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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, 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.
There are 6 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, Fa Sol La Si, 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
Cents
 
 
! colspan="2" |Notation
! Notation
 
 
!Supersoft
!Supersoft
Line 29: Line 29:
!Semihard
!Semihard
 
 
! Hard
!Hard
 
 
!Superhard
!Superhard
Line 36: Line 36:
 
 
!Diatonic
!Diatonic
! Napoli
!~15edf
!~15edf
 
 
Line 54: Line 52:
|-
|-
 
 
|Do#, Sol#
|Do#, Fa#, Sol#
|F#
|1\15, 46.154
|1\15, 46.154
 
 
Line 63: Line 59:
|2\18, 77.419
|2\18, 77.419
 
 
| rowspan="2" |1\7, 100
| rowspan="2" | 1\7, 100
 
 
|3\17, 124.138
|3\17, 124.138
 
 
| 2\10, 141.176
|2\10, 141.176
 
 
|3\13, 163.{{Overline|63}}
|3\13, 163.636
 
 
|-
|-
 
 
|Reb, Lab
|Reb, Solb, Lab
|Gb
|3\15, 138.462
|3\15, 138.462
 
 
Line 86: Line 80:
|1\10, 70.588
|1\10, 70.588
 
 
|1\13, 54.{{Overline|54}}
|1\13, 54.545
 
 
|-
|-
 
 
|'''Re, La'''
|'''Re, Sol, La'''
|'''G'''
|'''4\15,''' '''184.615'''
|'''4\15,''' '''184.615'''
 
 
Line 105: Line 97:
|'''3\10,''' '''211.765'''
|'''3\10,''' '''211.765'''
 
 
|'''4\13,''' '''218.{{Overline|18}}'''
|'''4\13,''' '''218.182'''
 
 
|-
|-
 
 
|Re#, La#
|Re#, Sol#, La#
|5\15, 230.769
|G#
| 5\15, 230.769
 
 
|4\11, 252.632
|4\11, 252.632
Line 118: Line 108:
|7\18, 270.968
|7\18, 270.968
 
 
| rowspan="2" |3\7, 300
| rowspan="2" | 3\7, 300
 
 
|8\17, 331.034
|8\17, 331.034
Line 124: Line 114:
|5\10, 352.941
|5\10, 352.941
 
 
|7\13, 381.{{Overline|81}}
|7\13, 381.818
 
 
|-
|-
 
 
|Mib, Sib
|Mib, Lab, Sib
|Ab
|7\15, 323.077
|7\15, 323.077
 
 
|5\11, 315.789
|5\11, 315.789
 
 
| 8\18, 309.677
|8\18, 309.677
 
 
|7\17, 289.655
|7\17, 289.655
 
 
| 4\10, 282.353
|4\10, 282.353
 
 
|5\13, 272.{{Overline|72}}
|5\13, 272.727
 
 
|-
|-
 
 
| Mi, Si
|Mi, La, Si
|A
|8\15, 369.231
|8\15, 369.231
 
 
|6\11, 378.947
|6\11, 378.947
 
 
| 10\18, 387.097
|10\18, 387.097
 
 
|4\7, 400
|4\7, 400
Line 158: Line 144:
|10\17, 413.793
|10\17, 413.793
 
 
| 6\10, 423.529
|6\10, 423.529
 
 
|8\13, 436.{{Overline|36}}
|8\13, 436.364
 
 
|-
|-
 
 
|Mi#, Si#
|Mi#, La#, Si#
|A#
|9\15, 415.385
|9\15, 415.385
 
 
| rowspan="2" |7\11, 442.105
| rowspan="2" | 7\11, 442.105
 
 
|12\18, 464.516
|12\18, 464.516
 
 
| 5\7, 500
|5\7, 500
 
 
|13\17, 537.069
|13\17, 537.069
Line 183: Line 167:
|-
|-
 
 
|Fab, Dob
|Fab, Sibb, Dob
|10\15, 461.538
| Bbb
| 10\15, 461.538
 
 
|11\18, 425.806
|11\18, 425.806
Line 196: Line 178:
|5\10, 352.941
|5\10, 352.941
 
 
| 6\13, 327.{{Overline|27}}
|6\13, 327.273
 
 
|-
|-
 
 
|'''Fa, Do'''
|'''Fa, Sib, Do'''
|'''Bb'''
|'''11\15,''' '''507.692'''
|'''11\15,''' '''507.692'''
 
 
Line 215: Line 195:
|'''7\10,''' '''494.118'''
|'''7\10,''' '''494.118'''
 
 
|'''9\13,''' '''490.{{Overline|90}}'''
|'''9\13,''' '''490.909'''
 
 
|-
|-
 
 
|Fa#, Do#
|Fa#, Si, Do#
|12\15, 553.846
|B
|12\15, 553.846
 
 
|9\11, 568.421
|9\11, 568.421
 
 
| 15\18, 580.645
|15\18, 580.645
 
 
|6\7, 600
|6\7, 600
Line 234: Line 212:
|9\10, 635.294
|9\10, 635.294
 
 
|12\13, 654.{{Overline|54}}
|12\13, 654.545
 
 
|-
|-
|Fax, Dox
|Fax, Si#, Dox
|B#
|13\15, 600
|13\15, 600
 
 
| rowspan="2" |10\11, 631.579
| rowspan="2" | 10\11, 631.579
 
 
|17\18, 658.064
|17\18, 658.064
Line 253: Line 229:
|11\10, 776.471
|11\10, 776.471
 
 
|15\13, 818.{{Overline|18}}
|15\13, 818.182
 
 
|-
|-
 
 
|Dob, Solb
|Dob, Fab, Solb
|Hb
|14\15, 646.154
|14\15, 646.154
| 16\18, 619.355
|16\18, 619.355
|6\7, 600
|6\7, 600
|14\17, 579.310
|14\17, 579.310
|8\10, 564.706
|8\10, 564.706
|10\13, 545.{{Overline|45}}
|10\13, 545.455
 
 
|-
|-
 
 
!Do, Sol
!Do, Fa, Sol
!H
!'''15\15,''' '''692.308'''
!'''15\15,''' '''692.308'''
 
 
Line 283: Line 256:
!'''10\10,''' '''705.882'''
!'''10\10,''' '''705.882'''
 
 
!'''13\13,''' '''709.'''{{Overline|09}}
!'''13\13,''' '''709.091'''
 
 
|-
|}
{| class="wikitable"
 
 
|Do#, Sol#
|+
 
 
|Η#
Cents
|16\15, 738.462
!Notation
!Supersoft
 
 
|12\11, 757.895
! Soft
 
 
|20\18, 774.194
!Semisoft
 
 
| rowspan="2" |8\8, 800
!Basic
 
 
|20\17, 827.586
!Semihard
 
 
|12\10, 847.059
! Hard
 
 
|16\13, 872.{{Overline|72}}
! Superhard
 
 
|-
|-
 
 
|Reb, Lab
!Napoli
! ~15edf
 
 
|Cb
! ~11edf
|18\15, 830.769
 
 
|13\11, 821.053
!~18edf
 
 
|21\18, 812.903
!~7edf
 
 
| 19\17, 786.207
!~17edf
 
 
|11\10, 776.471
!~10edf
 
 
|14\13, 763.{{Overline|63}}
!~13edf
 
 
|-
|-
 
 
|'''Re, La'''
|F#
|1\15, 46.154
 
 
|'''C'''
|1\11, 63.158
|'''19\15,''' '''876.923'''
 
 
|'''14\11,''' '''884.211'''
| 2\18, 77.419
 
 
|'''23\18,''' '''890.323'''
| rowspan="2" |1\7, 100
 
 
|'''9\5,''' '''900'''
|3\17, 124.138
 
 
|'''22\17,''' '''910.345'''
| 2\10, 141.176
 
 
|'''13\10,''' '''917.647'''
|3\13, 163.636
|'''17\13,''' '''927.{{Overline|27}}'''
 
 
|-
|-
 
 
|Re#, La#
| Gb, Ge
|3\15, 138.462
 
 
| C#
| 2\11. 126.316
|20\15, 923.077
 
 
|15\11, 947.368
|3\18, 116.129
 
 
|25\18, 967.742
|2\17, 82.759
 
 
| rowspan="2" |10\7, 1000
|1\10, 70.588
|25\17, 1034.483
|15\10, 1058.824
 
 
|20\13, 1090.{{Overline|90}}
|1\13, 54.545
 
 
|-
|-
 
 
|Mib, Sib
|'''G'''
|'''4\15,''' '''184.615'''
 
 
|Db
|'''3\11,''' '''189.474'''
|22\15, 1015.385
|'''5\18,''' '''193.548'''
 
 
|16\11, 1010.526
|'''2\7,''' '''200'''
 
 
|26\18, 1006.452
|'''5\17,''' '''206.897'''
 
 
|24\17, 993.103
|'''3\10,''' '''211.765'''
 
 
|14\10, 988.235
|'''4\13,''' '''218.182'''
|18\13, 981.{{Overline|81}}
 
 
|-
|-
 
 
|Mi, Si
|G#
|5\15, 230.769
 
 
| D
|4\11, 252.632
| 23\15, 1061.538
 
 
|17\11, 1073.684
|7\18, 270.968
 
 
|28\18, 1083.871
| rowspan="2" |3\7, 300
 
 
|11\7, 1100
| 8\17, 331.034
 
 
|27\17, 1117.241
|5\10, 352.941
| 16\10, 1129.412
 
 
|21\9, 1145.{{Overline|45}}
|7\13, 381.818
 
 
|-
|-
 
 
|Mi#, Si#
|Ab, Æ
|7\15, 323.077
 
 
|D#
|5\11, 315.789
|24\15, 1107.923
 
 
| rowspan="2" |18\11, 1136.842
|8\18, 309.677
 
 
|30\18, 1161.29
|7\17, 289.655
 
 
|12\7, 1200
|4\10, 282.353
 
 
| 30\17, 1241.379
|5\13, 272.727
 
 
|18\10, 1270.588
|-
 
 
| 24\13, 1309.{{Overline|09}}
|A
| 8\15, 369.231
 
 
|-
|6\11, 378.947
 
 
| Fab, Dob
|10\18, 387.097
 
 
|Ebb
| 4\7, 400
|25\15, 1153.846
 
 
|29\18, 1122.581
|10\17, 413.793
 
 
|11\7, 1100
|6\10, 423.529
 
 
|26\17, 1075.862
|8\13, 436.364
|15\10, 1058.824
|19\13, 1036.{{Overline|36}}
 
 
|-
|-
 
 
|'''Fa, Do'''
|A#
| 9\15, 415.385
 
 
|'''Eb'''
| rowspan="2" |7\11, 442.105
|'''26\15,''' '''1200'''
 
 
|'''19\11,''' '''1200'''
|12\18, 464.516
 
 
|'''31\18,''' '''1200'''
|5\7, 500
 
 
|'''12\7, 1200'''
|13\17, 537.069
 
 
|'''29\17,''' '''1200'''
|8\10, 564.706
 
 
|'''17\10,''' '''1200'''
|11\13, 600
|'''22\13,''' '''1200'''
 
 
|-
|-
 
 
|Fa#, Do#
|Bbb, Bee
|10\15, 461.538
 
 
| E
|11\18, 425.806
| 27\15, 1246.154
 
 
|20\11, 1263.158
|4\7, 400
 
 
|33\18, 1277.419
|9\17, 372.414
 
 
|13\7, 1300
| 5\10, 352.941
 
 
|32\17, 1324.138
|6\13, 327.273
|19\10, 1341.176
|25\13, 1363.{{Overline|63}}
 
 
|-
|-
 
 
|Fax, Dox
|'''Bb, Be'''
|'''11\15,''' '''507.692'''
 
 
|E#
|'''8\11,''' '''505.263'''
| 28\15, 1292.308
 
 
| rowspan="2" | 21\11, 1326.318
|'''13\18,''' '''503.226'''
 
 
| 35\18, 1354.834
|'''5\7, 500'''
 
 
|14\7, 1400
|'''12\17,''' '''496.552'''
 
 
|35\17, 1448.275
|'''7\10,''' '''494.118'''
|21\10, 1482.353
 
 
|28\13, 1527.{{Overline|27}}
|'''9\13,''' '''490.909'''
 
 
|-
|-
 
 
|Dob, Solb
|B
|12\15, 553.846
 
 
| Fb
|9\11, 568.421
|29\15, 1338.462
 
 
|34\18, 1316.129
|15\18, 580.645
 
 
|13\7, 1300
|6\7, 600
 
 
|31\17, 1282.759
| 15\17, 620.690
 
 
|18\10, 1270.588
|9\10, 635.294
 
 
|23\13, 1254.{{Overline|54}}
|12\13, 654.545
 
 
|-
|-
| B#
| 13\15, 600
 
 
!Do, Sol
| rowspan="2" |10\11, 631.579
 
 
!F
|17\18, 658.064
!30\15, 1384.615
 
 
! 22\11, 1389.473
|7\7, 700
 
 
!36\18, 1393.548
|18\17, 744.828
 
 
!14\7, 1400
|11\10, 776.471
 
 
!34\17, 1406.897
|15\13, 818.182
 
 
!20\10, 1411.765
|-
|Hb, He
|14\15, 646.154
| 16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
 
