f''' | |||
|'''29\11''' | |||
'''''1318.{{Overline|18}}''''' | |||
|'''21\8''' | |||
'''''1312.5''''' | |||
|'''34\13''' | |||
'''''1307; 1.{{Overline|4}}''''' | |||
|'''31\12''' | |||
'''''1291.{{Overline|6}}''''' | |||
|'''18\7''' | |||
'''''1285; 1.4''''' | |||
|'''23\9''' | |||
'''''1277.{{Overline|7}}''''' | |||
|- | |||
|Mi, Si | |||
|Si | |||
|F | |||
|8, F | |||
|9 | |||
|30\11 | |||
''1363.{{Overline|63}}'' | |||
|22\8 | |||
''1375'' | |||
|36\13 | |||
''1384; 1.625'' | |||
|14\5 | |||
''1400'' | |||
|34\12 | |||
''1416.{{Overline|6}}'' | |||
|20\7 | |||
''1428; 1.75'' | |||
|26\9 | |||
''1444.{{Overline|4}}'' | |||
|- | |||
|Mi#, Si# | |||
|Si# | |||
|F# | |||
|8#, F# | |||
|9# | |||
|31\11 | |||
''1409.{{Overline|09}}'' | |||
| rowspan="2" |23\8 | |||
''1437.5'' | |||
|38\13 | |||
''1461; 1, 1.1{{Overline|6}}'' | |||
|15\5 | |||
''1500'' | |||
|37\12 | |||
''1541.{{Overline|6}}'' | |||
|22\7 | |||
''1571; 2.{{Overline|3}}'' | |||
|29\9 | |||
''1611.1̄'' | |||
|- | |||
|Dob, Solb | |||
|Dob | |||
|Gf | |||
|9b, Gd | |||
|Af | |||
|32\11 | |||
''1454.{{Overline|54}}'' | |||
|37\13 | |||
''1423; 13'' | |||
|14\5 | |||
''1400'' | |||
|33\12 | |||
''1375'' | |||
|19\7 | |||
''1357; 7'' | |||
|24\9 | |||
''1333.{{Overline|3}}'' | |||
|- | |||
!Do, Sol | |||
!Do | |||
!G | |||
!'''9, G''' | |||
!A | |||
! colspan="7" |''1500'' | |||
|- | |||
|Do#, Sol# | |||
|Sol# | |||
|G# | |||
|9#, G# | |||
|A# | |||
|34\11 | |||
''1545.{{Overline|45}}'' | |||
|25\8 | |||
''1562.5'' | |||
|41\13 | |||
''1576; 1.08{{Overline|3}}'' | |||
| rowspan="2" |16\5 | |||
''1600'' | |||
|39\12 | |||
''1625'' | |||
|23\7 | |||
''1642; 1.1{{Overline|6}}'' | |||
|30\9 | |||
''1666.{{Overline|6}}'' | |||
|- | |||
|Reb, Lab | |||
|Lab | |||
|Jf, Af | |||
|Xb, Ad | |||
|Bf | |||
|36\11 | |||
''1636.{{Overline|36}}'' | |||
|26\8 | |||
''1625'' | |||
|42\13 | |||
''1615; 2.6'' | |||
|38\12 | |||
''1583.{{Overline|3}}'' | |||
|22\7 | |||
''1571; 2.{{Overline|3}}'' | |||
|28\9 | |||
''1555.5̄'' | |||
|- | |||
|'''Re, La''' | |||
|'''La''' | |||
|'''J, A''' | |||
|'''X, A''' | |||
|'''B''' | |||
|'''37\11''' | |||
'''''1681.{{Overline|81}}''''' | |||
|'''27\8''' | |||
'''''1687.5''''' | |||
|'''44\13''' | |||
'''''1692; 3.25''''' | |||
|'''17\5''' | |||
'''''1700''''' | |||
|'''41\12''' | |||
'''''1708.{{Overline|3}}''''' | |||
|'''24\7''' | |||
'''''1714; 3.5''''' | |||
|'''31\9''' | |||
'''''1722.{{Overline|2}}''''' | |||
|- | |||
|Re#, La# | |||
|La# | |||
|J#, A# | |||
|X#, A# | |||
|B# | |||
|38\11 | |||
''1727.{{Overline|27}}'' | |||
|28\8 | |||
''1750'' | |||
|46\13 | |||
''1769; 4.{{Overline|3}}'' | |||
| rowspan="2" |'''18\5''' | |||
'''''1800''''' | |||
|44\12 | |||
''1833.{{Overline|3}}'' | |||
|26\7 | |||
''1857; 7'' | |||
|34\9 | |||
''1888.{{Overline|8}}'' | |||
|- | |||
|'''Mib, Sib''' | |||
|'''Sib''' | |||
|'''Af, Bf''' | |||
|'''Eb, Bd''' | |||
|'''Cf''' | |||
|'''40\11''' | |||
'''''1818.{{Overline|18}}''''' | |||
|'''29\8''' | |||
'''''1812.5''''' | |||
|'''47\13''' | |||
'''''1807; 1.{{Overline|4}}''''' | |||
|'''43\12''' | |||
'''''1791.{{Overline|6}}''''' | |||
|'''25\7''' | |||
'''''1785; 1.4''''' | |||
|'''32\9''' | |||
'''''1777.{{Overline|7}}''''' | |||
|- | |||
|Mi, Si | |||
|Si | |||
|A, B | |||
|E, B | |||
|C | |||
|41\11 | |||
''1863.{{Overline|63}}'' | |||
|30\8 | |||
''1875'' | |||
|49\13 | |||
''1884; 1.625'' | |||
|19\5 | |||
''1900'' | |||
|46\12 | |||
''1916.{{Overline|6}}'' | |||
|27\7 | |||
''1928; 1.75'' | |||
|35\9 | |||
''1944.{{Overline|4}}'' | |||
|- | |||
|Mi#, Si# | |||
|Si# | |||
|A#, B# | |||
|E#, B# | |||
|C# | |||
|42\11 | |||
''1909.{{Overline|09}}'' | |||
| rowspan="2" |31\8 | |||
''1937.5'' | |||
|51\13 | |||
''1961; 1, 1.1{{Overline|6}}'' | |||
|20\5 | |||
''2000'' | |||
|49\12 | |||
''2041.{{Overline|6}}'' | |||
|29\7 | |||
''2071; 2.{{Overline|3}}'' | |||
|38\9 | |||
''2111.1̄'' | |||
|- | |||
|Dob, Solb | |||
|Dob | |||
|Bb, Cf | |||
|0b, Dd | |||
|Df | |||
|43\11 | |||
''1954.{{Overline|54}}'' | |||
|50\13 | |||
''1923; 13'' | |||
|19\5 | |||
''1900'' | |||
|45\12 | |||
''1875'' | |||
|26\7 | |||
''1857; 7'' | |||
|33\9 | |||
''1833.{{Overline|3}}'' | |||
|- | |||
!Do, Sol | |||
!Sol | |||
!B, C | |||
!0, D | |||
!D | |||
! colspan="7" |''2000'' | |||
|- | |||
|Do#, Sol# | |||
|Sol# | |||
|B#, C# | |||
|0#, D# | |||
|D# | |||
|45\11 | |||
''2045.{{Overline|45}}'' | |||
|33\8 | |||
''2062.5'' | |||
|54\13 | |||
''2076; 1.08{{Overline|3}}'' | |||
| rowspan="2" |21\5 | |||
''2100'' | |||
|51\12 | |||
''2125'' | |||
|30\7 | |||
''2142; 1.1{{Overline|6}}'' | |||
|39\9 | |||
''2166.{{Overline|6}}'' | |||
|- | |||
|Reb, Lab | |||
|Lab | |||
|Cf, Qf | |||
|1b, 1d | |||
|Ef | |||
|47\11 | |||
''2136.{{Overline|36}}'' | |||
|34\8 | |||
''2125'' | |||
|55\13 | |||
''2115; 2.6'' | |||
|50\12 | |||
''2083.{{Overline|3}}'' | |||
|29\7 | |||
''2071; 2.{{Overline|3}}'' | |||
|37\9 | |||
''2055.5̄'' | |||
|- | |||
|'''Re, La''' | |||
|'''La''' | |||
|'''C, Q''' | |||
|'''1''' | |||
|'''E''' | |||
|'''48\11''' | |||
'''''2181.{{Overline|81}}''''' | |||
|'''35\8''' | |||
'''''2187.5''''' | |||
|'''57\13''' | |||
'''''2192; 3.25''''' | |||
|'''22\5''' | |||
'''''2200''''' | |||
|'''53\12''' | |||
'''''2208.{{Overline|3}}''''' | |||
|'''31\7''' | |||
'''''2214; 3.5''''' | |||
|'''40\9''' | |||
'''''2222.{{Overline|2}}''''' | |||
|- | |||
|Re#, La# | |||
|La# | |||
|C#, Q# | |||
|1# | |||
|E# | |||
|49\11 | |||
''2227.{{Overline|27}}'' | |||
|36\8 | |||
''2250'' | |||
|59\13 | |||
''2269; 4.{{Overline|3}}'' | |||
| rowspan="2" |'''23\5''' | |||
'''''2300''''' | |||
|56\12 | |||
''2333.{{Overline|3}}'' | |||
|33\7 | |||
''2357; 7'' | |||
