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 /> |