 
!26\13, 1418.{{Overline|18}}
|}
{| class="wikitable"
|+Cents
! colspan="2" |Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
! Hard
!Superhard
|-
|-
!Bijou
!Hextone
! H
! ~15edf
!'''15\15,''' '''692.308'''
!~11edf
!~18edf
!'''11\11,''' '''694.737'''
! ~7edf
! ~17edf
!'''18\18,''' '''696.774'''
!~10edf
!~13edf
! 7\7, 700
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
|-
|-
|0#, D#
|0#, G#
|Η#
| 1\15, 46.154
|16\15, 738.462
|1\11, 63.158
|2\18, 77.419
|12\11, 757.895
| rowspan="2" |1\7, 100
|3\17, 124.138
|20\18, 774.194
|2\10, 141.176
|3\13, 163.{{Overline|63}}
| rowspan="2" |8\8, 800
|20\17, 827.586
|12\10, 847.059
|16\13, 872.727
|-
|-
|1b, 1c
|1f
|Cb, Ce
|3\15, 138.462
|18\15, 830.769
| 2\11. 126.316
|3\18, 116.129
|13\11, 821.053
|2\17, 82.759
|1\10, 70.588
|21\18, 812.903
| 1\13, 54.{{Overline|54}}
|19\17, 786.207
|11\10, 776.471
|14\13, 763.63
|-
|-
|'''1'''
|'''1'''
|'''C'''
|'''4\15,''' '''184.615'''
|'''19\15,''' '''876.923'''
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
|'''14\11,''' '''884.211'''
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|'''23\18,''' '''890.323'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.{{Overline|18}}'''
|'''9\5,''' '''900'''
|-
| 1#
|'''22\17,''' '''910.345'''
|1#
|5\15, 230.769
|'''13\10,''' '''917.647'''
| 4\11, 252.632
|7\18, 270.968
|'''17\13,''' '''927.273'''
| rowspan="2" |3\7, 300
|8\17, 331.034
|5\10, 352.941
| 7\13, 381.{{Overline|81}}
|-
|-
|2b, 2c
|2f
|C#
|7\15, 323.077
|20\15, 923.077
|5\11, 315.789
| 8\18, 309.677
|15\11, 947.368
|7\17, 289.655
| 4\10, 282.353
|25\18, 967.742
|5\13, 272.{{Overline|72}}
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|15\10, 1058.824
|20\13, 1090.909
|-
|-
|2
|2
| Db, De
|8\15, 369.231
|22\15, 1015.385
|6\11, 378.947
|10\18, 387.097
|16\11, 1010.526
|4\7, 400
|10\17, 413.793
|26\18, 1006.452
| 6\10, 423.529
|8\13, 436.{{Overline|36}}
|24\17, 993.103
|14\10, 988.235
|18\13, 981.818
|-
|-
|2#
|2#
|D
| 9\15, 415.385
|23\15, 1061.538
| rowspan="2" |7\11, 442.105
|12\18, 464.516
|17\11, 1073.684
|5\7, 500
|13\17, 537.069
|28\18, 1083.871
|8\10, 564.706
| 11\13, 600
|11\7, 1100
|27\17, 1117.241
|16\10, 1129.412
|21\9, 1145.455
|-
|-
|3b, 3c
|3f
|D#
|10\15, 461.538
|24\15, 1107.923
|11\18, 425.806
| 4\7, 400
| rowspan="2" |18\11, 1136.842
|9\17, 372.414
|5\10, 352.941
|30\18, 1161.29
|6\13, 327.{{Overline|27}}
|12\7, 1200
|30\17, 1241.379
|18\10, 1270.588
|24\13, 1309.091
|-
|-
|'''3'''
|'''3'''
|Ebb, Ëe
|'''11\15,''' '''507.692'''
|25\15, 1153.846
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
|29\18, 1122.581
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|11\7, 1100
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.{{Overline|90}}'''
|26\17, 1075.862
|15\10, 1058.824
| 19\13, 1036.364
|-
|-
| 3#
|3#
|'''Eb, Ë'''
| 12\15, 553.846
|'''26\15,''' '''1200'''
| 9\11, 568.421
|15\18, 580.645
|'''19\11,''' '''1200'''
| 6\7, 600
|15\17, 620.690
|'''31\18,''' '''1200'''
|9\10, 635.294
|12\13, 654.{{Overline|54}}
|'''12\7, 1200'''
|-
|3x
|'''29\17,''' '''1200'''
|3x
|13\15, 600
|'''17\10,''' '''1200'''
| rowspan="2" |10\11, 631.579
|17\18, 658.064
|'''22\13,''' '''1200'''
| 7\7, 700
|18\17, 744.828
|11\10, 776.471
|15\13, 818.{{Overline|18}}
|-
|-
|4b, 4c
|4f
|E
| 14\15, 646.154
|27\15, 1246.154
|16\18, 619.355
| 6\7, 600
|20\11, 1263.158
|14\17, 579.310
|8\10, 564.706
|33\18, 1277.419
|10\13, 545.{{Overline|45}}
|13\7, 1300
|32\17, 1324.138
|19\10, 1341.176
|25\13, 1363.636
|-
|-
!4
!4
|E#
!'''15\15,''' '''692.308'''
|28\15, 1292.308
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
| rowspan="2" |21\11, 1326.318
!7\7, 700
!'''17\17,''' '''703.448'''
|35\18, 1354.834
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.'''{{Overline|09}}
|14\7, 1400
|35\17, 1448.275
| 21\10, 1482.353
|28\13, 1527.273
|-
|-
|4#
|4#
| Fb, Fe
|16\15, 738.462
|29\15, 1338.462
|12\11, 757.895
|20\18, 774.194
|34\18, 1316.129
| rowspan="2" |8\8, 800
|20\17, 827.586
|13\7, 1300
| 12\10, 847.059
|16\13, 872.{{Overline|72}}
|31\17, 1282.759
|18\10, 1270.588
|23\13, 1254.545
|-
|-
|5b, 5c
|5
!F
|18\15, 830.769
!30\15, 1384.615
|13\11, 821.053
|21\18, 812.903
!22\11, 1389.473
|19\17, 786.207
| 11\10, 776.471
!36\18, 1393.548
|14\13, 763.{{Overline|63}}
|-
!14\7, 1400
|'''5'''
|'''5'''
!34\17, 1406.897
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
!20\10, 1411.765
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
!26\13, 1418.182
|'''22\17,''' '''910.345'''
|}
|'''13\10,''' '''917.647'''
 
|'''17\13,''' '''927.{{Overline|27}}'''
{| class="wikitable"
|+Cents
! Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
! Superhard
|-
|-
|5#
!Bijou
|5#
!~15edf
|20\15, 923.077
!~11edf
| 15\11, 947.368
!~18edf
|25\18, 967.742
!~7edf
| rowspan="2" |10\7, 1000
!~17edf
|25\17, 1034.483
!~10edf
|15\10, 1058.824
!~13edf
|20\13, 1090.{{Overline|90}}
|-
|-
|6b, 6c
|0#, D#
|6f
|1\15, 46.154
| 22\15, 1015.385
|1\11, 63.158
| 16\11, 1010.526
|2\18, 77.419
|26\18, 1006.452
| rowspan="2" |1\7, 100
|24\17, 993.103
|3\17, 124.138
|14\10, 988.235
|2\10, 141.176
|18\13, 981.{{Overline|81}}
|3\13, 163.636
|-
|-
|6
|1b, 1c
|6
|3\15, 138.462
|23\15, 1061.538
| 2\11. 126.316
| 17\11, 1073.684
|3\18, 116.129
|28\18, 1083.871
|2\17, 82.759
|11\7, 1100
|1\10, 70.588
|27\17, 1117.241
|1\13, 54.545
| 16\10, 1129.412
|21\9, 1145.{{Overline|45}}
|-
|-
|6#
|'''1'''
|6#
|'''4\15,''' '''184.615'''
|24\15, 1107.923
|'''3\11,''' '''189.474'''
| rowspan="2" | 18\11, 1136.842
|'''5\18,''' '''193.548'''
|30\18, 1161.290
|'''2\7,''' '''200'''
|12\7, 1200
|'''5\17,''' '''206.897'''
|30\17, 1241.379
|'''3\10,''' '''211.765'''
|18\10, 1270.588
|'''4\13,''' '''218.182'''
|24\13, 1309.{{Overline|09}}
|-
|-
|7b, 7c
|1#
|7f
|5\15, 230.769
| 25\15, 1153.846
|4\11, 252.632
|29\18, 1122.581
|7\18, 270.968
|11\7, 1100
| rowspan="2" |3\7, 300
|26\17, 1075.862
|8\17, 331.034
| 15\10, 1058.824
|5\10, 352.941
|19\13, 1036.{{Overline|36}}
|7\13, 381.818
|-
|-
|'''7'''
|2b, 2c
|'''7'''
|7\15, 323.077
|'''26\15,''' '''1200'''
|5\11, 315.789
|'''19\11,''' '''1200'''
| 8\18, 309.677
|'''31\18,''' '''1200'''
| 7\17, 289.655
|'''12\7, 1200'''
|4\10, 282.353
|'''29\17,''' '''1200'''
|5\13, 272.727
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|-
|7#
|2
|7#
|8\15, 369.231
|27\15, 1246.154
|6\11, 378.947
|20\11, 1263.158
|10\18, 387.097
|33\18, 1277.419
|4\7, 400
|13\7, 1300
|10\17, 413.793
|32\17, 1324.138
|6\10, 423.529
|19\10, 1341.176
|8\13, 436.364
|25\13, 1363.{{Overline|63}}
|-
|-
|7x
|2#
|7x
| 9\15, 415.385
|28\15, 1292.308
| rowspan="2" |7\11, 442.105
| rowspan="2" |21\11, 1326.318
|12\18, 464.516
|35\18, 1354.834
|5\7, 500
|14\7, 1400
|13\17, 537.069
|35\17, 1448.275
|8\10, 564.706
|21\10, 1482.353
|11\13, 600
|28\13, 1527.{{Overline|27}}
|-
|-
|8b, Fc
|3b, 3c
|8f
| 10\15, 461.538
|29\15, 1338.462
| 11\18, 425.806
|34\18, 1316.129
|4\7, 400
| 13\7, 1300
|9\17, 372.414
|31\17, 1282.759
|5\10, 352.941
|18\10, 1270.588
|6\13, 327.273
|23\13, 1254.{{Overline|54}}
|-
|-
!8, F
|'''3'''
!8
|'''11\15,''' '''507.692'''
!30\15, 1384.615
|'''8\11,''' '''505.263'''
!22\11, 1389.473
|'''13\18,''' '''503.226'''
! 36\18, 1393.548
|'''5\7, 500'''
!14\7, 1400
|'''12\17,''' '''496.552'''
!34\17, 1406.897
|'''7\10,''' '''494.118'''
!20\10, 1411.765
|'''9\13,''' '''490.909'''
!26\13, 1418.{{Overline|18}}
|-
|-
|8#, F#
|3#
|8#
|12\15, 553.846
|31\15, 1430.769
|9\11, 568.421
|23\11, 1452.632
|15\18, 580.645
|38\18, 1470.968
|6\7, 600
| rowspan="2" | 15\7, 1500
|15\17, 620.690
|37\17, 1531.034
|9\10, 635.294
|22\10, 1552.941
|12\13, 654.545
|29\13, 1581.{{Overline|81}}
|-
|-
|9b, Gc
|3x
|9f
|13\15, 600
|33\15, 1523.077
| rowspan="2" |10\11, 631.579
|24\11, 1515.789
|17\18, 658.064
|39\18, 1509.677
|7\7, 700
|36\17, 1489.655
|18\17, 744.828
| 21\10, 1482.759
|11\10, 776.471
|27\13, 1472.{{Overline|72}}
|15\13, 818.182
|-
|-
|'''9, G'''
|4b, 4c
|9
|14\15, 646.154
|'''34\15,''' '''1569.231'''
|16\18, 619.355
|'''25\11,''' '''1578.947'''
|6\7, 600
|'''41\18,''' '''1587.097'''
|14\17, 579.310
|'''16\7,''' '''1600'''
|8\10, 564.706
|'''39\17,''' '''1613.793'''
|10\13, 545.455
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.{{Overline|36}}'''
|-
|-
| 9#, G#
!4
|9#
!'''15\15,''' '''692.308'''
|35\15, 1615.385
!'''11\11,''' '''694.737'''
|26\11, 1642.105
!'''18\18,''' '''696.774'''
|43\18, 1664.516
!7\7, 700
| rowspan="2" |17\7, 1700
!'''17\17,''' '''703.448'''
|42\17, 1737.069
!'''10\10,''' '''705.882'''
| 25\10, 1764.706
!'''13\13,''' '''709.091'''
|33\13, 1800
|-
|-
|Xb, Ac
|4#
|Af
| 16\15, 738.462
|37\15, 1707.692
|12\11, 757.895
|27\11, 1705.263
|20\18, 774.194
|44\18, 1703.226
| rowspan="2" |8\8, 800
| 41\17, 1696.552
|20\17, 827.586
| 24\10, 1694.118
|12\10, 847.059
|31\13, 1690.{{Overline|90}}
| 16\13, 872.727
|-
|-
| X, A
|5b, 5c
|A
|18\15, 830.769
|38\15, 1753.846
|13\11, 821.053
|28\11, 1768.421
|21\18, 812.903
| 46\18, 1780.645
|19\17, 786.207
|18\7, 1800
|11\10, 776.471
|44\17, 1820.690
|14\13, 763.63
| 26\10, 1835.294
| 34\13, 1854.{{Overline|54}}
|-
|-
|X#, A#
|'''5'''
|A#
|'''19\15,''' '''876.923'''
|39\15, 1800
|'''14\11,''' '''884.211'''
| rowspan="2" |29\11, 1831.579
|'''23\18,''' '''890.323'''
|48\18, 1858.064
|'''9\5,''' '''900'''
|19\7, 1900
|'''22\17,''' '''910.345'''
|47\17, 1944.828
|'''13\10,''' '''917.647'''
|28\10, 1976.471
|'''17\13,''' '''927.273'''
|37\13, 2018.{{Overline|18}}
|-
|-
| Ebb, Ccc
|5#
|Ax
|20\15, 923.077
|40\15, 1846.154
|15\11, 947.368
| 47\18, 1819.355
|25\18, 967.742
|18\7, 1800
| rowspan="2" |10\7, 1000
|43\17, 1779.310
|25\17, 1034.483
|25\10, 1764.706
|15\10, 1058.824
|32\13, 1745.{{Overline|45}}
|20\13, 1090.909
|-
|-
|'''Eb, Cc'''
|6b, 6c
|'''Bf'''
|22\15, 1015.385
|'''41\15,''' '''1892.308'''
|16\11, 1010.526
|'''30\11,''' '''1894.737'''
|26\18, 1006.452
|'''49\18,''' '''1896.774'''
|24\17, 993.103
|'''19\7, 1900'''
|14\10, 988.235
|'''46\17,''' '''1903.448'''
|18\13, 981.818
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.{{Overline|09}}'''
|-
|-
|E, C
|6
|B
|23\15, 1061.538
|42\15, 1938.462
|17\11, 1073.684
|31\11, 1957.895
| 28\18, 1083.871
| 51\18, 1974.194
|11\7, 1100
|20\7, 2000
|27\17, 1117.241
| 49\17, 2027.586
|16\10, 1129.412
|29\10, 2047.059
|21\9, 1145.455
| 38\13, 2072.{{Overline|72}}
|-
|-
|Ex, Cx
|6#
|B#
|24\15, 1107.923
| 43\15, 1984.615
| rowspan="2" |18\11, 1136.842
| rowspan="2" |32\11, 2021.053
|30\18, 1161.290
|53\18, 2051.612
|12\7, 1200
|21\7, 2100
|30\17, 1241.379
|52\17, 2151.725
|18\10, 1270.588
|31\10, 2188.235
|24\13, 1309.091
| 41\13, 2236.{{Overline|36}}
|-
|-
|0b, Dc
| 7b, 7c
|Cf
|25\15, 1153.846
|44\15, 2030.769
|29\18, 1122.581
|52\18, 2012.903
|11\7, 1100
| 20\7, 2000
|26\17, 1075.862
| 48\17, 1986.207
|15\10, 1058.824
|28\10, 1976.471
|19\13, 1036.364
|36\13, 1963.{{Overline|63}}
|-
|-
!0, D
|'''7'''
!C
|'''26\15,''' '''1200'''
!45\15, 2076.923
|'''19\11,''' '''1200'''
!33\11, 2084.211
|'''31\18,''' '''1200'''
!54\18, 2090.323
|'''12\7, 1200'''
! 21\7, 2100
|'''29\17,''' '''1200'''
!51\17, 2110.345
|'''17\10,''' '''1200'''
!30\10, 2117.647
|'''22\13,''' '''1200'''
!39\13, 2127.{{Overline|27}}
|-
|-
|0#, D#
|7#
|C#
|27\15, 1246.154
|46\15, 2123.077
|20\11, 1263.158
|34\11, 2147.368
|33\18, 1277.419
|56\15, 2167.742
|13\7, 1300
| rowspan="2" |22\7, 2200
|32\17, 1324.138
|54\17, 2234.483
|19\10, 1341.176
|32\10, 2258.824
|25\13, 1363.636
|42\13, 2090.{{Overline|90}}
|-
|-
|1b, 1c
|7x
|Df
|28\15, 1292.308
|48\15, 2215.385
| rowspan="2" |21\11, 1326.318
|35\11, 2210.526
|35\18, 1354.834
|57\15, 2206.452
|14\7, 1400
|53\17, 2193.103
|35\17, 1448.275
|31\10, 2188.235
|21\10, 1482.353
|40\13, 2181.{{Overline|81}}
|28\13, 1527.273
|-
|-
|'''1'''
|8b, Fc
|'''D'''
|29\15, 1338.462
|'''49\15, 2261.538'''
|34\18, 1316.129
|'''36\11, 1073.684'''
|13\7, 1300
|'''59\18, 2283.871'''
|31\17, 1282.759
|'''23\7, 2300'''
|18\10, 1270.588
|'''56\17, 2317.241'''
|23\13, 1254.545
|'''33\10, 2329.412'''
|'''43\13,''' '''2345.{{Overline|45}}'''
|-
|-
|1#
!8, F
|D#
!30\15, 1384.615
|50\15, 2307.692
!22\11, 1389.473
|37\11, 2336.842
!36\18, 1393.548
|61\18, 2361.290
!14\7, 1400
| rowspan="2" |24\7, 2400
!34\17, 1406.897
|59\17, 2441.379
!20\10, 1411.765
|35\10, 2470.588
!26\13, 1418.182
|46\13, 2509.{{Overline|09}}
|-
|-
|2b, 2c
|8#, F#
|Ef
|31\15, 1430.769
|52\15, 2400
|23\11, 1452.632
|38\11, 2400
|38\18, 1470.968
|62\18, 2400
| rowspan="2" |15\7, 1500
|58\17, 2400
|37\17, 1531.034
|34\10, 2400
|22\10, 1552.941
|44\13, 2400
|29\13, 1581.818
|-
|-
|2
|9b, Gc
|E
|33\15, 1523.077
|53\15, 2446.154
|24\11, 1515.789
|39\11, 2463.158
|39\18, 1509.677
|64\18, 2477,419
|36\17, 1489.655
|25\7, 2500
|21\10, 1482.759
|61\17, 2524.138
|27\13, 1472.273
|36\10, 2541.176
|47\13, 2563.{{Overline|63}}
|-
|-
|2#
|'''9, G'''
|E#
|'''34\15,''' '''1569.231'''
|54\15, 2492.308
|'''25\11,''' '''1578.947'''
| rowspan="2" |40\11, 2526.316
|'''41\18,''' '''1587.097'''
|66\18, 2554.838
|'''16\7,''' '''1600'''
|26\7, 2600
|'''39\17,''' '''1613.793'''
|64\17, 2648.275
|'''23\10,''' '''1623.529'''
|38\10, 2682.353
|'''30\13,''' '''1636.364'''
|50\13, 2727.{{Overline|27}}
|-
|-
|3b, 3c
|9#, G#
|Fff
|35\15, 1615.385
|55\15,
|26\11, 1642.105
2538.462
|43\18, 1664.516
|65\18, 2516.129
| rowspan="2" |17\7, 1700
|25\7, 2500
|42\17, 1737.069
|60\17, 2482.759
|25\10, 1764.706
|35\10, 2470.588
|33\13, 1800
|45\13, 2454.{{Overline|54}}
|-
|-
|'''3'''
|Xb, Ac
|'''Ff'''
|37\15, 1707.692
|'''56\15, 2584.615'''
|27\11, 1705.263
|'''41\11, 2589.474'''
|44\18, 1703.226
|'''67\18, 2593.548'''
|41\17, 1696.552
|'''26\7, 2600'''
|24\10, 1694.118
|'''63\17, 2606.897'''
|31\13, 1690.909
|'''37\10, 2611.765'''
|'''48\13,''' '''2618.{{Overline|18}}'''
|-
|-
|3#
|X, A
|F
|38\15, 1753.846
|57\15, 2630.769
|28\11, 1768.421
|42\11, 2652.632
|46\18, 1780.645
|69\18, 2670.968
|18\7, 1800
|27\7, 2700
|44\17, 1820.690
|66\17, 2731.034
|26\10, 1835.294
|39\10, 2752.941
|34\13, 1854.545
|51\13, 2781.{{Overline|81}}
|-
|-
|3x
|X#, A#
|F#
|39\15, 1800
| rowspan="2" |58\15, 2676.923
| rowspan="2" |29\11, 1831.579
|43\11, 2715.789
|48\18, 1858.064
|71\18, 2748.387
|19\7, 1900
|28\7, 2800
|47\17, 1944.828
|69\17, 2855.172
|28\10, 1976.471
|41\10, 2894.118
|37\13, 2018.182
|54\13, 2945.{{Overline|45}}
|-
|-
|4bb, 4cc
|Ebb, Ccc
|0ff, Gff
|40\15, 1846.154
|42\11, 2652.632
|47\18, 1819.355
|68\18, 2632.258
|18\7, 1800
|26\7, 2600
|43\17, 1779.310
|62\17, 2565.517
|25\10, 1764.706
|36\10, 2541.176
|32\13, 1745.545
|46\13, 2509.{{Overline|09}}
|-
|-
|4b, 4c
|'''Eb, Cc'''
|0f, Gf
|'''41\15,''' '''1892.308'''
|59\15, 2723.077
|'''30\11,''' '''1894.737'''
|43\11, 2715.789
|'''49\18,''' '''1896.774'''
|70\18, 2709.677
|'''19\7, 1900'''
|27\7, 2700
|'''46\17,''' '''1903.448'''
|65\17, 2689.552
|'''27\10,''' '''1905.882'''
|38\10, 2682.353
|'''35\13,''' '''1909.091'''
|49\13, 2672.{{Overline|72}}
|-
|-
!4
|E, C
!0, G
|42\15, 1938.462
!60\15, 2769.231
|31\11, 1957.895
!44\11, 2778.947
|51\18, 1974.194
!72\18, 2787.097
|20\7, 2000
!28\7, 2800
|49\17, 2027.586
!68\17, 2813.793
|29\10, 2047.059
!40\10, 2823.529
|38\13, 2072.727
!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
|Ex, Cx
!Subdozenal
|43\15, 1984.615
| rowspan="2" |32\11, 2021.053
|53\18, 2051.612
|21\7, 2100
|52\17, 2151.725
|31\10, 2188.235
|41\13, 2236.364
|-
|0b, Dc
|44\15, 2030.769
|52\18, 2012.903
|20\7, 2000
|48\17, 1986.207
|28\10, 1976.471
|36\13, 1963.636
|-
! 0, D
!45\15, 2076.923
!33\11, 2084.211
!54\18, 2090.323
!21\7, 2100
!51\17, 2110.345
!30\10, 2117.647
!39\13, 2127.273
|}
 