|43\9 | |||
''2388.{{Overline|8}}'' | |||
|- | |||
|'''Mib, Sib''' | |||
|'''Sib''' | |||
|'''Qf, Df''' | |||
|'''2b, 2d''' | |||
|'''Ff''' | |||
|'''51\11''' | |||
'''''2318.{{Overline|18}}''''' | |||
|'''37\8''' | |||
'''''2312.5''''' | |||
|'''60\13''' | |||
'''''2307; 1.{{Overline|4}}''''' | |||
|'''55\12''' | |||
'''''2291.{{Overline|6}}''''' | |||
|'''32\7''' | |||
'''''2285; 1.4''''' | |||
|'''41\9''' | |||
'''''2277.{{Overline|7}}''''' | |||
|- | |||
|Mi, Si | |||
|Si | |||
|Q, D | |||
|2 | |||
|F | |||
|52\11 | |||
''2363.{{Overline|63}}'' | |||
|38\8 | |||
''2375'' | |||
|62\13 | |||
''2384; 1.625'' | |||
|24\5 | |||
''2400'' | |||
|58\12 | |||
''2416.{{Overline|6}}'' | |||
|34\7 | |||
''2428; 1.75'' | |||
|44\9 | |||
''2444.{{Overline|4}}'' | |||
|- | |||
|Mi#, Si# | |||
|Si# | |||
|Q#, D# | |||
|2# | |||
|F# | |||
|53\11 | |||
''2409.{{Overline|09}}'' | |||
| rowspan="2" |39\8 | |||
''2437.5'' | |||
|64\13 | |||
''2461; 1, 1.1{{Overline|6}}'' | |||
|25\5 | |||
''2500'' | |||
|61\12 | |||
''2541.{{Overline|6}}'' | |||
|36\7 | |||
''2571; 2.3̄'' | |||
|47\9 | |||
''2611.1̄'' | |||
|- | |||
|Dob, Solb | |||
|Dob | |||
|Df, Sf | |||
|3b, 3d | |||
|1f | |||
|54\11 | |||
''2454.{{Overline|54}}'' | |||
|63\13 | |||
''2423; 13'' | |||
|24\5 | |||
''2400'' | |||
|57\12 | |||
''2375'' | |||
|33\7 | |||
''2357; 7'' | |||
|42\9 | |||
''2333.{{Overline|3}}'' | |||
|- | |||
!Do, Sol | |||
!Do | |||
!D, S | |||
!3 | |||
!1 | |||
! colspan="7" |''2500'' | |||
|} | |||
==Intervals== | |||
{| class="wikitable" | |||
!Generators | |||
!Fourth notation | |||
!Interval category name | |||
!Generators | |||
!Notation of 4/3 inverse | |||
!Interval category name | |||
|- | |||
| colspan="6" |The 3-note MOS has the following intervals (from some root): | |||
|- | |||
|0 | |||
|Do, Sol | |||
|perfect unison | |||
|0 | |||
|Do, Sol | |||
|perfect fourth | |||
|- | |||
|1 | |||
|Mib, Sib | |||
|diminished third | |||
| -1 | |||
|Re, La | |||
|perfect second | |||
|- | |||
|2 | |||
|Reb, Lab | |||
|diminished second | |||
| -2 | |||
|Mi, Si | |||
|perfect third | |||
|- | |||
| colspan="6" |The chromatic 5-note MOS also has the following intervals (from some root): | |||
|- | |||
|3 | |||
|Dob, Solb | |||
|diminished fourth | |||
| -3 | |||
|Do#, Sol# | |||
|augmented unison (chroma) | |||
|- | |||
|4 | |||
|Mibb, Sibb | |||
|doubly diminished third | |||
| -4 | |||
|Re#, La# | |||
|augmented second | |||
|} | |||
==Genchain== | |||
The generator chain for this scale is as follows: | |||
{| class="wikitable" | |||
|Mibb | |||
Sibb | |||
|Dob | |||
Solb | |||
|Reb | |||
Lab | |||
|Mib | |||
Sib | |||
|Do | |||
Sol | |||
|Re | |||
La | |||
|Mi | |||
Si | |||
|Do# | |||
Sol# | |||
|Re# | |||
La# | |||
|Mi# | |||
Si# | |||
|- | |||
|dd3 | |||
|d4 | |||
|d2 | |||
|d3 | |||
|P1 | |||
|P2 | |||
|P3 | |||
|A1 | |||
|A2 | |||
|A3 | |||
|} | |||
==Modes== | |||
The mode names are based on the species of fourth: | |||
{| class="wikitable" | |||
!Mode | |||
!Scale | |||
![[Modal UDP Notation|UDP]] | |||
! colspan="2" |Interval type | |||
|- | |||
!name | |||
!pattern | |||
!notation | |||
!2nd | |||
!3rd | |||
|- | |||
|Major | |||
|LLs | |||
|<nowiki>2|0</nowiki> | |||
|P | |||
|P | |||
|- | |||
|Minor | |||
|LsL | |||
|<nowiki>1|1</nowiki> | |||
|P | |||
|d | |||
|- | |||
|Phrygian | |||
|LsLL | |||
|<nowiki>0|2</nowiki> | |||
|d | |||
|d | |||
|} | |||
==Temperaments== | |||
The most basic rank-2 temperament interpretation of diatonic is '''Mahuric'''. The name "Mahuric" comes from the “Mahur” scale in Persian and Arabic music. The major triad is spelled <code>root-2g-(p+g)</code> (p = 4/3, g = the whole tone) and approximates 4:5:6 in pental interpretations or 14:18:21 in septimal ones. Basic ~5ed4/3 fits both interpretations. | |||
==='''Mahuric-Meantone'''=== | |||
[[Subgroup]]: 4/3.5/4.3/2 | |||
[[Comma]] list: [[81/80]] | |||
[[POL2]] generator: ~9/8 = 193.6725 | |||
[[Mapping]]: [{{val|1 0 1}}, {{val|0 2 1}}] | |||
[[Optimal ET sequence]]: ~(5ed4/3, 8ed4/3, 13ed4/3) | |||
==='''Mahuric-Superpyth'''=== | |||
[[Subgroup]]: 4/3.9/7.3/2 | |||
[[Comma]] list: [[64/63]] | |||
[[POL2]] generator: ~8/7 = 216.7325 | |||
[[Mapping]]: [{{val|1 0 1}}, {{val|0 2 1}}] | |||
[[Optimal ET sequence]]: ~(5ed4/3, 7ed4/3, 9ed4/3, 11ed4/3) | |||
====Scale tree==== | |||
The spectrum looks like this: | |||
{| class="wikitable" | |||
! colspan="3" rowspan="2" |Generator | |||
(bright) | |||
! colspan="2" |Cents | |||
! rowspan="2" |L | |||
! rowspan="2" |s | |||
! rowspan="2" |L/s | |||
! rowspan="2" |Comments | |||
|- | |||
!Normalised<ref name=":05" /> | |||
!''ed5\12<ref name=":05" />'' | |||
|- | |||
|1\3 | |||
| | |||
| | |||
|171; 2.{{Overline|3}} | |||
|''166.{{Overline|6}}'' | |||
|1 | |||
|1 | |||
|1.000 | |||
|Equalised | |||
|- | |||
|6\17 | |||
| | |||
| | |||
|180 | |||
|''176; 2.125'' | |||
|6 | |||
|5 | |||
|1.200 | |||
| | |||
|- | |||
| | |||
|11\31 | |||
| | |||
|180; 1.21{{Overline|6}} | |||
|''177; 2, 2.6'' | |||
|11 | |||
|9 | |||
|1.222 | |||
| | |||
|- | |||
|5\14 | |||
| | |||
| | |||
|181.{{Overline|81}} | |||
|''178; 1.75'' | |||
|5 | |||
|4 | |||
|1.250 | |||
| | |||
|- | |||
| | |||
|14\39 | |||
| | |||
|182; 1, 1.5 | |||
|''179; 2, 19'' | |||
|14 | |||
|11 | |||
|1.273 | |||
| | |||
|- | |||
| | |||
|9\25 | |||
| | |||
|183; 19.{{Overline|6}} | |||
|''180'' | |||
|9 | |||
|7 | |||
|1.286 | |||
| | |||
|- | |||
|4\11 | |||
| | |||
| | |||
|184; 1.625 | |||
|''181.{{Overline|81}}'' | |||
|4 | |||
|3 | |||
|1.333 | |||
| | |||
|- | |||
| | |||
|15\41 | |||
| | |||
|185; 1.7{{Overline|63}} | |||
|''182; 1, 12.{{Overline|6}}'' | |||
|15 | |||
|11 | |||
|1.364 | |||
