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==Notation==
==Notation==
   
   
There are 4 main ways to notate the angel scale. One method uses a simple sesquitave (fifth) repeating notation consisting of 4 naturals (eg. Do Re Mi Fa, Sol La Si Do). Given that 1-5/4-5/3 is fifth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate angel scales as repeating at the double, triple or quadruple sesquitave (major ninth, thirteenth or seventeenth i. e. ~pentave), however it does make navigating the [[Generator|genchain]] harder. This way, 5/3 is its own pitch class, distinct from 10/9. Notating this way produces a major ninth which is the Aeolian mode of Napoli[6L 2s], a major thirteenth which is the Dorian mode of Bijou[9L 3s] or an ~pentave which is the Mixolydian mode of Hextone[12L 4s]. Since there are exactly 8 naturals in double sesquitave notation, 12 in triple sesquitave notation and 16 in quadruple sesquitave notation, letters A-H (FGABHCDEF) or dozenal or hex digits (0123456789XE0 or D1234567FGACD with flats written C molle or 0123456789ABCDEF0 or G123456789ABCDEFG with flats written F molle) may be used.
There are 4 main ways to notate the angel scale. One method uses a simple sesquitave (fifth) repeating notation consisting of 4 naturals (eg. Do Re Mi Fa, Sol La Si Do). Given that 1-5/4-5/3 is fifth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate angel scales as repeating at the double, triple, quadruple, quintuple or sextuple sesquitave (major ninth, thirteenth, seventeenth i. e. ~pentave or twenty-first or augmented twenty-fifth), however it does make navigating the [[Generator|genchain]] harder. This way, 5/3 is its own pitch class, distinct from 10/9. Notating this way produces a major ninth which is the Aeolian mode of Napoli[6L 2s], a major thirteenth which is the Dorian mode of Bijou[9L 3s], an ~pentave which is the Mixolydian mode of Hextone[12L 4s], a major twenty-first which is the Ionian mode of Guidotonic[15L 5s] or an augmented twenty-fifth which is the Lydian mode of Subdozenal[18L 6s]. Since there are exactly 8 naturals in double sesquitave notation, 12 in triple sesquitave notation, 16 in quadruple sesquitave notation, 20 in quintuple sesquitave notation and 24 in sextuple sesquitave notation, letters A-H (FGABHCDEF), dozenal or hex digits (0123456789XE0 or D1234567FGACD with flats written C molle or 0123456789ABCDEF0 or G123456789ABCDEFG with flats written F molle), the Guidonian names with F as the lowest ut or letters except I and O may be used.
 
 
{| class="wikitable"
{| class="wikitable"
Line 17: Line 17:
Cents<ref name=":0">Fractions repeating more than 4 digits written as continued fractions</ref>
Cents<ref name=":0">Fractions repeating more than 4 digits written as continued fractions</ref>
 
 
! colspan="4" |Notation
! colspan="4" | Notation
 
 
!Supersoft
!Supersoft
Line 37: Line 37:
!Diatonic
!Diatonic
 
 
!Napoli
! Napoli
 
 
!Bijou
!Bijou
Line 66: Line 66:
46; 6.5
46; 6.5
 
 
|1\11
| 1\11
63: 6.{{Overline|3}}
63: 6.{{Overline|3}}
 
 
Line 106: Line 106:
82; 1.3{{Overline|18}}
82; 1.3{{Overline|18}}
 
 
|1\10
| 1\10
70; 1.7
70; 1.7
 
 
Line 172: Line 172:
352; 1.0625
352; 1.0625
 
 
|7\13
| 7\13
 
 
381.{{Overline|81}}
381.{{Overline|81}}
Line 180: Line 180:
|Mib, Sib
|Mib, Sib
 
 
|Ab
| Ab
 
 
|2b, 2c
|2b, 2c
Line 193: Line 193:
309; 1, 2.1
309; 1, 2.1
 
 
|7\17
| 7\17
289; 1, 1.9
289; 1, 1.9
 
 
|4\10
| 4\10
282; 2.8{{Overline|3}}
282; 2.8{{Overline|3}}
 
 
|5\13
| 5\13
 
 
272.{{Overline|72}}
272.{{Overline|72}}
Line 227: Line 227:
413; 1, 3.8{{Overline|3}}
413; 1, 3.8{{Overline|3}}
 
 
|6\10
| 6\10
423; 1.{{Overline|8}}
423; 1.{{Overline|8}}
 
 
Line 236: Line 236:
|-
|-
 
 
|Mi#, Si#
| Mi#, Si#
 
 
|A#
|A#
Line 273: Line 273:
|3b, 3c
|3b, 3c
|3f
|3f
|10\15
| 10\15
461; 1, 1.1{{Overline|6}}
461; 1, 1.1{{Overline|6}}
 