{| class="wikitable"
|+Cents
!Notation
!Supersoft
!Soft
!Semisoft
! Basic
!Semihard
!Hard
!Superhard
|-
!Hextone
!~15edf
!~15edf
! ~11edf
!~11edf
!~18edf
!~18edf
!~7edf
!~7edf
Line 1,081: Line 1,097:
!~13edf
!~13edf
|-
|-
|F ut#
|0#, G#
|F#
|1\15, 46.154
|1\15, 46.154
|1\11, 63.158
|1\11, 63.158
Line 1,089: Line 1,104:
|3\17, 124.138
|3\17, 124.138
|2\10, 141.176
|2\10, 141.176
|3\13, 163.{{Overline|63}}
|3\13, 163.636
|-
|-
|G reb
| 1f
| Gb
|3\15, 138.462
|3\15, 138.462
|2\11. 126.316
|2\11. 126.316
| 3\18, 116.129
|3\18, 116.129
|2\17, 82.759
|2\17, 82.759
|1\10, 70.588
|1\10, 70.588
| 1\13, 54.{{Overline|54}}
|1\13, 54.545
|-
|-
|'''G re'''
|'''1'''
|'''G'''
|'''4\15,''' '''184.615'''
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
|'''3\11,''' '''189.474'''
Line 1,108: Line 1,121:
|'''5\17,''' '''206.897'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.{{Overline|18}}'''
|'''4\13,''' '''218.182'''
|-
|-
| G re#
|1#
|G#
|5\15, 230.769
|5\15, 230.769
|4\11, 252.632
|4\11, 252.632
|7\18, 270.968
|7\18, 270.968
| rowspan="2" | 3\7, 300
| rowspan="2" |3\7, 300
|8\17, 331.034
|8\17, 331.034
|5\10, 352.941
|5\10, 352.941
|7\13, 381.{{Overline|81}}
|7\13, 381.818
|-
|-
| A mib
|2f
|Hb
|7\15, 323.077
|7\15, 323.077
|5\11, 315.789
|5\11, 315.789
|8\18, 309.677
|8\18, 309.677
| 7\17, 289.655
|7\17, 289.655
|4\10, 282.353
|4\10, 282.353
|5\13, 272.{{Overline|72}}
|5\13, 272.727
|-
|-
|A mi
|2
|H
|8\15, 369.231
|8\15, 369.231
| 6\11, 378.947
|6\11, 378.947
|10\18, 387.097
|10\18, 387.097
|4\7, 400
| 4\7, 400
| 10\17, 413.793
|10\17, 413.793
| 6\10, 423.529
|6\10, 423.529
|8\13, 436.{{Overline|36}}
|8\13, 436.364
|-
|-
|A mi#
|2#
|H#
|9\15, 415.385
|9\15, 415.385
| rowspan="2" | 7\11, 442.105
| rowspan="2" |7\11, 442.105
|12\18, 464.516
|12\18, 464.516
|5\7, 500
|5\7, 500
Line 1,149: Line 1,158:
|11\13, 600
|11\13, 600
|-
|-
|B fa utb
|3f
|Jbb
| 10\15, 461.538
|10\15, 461.538
|11\18, 425.806
| 11\18, 425.806
|4\7, 400
|4\7, 400
|9\17, 372.414
|9\17, 372.414
|5\10, 352.941
|5\10, 352.941
| 6\13, 327.{{Overline|27}}
|6\13, 327.273
|-
|-
|'''B fa ut'''
|'''3'''
|'''Jb'''
|'''11\15,''' '''507.692'''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|'''8\11,''' '''505.263'''
Line 1,166: Line 1,173:
|'''12\17,''' '''496.552'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.{{Overline|90}}'''
|'''9\13,''' '''490.909'''
|-
|-
|B fa ut#
|3#
|J
|12\15, 553.846
|12\15, 553.846
|9\11, 568.421
|9\11, 568.421
Line 1,176: Line 1,182:
|15\17, 620.690
|15\17, 620.690
|9\10, 635.294
|9\10, 635.294
| 12\13, 654.{{Overline|54}}
|12\13, 654.545
|-
|-
|B fa utx
| 3x
|J#
|13\15, 600
|13\15, 600
| rowspan="2" |10\11, 631.579
| rowspan="2" | 10\11, 631.579
|17\18, 658.064
|17\18, 658.064
|7\7, 700
|7\7, 700
|18\17, 744.828
|18\17, 744.828
|11\10, 776.471
|11\10, 776.471
|15\13, 818.{{Overline|18}}
|15\13, 818.182
|-
|-
|C sol reb
|4f
|Kb
| 14\15, 646.154
|14\15, 646.154
|16\18, 619.355
|16\18, 619.355
|6\7, 600
|6\7, 600
|14\17, 579.310
|14\17, 579.310
|8\10, 564.706
|8\10, 564.706
| 10\13, 545.{{Overline|45}}
|10\13, 545.455
|-
|-
!C sol re
!4
!K
!'''15\15,''' '''692.308'''
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
!'''11\11,''' '''694.737'''
Line 1,205: Line 1,208:
!'''17\17,''' '''703.448'''
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.'''{{Overline|09}}
!'''13\13,''' '''709.091'''
|-
|-
|C sol re#
| 4#
|K#
|16\15, 738.462
|16\15, 738.462
|12\11, 757.895
|12\11, 757.895
Line 1,215: Line 1,217:
|20\17, 827.586
|20\17, 827.586
|12\10, 847.059
|12\10, 847.059
|16\13, 872.{{Overline|72}}
|16\13, 872.727
|-
|-
|D la mib
|5
|Lb
|18\15, 830.769
|18\15, 830.769
|13\11, 821.053
|13\11, 821.053
|21\18, 812.903
|21\18, 812.903
|19\17, 786.207
|19\17, 786.207
|11\10, 776.471
| 11\10, 776.471
|14\13, 763.{{Overline|63}}
|14\13, 763.63
|-
|-
|'''D la mi'''
|'''5'''
|'''L'''
|'''19\15,''' '''876.923'''
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
|'''14\11,''' '''884.211'''
Line 1,234: Line 1,234:
|'''22\17,''' '''910.345'''
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.{{Overline|27}}'''
|'''17\13,''' '''927.273'''
|-
|-
|D la mi#
|5#
|L#
|20\15, 923.077
|20\15, 923.077
|15\11, 947.368
|15\11, 947.368
|25\18, 967.742
| 25\18, 967.742
| rowspan="2" |10\7, 1000
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|25\17, 1034.483
|15\10, 1058.824
|15\10, 1058.824
|20\13, 1090.{{Overline|90}}
|20\13, 1090.909
|-
|-
|E fa utb
|6f
|Mb
|22\15, 1015.385
|22\15, 1015.385
|16\11, 1010.526
|16\11, 1010.526
Line 1,253: Line 1,251:
|24\17, 993.103
|24\17, 993.103
|14\10, 988.235
|14\10, 988.235
|18\13, 981.{{Overline|81}}
|18\13, 981.818
|-
|-
|E fa ut
|6
|M
|23\15, 1061.538
|23\15, 1061.538
|17\11, 1073.684
|17\11, 1073.684
Line 1,263: Line 1,260:
|27\17, 1117.241
|27\17, 1117.241
|16\10, 1129.412
|16\10, 1129.412
|21\9, 1145.{{Overline|45}}
|21\9, 1145.455
|-
|-
|E fa ut#
|6#
|M#
|24\15, 1107.923
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
| rowspan="2" |18\11, 1136.842
|30\18, 1161.29
|30\18, 1161.290
|12\7, 1200
|12\7, 1200
|30\17, 1241.379
|30\17, 1241.379
|18\10, 1270.588
|18\10, 1270.588
| 24\13, 1309.{{Overline|09}}
|24\13, 1309.091
|-
|-
|F sol re utb
| 7f
| Nbb
|25\15, 1153.846
|25\15, 1153.846
|29\18, 1122.581
|29\18, 1122.581
| 11\7, 1100
|11\7, 1100
|26\17, 1075.862
|26\17, 1075.862
|15\10, 1058.824
|15\10, 1058.824
|19\13, 1036.{{Overline|36}}
|19\13, 1036.364
|-
|-
|'''F sol re ut'''
|'''7'''
|'''Nb'''
|'''26\15,''' '''1200'''
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
|'''19\11,''' '''1200'''
Line 1,294: Line 1,288:
|'''22\13,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|-
|F sol re ut#
|7#
|N
|27\15, 1246.154
|27\15, 1246.154
|20\11, 1263.158
|20\11, 1263.158
Line 1,302: Line 1,295:
|32\17, 1324.138
|32\17, 1324.138
|19\10, 1341.176
|19\10, 1341.176
|25\13, 1363.{{Overline|63}}
|25\13, 1363.636
|-
|-
| F sol re utx
|7x
|N#
|28\15, 1292.308
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
| rowspan="2" |21\11, 1326.318
Line 1,312: Line 1,304:
|35\17, 1448.275
|35\17, 1448.275
|21\10, 1482.353
|21\10, 1482.353
|28\13, 1527.{{Overline|27}}
|28\13, 1527.273
|-
|-
|G la mi reb
|8f
| Pb
|29\15, 1338.462
|29\15, 1338.462
|34\18, 1316.129
| 34\18, 1316.129
|13\7, 1300
|13\7, 1300
|31\17, 1282.759
|31\17, 1282.759
|18\10, 1270.588
|18\10, 1270.588
|23\13, 1254.{{Overline|54}}
|23\13, 1254.545
|-
|-
!G la mi re
! 8
!P
!30\15, 1384.615
!30\15, 1384.615
!22\11, 1389.473
!22\11, 1389.473
Line 1,331: Line 1,321:
!34\17, 1406.897
!34\17, 1406.897
!20\10, 1411.765
!20\10, 1411.765
!26\13, 1418.{{Overline|18}}
!26\13, 1418.182
|-
|-
|G la mi re#
|8#
|P#
|31\15, 1430.769
|31\15, 1430.769
| rowspan="2" |23\11, 1452.632
|23\11, 1452.632
|38\18, 1470.968
| 38\18, 1470.968
|15\7, 1500
| rowspan="2" |15\7, 1500
|37\17, 1531.034
|37\17, 1531.034
| 22\10, 1552.941
|22\10, 1552.941
|29\13, 1581.{{Overline|81}}
|29\13, 1581.818
|-
|-
|A fab
|9f
|Qbb
|32\15, 1476.923
|37\18, 1432.258
|14\7, 1400
|33\17, 1365.517
|19\10, 1341.175
| 24\13, 1309.{{Overline|09}}
|-
|A fa
| Qb
|33\15, 1523.077
|33\15, 1523.077
|24\11, 1515.789
|24\11, 1515.789
|39\18, 1509.677
|39\18, 1509.677
|15\7, 1500
| 36\17, 1489.655
|36\17, 1489.655
|21\10, 1482.759
|21\10, 1482.759
|27\13, 1472.{{Overline|72}}
|27\13, 1472.273
|-
|-
|'''A mi'''
|9
|'''Q'''
|'''34\15,''' '''1569.231'''
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
|'''25\11,''' '''1578.947'''
Line 1,370: Line 1,347:
|'''39\17,''' '''1613.793'''
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.{{Overline|36}}'''
|'''30\13,''' '''1636.364'''
|-
|-
|A mi#
|9#
|Q#
|35\15, 1615.385
|35\15, 1615.385
|26\11, 1642.105
|26\11, 1642.105
Line 1,382: Line 1,358:
|33\13, 1800
|33\13, 1800
|-
|-
|B sol fa utb
|Af
|Rb
| 37\15, 1707.692
|37\15, 1707.692
| 27\11, 1705.263
|27\11, 1705.263
|44\18, 1703.226
|44\18, 1703.226
|41\17, 1696.552
|41\17, 1696.552
|24\10, 1694.118
|24\10, 1694.118
|31\13, 1690.{{Overline|90}}
|31\13, 1690.909
|-
|-
| B sol fa ut
|A
|R
| 38\15, 1753.846
|38\15, 1753.846
|28\11, 1768.421
|28\11, 1768.421
|46\18, 1780.645
|46\18, 1780.645
Line 1,399: Line 1,373:
|44\17, 1820.690
|44\17, 1820.690
|26\10, 1835.294
|26\10, 1835.294
|34\13, 1854.{{Overline|54}}
|34\13, 1854.545
|-
|-
|B sol fa ut#
|A#
|R#
| 39\15, 1800
|39\15, 1800
| rowspan="2" |29\11, 1831.579
| rowspan="2" |29\11, 1831.579
|48\18, 1858.064
| 48\18, 1858.064
| 19\7, 1900
|19\7, 1900
|47\17, 1944.828
|47\17, 1944.828
|28\10, 1976.471
|28\10, 1976.471
|37\13, 2018.{{Overline|18}}
|37\13, 2018.182
|-
|-
|C la sol reb
|Ax
|Sbb
|40\15, 1846.154
|40\15, 1846.154
|47\18, 1819.355
|47\18, 1819.355
Line 1,418: Line 1,390:
|43\17, 1779.310
|43\17, 1779.310
|25\10, 1764.706
|25\10, 1764.706
|32\13, 1745.{{Overline|45}}
|32\13, 1745.545
|-
|-
|'''C la sol re'''
|'''Bf'''
|'''Sb'''
|'''41\15,''' '''1892.308'''
|'''41\15,''' '''1892.308'''
|'''30\11,''' '''1894.737'''
|'''30\11,''' '''1894.737'''
Line 1,428: Line 1,399:
|'''46\17,''' '''1903.448'''
|'''46\17,''' '''1903.448'''
|'''27\10,''' '''1905.882'''
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.{{Overline|09}}'''
|'''35\13,''' '''1909.091'''
|-
|-
|C la sol re#
|B
|S#
|42\15, 1938.462
|42\15, 1938.462
|31\11, 1957.895
|31\11, 1957.895
Line 1,437: Line 1,407:
|20\7, 2000
|20\7, 2000
|49\17, 2027.586
|49\17, 2027.586
|29\10, 2047.059
| 29\10, 2047.059
|38\13, 2072.{{Overline|72}}
|38\13, 2072.727
|-
|-
| C la sol rex
|B#
| Sx
|43\15, 1984.615
|43\15, 1984.615
| rowspan="2" |32\11, 2021.053
| rowspan="2" |32\11, 2021.053
Line 1,448: Line 1,417:
|52\17, 2151.725
|52\17, 2151.725
|31\10, 2188.235
|31\10, 2188.235
|41\13, 2236.{{Overline|36}}
|41\13, 2236.364
|-
|-
| D la mib
|Cf
|Tb
|44\15, 2030.769
|44\15, 2030.769
|52\18, 2012.903
|52\18, 2012.903
Line 1,457: Line 1,425:
|48\17, 1986.207
|48\17, 1986.207
|28\10, 1976.471
|28\10, 1976.471
|36\13, 1963.{{Overline|63}}
|36\13, 1963.636
|-
|-
!D la mi
!C
!T
!45\15, 2076.923
!45\15, 2076.923
!33\11, 2084.211
!33\11, 2084.211
Line 1,467: Line 1,434:
!51\17, 2110.345
!51\17, 2110.345
!30\10, 2117.647
!30\10, 2117.647
!39\13, 2127.{{Overline|27}}
!39\13, 2127.273
|-
|-
|D la mib
|C#
|T#
|46\15, 2123.077
|46\15, 2123.077
|34\11, 2147.368
|34\11, 2147.368
|56\15, 2167.742
|56\15, 2167.742
| rowspan="2" |22\7, 2200
| rowspan="2" |22\7, 2200
| 54\17, 2234.483
|54\17, 2234.483
| 32\10, 2258.824
|32\10, 2258.824
|42\13, 2090.{{Overline|90}}
|42\13, 2090.909
|-
|-
|E fa utb
|Df
|Ub
|48\15, 2215.385
|48\15, 2215.385
|35\11, 2210.526
|35\11, 2210.526
Line 1,486: Line 1,451:
|53\17, 2193.103
|53\17, 2193.103
|31\10, 2188.235
|31\10, 2188.235
|40\13, 2181.{{Overline|81}}
|40\13, 2181.818
|-
|-
|'''E fa ut'''
|'''D'''
|'''U'''
|'''49\15, 2261.538'''
|'''49\15, 2261.538'''
| '''36\11, 1073.684'''
|'''36\11, 1073.684'''
|'''59\18, 2283.871'''
|'''59\18, 2283.871'''
|'''23\7, 2300'''
|'''23\7, 2300'''
| '''56\17, 2317.241'''
|'''56\17, 2317.241'''
|'''33\10, 2329.412'''
|'''33\10, 2329.412'''
|'''43\13,''' '''2345.{{Overline|45}}'''
|'''43\13,''' '''2345.455'''
|-
|-
|E fa ut#
|D#
|U
|50\15, 2307.692
|50\15, 2307.692
| 37\11, 2336.842
|37\11, 2336.842
|61\18, 2361.290
|61\18, 2361.290
| rowspan="2" |24\7, 2400
| rowspan="2" |24\7, 2400
|59\17, 2441.379
|59\17, 2441.379
|35\10, 2470.588
|35\10, 2470.588
| 46\13, 2509.{{Overline|09}}
|46\13, 2509.091
|-
|-
|F sol re utb
|Ef
|Vb
|52\15, 2400
|52\15, 2400
| 38\11, 2400
|38\11, 2400
|62\18, 2400
|62\18, 2400
|58\17, 2400
|58\17, 2400
|34\10, 2400
|34\10, 2400
|44\13, 2400
| 44\13, 2400
|-
|-
|F sol re ut
|E
|V
|53\15, 2446.154
|53\15, 2446.154
|39\11, 2463.158
| 39\11, 2463.158
|64\18, 2477,419
|64\18, 2477,419
|25\7, 2500
|25\7, 2500
|61\17, 2524.138
|61\17, 2524.138
|36\10, 2541.176
|36\10, 2541.176
|47\13, 2563.{{Overline|63}}
|47\13, 2563.636
|-
|-
|F sol re ut#
|E#
| V#
|54\15, 2492.308
|54\15, 2492.308
| rowspan="2" |40\11, 2526.316
| rowspan="2" |40\11, 2526.316
Line 1,535: Line 1,495:
|64\17, 2648.275
|64\17, 2648.275
|38\10, 2682.353
|38\10, 2682.353
|50\13, 2727.{{Overline|27}}
|50\13, 2727.273
|-
|-
|G la mi reb
|Fff
| Wbb
| 55\15, 2538.462
|55\15,
| 65\18, 2516.129
2538.462
|65\18, 2516.129
|25\7, 2500
|25\7, 2500
|60\17, 2482.759
|60\17, 2482.759
|35\10, 2470.588
|35\10, 2470.588
| 45\13, 2454.{{Overline|54}}
|45\13, 2454.545
|-
|-
|'''G la mi re'''
|'''Ff'''
|'''Wb'''
|'''56\15, 2584.615'''
| '''56\15, 2584.615'''
|'''41\11, 2589.474'''
|'''41\11, 2589.474'''
|'''67\18, 2593.548'''
|'''67\18, 2593.548'''
Line 1,555: Line 1,512:
|'''63\17, 2606.897'''
|'''63\17, 2606.897'''
|'''37\10, 2611.765'''
|'''37\10, 2611.765'''
|'''48\13,''' '''2618.{{Overline|18}}'''
|'''48\13,''' '''2618.182'''
|-
|-
| G la mi re#
|F
|W
|57\15, 2630.769
|57\15, 2630.769
|42\11, 2652.632
|42\11, 2652.632
|69\18, 2670.968
|69\18, 2670.968
| 27\7, 2700
|27\7, 2700
| 66\17, 2731.034
|66\17, 2731.034
|39\10, 2752.941
|39\10, 2752.941
|51\13, 2781.{{Overline|81}}
|51\13, 2781.818
|-
|-
|G la mi rex
| F#
|W#
| rowspan="2" |58\15, 2676.923
| rowspan="2" |58\15, 2676.923
|43\11, 2715.789
|43\11, 2715.789
|71\18, 2748.387
|71\18, 2748.387
|28\7, 2800
| 28\7, 2800
|69\17, 2855.172
|69\17, 2855.172
|41\10, 2894.118
|41\10, 2894.118
|54\13, 2945.{{Overline|45}}
|54\13, 2945.455
|-
|-
|A fab
|0ff, Gff
|Xbb
|42\11, 2652.632
|42\11, 2652.632
|68\18, 2632.258
|68\18, 2632.258
|26\7, 2600
|26\7, 2600
| 62\17, 2565.517
|62\17, 2565.517
|36\10, 2541.176
|36\10, 2541.176
|46\13, 2509.{{Overline|09}}
|46\13, 2509.091
|-
|-
|A fa
|0f, Gf
|Xb
|59\15, 2723.077
|59\15, 2723.077
|43\11, 2715.789
|43\11, 2715.789
| 70\18, 2709.677
|70\18, 2709.677
|27\7, 2700
|27\7, 2700
| 65\17, 2689.552
|65\17, 2689.552
|38\10, 2682.353
|38\10, 2682.353
| 49\13, 2672.{{Overline|72}}
|49\13, 2672.273
|-
|-
!A mi
!0, G
!X
!60\15, 2769.231
!60\15, 2769.231
!44\11, 2778.947
!44\11, 2778.947
Line 1,604: Line 1,556:
!68\17, 2813.793
!68\17, 2813.793
!40\10, 2823.529
!40\10, 2823.529
!52\13, 2836.{{Overline|36}}
!52\13, 2836.364
|}
 