| | |||
|- | |||
| | |||
|11\30 | |||
| | |||
|185, 1, 10.8{{Overline|3}} | |||
|''183.{{Overline|3}}'' | |||
|11 | |||
|8 | |||
|1.375 | |||
| | |||
|- | |||
| | |||
|7\19 | |||
| | |||
|186.{{Overline|6}} | |||
|''184; 4.75'' | |||
|7 | |||
|5 | |||
|1.400 | |||
| | |||
|- | |||
| | |||
|10\27 | |||
| | |||
|187.5 | |||
|''185.{{Overline|185}}'' | |||
|10 | |||
|7 | |||
|1.429 | |||
| | |||
|- | |||
| | |||
|13\35 | |||
| | |||
|187; 1, 19.75 | |||
|''185; 1.4'' | |||
|13 | |||
|9 | |||
|1.444 | |||
| | |||
|- | |||
| | |||
|16\43 | |||
| | |||
|188; 4.25 | |||
|''186; 21.5'' | |||
|16 | |||
|11 | |||
|1.4545 | |||
| | |||
|- | |||
|3\8 | |||
| | |||
| | |||
|189; 2.{{Overline|1}} | |||
|''187.5'' | |||
|3 | |||
|2 | |||
|1.500 | |||
|Mahuric-Meantone starts here | |||
|- | |||
| | |||
|17\45 | |||
| | |||
|190; 1, 1.{{Overline|12}} | |||
|''188.{{Overline|8}}'' | |||
|17 | |||
|11 | |||
|1.5455 | |||
| | |||
|- | |||
| | |||
|14\37 | |||
| | |||
|190.{{Overline|90}} | |||
|''189.{{Overline|189}}'' | |||
|14 | |||
|9 | |||
|1.556 | |||
| | |||
|- | |||
| | |||
|11\29 | |||
| | |||
|191; 3, 2.{{Overline|3}} | |||
|''189; 1, 1.9'' | |||
|11 | |||
|7 | |||
|1.571 | |||
| | |||
|- | |||
| | |||
|8\21 | |||
| | |||
|192 | |||
|''190; 2.1'' | |||
|8 | |||
|5 | |||
|1.600 | |||
| | |||
|- | |||
| | |||
| | |||
|13\34 | |||
|192.{{Overline|592}} | |||
|''191; 5.{{Overline|6}}'' | |||
|13 | |||
|8 | |||
|1.625 | |||
| | |||
|- | |||
| | |||
|5\13 | |||
| | |||
|193; 1, 1, 4.{{Overline|6}} | |||
|''192; 4.{{Overline|3}}'' | |||
|5 | |||
|3 | |||
|1.667 | |||
| | |||
|- | |||
| | |||
| | |||
|12\31 | |||
|194.{{Overline|594}} | |||
|''193; 1, 1, 4.{{Overline|6}}'' | |||
|12 | |||
|7 | |||
|1.714 | |||
| | |||
|- | |||
| | |||
|7\18 | |||
| | |||
|195; 2.8{{Overline|6}} | |||
|''194.{{Overline|4}}'' | |||
|7 | |||
|4 | |||
|1.750 | |||
| | |||
|- | |||
| | |||
|9\23 | |||
| | |||
|196.{{Overline|36}} | |||
|''195; 1.5{{Overline|3}}'' | |||
|9 | |||
|5 | |||
|1.800 | |||
| | |||
|- | |||
| | |||
|11\28 | |||
| | |||
|197; 67 | |||
|''196; 2.{{Overline|3}}'' | |||
|11 | |||
|6 | |||
|1.833 | |||
| | |||
|- | |||
| | |||
|13\33 | |||
| | |||
|197; 2.{{Overline|135}} | |||
|''196.{{Overline|96}}'' | |||
|13 | |||
|7 | |||
|1.857 | |||
| | |||
|- | |||
| | |||
|15\38 | |||
| | |||
|197; 1, 2, 1, 1.{{Overline|54}} | |||
|''197; 2, 1.4'' | |||
|15 | |||
|8 | |||
|1.875 | |||
| | |||
|- | |||
| | |||
|17\43 | |||
| | |||
|198; 17.1{{Overline|6}} | |||
|''197; 1, 2, 14'' | |||
|17 | |||
|9 | |||
|1.889 | |||
| | |||
|- | |||
| | |||
|19\48 | |||
| | |||
|198: 3, 1, 28 | |||
|''197.91{{Overline|6}}'' | |||
|19 | |||
|10 | |||
|1.900 | |||
| | |||
|- | |||
| | |||
|21\53 | |||
| | |||
|198; 2.3{{Overline|518}} | |||
|''198; 8.8{{Overline|3}}'' | |||
|21 | |||
|11 | |||
|1.909 | |||
| | |||
|- | |||
| | |||
|23\58 | |||
| | |||
|198; 1, 3, 1.7 | |||
|''198; 3.625'' | |||
|23 | |||
|12 | |||
|1.917 | |||
| | |||
|- | |||
| | |||
|25\63 | |||
| | |||
|198; 1, 2, 12.25 | |||
|''198; 2, 2.{{Overline|36}}'' | |||
|25 | |||
|13 | |||
|1.923 | |||
| | |||
|- | |||
| | |||
|27\68 | |||
| | |||
|198; 1, 3.{{Overline|405}} | |||
|''198; 1.{{Overline|8}}'' | |||
|27 | |||
|14 | |||
|1.929 | |||
| | |||
|- | |||
| | |||
|29\73 | |||
| | |||
|198; 1, 1.1{{Overline|6}} | |||
|''198; 1, 1.{{Overline|703}}'' | |||
|29 | |||
|15 | |||
|1.933 | |||
| | |||
|- | |||
| | |||
|31\78 | |||
| | |||
|198; 1, 12, 2.8 | |||
|''198; 1, 2.{{Overline|54}}'' | |||
|31 | |||
|16 | |||
|1.9375 | |||
| | |||
|- | |||
| | |||
|33\83 | |||
| | |||
|198; 1.{{Overline|005}} | |||
|''198; 1.2{{Overline|57}}'' | |||
|33 | |||
|17 | |||
|1.941 | |||
| | |||
|- | |||
| | |||
|35\88 | |||
| | |||
|199; 19.{{Overline|18}} | |||
|''198.8{{Overline|63}}'' | |||
|35 | |||
|18 | |||
|1.944 | |||
| | |||
|- | |||
|2\5 | |||
| | |||
| | |||
|200 | |||
|''200'' | |||
|2 | |||
|1 | |||
|2.000 | |||
|Mahuric-Meantone ends, Mahuric-Pythagorean begins | |||
|- | |||
| | |||
|17\42 | |||
| | |||
|201.{{Overline|9801}} | |||
|''202; 2.625'' | |||
|17 | |||
|8 | |||
|2.125 | |||
| | |||
|- | |||
| | |||
|15\37 | |||
| | |||
|202; 4.0{{Overline|45}} | |||
|''202.{{Overline|702}}'' | |||
|15 | |||
|7 | |||
|2.143 | |||
| | |||
|- | |||
| | |||
|13\32 | |||
| | |||
|202; 1, 1, 2.0{{Overline|6}} | |||
|''203.125'' | |||
|13 | |||
|6 | |||
|2.167 | |||
| | |||
|- | |||
| | |||
|11\27 | |||
| | |||
|203; 13 | |||
|''203.{{Overline|703}}'' | |||
|11 | |||
|5 | |||
|2.200 | |||
| | |||
|- | |||
| | |||
|9\22 | |||
| | |||
|203; 1, 3.41{{Overline|6}} | |||
|''204.{{Overline|54}}'' | |||
|9 | |||
|4 | |||
|2.250 | |||
| | |||
|- | |||
| | |||
|7\17 | |||
| | |||
|204; 1. 7.2 | |||
|''205; 1.1{{Overline|3}}'' | |||
|7 | |||
|3 | |||
|2.333 | |||
| | |||
|- | |||
| | |||
| | |||
|12\29 | |||
|205; 1.4 | |||
|''206; 1, 8.{{Overline|6}}'' | |||
|12 | |||
|5 | |||
|2.400 | |||
| | |||
|- | |||
| | |||
| | |||
|17\41 | |||
|206.{{Overline|06}} | |||
|''207; 3, 6.5'' | |||
|17 | |||
|7 | |||
|2.429 | |||
| | |||
|- | |||
| | |||
|5\12 | |||
| | |||
|206; 1, 8.{{Overline|6}} | |||
|''208.{{Overline|3}}'' | |||
|5 | |||
|2 | |||
|2.500 | |||
|Mahuric-Neogothic heartland is from here… | |||
|- | |||
| | |||
| | |||
|18\43 | |||
|207; 1.{{Overline|4}} | |||
|''209; 3, 4.{{Overline|3}}'' | |||
|18 | |||
|7 | |||
|2.571 | |||
| | |||
|- | |||
| | |||
| | |||
|13\31 | |||
|208 | |||
|''209; 1, 2.1'' | |||
|13 | |||
|5 | |||
|2.600 | |||
| | |||
|- | |||
| | |||
|8\19 | |||
| | |||
|208; 1.4375 | |||
|''210; 1.9'' | |||
|8 | |||
|3 | |||
|2.667 | |||
|…to here | |||
|- | |||
| | |||
|11\26 | |||
| | |||
|209; 1.{{Overline|90}} | |||
