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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"
 
 
|+
|+
 
 
Cents<ref name=":0">Fractions repeating more than 4 digits written as continued fractions</ref>
Cents
 
 
! colspan="4" | Notation
! Notation
 
 
!Supersoft
!Supersoft
Line 36: Line 36:
 
 
!Diatonic
!Diatonic
! Napoli
!Bijou
!Hextone
!~15edf
!~15edf
 
 
Line 57: Line 52:
|-
|-
 
 
|Do#, Sol#
|Do#, Fa#, Sol#
|1\15, 46.154
 
 
|F#
|1\11, 63.158
 
 
|0#, D#
|2\18, 77.419
|0#, G#
|1\15
46; 6.5
 
 
| 1\11
| rowspan="2" | 1\7, 100
63: 6.{{Overline|3}}
 
 
|2\18
|3\17, 124.138
77; 2, 2.6
 
 
| rowspan="2" |1\7
|2\10, 141.176
 
 
100
|3\13, 163.636
 
 
|3\17
|-
124; 7.25
 
 
|2\10
|Reb, Solb, Lab
141; 5.{{Overline|6}}
|3\15, 138.462
 
 
|3\13
|2\11. 126.316
 
 
163.{{Overline|63}}
|3\18, 116.129
 
 
|-
|2\17, 82.759
 
 
|Reb, Lab
|1\10, 70.588
 
 
|Gb
|1\13, 54.545
 
 
|1b, 1c
|-
|1f
|3\15
138; 3.25
 
 
|2\11
|'''Re, Sol, La'''
126; 3.1{{Overline|6}}
|'''4\15,''' '''184.615'''
 
 
|3\18
|'''3\11,''' '''189.474'''
116; 7.75
|'''5\18,''' '''193.548'''
 
 
|2\17
|'''2\7,''' '''200'''
82; 1.3{{Overline|18}}
 
 
| 1\10
|'''5\17,''' '''206.897'''
70; 1.7
 
 
|1\13
|'''3\10,''' '''211.765'''
 
 
54.{{Overline|54}}
|'''4\13,''' '''218.182'''
 
 
|-
|-
 
 
|'''Re, La'''
|Re#, Sol#, La#
|5\15, 230.769
 
 
|'''G'''
|4\11, 252.632
 
 
|'''1'''
|7\18, 270.968
|'''1'''
 
 
|'''4\15'''
| rowspan="2" | 3\7, 300
'''184; 1.625'''
 
 
|'''3\11'''
|8\17, 331.034
'''189; 2.{{Overline|1}}'''
|'''5\18'''
'''193; 1, 1, 4.{{Overline|6}}'''
 
 
|'''2\7'''
|5\10, 352.941
 
 
'''200'''
|7\13, 381.818
 
 
|'''5\17'''
|-
'''206; 1, 8.{{Overline|6}}'''
 
 
|'''3\10'''
|Mib, Lab, Sib
'''211; 1, 3.25'''
|7\15, 323.077
 
 
|'''4\13'''
|5\11, 315.789
 
 
'''218.{{Overline|18}}'''
|8\18, 309.677
 
 
|-
|7\17, 289.655
 
 
|Re#, La#
|4\10, 282.353
 
 
|G#
|5\13, 272.727
 
 
|1#
|-
|1#
|5\15
230; 1.3
|4\11
252; 1.58{{Overline|3}}
 
 
|7\18
|Mi, La, Si
270; 1.0{{Overline|3}}
|8\15, 369.231
 
 
| rowspan="2" |3\7
|6\11, 378.947
 
 
300
|10\18, 387.097
 
 
|8\17
|4\7, 400
331; 29
 
 
|5\10
|10\17, 413.793
352; 1.0625
 
 
| 7\13
|6\10, 423.529
 
 
381.{{Overline|81}}
|8\13, 436.364
 
 
|-
|-
 
 
|Mib, Sib
|Mi#, La#, Si#
|9\15, 415.385
 
 
| Ab
| rowspan="2" | 7\11, 442.105
 
 
|2b, 2c
|12\18, 464.516
|2f
|7\15
323; 13
 
 
|5\11
|5\7, 500
315; 1.2{{Overline|6}}
 
 
|8\18
|13\17, 537.069
309; 1, 2.1
 
 
| 7\17
|8\10, 564.706
289; 1, 1.9
 
 
| 4\10
|11\13, 600
282; 2.8{{Overline|3}}
 
 
| 5\13
|-
|Fab, Sibb, Dob
|10\15, 461.538
 
 
272.{{Overline|72}}
|11\18, 425.806
 
 
|-
|4\7, 400
 
 
|Mi, Si
|9\17, 372.414
 
 
|A
|5\10, 352.941
 
 
|2
|6\13, 327.273
|2
|8\15
369; 4.{{Overline|3}}
 
 
|6\11
|-
378; 1.0{{Overline|5}}
 
 
|10\18
|'''Fa, Sib, Do'''
387; 10.{{Overline|3}}
|'''11\15,''' '''507.692'''
 
 
|4\7
|'''8\11,''' '''505.263'''
 