 
Line 329: Line 329:
|Fa#, Do#
|Fa#, Do#
 
 
|B
| B
 
 
|3#
|3#
|3#
| 3#
|12\15
|12\15
553; 1.{{Overline|18}}
553; 1.{{Overline|18}}
Line 395: Line 395:
 
 
|Dob, Solb
|Dob, Solb
|Hb
| Hb
|4b, 4c
|4b, 4c
|4f
|4f
|14\15
| 14\15
   
   
646; 6.5
646; 6.5
Line 404: Line 404:
   
   
619; 2.{{Overline|81}}
619; 2.{{Overline|81}}
|6\7
| 6\7
   
   
600
600
Line 420: Line 420:
!Do, Sol
!Do, Sol
 
 
!H
! H
 
 
!4
!4
Line 458: Line 458:
|Η#
|Η#
 
 
|4#
| 4#
|4#
|4#
|16\15
|16\15
Line 464: Line 464:
738; 2.1{{Overline|6}}
738; 2.1{{Overline|6}}
 
 
|12\11
| 12\11
 
 
757; 1, 8.5
757; 1, 8.5
Line 484: Line 484:
847; 17
847; 17
 
 
|16\13
| 16\13
 
 
872.{{Overline|72}}
872.{{Overline|72}}
Line 561: Line 561:
|Re#, La#
|Re#, La#
 
 
|C#
| C#
 
 
|5#
| 5#
|5#
|5#
|20\15
|20\15
Line 569: Line 569:
923: 13
923: 13
 
 
|15\11
| 15\11
 
 
947; 2, 1.4
947; 2, 1.4
Line 601: Line 601:
|6b, 6c
|6b, 6c
|6f
|6f
|22\15
| 22\15
 
 
1015; 2.6
1015; 2.6
Line 668: Line 668:
 
 
|6#
|6#
|6#
| 6#
|24\15
|24\15
 
 
Line 685: Line 685:
1200
1200
 
 
|30\17
| 30\17
 
 
1241; 2.{{Overline|63}}
1241; 2.{{Overline|63}}
 
 
|18\10
| 18\10
 
 
1270; 1.7
1270; 1.7
Line 709: Line 709:
1153; 1.{{Overline|18}}
1153; 1.{{Overline|18}}
 
 
|29\18
| 29\18
 
 
1121; 1, 1, 2.6
1121; 1, 1, 2.6
 
 
|11\7
| 11\7
 
 
1100
1100
 
 
|26\17
| 26\17
 
 
1075; 1.16
1075; 1.16
Line 768: Line 768:
|-
|-
 
 
|Fa#, Do#
| Fa#, Do#
 
 
|E
|E
Line 778: Line 778:
1246; 6.5
1246; 6.5
 
 
|20\11
| 20\11
 
 
1263; 6.{{Overline|3}}
1263; 6.{{Overline|3}}
Line 808: Line 808:
|E#
|E#
 
 
|7x
| 7x
|7x
|7x
|28\15
|28\15
Line 822: Line 822:
1354; 1, 5.2
1354; 1, 5.2
 
 
|14\7
| 14\7
 
 
1400
1400
Line 834: Line 834:
1482; 2.8{{Overline|3}}
1482; 2.8{{Overline|3}}
 
 
|28\13
| 28\13
 
 
1527.{{Overline|27}}
1527.{{Overline|27}}
Line 866: Line 866:
1270; 1.7
1270; 1.7
 
 
|23\13
| 23\13
 
 
1254.{{Overline|54}}
1254.{{Overline|54}}
Line 886: Line 886:
1389; 2.{{Overline|1}}
1389; 2.{{Overline|1}}
 
 
!36\18
! 36\18
 
 
1393; 1, 1, 4.{{Overline|6}}
1393; 1, 1, 4.{{Overline|6}}
Line 894: Line 894:
1400
1400
 
 
!34\17
! 34\17
 
 
1406; 1, 8.{{Overline|6}}
1406; 1, 8.{{Overline|6}}
Line 949: Line 949:
 
 
|9b, Gc
|9b, Gc
|9f
| 9f
|33\15
|33\15
 
 
Line 981: Line 981:
 
 
|'''9, G'''
|'''9, G'''
|9
| 9
|'''34\15'''
|'''34\15'''
 