|''211; 1, 1.1{{Overline|6}}'' | |||
|11 | |||
|4 | |||
|2.750 | |||
| | |||
|- | |||
| | |||
|14\33 | |||
| | |||
|210 | |||
|''212.{{Overline|12}}'' | |||
|14 | |||
|5 | |||
|2.800 | |||
| | |||
|- | |||
| | |||
|17\40 | |||
| | |||
|210; 3.2{{Overline|3}} | |||
|''212.5'' | |||
|17 | |||
|6 | |||
|2.833 | |||
| | |||
|- | |||
| | |||
|20\47 | |||
| | |||
|210; 1.9 | |||
|''212; 1.{{Overline|30}}'' | |||
|20 | |||
|7 | |||
|2.857 | |||
| | |||
|- | |||
| | |||
|23\54 | |||
| | |||
|210; 1.4{{Overline|5}} | |||
|''212.{{Overline|962}}'' | |||
|23 | |||
|8 | |||
|2.875 | |||
| | |||
|- | |||
| | |||
|26\61 | |||
| | |||
|210.{{Overline|810}} | |||
|''213; 8, 1.4'' | |||
|26 | |||
|9 | |||
|2.889 | |||
| | |||
|- | |||
|3\7 | |||
| | |||
| | |||
|211; 1, 3.25 | |||
|''214; 3.5'' | |||
|3 | |||
|1 | |||
|3.000 | |||
|Mahuric-Pythagorean ends, Mahuric-Superpyth begins | |||
|- | |||
| | |||
|22\51 | |||
| | |||
|212; 1, 9.{{Overline|3}} | |||
|''215; 1, 2,1875'' | |||
|22 | |||
|7 | |||
|3.143 | |||
| | |||
|- | |||
| | |||
|19\44 | |||
| | |||
|213; 11.{{Overline|8}} | |||
|''215.{{Overline|90}}'' | |||
|19 | |||
|6 | |||
|3.167 | |||
| | |||
|- | |||
| | |||
|16\37 | |||
| | |||
|213.3̄ | |||
|''216.{{Overline|216}}'' | |||
|16 | |||
|5 | |||
|3.200 | |||
| | |||
|- | |||
| | |||
|13\30 | |||
| | |||
|213; 1, 2.3{{Overline|18}} | |||
|''216.{{Overline|6}}'' | |||
|13 | |||
|4 | |||
|3.250 | |||
| | |||
|- | |||
| | |||
|10\23 | |||
| | |||
|214; 3.5 | |||
|''217; 5.75'' | |||
|10 | |||
|3 | |||
|3.333 | |||
| | |||
|- | |||
| | |||
|7\16 | |||
| | |||
|215; 2.6 | |||
|''218.75'' | |||
|7 | |||
|2 | |||
|3.500 | |||
| | |||
|- | |||
| | |||
| | |||
|18\41 | |||
|216 | |||
|''219; 1, 1.05'' | |||
|18 | |||
|5 | |||
|3.600 | |||
| | |||
|- | |||
| | |||
|11\25 | |||
| | |||
|216; 2.541{{Overline|6}} | |||
|''220'' | |||
|11 | |||
|3 | |||
|3.667 | |||
| | |||
|- | |||
| | |||
|15\34 | |||
| | |||
|216; 1.152{{Overline|7}} | |||
|''220; 1.7'' | |||
|15 | |||
|4 | |||
|3.750 | |||
| | |||
|- | |||
| | |||
|19\43 | |||
| | |||
|217; 7 | |||
|''220; 1, 7.6'' | |||
|19 | |||
|5 | |||
|3.800 | |||
| | |||
|- | |||
| | |||
|23\52 | |||
| | |||
|217; 3, 10.25 | |||
|''221; 6.5'' | |||
|23 | |||
|6 | |||
|3.833 | |||
| | |||
|- | |||
|4\9 | |||
| | |||
| | |||
|218.{{Overline|18}} | |||
|''222.{{Overline|2}}'' | |||
|4 | |||
|1 | |||
|4.000 | |||
| | |||
|- | |||
| | |||
|17\38 | |||
| | |||
|219; 1, 2.{{Overline|90}} | |||
|''223; 1.58{{Overline|3}}'' | |||
|17 | |||
|4 | |||
|4.250 | |||
| | |||
|- | |||
| | |||
|13\29 | |||
| | |||
|219; 1, 2.55 | |||
|''224; 7.25'' | |||
|13 | |||
|3 | |||
|4.333 | |||
| | |||
|- | |||
| | |||
|9\20 | |||
| | |||
|220; 2.45 | |||
|''225'' | |||
|9 | |||
|2 | |||
|4.500 | |||
| | |||
|- | |||
| | |||
|14\31 | |||
| | |||
|221; 19 | |||
|''225; 1.24'' | |||
|14 | |||
|3 | |||
|4.667 | |||
| | |||
|- | |||
| | |||
|19\42 | |||
| | |||
|221; 2.{{Overline|783}} | |||
|''226; 4.2'' | |||
|19 | |||
|4 | |||
|4.750 | |||
| | |||
|- | |||
|5\11 | |||
| | |||
| | |||
|222.{{Overline|2}} | |||
|''227.{{Overline|27}}'' | |||
|5 | |||
|1 | |||
|5.000 | |||
|Mahuric-Superpyth ends | |||
|- | |||
| | |||
|16\35 | |||
| | |||
|223; 3.{{Overline|90}} | |||
|''228; 1.75'' | |||
|16 | |||
|3 | |||
|5.333 | |||
| | |||
|- | |||
| | |||
|11\24 | |||
| | |||
|223; 1, 2.6875 | |||
|''229.1{{Overline|6}}'' | |||
|11 | |||
|2 | |||
|5.500 | |||
| | |||
|- | |||
| | |||
|17\37 | |||
| | |||
|224; 5.7{{Overline|2}} | |||
|''229.{{Overline|729}}'' | |||
|17 | |||
|3 | |||
|5.667 | |||
| | |||
|- | |||
|6\13 | |||
| | |||
| | |||
|225 | |||
|''230; 1.3'' | |||
|6 | |||
|1 | |||
|6.000 | |||
| | |||
|- | |||
|1\3 | |||
| | |||
| | |||
|240 | |||
|''250'' | |||
|1 | |||
|0 | |||
|→ inf | |||
|Paucitonic | |||
|} | |||
== See also == | |||
[[2L 1s (4/3-equivalent)]] - idealized tuning<references /> |
Revision as of 05:30, 26 May 2023
2L 1s<fourth>, is a fourth-repeating MOS scale. The notation "<fourth>" means the period of the MOS is a fourth, disambiguating it from octave-repeating 2L 1s.
The generator range is 171.4 to 240 cents, placing it near the diatonic major second, usually representing a major second of some type. The dark (chroma-negative) generator is, however, its fourth complement (240 to 342.9 cents).
In the fourth-repeating version of the diatonic scale, each tone has a 4/3 perfect fourth above it. The scale has one major chord and two minor chords.
Basic diatonic is in 5ed4/3, which is a very good fourth-based equal tuning similar to 12edo.
Notation
There are 4 main ways to notate this scale. One method uses a simple fourth repeating notation consisting of 3 naturals (eg. Do Re Mi, Sol La Si). Given that 1-5/4-3/2 is fourth-equivalent to a tone cluster of 1-9/8-5/4, it may be more convenient to notate diatonic scales as repeating at the double, triple, quadruple or quintuple fourth (minor seventh, tenth, thirteenth or sixteenth), however it does make navigating the genchain harder. This way, 3/2 is its own pitch class, distinct from 9/8. Notating this way produces a minor tenth which is the Dorian mode of Middletown[6L 3s], also known as the Mahur scale in Persian/Arabic music, a minor thirteenth which is the Aeolian mode of Bijou[8L 4s] or a minor sixteenth which is the Phrygian mode of Hyperionic. Since there are exactly 9 naturals in triple fourth notation, 12 in quadruple fourth and 15 in quintuple fourth notation, letters A-G plus J, Q or Q, S (GJABCQDEF or GABCQDSEF, flats written F molle) or dozenal or hex digits (0123456789XE0 or E1234567GABDE with flats written D molle or 123456789ABCDEF1 with flats written F molle) may be used.