{| class="wikitable"
|+Cents
!Notation
!Supersoft
!Soft
! Semisoft
! Basic
!Semihard
!Hard
!Superhard
|-
|-
|A mi#
!Guidotonic
|X#
!~15edf
|61\15
!~11edf
2815; 2.6
!~18edf
|45\11
!~7edf
2842; 9.5
!~17edf
|74\18
!~10edf
2864; 1.9375
!~13edf
| rowspan="2" |29\7
2900
|71\17
2937; 1, 13.5
|42\10
2964; 1, 2.4
|55\13
3000
|-
|-
|B sol fab
|F ut#
| Yb
|1\15, 46.154
|63\15
|1\11, 63.158
2907; 1, 2, 4
|2\18, 77.419
|46\11
| rowspan="2" |1\7, 100
2905; 3.8
|3\17, 124.138
|75\18
|2\10, 141.176
2903; 4, 2, 3
|3\13, 163.636
| 70\17
2896; 1.8125
|41\10
2894; 8.5
|53\13
2890.{{Overline|90}}
|-
|'''B sol fa'''
|'''Y'''
|'''64\15'''
'''2953; 1, 5.5'''
|'''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#
|G reb
|Y#
|3\15, 138.462
|65\15
|2\11. 126.316
3000
|3\18, 116.129
| 48\11
|2\17, 82.759
3031; 1, 1.375
|1\10, 70.588
| 79\18
|1\13, 54.545
3058; 15.5
| rowspan="2" |31\7
3100
|76\17
3144; 1, 4.8
|45\10
3176: 2, 8
| 59\13
3218.{{Overline|18}}
|-
|-
|C la solb
|'''G re'''
| Zb
|'''4\15,''' '''184.615'''
|67\15
|'''3\11,''' '''189.474'''
3092; 3, 4
|'''5\18,''' '''193.548'''
|49\11
|'''2\7,''' '''200'''
3094; 1, 2.8
|'''5\17,''' '''206.897'''
|80\18
|'''3\10,''' '''211.765'''
3096; 1, 3, 2, 3
|'''4\13,''' '''218.182'''
| 75\17
3103; 2, 2, 6
|44\10
3105; 1, 7.5
|57\13
3109.{{Overline|09}}
|-
|-
| C la sol
|G re#
|Z
|5\15, 230.769
| 68\15
|4\11, 252.632
3138; 2, 6
|7\18, 270.968
|50\11
| rowspan="2" |3\7, 300
3157; 1, 8.5
|8\17, 331.034
|82\18
|5\10, 352.941
3174; 5, 6
|7\13, 381.818
|32\7
3200
|78\17
3227; 1, 1, 2.4
|46\10
3247; 17
|60\13
3272.{{Overline|72}}
|-
|-
|C la sol#
|A mib
|Z#
|7\15, 323.077
|69\15
|5\11, 315.789
3184; 1.625
|8\18, 309.677
| rowspan="2" |51\11
|7\17, 289.655
3221: 19
|4\10, 282.353
|84\18
|5\13, 272.727
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 labb
|Ab
|70\15
3230; 1.3
|83\18
3212;  1, 9, 3
|32\7
3200
|77\17
3186; 4, 3
| 45\10
3176: 2, 8
| 58\13
3163.{{Overline|63}}
|-
|-
|'''D lab'''
|A mi
|'''A'''
|8\15, 369.231
|'''71\15'''
| 6\11, 378.947
'''3276; 1, 12'''
|10\18, 387.097
|'''52\11'''
|4\7, 400
'''3284; 4.75'''
|10\17, 413.793
|'''85\18'''
|6\10, 423.529
'''3290; 3.1'''
|8\13, 436.364
|'''33\7'''
'''3300'''
|'''80\17'''
'''3310; 2.9'''
|'''47\10'''
'''3317; 1, 1, 1.2'''
|'''61\13'''
'''3327.{{Overline|27}}'''
|-
|-
|D la
| A mi#
|A#
|9\15, 415.385
|72\15
| rowspan="2" |7\11, 442.105
3323; 13
|12\18, 464.516
|53\11
|5\7, 500
3347; 2, 1.4
|13\17, 537.069
|87\18
|8\10, 564.706
3367; 1, 2.875
|11\13, 600
|34\7
3400
|83\17
3434; 2, 14
|49\10
3458; 1, 4, 1.5
|64\13
3490.{{Overline|90}}
|-
|-
|D la#
|B fa utb
|Ax
|10\15, 461.538
|73\15
|11\18, 425.806
3369; 4, 3
|4\7, 400
| rowspan="2" |54\15
|9\17, 372.414
3410; 1.9
|5\10, 352.941
|89\18
|6\13, 327.273
3445; 6.2
|35\7
3500
|86\17
3558; 1, 1, 1, 1.75
|51\10
3600
|67\13
3654.{{Overline|54}}
|-
|-
|F utb
|'''B fa ut'''
|Bb
|'''11\15,''' '''507.692'''
| 74\15
|'''8\11,''' '''505.263'''
3415; 2.6
|'''13\18,''' '''503.226'''
|88\18
|'''5\7, 500'''
3406; 2, 4, 1.5
|'''12\17,''' '''496.552'''
|34\7
|'''7\10,''' '''494.118'''
3400
|'''9\13,''' '''490.909'''
|82\17
3393; 9, 1.5
|48\10
3388; 4, 4
|62\13
3381.{{Overline|81}}
|-
!F ut
! B
!75\15
3461; 1, 1, 6
!55\11
3473; 1, 2, 6
! 90\18
3483; 1, 6.75
!35\7
3500
!85\17
3517; 4, 7
!50\10
3529; 2, 2, 3
!65\13
3545.{{Overline|45}}
|-
|-
|F ut#
|B fa ut#
|B#
|12\15, 553.846
| 76\15
|9\11, 568.421
3507; 1, 2, 4
|15\18, 580.645
|56\15
|6\7, 600
3536; 1, 5, 3
|15\17, 620.690
|92\18
|9\10, 635.294
3561: 3, 2, 4
|12\13, 654.545
| rowspan="2" |36\7
3600
|88\17
3641; 2, 1, 1.75
|52\10
3670; 1.7
|68\13
3709.{{Overline|09}}
|-
|-
|G reb
|B fa utx
|Cb
| 13\15, 600
| 78\15
| rowspan="2" |10\11, 631.579
3600
|17\18, 658.064
|57\15
|7\7, 700
3600
|18\17, 744.828
|93\18
|11\10, 776.471
3600
|15\13, 818.182
|87\17
3600
|51\10
3600
|66\13
3600
|-
|-
|'''G re'''
|C sol re utb
|'''C'''
| 14\15, 646.154
|'''79\15'''
|16\18, 619.355
'''3646; 6.5'''
|6\7, 600
|'''58\11'''
|14\17, 579.310
'''3663; 6, 3'''
|8\10, 564.706
|'''95\18'''
|10\13, 545.455
'''3677; 2, 2.6'''
|'''37\7'''
'''3700'''
|'''90\17'''
'''3724; 7, 4'''
|'''53\17'''
'''3741; 5, 1.5'''
|'''69\13'''
'''3763.{{Overline|63}}'''
|-
|-
|G re#
!C sol re ut
|C#
!'''15\15,''' '''692.308'''
|80\15
!'''11\11,''' '''694.737'''
3692; 4, 3
!'''18\18,''' '''696.774'''
|59\11
!7\7, 700
3726; 3, 6
!'''17\17,''' '''703.448'''
|97\18
!'''10\10,''' '''705.882'''
3755; 5.2
!'''13\13,''' '''709.091'''
| rowspan="2" |38\7
3800
|93\17
3848; 3.625
|55\17
3882; 2, 1.2
|72\13
3927.{{Overline|27}}
|-
|-
|A mib
|C sol re ut#
| Db
|16\15, 738.462
|82\15
|12\11, 757.895
3784; 1.625
|20\18, 774.194
|60\11
| rowspan="2" |8\8, 800
3789; 2,9
|20\17, 827.586
|98\18
|12\10, 847.059
3793; 1, 1, 4, 1.5
|16\13, 872.727
|92\17
3806; 1, 8, 1.5
| 54\17
3811; 1, 3, 4
|70\13
3818.{{Overline|18}}
|-
|-
|A mi
|D la mi reb
|D
|18\15, 830.769
|83\15
|13\11, 821.053
3830, 1.3
|21\18, 812.903
|61\11
|19\17, 786.207
3852; 1, 1, 1.4
|11\10, 776.471
|100\18
|14\13, 763.63
3870; 1, 30
|39\7
3900
|95\17
3931; 29
|56\17
3952; 1, 16
| 73\13
3981.{{Overline|81}}
|-
|-
|A mi#
|'''D la mi re'''
|D#
|'''19\15,''' '''876.923'''
|84\15
|'''14\11,''' '''884.211'''
3876; 1, 12
|'''23\18,''' '''890.323'''
| rowspan="2" |62\11
|'''9\5,''' '''900'''
3915; 1, 3.75
|'''22\17,''' '''910.345'''
|102\18
|'''13\10,''' '''917.647'''
3948; 2, 1, 1.4
|'''17\13,''' '''927.273'''
|40\7
4000
|98\17
4055; 5.8
|58\10
4094; 8.5
|76\13
4145.{{Overline|45}}
|-
|-
|B fa utb
|D la mi re#
|Ebb
|20\15, 923.077
|85\15
| rowspan="2" |15\11, 947.368
3923; 13
|25\18, 967.742
|101\18
|10\7, 1000
3909; 1, 2.1
|25\17, 1034.483
|39\7
|15\10, 1058.824
3900
|20\13, 1090.909
|94\17
3889; 1, 1.9
|55\10
3882; 2, 1.2
|71\13
3872.{{Overline|72}}
|-
|-
|'''B fa ut'''
|E fa utb
|'''Eb'''
|21\15, 969.231
|'''86\15'''
|24\18, 929.032
'''3969; 4, 3'''
| 9\5, 900
|'''63\11'''
|21\17, 868.966
'''3978; 1, 3.75'''
|12\10, 847.059
|'''103\18'''
|15\13, 818.182
'''3987; 10, 3'''
|'''40\7'''
'''4000'''
|'''97\17'''
'''4013; 1, 3, 1.2'''
|'''57\10'''
'''4023; 1, 1, 8'''
|'''74\13'''
'''4036.{{Overline|36}}'''
|-
|-
|B fa ut#
|E fa ut
| E
| 22\15, 1015.385
|87\15
|16\11, 1010.526
4015; 2.6
|26\18, 1006.452
|64\11
|10\7, 1000
4042; 9.5
|24\17, 993.103
|105\18
|14\10, 988.235
4064; 1.9375
|18\13, 981.818
|41\7
4100
| 100\17
4137; 1, 13.5
|59\10
4164; 1, 2.4
|77\13
4200
|-
|-
| B fa utx
|E si mi re
|E#
|23\15, 1061.538
|88\15
|17\11, 1073.684
4061; 1, 1, 6
|28\18, 1083.871
| rowspan="2" |65\11
|11\7, 1100
4105; 3.8
|27\17, 1117.241
|107\18
|16\10, 1129.412
4141; 1, 14.5
|21\9, 1145.455
|42\7
4200
|103\17
4262; 14.5
|61\10
4305; 1, 7.5
|80\13
4363.{{Overline|63}}
|-
|-
| C sol reb
| E si mi re#
|Fb
|24\15, 1107.923
|89\15
| rowspan="2" |18\11, 1136.842
4107; 1.3
|30\18, 1161.29
|106\18
|12\7, 1200
4103; 4, 2, 3
|30\17, 1241.379
| 41\7
| 18\10, 1270.588
4100
|24\13, 1309.091
|99\17
4096; 1.8125
|58\10
4094; 8.5
|75\13
4090.{{Overline|90}}
|-
|-
!C sol re
|F sol fa ut reb
!F
|25\15, 1153.846
!90\15
|29\18, 1122.581
4153; 1, 5.5
|11\7, 1100
!66\11
|26\17, 1075.862
4168; 2.375
|15\10, 1058.824
!108\18
|19\13, 1036.364
4180; 1.55
!42\7
4200
!102\17
4220; 1.45
!60\10
4235; 3.4
!78\13
4254.{{Overline|54}}
|}
==Intervals==
{| class="wikitable"
!Generators
!Sesquitave notation
!Interval category name
!Generators
!Notation of 3/2 inverse
!Interval category name
|-
|-
| colspan="6" |The 4-note MOS has the following intervals (from some root):
|'''F sol fa ut re'''
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|-
|0
|F sol fa ut re#
|Do, Sol
|27\15, 1246.154
|perfect unison
|20\11, 1263.158
|0
|33\18, 1277.419
|Do, Sol
|13\7, 1300
|sesquitave (just fifth)
|32\17, 1324.138
| 19\10, 1341.176
| 25\13, 1363.636
|-
|-
|1
|F sol fa ut rex
|Fa, Do
|28\15, 1292.308
|perfect fourth
| rowspan="2" |21\11, 1326.318
| -1
|35\18, 1354.834
|Re, La
| 14\7, 1400
|perfect second
|35\17, 1448.275
|21\10, 1482.353
|28\13, 1527.273
|-
|-
|2
|G la sol re mib
|Mib, Sib
| 29\15, 1338.462
|minor third
|34\18, 1316.129
| -2
| 13\7, 1300
|Mi, Si
|31\17, 1282.759
|major third
|18\10, 1270.588
|23\13, 1254.545
|-
|-
|3
!G la sol re mi
|Reb, Lab
!30\15, 1384.615
|diminished second
!22\11, 1389.473
| -3
!36\18, 1393.548
|Fa#, Do#
!14\7, 1400
|augmented fourth
!34\17, 1406.897
!20\10, 1411.765
!26\13, 1418.182
|-
|-
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|G la sol re mi#
|31\15, 1430.769
|23\11, 1452.632
|38\18, 1470.968
| rowspan="2" |15\7, 1500
|37\17, 1531.034
|22\10, 1552.941
|29\13, 1581.818
|-
|-
|4
|A si la mi fab
|Dob, Solb
|33\15, 1523.077
|diminished sesquitave
| 24\11, 1515.789
| -4
|39\18, 1509.677
|Do#, Sol#
|36\17, 1489.655
|augmented unison (chroma)
|21\10, 1482.759
| 27\13, 1472.273
|-
|-
|5
|'''A si la mi fa'''
|Fab, Dob
|'''34\15,''' '''1569.231'''
| diminished fourth
|'''25\11,''' '''1578.947'''
| -5
|'''41\18,''' '''1587.097'''
|Re#, La#
|'''16\7,''' '''1600'''
|augmented second
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.364'''
|-
|-
|6
|A si la mi fa#
|Mibb, Sibb
| 35\15, 1615.385
|diminished third
| rowspan="2" |26\11, 1642.105
| -6
|43\18, 1664.516
|Mi#, Si#
|17\7, 1700
|augmented third
|42\17, 1737.069
|}
| 25\10, 1764.706
|33\13, 1800
==Genchain==
|-
|B sol fa utb
The generator chain for this scale is as follows:
|36\61, 1661.538
{| class="wikitable"
|42\18, 1625.806
|Mibb
|16\7, 1600
|38\29, 1572.414
Sibb
|22\10, 1552.941
|Fab
|28\13, 1527.273
|-
Dob
|B sol fa ut
|Dob
|37\15, 1707.692
|27\11, 1705.263
Solb
| 44\18, 1703.226
|Reb
| 17\7, 1700
|41\17, 1696.552
Lab
|24\10, 1694.118
|Mib
|31\13, 1690.909
|-
Sib
|B si
|Fa
|38\15, 1753.846
| 28\11, 1768.421
Do
|46\18, 1780.645
|Do
|18\7, 1800
|44\17, 1820.690
Sol
|26\10, 1835.294
|Re
|34\13, 1854.545
|-
La
|B si
|Mi
|39\15, 1800
| rowspan="2" |29\11, 1831.579
Si
|48\18, 1858.064
|Fa#
|19\7, 1900
|47\17, 1944.828
Do#
|28\10, 1976.471
|Do#
|37\13, 2018.182
|-
Sol#
|C la sol re utb
|Re#
|40\15, 1846.154
|47\18, 1819.355
La#
| 18\7, 1800
|Mi#
| 43\17, 1779.310
|25\10, 1764.706
Si#
|32\13, 1745.545
|-
|'''C la sol re ut'''
|'''41\15,''' '''1892.308'''
|'''30\11,''' '''1894.737'''
|'''49\18,''' '''1896.774'''
|'''19\7, 1900'''
|'''46\17,''' '''1903.448'''
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
|-
|C la sol re ut#
|42\15, 1938.462
|31\11, 1957.895
|51\18, 1974.194
|20\7, 2000
|49\17, 2027.586
| 29\10, 2047.059
|38\13, 2072.727
|-
|-
|d3
|C la sol re utx
|d4
| rowspan="2" |43\15, 1984.615
|d5
|32\11, 2021.053
|d2
|53\18, 2051.612
|m3
|21\7, 2100
|P4
|52\17, 2151.725
|P1
|31\10, 2188.235
|P2
|41\13, 2236.364
|M3
|A4
|A1
|A2
|A3
|}
==Modes==
The mode names are based on the species of fifth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
|-
|-
!name
|D fa la mi reb
!pattern
|31\11, 1957.895
!notation
|50\18, 1935.484
!2nd
|19\7, 1900
!3rd
|45\17, 1862.069
!4th
|26\10, 1835.294
|33\13, 1800
|-
|-
|Lydian
|D fa la mi re
|LLLs
|44\15, 2030.769
|<nowiki>3|0</nowiki>
|32\11, 2021.053
|P
|52\18, 2012.903
|M
|20\7, 2000
|A
|48\17, 1986.207
|28\10, 1976.471
|36\13, 1963.636
|-
!D si la mi re
!45\15, 2076.923
!33\11, 2084.211
!54\18, 2090.323
!21\7, 2100
! 51\17, 2110.345
!30\10, 2117.647
!39\13, 2127.273
|-
|-
|Major
|D si la mi re#
|LLsL
|46\15, 2123.077
|<nowiki>2|1</nowiki>
| rowspan="2" |34\11, 2147.368
|P
|56\18, 2167.742
|M
|22\7, 2200
|P
|54\17, 2234.483
| 32\10, 2258.824
|42\13, 2090.909
|-
|-
|Minor
|E fab
|LLsL
|47\26, 2169.231
|<nowiki>1|2</nowiki>
|55\16, 2129.032
|P
|21\7, 2100
|m
|50\17, 2068.966
|P
|29\10, 2047.059
|37\13, 2018.182
|-
|-
|Phrygian
|E fa
|sLLL
|48\15, 2215.385
|<nowiki>0|3</nowiki>
|35\11, 2210.526
|d
|57\18, 2206.452
|m
|23\7, 2300
|P
|53\17, 2193.103
|}
|31\10, 2188.235
|40\13, 2181.818
==Temperaments==
|-
|E si mi
The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
|49\15, 2261.538
==='''Napoli-Meantone'''===
|36\11, 1073.684
|59\18, 2283.871
[[Subgroup]]: 3/2.6/5.8/5
|24\7, 2400
|56\17, 2317.241
[[Comma]] list: [[81/80]]
|33\10, 2329.412
 