 
400
|'''13\18,''' '''503.226'''
 
 
|10\17
|'''5\7, 500'''
413; 1, 3.8{{Overline|3}}
 
 
| 6\10
|'''12\17,''' '''496.552'''
423; 1.{{Overline|8}}
 
 
|8\13
|'''7\10,''' '''494.118'''
 
 
436.{{Overline|36}}
|'''9\13,''' '''490.909'''
 
 
|-
|-
 
 
| Mi#, Si#
|Fa#, Si, Do#
|12\15, 553.846
 
 
|A#
|9\11, 568.421
 
 
|2#
|15\18, 580.645
|2#
|9\15
415; 2.6
 
 
| rowspan="2" |7\11
|6\7, 600
442; 9.5
 
 
|12\18
|15\17, 620.690
464; 1.0625
 
 
|5\7
|9\10, 635.294
 
 
500
|12\13, 654.545
 
 
|13\17
|-
537; 14.5
|Fax, Si#, Dox
|13\15, 600
 
 
|8\10
| rowspan="2" | 10\11, 631.579
564; 1.41{{Overline|6}}
 
 
|11\13
|17\18, 658.064
 
 
600
|7\7, 700
 
 
|-
|18\17, 744.828
 
 
|Fab, Dob
|11\10, 776.471
 
 
|Bbb
|15\13, 818.182
 
 
|3b, 3c
|-
|3f
| 10\15
461; 1, 1.1{{Overline|6}}
 
 
|11\18
|Dob, Fab, Solb
425; 1.24
|14\15, 646.154
|16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
 
 
|4\7
|-
 
 
400
!Do, Fa, Sol
!'''15\15,''' '''692.308'''
 
 
|9\17
!'''11\11,''' '''694.737'''
372; 2.41{{Overline|6}}
 
 
|5\10
!'''18\18,''' '''696.774'''
352; 1.0625
 
 
|6\13
!7\7, 700
 
 
327.{{Overline|27}}
!'''17\17,''' '''703.448'''
 
 
|-
!'''10\10,''' '''705.882'''
 
 
|'''Fa, Do'''
!'''13\13,''' '''709.091'''
 
 
|'''Bb'''
|}
 
 
|'''3'''
{| class="wikitable"
|'''3'''
 
 
|'''11\15'''
|+
'''507; 1.{{Overline|4}}'''
 
 
|'''8\11'''
Cents
'''505; 3.8'''
!Notation
!Supersoft
 
 
|'''13\18'''
! Soft
'''503; 4, 2.{{Overline|3}}'''
 
 
|'''5\7'''
!Semisoft
 
 
'''500'''
!Basic
 
 
|'''12\17'''
!Semihard
'''496; 1.8125'''
 
 
|'''7\10'''
! Hard
'''494; 8.5'''
 
 
|'''9\13'''
! Superhard
'''490.{{Overline|90}}'''
 
 
|-
|-
 
 
|Fa#, Do#
!Napoli
! ~15edf
 
 
| B
! ~11edf
 
 
|3#
!~18edf
| 3#
|12\15
553; 1.{{Overline|18}}
 
 
|9\11
!~7edf
568; 2.375
 
 
|15\18
!~17edf
580; 1.55
 
 
|6\7
!~10edf
 
 
600
!~13edf
 
 
|15\17
|-
620; 1.45
 
 
|9\10
|F#
635; 3.4
|1\15, 46.154
 
 
|12\13
|1\11, 63.158
 
 
654.{{Overline|54}}
| 2\18, 77.419
 
 
|-
| rowspan="2" |1\7, 100
|Fax, Dox
 
 
|B#
|3\17, 124.138
 
 
|3x
| 2\10, 141.176
|3x
|13\15
 
 
600
|3\13, 163.636
 
 
| rowspan="2" |10\11
|-
 
 
631; 1.{{Overline|72}}
| Gb, Ge
|3\15, 138.462
 
 
|17\18
| 2\11. 126.316
 
 
658; 15.5
|3\18, 116.129
 
 
|7\7
|2\17, 82.759
 
 
700
|1\10, 70.588
 
 
|18\17
|1\13, 54.545
 
 
744; 1.208{{Overline|3}}
|-
 
 
|11\10
|'''G'''
|'''4\15,''' '''184.615'''
 