 
Line 1,017: Line 1,017:
 
 
|9#, G#
|9#, G#
|9#
| 9#
|35\15
|35\15
 
 
Line 1,054: Line 1,054:
|Xb, Ac
|Xb, Ac
|Af
|Af
|37\15
| 37\15
 
 
1707; 1.{{Overline|4}}
1707; 1.{{Overline|4}}
Line 1,080: Line 1,080:
|-
|-
 
 
|Mi, Si
| Mi, Si
 
 
|A
|A
Line 1,086: Line 1,086:
|X, A
|X, A
|A
|A
|38\15
| 38\15
 
 
1753; 1.{{Overline|18}}
1753; 1.{{Overline|18}}
Line 1,098: Line 1,098:
1780; 1.55
1780; 1.55
 
 
|18\7
| 18\7
 
 
1800
1800
Line 1,116: Line 1,116:
|-
|-
 
 
|Mi#, Si#
| Mi#, Si#
 
 
|A#
|A#
Line 1,174: Line 1,174:
1779; 3.{{Overline|2}}
1779; 3.{{Overline|2}}
 
 
|25\10
| 25\10
 
 
1764; 1.41{{Overline|6}}
1764; 1.41{{Overline|6}}
Line 1,222: Line 1,222:
|Fa#, Do#
|Fa#, Do#
 
 
|B
| B
 
 
|E, C
| E, C
|B#
| B#
|42\15
|42\15
 
 
1938; 2.1{{Overline|6}}
1938; 2.1{{Overline|6}}
 
 
|31\11
| 31\11
 
 
1957; 1, 8.5
1957; 1, 8.5
Line 1,246: Line 1,246:
2027; 1, 1.41{{Overline|6}}
2027; 1, 1.41{{Overline|6}}
 
 
|29\10
| 29\10
 
 
2047; 17
2047; 17
Line 1,282: Line 1,282:
2151; 2.625
2151; 2.625
 
 
|31\10
| 31\10
 
 
2188; 4.25
2188; 4.25
 
 
|41\13
| 41\13
 
 
2236.{{Overline|36}}
2236.{{Overline|36}}
Line 1,292: Line 1,292:
|-
|-
 
 
|Dob, Solb
| Dob, Solb
 
 
|Hb
|Hb
Line 1,298: Line 1,298:
|0b, Dc
|0b, Dc
|Cf
|Cf
|44\15
| 44\15
 
 
2030; 1.3
2030; 1.3
Line 1,329: Line 1,329:
 