|43\13, 2345.455
[[POL2]] generator: ~9/8 = 192.6406¢
|-
 
|E si mi#
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
|50\15, 2307.692
 
| rowspan="2" |37\11, 2336.842
[[Optimal ET sequence]]: ~(7edf, 11edf, 18edf)
|61\18, 2361.290
==='''Napoli-Archy'''===
| rowspan="2" |23\7, 2300
| 59\17, 2441.379
[[Subgroup]]: 3/2.7/6.14/9
|35\10, 2470.588
|46\13, 2509.091
[[Comma]] list: [[64/63]]
|-
 
|F sol fa utb
[[POL2]] generator: ~8/7 = 218.6371¢
|51\15, 2353.846
 
|60\18, 2322.581
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
|55\17, 2275.862
 
|32\10, 2258.824
[[Optimal ET sequence]]: ~(7edf, 10edf, 13edf, 16edf)
|41\13, 2236.364
===Scale tree===
|-
|F sol fa ut
The spectrum looks like this:
|52\15, 2400
{| class="wikitable"
|38\11, 2400
! colspan="3" |Generator
|62\18, 2400
|24\7, 2400
(bright)
|58\17, 2400
!Cents
|34\10, 2400
!L
|44\13, 2400
!s
!L/s
!Comments
|-
|-
|1\4
|F sol fa ut#
|
|53\15, 2446.154
|
|39\11, 2463.158
|171.429
|64\18, 2477,419
|1
| rowspan="2" |25\7, 2500
|1
|61\17, 2524.138
|1.000
|36\10, 2541.176
|Equalised
|47\13, 2563.636
|-
|-
|6\23
|G la sol reb
|
|55\15, 2538.462
|
|40\11, 2526.316
|180.000
|65\18, 2516.129
|6
|60\17, 2482.759
|5
|35\10, 2470.588
|1.200
|45\13, 2454.545
|
|-
|-
|5\19
|'''G la sol re'''
|
|'''56\15, 2584.615'''
|
|'''41\11, 2589.474'''
|181.{{Overline|81}}
|'''67\18, 2593.548'''
|5
|'''26\7, 2600'''
|4
|'''63\17, 2606.897'''
|1.250
|'''37\10, 2611.765'''
|
|'''48\13,''' '''2618.182'''
|-
|-
|
|G la sol re#
|14\53
|57\15, 2630.769
|
|42\11, 2652.632
|182.609
|69\18, 2670.968
|14
| rowspan="2" |27\7, 2700
|11
|66\17, 2731.034
|1.273
|39\10, 2752.941
|
|51\13, 2781.818
|-
|A si la mib
|59\15, 2723.077
|43\11, 2715.789
|70\18, 2709.677
|65\17, 2689.552
|38\10, 2682.353
|49\13, 2672.273
|-
!A si la mi
!60\15, 2769.231
!44\11, 2778.947
!72\18, 2787.097
!28\7, 2800
!68\17, 2813.793
!40\10, 2823.529
!52\13, 2836.364
|-
|-
|
|A si la mi#
|9\34
|61\15, 2815.385
|
| rowspan="2" |45\11, 2842.105
| 183.051
| 74\18, 2864.516
|9
|29\7, 2900
|7
|71\17, 2937.069
| 1.286
|42\10, 2964.706
|
|55\13, 3000
|-
|-
|4\15
|B fab
|
|62\15, 2861.538
|
|73\18, 2825.806
|184.615
| 28\7, 2800
|4
|67\17, 2772.414
|3
|39\10, 2752.941
|1.333
|50\13, 2727.273
|
|-
|-
|
|B fa
|11\41
|63\15, 2907.692
|
|46\11, 2905.263
|185.915
|75\18, 2903.226
|11
|29\7, 2900
|8
|70\17, 2896.552
|1.375
|41\10, 2894.118
|
|53\13, 2890.909
|-
|'''B si'''
|'''64\15, 2953.846'''
|'''47\11, 2968.421'''
|'''77\18, 2980.645'''
|'''30\7, 3000'''
|'''73\17, 3020.690'''
|'''43\10, 3035.294'''
|'''56\13, 3054.545'''
|-
|B si#
|65\15, 3000
|48\11, 3031.579
|79\18, 3058.064
| rowspan="2" |31\7, 3100
|76\17, 3144.828
|45\10, 3176.471
|59\13, 3218.182
|-
|-
|
|C solb
|7\26
|67\15, 3092.308
|
|49\11, 3094.737
|186.{{Overline|6}}
|80\18, 3096.774
|7
|75\17, 3103.448
|5
|44\10, 3105.882
|1.400
|57\13, 3109.091
|
|-
|-
|
|C sol
|10\37
|68\15, 3138.462
|
|50\11, 3157.895
|187.5
| 82\18, 3174.194
|10
|32\7, 3200
| 7
|78\17, 3227.586
| 1.429
| 46\10, 3247.059
|
|60\13, 3272.273
|-
|-
|
|C sol#
|13\48
| 69\15, 3184.615
|
| rowspan="2" |51\11, 3221.053
| 187.952
|84\18, 3251.612
|13
|33\7, 3300
|9
|81\17, 3351.725
|1.444
|48\10, 3388.235
|
|63\13, 3436.364
|-
|-
|
|D labb
|16\59
|70\15, 3230.769
|
|83\18, 3212.903
|188.253
|32\7, 3200
|16
|77\17, 3186.207
|11
|45\10, 3176.471
|1.455
|58\13, 3163.636
|
|-
|'''D lab'''
|'''71\15,''' '''3276.923'''
|'''52\11,''' '''3284.211'''
|'''85\18,''' '''3290.323'''
|'''33\7, 3300'''
|'''80\17,''' '''3310.345'''
|'''47\10,''' '''3317.647'''
|'''61\13,''' '''3327.{{Overline|27}}'''
|-
|-
|3\11
|D la
|
|72\15, 3323.077
|
|53\11, 3347.368
|189.474
|87\18, 3367.742
|3
|34\7, 3400
|2
|83\17, 3434.583
|1.500
|49\10, 3458.824
| Napoli-Meantone starts here
|64\13, 3490.909
|-
|-
|
|D la#
|14\51
|73\15, 3369.231
|
| rowspan="2" |54\11, 3410.625
|190.{{Overline|90}}
|89\18, 3445.162
|14
|35\7, 3500
|9
|86\17, 3558.621
|1.556
|51\10, 3600
|
|67\13, 3654.545
|-
|-
|
|F utb
|11\40
|74\15, 3415.385
|
|88\18, 3406.452
|191.304
|34\7, 3400
|11
|82\17, 3393.103
|7
|48\10, 3388.235
| 1.571
|62\13, 3381.818
|
|-
|-
|
!F ut
|8\29
!75\15, 3461.538
|
!55\11, 3473.684
|192.000
!90\18, 3483.871
|8
!35\7, 3500
|5
!85\17, 3517.241
|1.600
!50\10, 3529.412
|
!65\13, 3545.455
|}
 