Notation | Supersoft | Soft | Semisoft | Basic | Semihard | Hard | Superhard | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
Diatonic | Mahur | Bijou | Hyperionic | ~11ed4/3 | ~8ed4/3 | ~13ed4/3 | ~5ed4/3 | ~12ed4/3 | ~7ed4\3 | ~9ed4/3 | |
Fourth | Seventh | ||||||||||
Do#, Sol# | Sol# | G# | 0#, D# | 1# | 1\11
46; 6.5 |
1\8
63; 6.3 |
2\13
77; 2, 2.6 |
1\5
100 |
3\12
124; 7.25 |
2\7
141; 5.6 |
3\9
163.63 |
Reb, Lab | Lab | Jf, Af | 1b, 1d | 2f | 3\11
138; 3.25 |
2\8
126; 3.16 |
3\13
116; 7.75 |
2\12
82; 1.318 |
1\7
70; 1.7 |
1\9
54.54 | |
Re, La | La | J, A | 1 | 2 | 4\11
184; 1.625 |
3\8
189; 2.1 |
5\13
193; 1, 1, 4.6 |
2\5
200 |
5\12
206; 1, 8.6 |
3\7
211; 1, 3.25 |
4\9
218.18 |
Re#, La# | La# | J#, A# | 1# | 2# | 5\11
230; 1.3 |
4\8
252; 1.583 |
7\13
270; 1.03 |
3\5
300 |
8\12
331; 29 |
5\7
352; 1.0625 |
7\9
381.81 |
Mib, Sib | Sib | Af, Bf | 2b, 2d | 3f | 7\11
323; 13 |
5\8
315; 1.26 |
8\13
309; 1, 2.1 |
7\12
289; 1, 1.9 |
4\7
282; 2.83 |
5\9
272.72 | |
Mi, Si | Si | A, B | 2 | 3 | 8\11
369; 4.3 |
6\8
378; 1.05 |
10\13
387; 10.3 |
4\5
400 |
10\12
413; 1, 3.83 |
6\7
423; 1.8 |
8\9
436.36 |
Mi#, Si# | Si# | A#, B# | 2# | 3# | 9\11
415; 2.6 |
7\8
442; 9.5 |
12\13
464; 1.9375 |
5\5
500 |
13\12
537; 14.5 |
8\7
564; 1.416 |
11\9
600 |
Dob, Solb | Dob | Bb, Cf | 3b, 3d | 4f | 10\11
461; 1, 1.16 |
11\13
425; 1.24 |
4\5
400 |
9\12
372; 2.416 |
5\7
352; 1.0625 |
6\9
327.27 | |
Do, Sol | Do | B, C | 3 | 4 | 11\11
507; 1.4 |
8\8
505; 3.8 |
13\13
503; 4, 2.3 |
5\5
500 |
12\12
496; 1.8125 |
7\7
494; 8.5 |
9\9
490.90 |
Do#, Sol# | Do# | B#, C# | 3# | 4# | 12\11
553; 1.18 |
9\8
568; 2.375 |
15\13
580; 1.55 |
6\5
600 |
15\12
620; 1.45 |
9\7
635; 3.4 |
12\9
654.54 |
Reb, Lab | Reb | Cf, Qf | 4b, 4d | 5f | 14\11
646; 6.5 |
10\8
631; 1.72 |
16\13
619; 2.81 |
14\12
579; 3.2 |
8\7
564; 1.416 |
10\9
545.45 | |
Re, La | Re | C, Q | 4 | 5 | 15\11
692; 3.25 |
11\8
694; 1, 2.8 |
18\13
696; 1.2916 |
7\5
700 |
17\12
703; 2, 2.16 |
10\7
705; 1.13 |
13\9
709.09 |
Re#, La# | Re# | C#, Q# | 4# | 5# | 16\11
738; 2.16 |
12\8
757; 1, 8.5 |
20\13
774; 5.16 |
8\5
800 |
20\12
827; 1, 1.416 |
12\7
847; 17 |
16\9
872.72 |
Mib, Sib | Mib | Qf, Df | 5b, 5d | 6f | 18\11
830; 1.3 |
13\8
821; 19 |
21\13
812; 1, 9.3 |
19\12
786; 4.83 |
11\7
776; 2.125 |
14\9
763.63 | |
Mi, Si | Mi | Q, D | 5 | 6 | 19\11
876; 1.083 |
14\8
884; 4.75 |
23\13
890; 3.1 |
9\5
900 |
22\12
910; 2.9 |
13\7
917; 1.54 |
17\9
927.27 |
Mi#, Si# | Mi# | Q#, D# | 5# | 6# | 20\11
923: 13 |
15\8
947; 2, 1.4 |
25\13
967; 1, 2.875 |
10\5
1000 |
25\12
1034; 2, 14 |
15\7
1058; 1, 4.6 |
20\9
1090.90 |
Dob, Solb | Solb | Df, Sf | 6b, 6d | 7f | 21\11
969; 4.3 |
24\13
929; 31 |
9\5
900 |
21\12
868; 1, 28 |
11\7
776; 2.125 |
15\9
818.18 | |
Do, Sol | Sol | D, S | 6 | 7 | 22\11
1015; 2.6 |
16\8
1010; 1.9 |
26\13
1006; 2, 4.6 |
10\5
1000 |
24\12
993; 9.6 |
14\7
988; 4.25 |
18\9
981.81 |
Do#, Sol# | Sol# | D#, S# | 6# | 7# | 23\11
1061; 1, 1.16 |
17\8
1073; 1, 2.16 |
28\13
1083; 1.148 |
11\5
1100 |
27\12
1117; 4, 7 |
16\7
1129; 2, 2.3 |
24\9
1309.09 |
Reb, Lab | Lab | Ef | 7b, 7d | 8f | 25\11
1153; 1.18 |
18\8
1136; 1.1875 |
29\13
1122; 1.72 |
26\12
1075; 1.16 |
15\7
1058; 1, 4.6 |
19\9
1036.36 | |
Re, La | La | E | 7 | 8 | 26\11
1200 |
19\8
1200 |
31\13
1200 |
12\5
1200 |
29\12
1200 |
17\7
1200 |
22\9
1200 |
Re#, La# | La# | E# | 7# | 8# | 27\11
1246; 6,5 |
20\8
1263; 6.3 |
33\13
1277; 2, 2.6 |
13\5
1300 |
32\12
1324; 7.25 |
19\7
1341; 5.6 |
25\9
1363.63 |
Mib, Sib | Sib | Ff | 8b, Fd | 9f | 29\11
1338; 3.25 |
21\8
1326; 3.16̄ |
34\13
1316; 7.75 |
31\12
1282; 1.318 |
18\7
1270; 1.7 |
23\9
1254.54 | |
Mi, Si | Si | F | 8, F | 9 | 30\11
1384; 1.625 |
22\8
1389; 2.1̄ |
36\13
1393; 1, 1, 4.6 |
14\5
1400 |
34\12
1406; 1, 8.6 |
20\7
1411; 1, 3.25 |
26\9
1418.18 |
Mi#, Si# | Si# | F# | 8#, F# | 9# | 31\11
1430; 1.3 |
23\8
1452; 1.583 |
38\13
1470; 1.03 |
15\5
1500 |
37\12
1531; 29 |
22\7
1552; 1.0625 |
29\9
1581.81 |
Dob, Solb | Dob | Gf | 9b, Gd | Af | 32\11
1476; 1.083 |
37\13
1432: 3.875 |
14\5
1400 |
33\12
1365; 1.93 |
19\7
1341; 5.3 |
24\9
1309.09 | |
Do, Sol | Do | G | 9, G | A | 33\11
1523; 13 |
24\8
1515; 1.26 |
39\13
1509; 1, 2.1 |
15\5
1500 |
36\12
1489; 1, 1.9 |
21\7
1482; 2.83 |
27\9
1472.72 |
Do#, Sol# | Do# | G# | 9#, G# | A# | 34\11
1569; 4.3 |
25\8
1578; 1.05̄ |
41\13
1587; 10.3 |
16\5
1600 |
39\12
1613; 1, 3.83 |
23\7
1623; 1.8 |
30\9
1636.36 |
Reb, Lab | Reb | Jf, Af | Xb, Ad | Bf | 36\11
1661; 1, 1.16 |
26\8
1642; 9.5 |
42\13
1625; 1.24 |
38\12
1572; 29 |
22\7
1552; 1.0625 |
28\9
1527.27 | |
Re, La | Re | J, A | X, A | B | 37\11
1707; 1.4 |
27\8
1705; 3.8 |
44\13
1703; 4, 2.3̄ |
17\5
1700 |
41\12
1696; 1.8125 |
24\7
1694; 8.5 |
31\9
1690.90 |
Re#, La# | Re# | J#, A# | X#, A# | B# | 38\11
1753; 1.18 |
28\8
1768; 2.375 |
46\13