 
!0, D
!0, D
!C
! C
!45\15
! 45\15
 
 
2076; 1.08'''{{Overline|3}}'''
2076; 1.08'''{{Overline|3}}'''
Line 1,372: Line 1,372:
|54\17
|54\17
2234; 2, 14
2234; 2, 14
|32\10
| 32\10
2258; 1, 4.{{Overline|6}}
2258; 1, 4.{{Overline|6}}
|42\13
|42\13
Line 1,430: Line 1,430:
|35\10
|35\10
2470; 1.7
2470; 1.7
|46\13
| 46\13
2509.{{Overline|09}}
2509.{{Overline|09}}
|-
|-
|Mib, Sib
|Mib, Sib
|Db
|Db
|2b, 2c
| 2b, 2c
|Ef
|Ef
|52\15
|52\15
Line 1,496: Line 1,496:
|65\18
|65\18
2516; 7.75
2516; 7.75
|25\7
| 25\7
2500
2500
|60\17
|60\17
Line 1,534: Line 1,534:
|69\18
|69\18
2670; 1.0{{Overline|3}}
2670; 1.0{{Overline|3}}
|27\7
| 27\7
2700
2700
|66\17
|66\17
Line 1,568: Line 1,568:
|59\15
|59\15
2723; 13
2723; 13
|70\18
|70\18
2709; 1, 2.1
2709; 1, 2.1
|27\7
|27\7
2700
2700
|65\17
|65\17
2689; 1, 1.9
2689; 1, 1.9
|38\10
|38\10
2682; 2.8{{Overline|3}}
2682; 2.8{{Overline|3}}
|49\13
|49\13
2672.{{Overline|72}}
2672.{{Overline|72}}
|-
!Do, Sol
!F
!4
!0, G
! 60\15
2769; 4.'''{{Overline|3}}'''
! 44\11
2778; 1.0{{Overline|5}}
! 72\18
2787; 3.1
!28\7
2800
!68\17
2813; 1, 3.8{{Overline|3}}
! 40\10
2823; 1.{{Overline|8}}
!52\13
2836.{{Overline|36}}
|}
{| class="wikitable"
|+Cents<ref name=":04">Fractions repeating more than 4 digits written as continued fractions</ref>
! colspan="2" | Notation
!Supersoft
!Soft
!Semisoft
!Basic
! Semihard
!Hard
!Superhard
|-
!Guidotonic
!Subdozenal
!~15edf
!~11edf
!~18edf
!~7edf
! ~17edf
!~10edf
! ~13edf
|-
|F ut#
|F#
|1\15
46; 6.5
|1\11
63: 6.{{Overline|3}}
|2\18
77; 2, 2.6
| rowspan="2" |1\7
100
|3\17
124; 7.25
|2\10
141; 5.{{Overline|6}}
|3\13
163.{{Overline|63}}
|-
|G reb
| Gb
|3\15
138; 3, 4
|2\11
126; 3, 6
|3\18
116; 7.75
|2\17
82; 1.3{{Overline|18}}
|1\10
70; 1.7
|1\13
54.{{Overline|54}}
|-
|'''G re'''
|'''G'''
|'''4\15'''
'''184; 1.625'''
|'''3\11'''
'''189; 2.{{Overline|1}}'''
|'''5\18'''
'''193; 1, 1, 4.{{Overline|6}}'''
|'''2\7'''
'''200'''
|'''5\17'''
'''206; 1, 8.{{Overline|6}}'''
|'''3\10'''
'''211; 1, 3.25'''
|'''4\13'''
'''218.{{Overline|18}}'''
|-
|G re
|G#
| 5\15
230; 1.3
|4\11
252; 1.58{{Overline|3}}
|7\18
270; 1.0{{Overline|3}}
| rowspan="2" |3\7
300
|8\17
331; 29
|5\10
352; 1, 16
|7\13
381.{{Overline|81}}
|-
|A mib
|Ab
|7\15
323; 13
|5\11
315; 1.2{{Overline|6}}
| 8\18
309; 1, 2.1
|7\17
289; 1, 1.9
|4\10
282; 2.8{{Overline|3}}
|5\13
272.{{Overline|72}}
|-
|A mi
|A
| 8\15
369; 4.{{Overline|3}}
|6\11
378; 1.0{{Overline|5}}
|10\18
387; 10.{{Overline|3}}
|4\7
400
| 10\17
413; 1, 3.8{{Overline|3}}
|6\10
423; 1.{{Overline|8}}
|8\13
436.{{Overline|36}}
|-
|A mi#
| A#
|9\15
415; 2.6
| rowspan="2" |7\11
442; 9.5
| 12\18
464; 1.9375
|5\7
500
| 13\17
537; 14.5
|8\10
564; 1.41{{Overline|6}}
|11\13
600
|-
|B fa utb
|Bbb
|10\15
461; 1, 1, 6
|11\18
425; 1.24
|4\7
400
|9\17
372; 2.41{{Overline|6}}
|5\10
352; 1, 16
| 6\13
327.{{Overline|27}}
|-
|'''B fa ut'''
|'''Bb'''
|'''11\15'''
'''507; 1.{{Overline|4}}'''
|'''8\11'''
'''505; 3.8'''
|'''13\18'''
'''503; 4, 2.{{Overline|3}}'''
|'''5\7'''
'''500'''
|'''12\17'''
'''496; 1.8125'''