{| class="wikitable"
|+Cents
!Notation
!Supersoft
!Soft
! Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
|-
|
!Subdozenal
|5\18
!~15edf
|
!~11edf
|193.548
!~18edf
|5
!~7edf
|3
!~17edf
|1.667
!~10edf
|
!~13edf
|-
|-
|
|F#
|
|1\15, 46.154
|12\43
|1\11, 63.158
|194.{{Overline|594}}
|2\18, 77.419
|12
| rowspan="2" |1\7, 100
|7
|3\17, 124.138
|1.714
|2\10, 141.176
|
|3\13, 163.636
|-
|-
|
|Gb, Ge
|7\25
|3\15, 138.462
|
|2\11. 126.316
|195.348
|3\18, 116.129
|7
|2\17, 82.759
|4
|1\10, 70.588
|1.750
|1\13, 54.545
|
|-
|-
|
|'''G'''
|9\32
|'''4\15,''' '''184.615'''
|
|'''3\11,''' '''189.474'''
|196.{{Overline|36}}
|'''5\18,''' '''193.548'''
|9
|'''2\7,''' '''200'''
|5
|'''5\17,''' '''206.897'''
|1.800
|'''3\10,''' '''211.765'''
|
|'''4\13,''' '''218.182'''
|-
|-
|
|G#
|11\39
|5\15, 230.769
|
|4\11, 252.632
|197.015
|7\18, 270.968
|11
| rowspan="2" |3\7, 300
|6
|8\17, 331.034
|1.833
|5\10, 352.941
|
|7\13, 381.818
|-
|-
|
|Hb, He
|13\46
|7\15, 323.077
|
|5\11, 315.789
|197.468
|8\18, 309.677
|13
|7\17, 289.655
|7
|4\10, 282.353
|1.857
|5\13, 272.727
|
|-
|-
|
|H
| 15\53
|8\15, 369.231
|
|6\11, 378.947
|197.802
|10\18, 387.097
|15
|4\7, 400
|8
|10\17, 413.793
|1.875
|6\10, 423.529
|
|8\13, 436.364
|-
|-
|
|H#
|17\60
|9\15, 415.385
|
| rowspan="2" |7\11, 442.105
|198.058
|12\18, 464.516
|17
|5\7, 500
|9
|13\17, 537.069
|1.889
|8\10, 564.706
|
|11\13, 600
|-
|-
|
|Jbb, Jee
|19\67
|10\15, 461.538
|
|11\18, 425.806
|198.261
|4\7, 400
|19
|9\17, 372.414
|10
|5\10, 352.941
|1.900
|6\13, 327.273
|
|-
|-
|
|'''Jb, Je'''
|21\74
|'''11\15,''' '''507.692'''
|
|'''8\11,''' '''505.263'''
|198.425
|'''13\18,''' '''503.226'''
|21
|'''5\7, 500'''
|11
|'''12\17,''' '''496.552'''
|1.909
|'''7\10,''' '''494.118'''
|
|'''9\13,''' '''490.909'''
|-
|-
|
|J
|23\81
|12\15, 553.846
|
|9\11, 568.421
|198.561
|15\18, 580.645
|23
|6\7, 600
|12
|15\17, 620.690
|1.917
|9\10, 635.294
|
|12\13, 654.545
|-
|-
|
|J#
|25\88
|13\15, 600
|
| rowspan="2" |10\11, 631.579
|198.675
|17\18, 658.064
|25
|7\7, 700
|13
|18\17, 744.828
|1.923
|11\10, 776.471
|
|15\13, 818.182
|-
|-
|
|Kb, Ke
|27\95
|14\15, 646.154
|
|16\18, 619.355
|198.773
|6\7, 600
|27
|14\17, 579.310
|14
|8\10, 564.706
|1.929
|10\13, 545.455
|
|-
|-
|
!K
|29\102
!'''15\15,''' '''692.308'''
|
!'''11\11,''' '''694.737'''
| 198.857
!'''18\18,''' '''696.774'''
|29
!7\7, 700
|15
!'''17\17,''' '''703.448'''
|1.933
!'''10\10,''' '''705.882'''
|
!'''13\13,''' '''709.091'''
|-
|-
|
|K#
|31\109
|16\15, 738.462
|
|12\11, 757.895
|198.930
|20\18, 774.194
| 31
| rowspan="2" |8\8, 800
|16
|20\17, 827.586
|1.9375
|12\10, 847.059
|
|16\13, 872.727
|-
|-
|
|Lb, Le
|33\116
|18\15, 830.769
|
|13\11, 821.053
|198.995
|21\18, 812.903
|33
|19\17, 786.207
| 17
|11\10, 776.471
|1.941
|14\13, 763.63
|
|-
|-
|2\7
|'''L'''
|
|'''19\15,''' '''876.923'''
|
|'''14\11,''' '''884.211'''
|199.009
|'''23\18,''' '''890.323'''
| 2
|'''9\5,''' '''900'''
|1
|'''22\17,''' '''910.345'''
|2.000
|'''13\10,''' '''917.647'''
|Napoli-Meantone ends, Napoli-Pythagorean begins
|'''17\13,''' '''927.273'''
|-
|-
|
|L#
|17\59
|20\15, 923.077
|
| rowspan="2" |15\11, 947.368
| 200
|25\18, 967.742
|17
|10\7, 1000
|8
|25\17, 1034.483
|2.125
|15\10, 1058.824
|
|20\13, 1090.909
|-
|-
|
|Mbb, Mee
|15\52
|21\15, 969.231
|
|24\18, 929.032
|201.{{Overline|9801}}
|9\5, 900
|15
|21\17, 868.966
|7
|12\10, 847.059
|2.143
|15\13, 818.182
|
|-
|-
|
|Mb, Me
|13\45
|22\15, 1015.385
|
|16\11, 1010.526
|202.247
|26\18, 1006.452
|13
|10\7, 1000
|6
|24\17, 993.103
|2.167
|14\10, 988.235
|
|18\13, 981.818
|-
|-
|
|M
|11\38
|23\15, 1061.538
|
|17\11, 1073.684
|202.597
|28\18, 1083.871
|11
|11\7, 1100
|5
|27\17, 1117.241
|2.200
|16\10, 1129.412
|
|21\9, 1145.455
|-
|M#
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
|30\18, 1161.29
|12\7, 1200
|30\17, 1241.379
|18\10, 1270.588
|24\13, 1309.091
|-
|-
|
|Nbb, Nee
|9\31
|25\15, 1153.846
|
|29\18, 1122.581
|203.077
|11\7, 1100
|9
|26\17, 1075.862
|4
|15\10, 1058.824
|2.250
|19\13, 1036.364
|
|-
|-
|
|'''Nb, Ne'''
|7\24
|'''26\15,''' '''1200'''
|
|'''19\11,''' '''1200'''
|203.774
|'''31\18,''' '''1200'''
|7
|'''12\7, 1200'''
|3
|'''29\17,''' '''1200'''
|2.333
|'''17\10,''' '''1200'''
|
|'''22\13,''' '''1200'''
|-
|-
|
|N
|
|27\15, 1246.154
| 12\41
|20\11, 1263.158
|204.878
|33\18, 1277.419
|12
|13\7, 1300
| 5
|32\17, 1324.138
|2.400
|19\10, 1341.176
|
|25\13, 1363.636
|-
|-
|
|N#
|5\17
|28\15, 1292.308
|
| rowspan="2" |21\11, 1326.318
|205.714
|35\18, 1354.834
|5
|14\7, 1400
|2
|35\17, 1448.275
|2.500
|21\10, 1482.353
|Napoli-Neogothic heartland is from here…
|28\13, 1527.273
|-
|-
|
|Pb, Pe
|
|29\15, 1338.462
|18\61
|34\18, 1316.129
|206.897
|13\7, 1300
|18
|31\17, 1282.759
|7
|18\10, 1270.588
|2.571
|23\13, 1254.545
|
|-
|-
|
!P
|8\27
!30\15, 1384.615
|
!22\11, 1389.473
|207.693
!36\18, 1393.548
|8
!14\7, 1400
|3
!34\17, 1406.897
|2.667
!20\10, 1411.765
|…to here
!26\13, 1418.182
|-
|-
|
|P#
|11\37
|31\15, 1430.769
|
|23\11, 1452.632
|208.000
|38\18, 1470.968
| 11
| rowspan="2" |15\7, 1500
| 4
|37\17, 1531.034
|2.750
|22\10, 1552.941
|
|29\13, 1581.818
|-
|-
|
|Qb, Qe
|14\47
|33\15, 1523.077
|
|24\11, 1515.789
|208.696
|39\18, 1509.677
|14
|36\17, 1489.655
|5
|21\10, 1482.759
|2.800
|27\13, 1472.273
|
|-
|-
| 3\10
|'''Q'''
|
|'''34\15,''' '''1569.231'''
|
|'''25\11,''' '''1578.947'''
|209.524
|'''41\18,''' '''1587.097'''
| 3
|'''16\7,''' '''1600'''
|1
|'''39\17,''' '''1613.793'''
|3.000
|'''23\10,''' '''1623.529'''
|Napoli-Pythagorean ends, Napoli-Archy begins
|'''30\13,''' '''1636.364'''
|-
|-
|
|Q#
|22\73
|35\15, 1615.385
|
| rowspan="2" |26\11, 1642.105
|210.000
|43\18, 1664.516
|22
|17\7, 1700
|7
|42\17, 1737.069
|3.143
|25\10, 1764.706
|
|33\13, 1800
|-
|-
|
|Rb, Re
|19\63
|36\61, 1661.538
|
|42\18, 1625.806
|211.755
|16\7, 1600
|19
|38\29, 1572.414
|6
|22\10, 1552.941
|3.167
|28\13, 1527.273
|
|-
|-
|
|R
|16\53
|37\15, 1707.692
|
|27\11, 1705.263
|212.903
|44\18, 1703.226
|16
|17\7, 1700
|5
|41\17, 1696.552
|3.200
|24\10, 1694.118
|
|31\13, 1690.909
|-
|-
|
|R#
|13\43
|38\15, 1753.846
|
|28\11, 1768.421
|213.084
|46\18, 1780.645
|13
|18\7, 1800
|4
|44\17, 1820.690
|3.250
|26\10, 1835.294
|
|34\13, 1854.545
|-
|-
|
|R#
|10\33
|39\15, 1800
|
| rowspan="2" |29\11, 1831.579
|213.{{Overline|3}}
|48\18, 1858.064
| 10
|19\7, 1900
|3
|47\17, 1944.828
|3.333
|28\10, 1976.471
|
|37\13, 2018.182
|-
|-
|
|Sb, Se
|7\23
|40\15, 1846.154
|
|47\18, 1819.355
|213.699
|18\7, 1800
|7
|43\17, 1779.310
|2
|25\10, 1764.706
|3.500
|32\13, 1745.545
|
|-
|-
|
|'''S'''
|11\36
|'''41\15,''' '''1892.308'''
|
|'''30\11,''' '''1894.737'''
|214.286
|'''49\18,''' '''1896.774'''
|11
|'''19\7, 1900'''
|3
|'''46\17,''' '''1903.448'''
| 3.667
|'''27\10,''' '''1905.882'''
|
|'''35\13,''' '''1909.091'''
|-
|-
|
|S#
|15\49
|42\15, 1938.462
|
|31\11, 1957.895
| 215.385
|51\18, 1974.194
|15
|20\7, 2000
|4
|49\17, 2027.586
| 3.750
|29\10, 2047.059
|
|38\13, 2072.727
|-
|Sx
|43\15, 1984.615
| rowspan="2" |32\11, 2021.053
|53\18, 2051.612
|21\7, 2100
|52\17, 2151.725
|31\10, 2188.235
|41\13, 2236.364
|-
|-
|
|Tb, Te
|19\62
|44\15, 2030.769
|
|52\18, 2012.903
| 216.393
|20\7, 2000
|19
|48\17, 1986.207
|5
|28\10, 1976.471
|3.800
|36\13, 1963.636
|
|-
|-
|4\13
!T
|
!45\15, 2076.923
|
!33\11, 2084.211
|216.867
!54\18, 2090.323
|4
!21\7, 2100
|1
!51\17, 2110.345
|4.000
!30\10, 2117.647
|
!39\13, 2127.273
|-
|-
|
|T#
|13\42
|46\15, 2123.077
|
| rowspan="2" |34\11, 2147.368
|217.143
|56\18, 2167.742
|13
|22\7, 2200
|3
|54\17, 2234.483
|4.333
|32\10, 2258.824
|
|42\13, 2090.909
|-
|-
|
|Ub, Üe
|9\29
|47\26, 2169.231
|
|55\16, 2129.032
|218.{{Overline|18}}
|21\7, 2100
|9
|50\17, 2068.966
|2
|29\10, 2047.059
|4.500
|37\13, 2018.182
|
|-
|-
|
|Ub, Ü
|14\45
|48\15, 2215.385
|
|35\11, 2210.526
|219.718
|57\18, 2206.452
|14
|23\7, 2300
|3
|53\17, 2193.103
|4.667
|31\10, 2188.235
|
|40\13, 2181.818
|-
|-
|5\16
|U
|
|49\15, 2261.538
|
|36\11, 1073.684
| 220.408
|59\18, 2283.871
| 5
|24\7, 2400
|1
|56\17, 2317.241
|5.000
|33\10, 2329.412
|Napoli-Archy ends
|43\13, 2345.455
|-
|-
|
|U#
|16\51
|50\15, 2307.692
|
| rowspan="2" |37\11, 2336.842
|221.053
|61\18, 2361.290
|16
| rowspan="2" |23\7, 2300
| 3
|59\17, 2441.379
|5.333
|35\10, 2470.588
|
|46\13, 2509.091
|-
|-
|
|Vb, Ve
|11\35
|51\15, 2353.846
|
|60\18, 2322.581
|222.{{Overline|2}}
|55\17, 2275.862
|11
|32\10, 2258.824
|2
|41\13, 2236.364
|5.500
|
|-
|-
|
|V
|17\54
|52\15, 2400
|
|38\11, 2400
|223.728
|62\18, 2400
|17
|24\7, 2400
|3
|58\17, 2400
| 5.667
|34\10, 2400
|
|44\13, 2400
|-
|-
|6\19
|V#
|
|53\15, 2446.154
|
|39\11, 2463.158
|224.176
|64\18, 2477,419
|6
| rowspan="2" |25\7, 2500
|1
|61\17, 2524.138
|6.000
|36\10, 2541.176
|
|47\13, 2563.636
|-
|-
| 1\3
|Wb, We
|
|55\15, 2538.462
|
|40\11, 2526.316
|225.000
|65\18, 2516.129
|1
|60\17, 2482.759
|0
|35\10, 2470.588
|→ inf
|45\13, 2454.545
|Paucitonic
|-
|'''Wb'''