1780; 1.55 |
18\5
1800 |
44\12
1820; 1.45 |
26\7
1835; 3,4 |
34\9
1854.54 |
Mib, Sib | Mib | Af, Bf | Eb, Bd | Cf | 40\11
1846; 6.5 |
29\8
1831; 1.72 |
47\13
1819; 2.81 |
43\12
1779; 3.2 |
25\7
1764; 1, 3.25 |
32\9
1745.45 | |
Mi, Si | Mi | A, B | E, B | C | 41\11
1892; 3.25 |
30\8
1894; 1, 2.8 |
49\13
1896; 1.2916 |
19\5
1900 |
46\12
1903; 2, 2.16 |
27\7
1905; 1, 7.5 |
35\9
1909.09 |
Mi#, Si# | Mi# | A#, B# | E#, B# | C# | 42\11
1938; 2.16 |
31\8
1957; 1, 8.5 |
51\13
1974; 5.16 |
20\5
2000 |
49\12
2027; 1, 1.416 |
29\7
2047; 17 |
38\9
2072.72 |
Dob, Solb | Solb | Bb, Cf | 0b, Dd | Df | 43\15
1984; 1.625 |
50\13
1935; 2.06 |
19\5
1900 |
45\12
1862; 14.5 |
26\7
1835; 3,4 |
33\9
1800 | |
Do, Sol | Sol | B, C | 0, D | D | 44\11
2030; 1.3 |
32\8
2021; 19 |
52\13
2012; 1, 9.3 |
20\5
2000 |
48\12
1986; 4.83 |
28\7
1976; 2.125 |
36\9
1963.63 |
Do#, Sol# | Sol# | B#, C# | 0#, D# | D# | 45\11
2076; 1.083 |
33\8
2084; 4.75 |
54\13
2090; 3.1 |
21\5
2100 |
51\12
2110; 2.9 |
30\7
2117; 1.54 |
39\9
2127.27 |
Reb, Lab | Lab | Cf, Qf | 1b, 1d | Ef | 47\11
2169; 4.3 |
34\8
2147; 2, 1.4 |
55\13
2129; 31 |
50\12
2068; 1, 28 |
29\7
2047; 17 |
37\9
2018.18 | |
Re, La | La | C, Q | 1 | E | 48\11
2215; 2.6 |
35\8
2210; 1.9 |
57\13
2206; 2, 4.6 |
22\5
2200 |
53\12
2193; 9.6 |
31\7
2188; 4.25 |
40\9
2181.81 |
Re#, La# | La# | C#, Q# | 1# | E# | 49\11
2261; 1, 1.16 |
36\8
2273; 1, 2.16 |
59\13
2083; 1.148 |
23\5
2300 |
56\12
2327; 4, 7 |
33\7
2329; 2, 2.3 |
43\9
2345.45 |
Mib, Sib | Sib | Qf, Df | 2b, 2d | Ff | 51\11
2353; 1.18 |
37\8
2336; 1.1875 |
61\13
2322; 1.72 |
55\12
2275; 1.16 |
32\7
2258; 1, 4.6 |
41\9
2236.36 | |
Mi, Si | Si | Q, D | 2 | F | 52\11
2400 |
38\8
2400 |
62\13
2400 |
24\5
2400 |
58\12
2400 |
34\7
2400 |
44\9
2400 |
Mi#, Si# | Si# | Q#, D# | 2# | F# | 53\11
2446; 6.5 |
39\8
2463; 6.3 |
64\13
2477; 2, 2.6 |
25\5
2500 |
61\12
2524; 7.25 |
36\7
2541; 5.6 |
47/9
2563.63 |
Dob, Solb | Dob | Df, Sf | 3b, 3d | 1f | 54\11
2492; 3.25 |
63\13
2438; 1.136 |
24\5
2400 |
57\12
2358; 1.61̄ |
33\7
2329; 2, 2.3 |
42\9
2390.90 | |
Do, Sol | Do | D, S | 3 | 1 | 55\11
2538; 2.16 |
40\8
2526; 3.16 |
65\13
2516; 7.75 |
25\5
2500 |
60\12
2482; 1.318 |
35\7
2470; 1.7 |
45\9
2454.54 |
Notation | Supersoft | Soft | Semisoft | Basic | Semihard | Hard | Superhard | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
Diatonic | Mahur | Bijou | Hyperionic | ~11ed4/3 | ~8ed4/3 | ~13ed4/3 | ~5ed4/3 | ~12ed4/3 | ~7ed4\3 | ~9ed4/3 | |
Fourth | Seventh | ||||||||||
Do#, Sol# | Sol# | G# | 0#, D# | 1# | 1\11
45.45 |
1\8
62.5 |
2\13
76; 1.083 |
1\5
100 |
3\12
125 |
2\7
142; 1.16 |
3\9
166.6 |
Reb, Lab | Lab | Jf, Af | 1b, 1d | 2f | 3\11
136.36 |
2\8
125 |
3\13
115; 2.6 |
2\12
83.3 |
1\7
71; 2.3 |
1\9
55.5̄ | |
Re, La | La | J, A | 1 | 2 | 4\11
181.81 |
3\8
187.5 |
5\13
192; 3.25 |
2\5
200 |
5\12
208.3 |
3\7
214; 3.5 |
4\9
222.2 |
Re#, La# | La# | J#, A# | 1# | 2# | 5\11
227.27 |
4\8
250 |
7\13
269; 4.3 |
3\5
300 |
8\12
333.3 |
5\7
357; 7 |
7\9
388.8 |
Mib, Sib | Sib | Af, Bf | 2b, 2d | 3f | 7\11
318.18 |
5\8
312.5 |
8\13
307; 1.4 |
7\12
291.6̄ |
4\7
285; 1.4 |
5\9
277.7 | |
Mi, Si | Si | A, B | 2 | 3 | 8\11
363.63 |
6\8
375 |
10\13
384; 1.625 |
4\5
400 |
10\12
416.6 |
6\7
428; 1.75 |
8\9
444.4 |
Mi#, Si# | Si# | A#, B# | 2# | 3# | 9\11
409.09 |
7\8
437.5 |
12\13
461; 1, 1.16 |
5\5
500 |
13\12
541.6 |
8\7
571; 2.3 |
11\9
611.1̄ |
Dob, Solb | Dob | Bb, Cf | 3b, 3d | 4f | 10\11
454.54 |
11\13
423; 13 |
4\5
400 |
9\12
375 |
5\7
357; 7 |
6\9
333.3 | |
Do, Sol | Do | B, C | 3 | 4 | 500 | ||||||
Do#, Sol# | Do# | B#, C# | 3# | 4# | 12\11
545.45 |
9\8
562.5 |
15\13
576; 1.083 |
6\5
600 |
15\12
625 |
9\7
642; 1.16 |
12\9
666.6 |
Reb, Lab | Reb | Cf, Qf | 4b, 4d | 5f | 14\11
636.36 |
10\8
625 |
16\13
615; 2.6 |
14\12
583.3 |
8\7
571; 2.3 |
10\9
555.5̄ | |
Re, La | Re | C, Q | 4 | 5 | 15\11
681.81 |
11\8
687.5 |
18\13
692; 3.25 |
7\5
700 |
17\12
708.3 |
10\7
714; 3.5 |
13\9
722.2 |
Re#, La# | Re# | C#, Q# | 4# | 5# | 16\11
727.27 |
12\8
750 |
20\13
769; 4.3 |
8\5
800 |
20\12
833.3 |
12\7
857; 7 |
16\9
888.8 |
Mib, Sib | Sib | Qf, Df | 5b, 5d | 6f | 18\11
818.18 |
13\8
812.5 |
21\13
807; 1.4 |
19\12
791.6 |
11\7
785; 1.4 |
14\9
777.7 | |
Mi, Si | Si | Q, D | 5 | 6 | 19\11
863.63 |
14\8
875 |
23\13
884; 1.625 |
9\5
900 |
22\12
916.6 |
13\7
928; 1.75 |
17\9
944.4 |
Mi#, Si# | Si# | Q#, D# | 5# | 6# | 20\11
909.09 |
15\8
937.5 |
25\13
961; 1, 1.16 |
10\5
1000 |
25\12
1041.6 |
15\7
1071; 2.3 |
20\9
1111.1̄ |
Dob, Solb | Solb | Df, Sf | 6b, 6d | 7f | 21\11
954.54 |
24\13
923; 13 |
9\5
900 |
21\12
875 |
12\7
857; 7 |
15\9
833.3 | |
Do, Sol | Sol | D, S | 6 | 7 | 1000 | ||||||
Do#, Sol# | Sol# | D#, S# | 6# | 7# | 23\11
1045.45 |
17\8
1062.5 |
28\13
1076; 1.083 |
11\5
1100 |
27\12
1125 |
16\7
1142; 1.16 |
21\9
1166.6 |