|'''7\10'''
'''494; 8.5'''
|'''9\13'''
'''490.{{Overline|90}}'''
|-
|B fa ut#
|B
| 12\15
553; 1.{{Overline|18}}
|9\11
568; 2.375
|15\18
580; 1.55
| 6\7
600
|15\17
620; 1.45
|9\10
635; 3.4
|12\13
654.{{Overline|54}}
|-
|B fa utx
|B#
|13\15
600
| rowspan="2" |10\11
631; 1.{{Overline|72}}
|17\18
658; 15.5
|7\7
700
|18\17
744; 1.208{{Overline|3}}
|11\10
776; 2, 8
|15\13
818.{{Overline|18}}
|-
|C sol reb
|Hb
|14\15
646; 6.5
|16\18
619; 2.{{Overline|81}}
|6\7
600
|14\17
579; 3.{{Overline|2}}
|8\10
564; 1.41{{Overline|6}}
|10\13
545.{{Overline|45}}
|-
!C sol re
!H
!'''15\15'''
'''692; 3.25'''
!'''11\11'''
'''694; 1, 2.8'''
!'''18\18'''
'''696; 1.291'''{{Overline|6}}
!'''7\7'''
'''700'''
!'''17\17'''
'''703; 2, 2, 6'''
!'''10\10'''
'''705; 1.1'''{{Overline|3}}
!'''13\13'''
'''709.'''{{Overline|09}}
|-
|C sol re#
| Η#
|16\15
738; 2.1{{Overline|6}}
|12\11
757; 1, 8.5
|20\18
774; 5, 6
| rowspan="2" |8\8
800
|20\17
827; 1, 1.41{{Overline|6}}
|12\10
847; 17
| 16\13
872.{{Overline|72}}
|-
|D la mib
|Cb
|18\15
830; 1.3
|13\11
821; 19
|21\18
812; 1, 9.{{Overline|3}}
|19\17
786; 4.8{{Overline|3}}
|11\10
776; 2, 8
|14\13
763.{{Overline|63}}
|-
|'''D la mi'''
|'''C'''
|'''19\15'''
'''876; 1, 12'''
|'''14\11'''
'''884; 4.75'''
|'''23\18'''
'''890; 3.1'''
|'''9\5'''
'''900'''
|'''22\17'''
'''910; 2.9'''
|'''13\10'''
'''917; 1.{{Overline|54}}'''
|'''17\13'''
'''927.{{Overline|27}}'''
|-
|D la mib
|C#
|20\15
923: 13
|15\11
947; 2, 1.4
|25\18
967; 1, 2.875
| rowspan="2" |10\7
1000
|25\17
1034; 2, 14
|15\10
1058; 1, 4.{{Overline|6}}
|20\13
1090.{{Overline|90}}
|-
|E fa utb
|Db
|22\15
1015; 2.6
|16\11
1010; 1.9
|26\18
1006; 2, 4.{{Overline|6}}
|24\17
993; 9.{{Overline|6}}
|14\10
988; 4, 4
|18\13
981.{{Overline|81}}
|-
|E fa ut
|D
|23\15
1061; 1, 1, 6
|17\11
1073; 1, 2, 6
|28\18
1083; 1.{{Overline|148}}
|11\7
1100
|27\17
1117; 4, 7
|16\10
1129; 2, 2.{{Overline|3}}
|21\9
1145.{{Overline|45}}
|-
|E fa ut#
|D#
|24\15
1107; 1.{{Overline|4}}
| rowspan="2" |18\11
1136; 1.1875
|30\18
1161; 3.{{Overline|4}}
|12\7
1200
|30\17
1241; 2.{{Overline|63}}
|18\10
1270; 1.7
| 24\13
1309.{{Overline|09}}
|-
|F sol re utb
|Ebb
|25\15
1153; 1.{{Overline|18}}
|29\18
1121; 1, 1, 2.6
|11\7
1100
|26\17
1075; 1.16
|15\10
1058; 1, 4.{{Overline|6}}
|19\13
1036.{{Overline|36}}
|-
|'''F sol re ut'''
|'''Eb'''
|'''26\15'''
'''1200'''
|'''19\11'''
'''1200'''
|'''31\18'''
'''1200'''
|'''12\7'''
'''1200'''
|'''29\17'''
'''1200'''
|'''17\10'''
'''1200'''
|'''22\13'''
'''1200'''
|-
|F sol re ut#
|E
|27\15
1246; 6.5
|20\11
1263; 6.{{Overline|3}}
|33\18
1277; 2, 2.6
|13\7
1300
|32\17
1324; 7.25
| 19\10
1341; 5.{{Overline|6}}
|25\13
1363.{{Overline|63}}
|-
|F sol re utx
| E#
|28\15
1292; 3, 4
| rowspan="2" |21\11
1326; 3, 6
|35\18
1354; 1, 5.2
|14\7
1400
|35\17
1448; 3.625
|21\10
1482; 2.8{{Overline|3}}
|28\13
1527.{{Overline|27}}
|-
|G la mi reb
| Fb
| 29\15
1338; 2, 6
|34\18
1316; 7.75
|13\7
1300
|31\17
1282; 1.3{{Overline|18}}
|18\10
1270; 1.7
|23\13
1254.{{Overline|54}}
|-
!G la mi re
!F
!30\15