|'''56\15, 2584.615'''
|'''41\11, 2589.474'''
|'''67\18, 2593.548'''
|'''26\7, 2600'''
|'''63\17, 2606.897'''
|'''37\10, 2611.765'''
|'''48\13,''' '''2618.182'''
|-
|W#
|57\15, 2630.769
|42\11, 2652.632
|69\18, 2670.968
| rowspan="2" |27\7, 2700
|66\17, 2731.034
|39\10, 2752.941
|51\13, 2781.818
|-
|Xb, Xe
|59\15, 2723.077
|43\11, 2715.789
|70\18, 2709.677
|65\17, 2689.552
|38\10, 2682.353
|49\13, 2672.273
|-
|-
!X
!60\15, 2769.231
!44\11, 2778.947
!72\18, 2787.097
!28\7, 2800
!68\17, 2813.793
!40\10, 2823.529
!52\13, 2836.364
|-
|X#
|61\15, 2815.385
| rowspan="2" |45\11, 2842.105
|74\18, 2864.516
|29\7, 2900
|71\17, 2937.069
|42\10, 2964.706
|55\13, 3000
|-
|Ybb, Yee
|62\15, 2861.538
|73\18, 2825.806
|28\7, 2800
|67\17, 2772.414
|39\10, 2752.941
|50\13, 2727.273
|-
|Yb, Ye
|63\15, 2907.692
|46\11, 2905.263
|75\18, 2903.226
|29\7, 2900
|70\17, 2896.552
|41\10, 2894.118
|53\13, 2890.909
|-
|'''Y'''
|'''64\15, 2953.846'''
|'''47\11, 2968.421'''
|'''77\18, 2980.645'''
|'''30\7, 3000'''
|'''73\17, 3020.690'''
|'''43\10, 3035.294'''
|'''56\13, 3054.545'''
|-
|Y#
|65\15, 3000
|48\11, 3031.579
|79\18, 3058.064
| rowspan="2" |31\7, 3100
|76\17, 3144.828
|45\10, 3176.471
|59\13, 3218.182
|-
|Zb. Ze
|67\15, 3092.308
|49\11, 3094.737
|80\18, 3096.774
|75\17, 3103.448
|44\10, 3105.882
|57\13, 3109.091
|-
|Z
|68\15, 3138.462
|50\11, 3157.895
|82\18, 3174.194
|32\7, 3200
|78\17, 3227.586
|46\10, 3247.059
|60\13, 3272.273
|-
|Z#
|69\15, 3184.615
| rowspan="2" |51\11, 3221.053
|84\18, 3251.612
|33\7, 3300
|81\17, 3351.725
|48\10, 3388.235
|63\13, 3436.364
|-
|Ab, Æ
|70\15, 3230.769
|83\18, 3212.903
|32\7, 3200
|77\17, 3186.207
|45\10, 3176.471
|58\13, 3163.636
|-
|'''A'''
|'''71\15,''' '''3276.923'''
|'''52\11,''' '''3284.211'''
|'''85\18,''' '''3290.323'''
|'''33\7, 3300'''
|'''80\17,''' '''3310.345'''
|'''47\10,''' '''3317.647'''
|'''61\13,''' '''3327.{{Overline|27}}'''
|-
|A#
|72\15, 3323.077
|53\11, 3347.368
|87\18, 3367.742
|34\7, 3400
|83\17, 3434.583
|49\10, 3458.824
|64\13, 3490.909
|-
|Ax
|73\15, 3369.231
| rowspan="2" |54\11, 3410.625
|89\18, 3445.162
|35\7, 3500
|86\17, 3558.621
|51\10, 3600
|67\13, 3654.545
|-
|Bb, Be
|74\15, 3415.385
|88\18, 3406.452
|34\7, 3400
|82\17, 3393.103
|48\10, 3388.235
|62\13, 3381.818
|-
!B
!75\15, 3461.538
!55\11, 3473.684
!90\18, 3483.871
!35\7, 3500
!85\17, 3517.241
!50\10, 3529.412
!65\13, 3545.455
|-
|B#
|76\15, 3507.692
|56\11, 3536.842
|92\18, 3561.290
| rowspan="2" |36\7, 3600
|88\17, 3641.379
|52\10, 3670.588
|68\13, 3709.091
|-
|Cb, Ce
|78\15, 3600
|57\11, 3600
|93\18, 3600
|87\17, 3600
|51\10, 3600
|66\13, 3600
|-
|'''C'''
|'''79\15,''' '''3646.154'''
|'''58\11,''' '''3663.158'''
|'''95\18,''' '''3677.419'''
|'''37\7,''' '''3700'''
|'''90\17,''' '''3724.138'''
|'''53\10,''' '''3741.176'''
|'''69\13,''' '''3763.636'''
|-
|C#
|80\15, 3692.308
|59\11, 3726.316
|97\18, 3755.838
| rowspan="2" |38\7, 3800
|93\17, 3848.275
|55\10, 3882.353
|72\13, 3927.273
|-
|Db, De
|82\15, 3784.615
|60\11, 3789.474
|98\18, 3793.548
|92\17, 3806.897
|54\10, 3811.765
|70\13, 3818.182
|-
|D
|83\15, 3830.769
|61\11, 3852.632
|100\18, 3870.968
|39\7, 3900
|95\17, 3931.03$
|56\10, 3952.941
|73\13, 3981.818
|-
|D#
|84\15, 3876.923
| rowspan="2" |62\11, 3915.789
|102\18, 3948.387
|40\7, 4000
|98\17, 4055.172
|58\10, 4094.118
|76\13, 4145.455
|-
|Ebb, Ëe
|85\15, 3923.077
|101\18, 3909.677
|39\7, 3900
|94\17, 3889.552
|55\10, 3882.353
|71\13, 3872.727
|-
|'''Eb, Ë'''
|'''86\15,''' '''3969.231'''
|'''63\11,''' '''3978.947'''
|'''103\18,''' '''3987.097'''
|'''40\7, 4000'''
|'''97\17,''' '''4013.793'''
|'''57\10,''' '''4023.529'''
|'''74\13,''' '''4036.364'''
|-
|E
|87\15, 4015.385
|64\11, 4042.105
|105\18, 4064.516
|41\7, 4100
|100\17, 4137.931
|59\10, 4164.706
|77\13, 4200
|-
|E#
|88\15, 4061.583
| rowspan="2" |65\11, 4105.263
|107\18, 4141.956
|42\7, 4200
|103\17, 4262.069
|61\10, 4305.882
|80\13, 4363.636
|-
|Fb, Fe
|89\15, 4107.692
|106\18, 4103.226
|41\7, 4100
|99\17, 4096.552
|58\10, 4094.118
|75\13, 4090.909
|-
!F
!90\15, 4153.846
!66\11, 4168.421
!108\18, 4180.645
!42\7, 4200
!102\17, 4220.690
!60\10, 4235.294
!78\13, 4254.545
|}
==Intervals==
{| class="wikitable"
!Generators
!Sesquitave notation
!Interval category name
!Generators
!Notation of 3/2 inverse
!Interval category name
|-
| colspan="6" |The 4-note MOS has the following intervals (from some root):
|-
|0
|Do, Fa, Sol
|perfect unison
|0
|Do, Fa, Sol
|sesquitave (just fifth)
|-
|1
|Fa, Sib, Do
|perfect fourth
| -1
|Re, Sol, La
|perfect second
|-
|2
|Mib, Lab, Sib
|minor third
| -2
|Mi, La, Si
|major third
|-
|3
|Reb, Solb, Lab
|diminished second
| -3
|Fa#, Si, Do#
|augmented fourth
|-
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|-
|4
|Dob, Fab, Solb
|diminished sesquitave
| -4
|Do#, Fa#, Sol#
|augmented unison (chroma)
|-
|5
|Fab, Sibb, Dob
|diminished fourth
| -5
|Re#, Sol#, La#
|augmented second
|-
|6
|Mibb, Labb, Sibb
|diminished third
| -6
|Mi#, La#, Si#
|augmented third
|}
==Genchain==
The generator chain for this scale is as follows:
{| class="wikitable"
|Mibb
Labb
Sibb
|Fab
Sibb
Dob
|Dob
Fab
Solb
|Reb
Solb
Lab
|Mib
Lab
Sib
|Fa
Sib
Do
|Do
Fa
Sol
|Re
Sol
La
|Mi
La
Si
|Fa#
Si
Do#
|Do#
Fa#
Sol#
|Re#
Sol#
La#
|Mi#
La#
Si#
|-
|d3
|d4
|d5
|d2
|m3
|P4
|P1
|P2
|M3
|A4
|A1
|A2
|A3
|}
==Modes==
The mode names are based on the species of fifth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
|-
|Lydian
|LLLs
|<nowiki>3|0</nowiki>
|P
|M
|A
|-
|Major
|LLsL
|<nowiki>2|1</nowiki>
|P
|M
|P
|-
|Minor
|LsLL
|<nowiki>1|2</nowiki>
|P
|m
|P
|-
|Phrygian
|sLLL
|<nowiki>0|3</nowiki>
|d
|m
|P
|}
==Temperaments==
The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
==='''Napoli-Meantone (Hex meantone)'''===
[[Subgroup]]: 3/2.6/5.8/5 (5.2.3)
[[Comma]] list: [[81/80]]
[[POL2]] generator: ~9/8 = 192.6406¢
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
[[Optimal ET sequence]]: *[[28ed5]], [[44ed5]], [[72ed5]] ≈ [[7edf]], [[11edf]], [[18edf]]
==='''Napoli-Archy (Hex Archytas)'''===
[[Subgroup]]: 3/2.7/6.14/9 (36/7.2.3)
[[Comma]] list: [[64/63]]
[[POL2]] generator: ~8/7 = 218.6371¢
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
[[Optimal ET sequence]]: *[[28ed36/7]], [[40ed36/7]], [[52ed36/7]] ≈ [[7edf]], [[10edf]], [[13edf]]
===Scale tree===
The spectrum looks like this:
{| class="wikitable"
!Generator
(bright)
!Cents
!L
!s
!L/s
!Comments
|-
|1\4
|171.429
|1
|1
|1.000
|Equalised
|-
|6\23
|180.000
|6
|5
|1.200
|
|-
|5\19
|181.818
|5
|4
|1.250
|
|
|
|-
|
|14\53
|240.000
|182.609
|
|14
|
|11
|
|1.273
|
|
|}
|-
|9\34
|183.051
|9
|7
|1.286
|
|-
|4\15
|184.615
|4
|3
|1.333
|
|-
|11\41
|185.915
|11
|8
|1.375
|
|-
|7\26
|186.667
|7
|5
|1.400
|
|-
|10\37
|187.5
|10
|7
|1.429
|
|-
|13\48
|187.952
|13
|9
|1.444
|
|-
|16\59
|188.253
|16
|11
|1.455
|
|-
|3\11
|189.474
|3
|2
|1.500
|Napoli-Meantone starts here
|-
|14\51
|190.909
|14
|9
|1.556
|
|-
|11\40
|191.304
|11
|7
|1.571
|
|-
|8\29
|192.000
|8
|5
|1.600
|
|-
|5\18
|193.548
|5
|3
|1.667
|
|-
|12\43
|194.595
|12
|7
|1.714
|
|-
|7\25
|195.348
|7
|4
|1.750
|
|-
|9\32
|196.364
|9
|5
|1.800
|
|-
|11\39
|197.015
|11
|6
|1.833
|
|-
|13\46
|197.468
|13
|7
|1.857
|
|-
|15\53
|197.802
|15
|8
|1.875
|
|-
|17\60
|198.058
|17
|9
|1.889
|
|-
|19\67
|198.261
|19
|10
|1.900
|
|-
|21\74
|198.425
|21
|11
|1.909
|
|-
|23\81
|198.561
|23
|12
|1.917
|
|-
|25\88
|198.675
|25
|13
|1.923
|
|-
|27\95
|198.773
|27
|14
|1.929
|
|-
|29\102
|198.857
|29
|15
|1.933
|
|-
|31\109
|198.930
|31
|16
|1.9375
|
|-
|33\116
|198.995
|33
|17
|1.941
|
|-
|35\123
|199.009
|35
|18
|1.944
|
|-
|2\7
|200
|2
|1
|2.000
|Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|17\59
|201.980
|17
|8
|2.125
|
|-
|15\52
|202.247
|15
|7
|2.143
|
|-
|13\45
|202.597
|13
|6
|2.167
|
|-
|11\38
|203.077
|11
|5
|2.200
|
|-
|9\31
|203.774
|9
|4
|2.250
|
|-
|7\24
|204.878
|7
|3
|2.333
|
|-
|12\41
|205.714
|12
|5
|2.400
|
|-
|5\17
|206.897
|5
|2
|2.500
|Napoli-Neogothic heartland is from here…
|-
|18\61
|207.693
|18
|7
|2.571
|
|-
|13\44
|208.000
|13
|5
|2.600
|
|-
|8\27
|208.696
|8
|3
|2.667
|…to here
|-
|11\37
|209.524
|11
|4
|2.750
|
|-
|14\47
|210.000
|14
|5
|2.800
|
|-
|3\10
|211.765
|3
|1
|3.000
|Napoli-Pythagorean ends, Napoli-Archy begins
|-
|22\73
|212.903
|22
|7
|3.143
|
|-
|19\63
|213.084
|19
|6
|3.167
|
|-
|16\53
|213.333
|16
|5
|3.200
|
|-
|13\43
|213.699
|13
|4
|3.250
|
|-
|10\33
|214.286
|10
|3
|3.333
|
|-
|7\23
|215.385
|7
|2
|3.500
|
|-
|11\36
|216.393
|11
|3
|3.667
|
|-
|15\49
|216.867
|15
|4
|3.750
|
|-
|19\62
|217.143
|19
|5
|3.800
|
|-
|4\13
|218.182
|4
|1
|4.000
|
|-
|13\42
|219.718
|13
|3
|4.333
|
|-
|9\29
|220.408
|9
|2
|4.500
|
|-
|14\45
|221.053
|14
|3
|4.667
|
|-
|5\16
|222.222
|5
|1
|5.000
|Napoli-Archy ends
|-
|11\35
|223.728
|11
|2
|5.500
|
|-
|17\54
|224.176
|17
|3
|5.667
|
|-
|6\19
|225.000
|6
|1
|6.000
|
|-
|1\3
|240.000
|1
|0
|→ inf
|Paucitonic
|}
 