Reb, Lab | Lab | Ef | 7b, 7d | 8f | 25\11
1136.36 |
18\8
1125 |
29\13
1115; 2.6 |
26\12
1083.3 |
22\7
1571; 2.3 |
19\9
1055.5̄ | |
Re, La | La | E | 7 | 8 | 26\11
1181.81 |
19\8
1187.5 |
31\13
1192; 3.25 |
12\5
1200 |
29\12
1208.3 |
17\7
1214; 3.5 |
22\9
1222.2 |
Re#, La# | La# | E# | 7# | 8# | 27\11
1227.27 |
20\8
1250 |
33\13
1269; 4.3 |
13\5
1300 |
32\12
1333.3 |
19\7
1357; 7 |
25\9
1388.8 |
Mib, Sib | Sib | Ff | 8b, Fd | 9f | 29\11
1318.18 |
21\8
1312.5 |
34\13
1307; 1.4 |
31\12
1291.6 |
18\7
1285; 1.4 |
23\9
1277.7 | |
Mi, Si | Si | F | 8, F | 9 | 30\11
1363.63 |
22\8
1375 |
36\13
1384; 1.625 |
14\5
1400 |
34\12
1416.6 |
20\7
1428; 1.75 |
26\9
1444.4 |
Mi#, Si# | Si# | F# | 8#, F# | 9# | 31\11
1409.09 |
23\8
1437.5 |
38\13
1461; 1, 1.16 |
15\5
1500 |
37\12
1541.6 |
22\7
1571; 2.3 |
29\9
1611.1̄ |
Dob, Solb | Dob | Gf | 9b, Gd | Af | 32\11
1454.54 |
37\13
1423; 13 |
14\5
1400 |
33\12
1375 |
19\7
1357; 7 |
24\9
1333.3 | |
Do, Sol | Do | G | 9, G | A | 1500 | ||||||
Do#, Sol# | Sol# | G# | 9#, G# | A# | 34\11
1545.45 |
25\8
1562.5 |
41\13
1576; 1.083 |
16\5
1600 |
39\12
1625 |
23\7
1642; 1.16 |
30\9
1666.6 |
Reb, Lab | Lab | Jf, Af | Xb, Ad | Bf | 36\11
1636.36 |
26\8
1625 |
42\13
1615; 2.6 |
38\12
1583.3 |
22\7
1571; 2.3 |
28\9
1555.5̄ | |
Re, La | La | J, A | X, A | B | 37\11
1681.81 |
27\8
1687.5 |
44\13
1692; 3.25 |
17\5
1700 |
41\12
1708.3 |
24\7
1714; 3.5 |
31\9
1722.2 |
Re#, La# | La# | J#, A# | X#, A# | B# | 38\11
1727.27 |
28\8
1750 |
46\13
1769; 4.3 |
18\5
1800 |
44\12
1833.3 |
26\7
1857; 7 |
34\9
1888.8 |
Mib, Sib | Sib | Af, Bf | Eb, Bd | Cf | 40\11
1818.18 |
29\8
1812.5 |
47\13
1807; 1.4 |
43\12
1791.6 |
25\7
1785; 1.4 |
32\9
1777.7 | |
Mi, Si | Si | A, B | E, B | C | 41\11
1863.63 |
30\8
1875 |
49\13
1884; 1.625 |
19\5
1900 |
46\12
1916.6 |
27\7
1928; 1.75 |
35\9
1944.4 |
Mi#, Si# | Si# | A#, B# | E#, B# | C# | 42\11
1909.09 |
31\8
1937.5 |
51\13
1961; 1, 1.16 |
20\5
2000 |
49\12
2041.6 |
29\7
2071; 2.3 |
38\9
2111.1̄ |
Dob, Solb | Dob | Bb, Cf | 0b, Dd | Df | 43\11
1954.54 |
50\13
1923; 13 |
19\5
1900 |
45\12
1875 |
26\7
1857; 7 |
33\9
1833.3 | |
Do, Sol | Sol | B, C | 0, D | D | 2000 | ||||||
Do#, Sol# | Sol# | B#, C# | 0#, D# | D# | 45\11
2045.45 |
33\8
2062.5 |
54\13
2076; 1.083 |
21\5
2100 |
51\12
2125 |
30\7
2142; 1.16 |
39\9
2166.6 |
Reb, Lab | Lab | Cf, Qf | 1b, 1d | Ef | 47\11
2136.36 |
34\8
2125 |
55\13
2115; 2.6 |
50\12
2083.3 |
29\7
2071; 2.3 |
37\9
2055.5̄ | |
Re, La | La | C, Q | 1 | E | 48\11
2181.81 |
35\8
2187.5 |
57\13
2192; 3.25 |
22\5
2200 |
53\12
2208.3 |
31\7
2214; 3.5 |
40\9
2222.2 |
Re#, La# | La# | C#, Q# | 1# | E# | 49\11
2227.27 |
36\8
2250 |
59\13
2269; 4.3 |
23\5
2300 |
56\12
2333.3 |
33\7
2357; 7 |
43\9
2388.8 |
Mib, Sib | Sib | Qf, Df | 2b, 2d | Ff | 51\11
2318.18 |
37\8
2312.5 |
60\13
2307; 1.4 |
55\12
2291.6 |
32\7
2285; 1.4 |
41\9
2277.7 | |
Mi, Si | Si | Q, D | 2 | F | 52\11
2363.63 |
38\8
2375 |
62\13
2384; 1.625 |
24\5
2400 |
58\12
2416.6 |
34\7
2428; 1.75 |
44\9
2444.4 |
Mi#, Si# | Si# | Q#, D# | 2# | F# | 53\11
2409.09 |
39\8
2437.5 |
64\13
2461; 1, 1.16 |
25\5
2500 |
61\12
2541.6 |
36\7
2571; 2.3̄ |
47\9
2611.1̄ |
Dob, Solb | Dob | Df, Sf | 3b, 3d | 1f | 54\11
2454.54 |
63\13
2423; 13 |
24\5
2400 |
57\12
2375 |
33\7
2357; 7 |
42\9
2333.3 | |
Do, Sol | Do | D, S | 3 | 1 | 2500 |
Intervals
Generators | Fourth notation | Interval category name | Generators | Notation of 4/3 inverse | Interval category name |
---|---|---|---|---|---|
The 3-note MOS has the following intervals (from some root): | |||||
0 | Do, Sol | perfect unison | 0 | Do, Sol | perfect fourth |
1 | Mib, Sib | diminished third | -1 | Re, La | perfect second |
2 | Reb, Lab | diminished second | -2 | Mi, Si | perfect third |
The chromatic 5-note MOS also has the following intervals (from some root): | |||||
3 | Dob, Solb | diminished fourth | -3 | Do#, Sol# | augmented unison (chroma) |
4 | Mibb, Sibb | doubly diminished third | -4 | Re#, La# | augmented second |
Genchain
The generator chain for this scale is as follows:
Mibb
Sibb |
Dob
Solb |
Reb
Lab |
Mib
Sib |
Do
Sol |
Re
La |
Mi
Si |
Do#
Sol# |
Re#
La# |
Mi#
Si# |
dd3 | d4 | d2 | d3 | P1 | P2 | P3 | A1 | A2 | A3 |
Modes
The mode names are based on the species of fourth:
Mode | Scale | UDP | Interval type | |
---|---|---|---|---|
name | pattern | notation | 2nd | 3rd |
Major | LLs | 2|0 | P | P |
Minor | LsL | 1|1 | P | d |
Phrygian | LsLL | 0|2 | d | d |
Temperaments
The most basic rank-2 temperament interpretation of diatonic is Mahuric. The name "Mahuric" comes from the “Mahur” scale in Persian and Arabic music. The major triad is spelled root-2g-(p+g)
(p = 4/3, g = the whole tone) and approximates 4:5:6 in pental interpretations or 14:18:21 in septimal ones. Basic ~5ed4/3 fits both interpretations.