1384; 1.625
! 22\11
1389; 2.{{Overline|1}}
!36\18
1393; 1, 1, 4.{{Overline|6}}
!14\7
1400
!34\17
1406; 1, 8.{{Overline|6}}
!20\10
1411; 1, 3, 4
!26\13
1418.{{Overline|18}}
|-
|G la mi re#
|F#
|31\15
1430; 1.3
| rowspan="2" |23\11
1452; 1.58{{Overline|3}}
|38\18
1470; 1.0{{Overline|3}}
|15\7
1500
|37\17
1531; 29
|22\10
1552; 1, 16
|29\13
1581.{{Overline|81}}
|-
|A fab
|
|32\15
1476; 1, 12
|37\18
1432; 3.875
|14\7
1400
|33\29
1365; 1.9{{Overline|3}}
|19\10
1341; 5.{{Overline|6}}
|24\13
1309.{{Overline|09}}
|-
|A fa
|Gb
|33\15
1523; 13
|24\11
1515; 1.2{{Overline|6}}
|39\18
1509; 1, 2.1
|15\7
1500
|36\17
1489; 1, 1.9
|21\10
1482; 2.8{{Overline|3}}
|27\13
1472.{{Overline|72}}
|-
|'''A mi'''
|'''G'''
|'''34\15'''
'''1569; 4.{{Overline|3}}'''
|'''25\11'''
'''1578; 1.0{{Overline|5}}'''
|'''41\18'''
'''1587; 10.{{Overline|3}}'''
|'''16\7'''
'''1600'''
|'''39\17'''
'''1613; 1, 3.8{{Overline|3}}'''
|'''23\10'''
'''1623; 1.{{Overline|8}}'''
|'''30\13'''
'''1636.{{Overline|36}}'''
|-
|A mi#
|G#
|35\15
1615; 2.6
|26\11
1642; 9.5
| 43\18
1664; 1.9375
| rowspan="2" |17\7
1700
|42\17
1737; 14.5
|25\10
1764; 1.41{{Overline|6}}
| 33\13
1800
|-
|B sol fa utb
|Ab
|37\15
1707; 1.{{Overline|4}}
|27\11
1705; 3.8
|44\18
1703; 4, 2.{{Overline|3}}
|41\17
1696; 1.8125
|24\10
1694; 8.5
|31\13
1690.{{Overline|90}}
|-
| B sol fa ut
|A
| 38\15
1753; 1.{{Overline|18}}
|28\11
1768; 2.375
|46\18
1780; 1.55
| 18\7
1800
|44\17
1820; 1.45
|26\10
1835; 3.4
|34\13
1854.{{Overline|54}}
|-
|B sol fa ut#
|A#
| 39\15
1800
| rowspan="2" |29\11
1831; 1.{{Overline|72}}
|48\18
1858; 15.5
|19\7
1900
| 47\17
1944; 1.208{{Overline|3}}
|28\10
1976; 2, 8
|37\13
2018.{{Overline|18}}
|-
|C la sol reb
|Bbb
| 40\15
1846; 6.5
| 47\18
1819; 2.{{Overline|81}}
|18\7
1800
|43\17
1779; 3.{{Overline|2}}
|25\10
1764; 1.41{{Overline|6}}
|32\13
1745.{{Overline|45}}
|-
|'''C la sol re'''
|'''Bb'''
|'''41\15'''
'''1892; 3, 4'''
|'''30\11'''
'''1894; 1, 2.8'''
|'''49\18'''
'''1896; 1.291{{Overline|6}}'''
|'''19\7'''
'''1900'''
|'''46\17'''
'''1903; 2, 2, 6'''
|'''27\10'''
'''1905; 1.1{{Overline|3}}'''
|'''35\13'''
'''1909.{{Overline|09}}'''
|-
| C la sol re#
| B
| 42\15
1938; 2, 6
|31\11
1957; 1, 8.5
|51\18
1974; 5, 6
| 20\7
2000
|49\17
2027; 1, 1.41{{Overline|6}}
|29\10
2047; 17
|38\13
2072.{{Overline|72}}
|-
|C la sol rex
|B#
|43\15
1984; 1.625
| rowspan="2" |32\11
2021; 19
|53\18
2051; 1, 1, 1, 1.4
| 21\7
2100
|52\17
2151; 1, 2.625
|31\10
2188; 4.25
|41\13
2236.{{Overline|36}}
|-
|D la mib
| Hb
|44\15
2030; 1.3
|52\18
2012; 1, 9.{{Overline|3}}
|20\7
2000
|48\17
1986; 4.8{{Overline|3}}
|28\10
1976; 2, 8
|36\13
1963.{{Overline|63}}
|-
!D la mi
!H
!45\15
2076; 1, 12
!33\11
2084; 4.75
!54\18
2090; 3.1
! 21\7
2100
!51\17
2110; 2.9
!30\10
2117; 1.{{Overline|54}}
! 39\13
2127.{{Overline|27}}
|-
|D la mib
|Η#
|46\15
2123; 13
|34\11
2147; 2, 1.4
| 56\18
2167; 1, 2.875
| rowspan="2" |22\7
2200
| 54\17
2234; 2, 14
| 32\10
2258; 1, 4.{{Overline|6}}
|42\13
2290.{{Overline|90}}
|-
|E fa utb
|Cb
|48\15
2215; 2.6
|35\11