==See also==
[[3L 1s (3/2-equivalent)]] - idealized tuning
 
[[6L 2s (20/9-equivalent)]] - Neapolitan 1/2-comma meantone
 
[[6L 2s (88/39-equivalent)]] - Neapolitan gentle temperament
 
[[6L 2s (16/7-equivalent)]] - Neapolitan 1/2-comma archy
 
[[9L 3s (10/3-equivalent)]] - Bijou 1/3-comma meantone
 
[[9L 3s (44/13-equivalent)]] - Bijou gentle temperament
 
[[9L 3s (24/7-equivalent)]] - Bijou 1/3-comma archy
 
[[12L 4s (5/1-equivalent)]] - Hex meantone
 
[[12L 4s (56/11-equivalent)]] - Hextone gentle temperament
 
[[12L 4s (36/7-equivalent)]] - Hextone 1/4-comma archy
 
[[15L 5s (15/2-equivalent)]] - Guidotonic major 1/5-comma meantone
 
[[15L 5s (84/11-equivalent)]] - Guidotonic major gentle temperament
 
[[15L 5s (54/7-equivalent)]] - Guidotonic major 1/5-comma archy
 
[[18L 6s (11/1-equivalent)]] - Subdozenal harmonic tuning
 
[[18L 6s (56/5-equivalent)]] - Subdozenal low septimal (meantone) tuning
 
[[18L 6s (512/45-equivalent)]] - Subdozenal 1/6-comma meantone
 
[[18L 6s (80/7-equivalent)]] - Subdozenal high septimal tuning


==See also==
[[18L 6s (128/11-equivalent)]] - Subdozenal subharmonic tuning
[[3L 1s (3/2-equivalent)]] - idealized tuning
 
[[6L 2s (20/9-equivalent)]] - Neapolitan 1/2-comma meantone
 
[[6L 2s (52/23-equivalent)]] - Neapolitan gentle temperament
 
[[6L 2s (16/7-equivalent)]] - Neapolitan 1/2-comma archy
 
[[9L 3s (10/3-equivalent)]] - Bijou 1/3-comma meantone
 
[[9L 3s (22/13-equivalent]]) - Bijou gentle temperament
 
[[9L 3s (24/7-equivalent)]] - Bijou 1/3-comma archy
 
[[12L 4s (5/1-equivalent)]] - Hex meantone
 
[[12L 4s (56/11-equivalent)]] - Hextone gentle temperament
 
[[12L 4s (36/7-equivalent)]] - Hextone 1/4-comma archy
 
[[15L 5s (15/2-equivalent)]] - Guidotonic major 1/5-comma meantone
 
[[15L 5s (84/11-equivalent)]] - Guidotonic major gentle temperament
 
[[15L 5s (54/7-equivalent)]] - Guidotonic major 1/5-comma archy
 
[[18L 6s (11/1-equivalent)]] - Subdozenal harmonic tuning
 
[[18L 6s (56/5-equivalent)]] - Subdozenal low septimal tuning
 
[[18L 6s (80/7-equivalent)]] - Subdozenal high septimal tuning


[[18L 6s (128/11-equivalent)]] - Subdozenal subharmonic tuning<references />
[[18L 6s (11/1-equivalent)|18L 6s (12/1-equivalent)]] - Warped Pythagorean tuning
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/3L_1s_(perfect_fifth-equivalent)"