Mahuric-Meantone
Subgroup: 4/3.5/4.3/2
POL2 generator: ~9/8 = 193.6725
Mapping: [⟨1 0 1], ⟨0 2 1]]
Optimal ET sequence: ~(5ed4/3, 8ed4/3, 13ed4/3)
Mahuric-Superpyth
Subgroup: 4/3.9/7.3/2
POL2 generator: ~8/7 = 216.7325
Mapping: [⟨1 0 1], ⟨0 2 1]]
Optimal ET sequence: ~(5ed4/3, 7ed4/3, 9ed4/3, 11ed4/3)
Scale tree
The spectrum looks like this:
Generator
(bright) |
Cents | L | s | L/s | Comments | |||
---|---|---|---|---|---|---|---|---|
Normalised[1] | ed5\12[1] | |||||||
1\3 | 171; 2.3 | 166.6 | 1 | 1 | 1.000 | Equalised | ||
6\17 | 180 | 176; 2.125 | 6 | 5 | 1.200 | |||
11\31 | 180; 1.216 | 177; 2, 2.6 | 11 | 9 | 1.222 | |||
5\14 | 181.81 | 178; 1.75 | 5 | 4 | 1.250 | |||
14\39 | 182; 1, 1.5 | 179; 2, 19 | 14 | 11 | 1.273 | |||
9\25 | 183; 19.6 | 180 | 9 | 7 | 1.286 | |||
4\11 | 184; 1.625 | 181.81 | 4 | 3 | 1.333 | |||
15\41 | 185; 1.763 | 182; 1, 12.6 | 15 | 11 | 1.364 | |||
11\30 | 185, 1, 10.83 | 183.3 | 11 | 8 | 1.375 | |||
7\19 | 186.6 | 184; 4.75 | 7 | 5 | 1.400 | |||
10\27 | 187.5 | 185.185 | 10 | 7 | 1.429 | |||
13\35 | 187; 1, 19.75 | 185; 1.4 | 13 | 9 | 1.444 | |||
16\43 | 188; 4.25 | 186; 21.5 | 16 | 11 | 1.4545 | |||
3\8 | 189; 2.1 | 187.5 | 3 | 2 | 1.500 | Mahuric-Meantone starts here | ||
17\45 | 190; 1, 1.12 | 188.8 | 17 | 11 | 1.5455 | |||
14\37 | 190.90 | 189.189 | 14 | 9 | 1.556 | |||
11\29 | 191; 3, 2.3 | 189; 1, 1.9 | 11 | 7 | 1.571 | |||
8\21 | 192 | 190; 2.1 | 8 | 5 | 1.600 | |||
13\34 | 192.592 | 191; 5.6 | 13 | 8 | 1.625 | |||
5\13 | 193; 1, 1, 4.6 | 192; 4.3 | 5 | 3 | 1.667 | |||
12\31 | 194.594 | 193; 1, 1, 4.6 | 12 | 7 | 1.714 | |||
7\18 | 195; 2.86 | 194.4 | 7 | 4 | 1.750 | |||
9\23 | 196.36 | 195; 1.53 | 9 | 5 | 1.800 | |||
11\28 | 197; 67 | 196; 2.3 | 11 | 6 | 1.833 | |||
13\33 | 197; 2.135 | 196.96 | 13 | 7 | 1.857 | |||
15\38 | 197; 1, 2, 1, 1.54 | 197; 2, 1.4 | 15 | 8 | 1.875 | |||
17\43 | 198; 17.16 | 197; 1, 2, 14 | 17 | 9 | 1.889 | |||
19\48 | 198: 3, 1, 28 | 197.916 | 19 | 10 | 1.900 | |||
21\53 | 198; 2.3518 | 198; 8.83 | 21 | 11 | 1.909 | |||
23\58 | 198; 1, 3, 1.7 | 198; 3.625 | 23 | 12 | 1.917 | |||
25\63 | 198; 1, 2, 12.25 | 198; 2, 2.36 | 25 | 13 | 1.923 | |||
27\68 | 198; 1, 3.405 | 198; 1.8 | 27 | 14 | 1.929 | |||
29\73 | 198; 1, 1.16 | 198; 1, 1.703 | 29 | 15 | 1.933 | |||
31\78 | 198; 1, 12, 2.8 | 198; 1, 2.54 | 31 | 16 | 1.9375 | |||
33\83 | 198; 1.005 | 198; 1.257 | 33 | 17 | 1.941 | |||
35\88 | 199; 19.18 | 198.863 | 35 | 18 | 1.944 | |||
2\5 | 200 | 200 | 2 | 1 | 2.000 | Mahuric-Meantone ends, Mahuric-Pythagorean begins | ||
17\42 | 201.9801 | 202; 2.625 | 17 | 8 | 2.125 | |||
15\37 | 202; 4.045 | 202.702 | 15 | 7 | 2.143 | |||
13\32 | 202; 1, 1, 2.06 | 203.125 | 13 | 6 | 2.167 | |||
11\27 | 203; 13 | 203.703 | 11 | 5 | 2.200 | |||
9\22 | 203; 1, 3.416 | 204.54 | 9 | 4 | 2.250 | |||
7\17 | 204; 1. 7.2 | 205; 1.13 | 7 | 3 | 2.333 | |||
12\29 | 205; 1.4 | 206; 1, 8.6 | 12 | 5 | 2.400 | |||
17\41 | 206.06 | 207; 3, 6.5 | 17 | 7 | 2.429 | |||
5\12 | 206; 1, 8.6 | 208.3 | 5 | 2 | 2.500 | Mahuric-Neogothic heartland is from here… | ||
18\43 | 207; 1.4 | 209; 3, 4.3 | 18 | 7 | 2.571 | |||
13\31 | 208 | 209; 1, 2.1 | 13 | 5 | 2.600 | |||
8\19 | 208; 1.4375 | 210; 1.9 | 8 | 3 | 2.667 | …to here | ||
11\26 | 209; 1.90 | 211; 1, 1.16 | 11 | 4 | 2.750 | |||
14\33 | 210 | 212.12 | 14 | 5 | 2.800 | |||
17\40 | 210; 3.23 | 212.5 | 17 | 6 | 2.833 | |||
20\47 | 210; 1.9 | 212; 1.30 | 20 | 7 | 2.857 | |||
23\54 | 210; 1.45 | 212.962 | 23 | 8 | 2.875 | |||
26\61 | 210.810 | 213; 8, 1.4 | 26 | 9 | 2.889 | |||
3\7 | 211; 1, 3.25 | 214; 3.5 | 3 | 1 | 3.000 | Mahuric-Pythagorean ends, Mahuric-Superpyth begins | ||
22\51 | 212; 1, 9.3 | 215; 1, 2,1875 | 22 | 7 | 3.143 | |||
19\44 | 213; 11.8 | 215.90 | 19 | 6 | 3.167 | |||
16\37 | 213.3̄ | 216.216 | 16 | 5 | 3.200 | |||
13\30 | 213; 1, 2.318 | 216.6 | 13 | 4 | 3.250 | |||
10\23 | 214; 3.5 | 217; 5.75 | 10 | 3 | 3.333 | |||
7\16 | 215; 2.6 | 218.75 | 7 | 2 | 3.500 | |||
18\41 | 216 | 219; 1, 1.05 | 18 | 5 | 3.600 | |||
11\25 | 216; 2.5416 | 220 | 11 | 3 | 3.667 | |||
15\34 | 216; 1.1527 | 220; 1.7 | 15 | 4 | 3.750 | |||
19\43 | 217; 7 | 220; 1, 7.6 | 19 | 5 | 3.800 | |||
23\52 | 217; 3, 10.25 | 221; 6.5 | 23 | 6 | 3.833 | |||
4\9 | 218.18 | 222.2 | 4 | 1 | 4.000 | |||
17\38 | 219; 1, 2.90 | 223; 1.583 | 17 | 4 | 4.250 | |||
13\29 | 219; 1, 2.55 | 224; 7.25 | 13 | 3 | 4.333 | |||
9\20 | 220; 2.45 | 225 | 9 | 2 | 4.500 | |||
14\31 | 221; 19 | 225; 1.24 | 14 | 3 | 4.667 | |||
19\42 | 221; 2.783 | 226; 4.2 | 19 | 4 | 4.750 | |||
5\11 | 222.2 | 227.27 | 5 | 1 | 5.000 | Mahuric-Superpyth ends | ||
16\35 | 223; 3.90 | 228; 1.75 | 16 | 3 | 5.333 | |||
11\24 | 223; 1, 2.6875 | 229.16 | 11 | 2 | 5.500 | |||
17\37 | 224; 5.72 | 229.729 | 17 | 3 | 5.667 | |||
6\13 | 225 | 230; 1.3 | 6 | 1 | 6.000 | |||
1\3 | 240 | 250 | 1 | 0 | → inf | Paucitonic |
See also
2L 1s (4/3-equivalent) - idealized tuning