2210; 1.9
|57\18
2206; 2, 4.{{Overline|6}}
|53\17
2193; 9.{{Overline|6}}
|31\10
2188; 4, 4
|40\13
2181.{{Overline|81}}
|-
|'''E fa ut'''
|'''C'''
|'''49\15'''
'''2261; 1, 1, 6'''
|'''36\11'''
'''2273; 1, 2, 6'''
|'''59\18'''
'''2283; 1.{{Overline|148}}'''
|'''23\7'''
'''2300'''
|'''56\17'''
'''2317; 4, 7'''
|'''33\10'''
'''2329; 2, 2.{{Overline|3}}'''
|'''43\13'''
'''2245.{{Overline|45}}'''
|-
|E fa ut#
|C#
|50\15
2307; 1.{{Overline|4}}
|37\11
2336; 1.1875
|61\18
2361; 3.{{Overline|4}}
| rowspan="2" |24\7
2400
|59\17
2441; 2.{{Overline|63}}
|35\10
2470; 1.7
|46\13
2509.{{Overline|09}}
|-
|F sol re utb
|Db
|52\15
2400
|38\11
2400
|62\18
2400
|58\17
2400
|34\10
2400
|44\13
2400
|-
|F sol re ut
|D
|53\15
2446; 6.5
|39\11
2463; 6.{{Overline|3}}
|64\18
2477; 2, 2.6
|25\7
2500
|61\17
2524; 7.25
|36\10
2541; 5.{{Overline|6}}
| 47\13
2563.{{Overline|63}}
|-
|F sol re ut#
|D#
|54\15
2492; 3, 4
| rowspan="2" |40\11
2526; 3.1
| 66\18
2554; 1, 5.2
|26\7
2600
|64\17
2648; 3.625
|38\10
2682; 2.8{{Overline|3}}
|50\13
2727.{{Overline|27}}
|-
|G la mi reb
|Ebb
|55\15
2538; 2, 6
|65\18
2516; 7.75
| 25\7
2500
|60\17
2482; 1.3{{Overline|18}}
|35\10
2470; 1.7
|45\13
2454.{{Overline|54}}
|-
|'''G la mi re'''
|'''Eb'''
|'''56\15'''
'''2584; 1.625'''
|'''41\11'''
'''2589; 2.{{Overline|1}}'''
|'''67\18'''
'''2593; 1, 1, 4.{{Overline|6}}'''
|'''26\7'''
'''2600'''
|'''63\17'''
'''2606; 1, 8.{{Overline|6}}'''
|'''37\10'''
'''2611; 1, 3, 4'''
|'''48\13'''
'''2618.{{Overline|18}}'''
|-
|G la mi re#
|E
|57\15
2630; 1.3
|42\11
2652; 1.58{{Overline|3}}
|69\18
2670; 1.0{{Overline|3}}
| 27\7
2700
|66\17
2731; 29
|39\10
2752; 1, 16
|51\13
2781.{{Overline|81}}
|-
|G la mi rex
|E#
| rowspan="2" | 58\15
2676; 1, 12
|43\11
2715; 1.2{{Overline|6}}
|71\18
2748; 2.58{{Overline|3}}
|28\7
2800
|69\17
2855; 4.8
|41\10
2894; 8.5
|54\13
2945.{{Overline|45}}
|-
|A fab
|
|42\11
2652; 1.58{{Overline|3}}
|68\18
2632; 3.875
|26\7
2600
|62\17
2565; 1.9{{Overline|3}}
|36\10
2541; 5.{{Overline|6}}
|46\13
2509.{{Overline|09}}
|-
|A fa
|Fb
|59\15
2723; 13
|43\11
2715; 1.2{{Overline|6}}
|70\18
2709; 1, 2.1
|27\7
2700
|65\17
2689; 1, 1.9
|38\10
2682; 2.8{{Overline|3}}
|49\13
2672.{{Overline|72}}
|-
!A mi
!F
!60\15
2769; 4.'''{{Overline|3}}'''
!44\11
2778; 1.0{{Overline|5}}
!72\18
2787; 3.1
!28\7
2800
!68\17
2813; 1, 3.8{{Overline|3}}
!40\10
2823; 1.{{Overline|8}}
!52\13
2836.{{Overline|36}}
|-
|A mi#
|
|61\15
2815; 2.6
|45\11
2842; 9.5
|74\18
2864; 1.9375
| rowspan="2" |29\7
2900
|71\17
2937; 14.5
|42\10
2964; 1.41{{Overline|6}}
|55\13
3000
|-
|B sol fab
|
|63\15
2907; 1.{{Overline|4}}
|46\11
2905; 3.8
|75\18
2903; 4, 2.{{Overline|3}}
|70\17
2896; 1.8125
|41\10
2894; 8.5
|53\13
2890.{{Overline|90}}
|-
|'''B sol fa'''
|
|'''64\15'''
'''2953; 1.{{Overline|18}}'''
|'''47\11'''
'''2968; 2.375'''
|'''77\18'''
'''2980; 1.55'''
|'''30\7'''
'''3000'''
|'''73\17'''
'''3020; 1.45'''
|'''43\10'''
'''3035; 3.4'''
|'''56\13'''
'''3054.{{Overline|54}}'''
|-
|B sol fa#
|
|65\15
3000
|48\11
3031; 1.{{Overline|72}}
|79\18
3058; 15.5
| rowspan="2" |31\7
3100
|76\17
3144; 1.208{{Overline|3}}
|45\10
3176: 2, 8
|59\13
3218.{{Overline|18}}
|-
|C la solb
|
|67\15
3092; 3, 4
|49\11
3094; 1, 2.8
|80\18
3096; 1.291{{Overline|6}}
|75\17
3103; 2, 2, 6
|44\10
3105; 1.1{{Overline|3}}
|57\13
3109.{{Overline|09}}
|-
|C la sol
|
|68\15
3138; 2, 6
|50\11
3157; 1, 8.5
|82\18
3174; 5, 6
|32\7
3200
|78\17
3227; 1, 1.41{{Overline|6}}
|46\10
3247; 17
|60\13
3272.{{Overline|72}}
|-
|C la sol#
|
|69\15
3184; 1.625
| rowspan="2" |51\11
3221: 19
|84\18
3251; 1, 1, 1, 1.4
|33\7
3300
|81\17
3351; 1, 2.625
|48\10
3388; 4, 4
|63\13
3436.{{Overline|36}}
|-
|D lab
|
|70\15
3230; 1.3
|83\18
3212;  1, 9.{{Overline|3}}
|32\7
3200
|77\17
3186; 4.{{Overline|3}}
|45\10
3176: 2, 8
|58\13
3172.{{Overline|72}}
|-
|'''D la'''
|
|'''71\15'''
'''3276; 1, 12'''
|'''52\11'''
'''3284; 4.75'''
|'''85\18'''
'''3290; 3.1'''
|'''33\7'''
'''3300'''
|'''80\17'''
'''3310; 2.9'''
|'''47\10'''
'''3317; 1.5{{Overline|4}}'''
|'''61\13'''
'''3327.{{Overline|27}}'''
|-
|D la#
|
|72\15
3323; 13
|53\11
3347; 2, 1.4
|87\18
3367; 1, 2.875
| rowspan="2" |34\7
3400
|83\17
3434; 2, 14
|49\10
3458; 1, 4.{{Overline|6}}
|64\13
3490.{{Overline|90}}
|-
|F utb
|
|74\15
3415; 2.6
|54\15
3410; 1.9
|88\18
3406; 2, 4.{{Overline|6}}
|82\17
3393; 9.{{Overline|6}}
|48\10
3388; 4, 4
|62\13
3381.{{Overline|81}}
|-
|-
!Do, Sol
!F ut
!F
!
!4
!75\15
!0, G
3461;  1, 1, 6
!60\15
!55\11
2769; 4.'''{{Overline|3}}'''
3473; 1, 2, 6
!44\11
!90\18
2778; 1.0{{Overline|5}}
3483; 1.'''{{Overline|148}}'''
!72\18
!35\7
2787; 3.1
3500
!28\7
!85\17
2800
3517; 4, 7
!68\17
!50\10
2813; 1, 3.8{{Overline|3}}
3529; 2, 2.{{Overline|3}}q
!40\10
!65\13
2823; 1.{{Overline|8}}
3545.{{Overline|45}}
!52\13
2836.{{Overline|36}}
|}
|}
==Intervals==
==Intervals==
Line 1,630: Line 2,733:
|major third
|major third
|-
|-
|3
| 3
|Reb, Lab
|Reb, Lab
|diminished second
|diminished second
Line 1,643: Line 2,746:
|diminished sesquitave
|diminished sesquitave
| -4
| -4
|Do#, Sol#
| Do#, Sol#
|augmented unison (chroma)
|augmented unison (chroma)
|-
|-
Line 1,755: Line 2,858:
|P
|P
|m
|m
|P
| P
|-
|-
|Phrygian
|Phrygian
|sLLL
| sLLL
|<nowiki>0|3</nowiki>
|<nowiki>0|3</nowiki>
|d
|d
Line 1,888: Line 2,991:
|
|
|<u>187.5</u>
|<u>187.5</u>
|10
| 10
|7
|7
|1.429
|1.429
Line 1,908: Line 3,011:
|16
|16
|11
|11
|1.455
| 1.455
|
|
|-
|-
Line 2,005: Line 3,108:
|
|
|<u>197; 2.{{Overline|135}}</u>
|<u>197; 2.{{Overline|135}}</u>
|13
| 13
|7
|7
|1.857
|1.857
Line 2,137: Line 3,240:
|-
|-
|
|
|7\24
| 7\24
|
|
|<u>204; 1. 7.2</u>
|<u>204; 1. 7.2</u>
|7
| 7
|3
|3
|2.333
|2.333
Line 2,313: Line 3,416:
|15
|15
|4
|4
|3.750
| 3.750
|
|
|-
|-
Line 2,392: Line 3,495:
|
|
|<u>224; 5.7{{Overline|2}}</u>
|<u>224; 5.7{{Overline|2}}</u>
|17
| 17
|3
|3
|5.667
|5.667
Line 2,416: Line 3,519:
|}
|}


== See also ==
==See also==
[[3L 1s (3/2-equivalent)]] - idealized tuning
[[3L 1s (3/2-equivalent)]] - idealized tuning


Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/3L_1s_(perfect_fifth-equivalent)"