 
776; 2.125
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
 
 
|15\13
|'''2\7,''' '''200'''
 
 
818.{{Overline|18}}
|'''5\17,''' '''206.897'''
 
 
|-
|'''3\10,''' '''211.765'''
 
 
|Dob, Solb
|'''4\13,''' '''218.182'''
| Hb
|4b, 4c
|4f
| 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}}
 
 
|-
|-
 
 
!Do, Sol
|G#
|5\15, 230.769
 
 
! H
|4\11, 252.632
 
 
!4
|7\18, 270.968
!4
!'''15\15'''
 
 
'''692; 3.25'''
| rowspan="2" |3\7, 300
 
 
!'''11\11'''
| 8\17, 331.034
'''694; 1, 2.8'''
 
 
!'''18\18'''
|5\10, 352.941
 
 
'''696; 1.291'''{{Overline|6}}
|7\13, 381.818
 
 
!'''7\7'''
|-
 
 
'''700'''
|Ab, Æ
|7\15, 323.077
 
 
!'''17\17'''
|5\11, 315.789
 
 
'''703; 2, 2.1'''{{Overline|6}}
|8\18, 309.677
 
 
!'''10\10'''
|7\17, 289.655
 
 
'''705; 1.1'''{{Overline|3}}
|4\10, 282.353
 
 
!'''13\13'''
|5\13, 272.727
'''709.'''{{Overline|09}}
 
 
|-
|-
 
 
|Do#, Sol#
|A
| 8\15, 369.231
 
 
|Η#
|6\11, 378.947
 
 
| 4#
|10\18, 387.097
|4#
|16\15
 
 
738; 2.1{{Overline|6}}
| 4\7, 400
 
 
| 12\11
|10\17, 413.793
 
 
757; 1, 8.5
|6\10, 423.529
 
 
|20\18
|8\13, 436.364
 
 
774; 5, 6
|-
 
 
| rowspan="2" |8\8
|A#
| 9\15, 415.385
 
 
800
| rowspan="2" |7\11, 442.105
 
 
|20\17
|12\18, 464.516
 
 
827; 1, 1.41{{Overline|6}}
|5\7, 500
 
 
|12\10
|13\17, 537.069
 
 
847; 17
|8\10, 564.706
 
 
| 16\13
|11\13, 600
872.{{Overline|72}}
 
 
|-
|-
 
 
|Reb, Lab
|Bbb, Bee
|10\15, 461.538
 
 
|Cb
|11\18, 425.806
 
 
|5b, 5c
|4\7, 400
|5
|18\15
 
 
830; 1.3
|9\17, 372.414
 
 
|13\11
| 5\10, 352.941
 
 
821; 19
|6\13, 327.273
 
 
|21\18
|-
 
 
812; 1, 9.{{Overline|3}}
|'''Bb, Be'''
|'''11\15,''' '''507.692'''
 
 
|19\17
|'''8\11,''' '''505.263'''
 
 
786; 4.8{{Overline|3}}
|'''13\18,''' '''503.226'''
 
 
|11\10
|'''5\7, 500'''
 
 
776; 2.125
|'''12\17,''' '''496.552'''
 
 
|14\13
|'''7\10,''' '''494.118'''
 
 
763.{{Overline|63}}
|'''9\13,''' '''490.909'''
 
 
|-
|-
 
 
|'''Re, La'''
|B
|12\15, 553.846
 
 
|'''C'''
|9\11, 568.421
 
 
|'''5'''
|15\18, 580.645
|'''5'''
 
 
|'''19\15'''
|6\7, 600
 
 
'''876; 1.08{{Overline|3}}'''
| 15\17, 620.690
 
 
|'''14\11'''
|9\10, 635.294
 
 
'''884; 4.75'''
|12\13, 654.545
 
 
|'''23\18'''
|-
| B#
| 13\15, 600
 
 
'''890; 3.1'''
| rowspan="2" |10\11, 631.579
 
 
|'''9\5'''
|17\18, 658.064
 
 
'''900'''
|7\7, 700
 
 
|'''22\17'''
|18\17, 744.828
 
 
'''910; 2.9'''
|11\10, 776.471
 
 
|'''13\10'''
|15\13, 818.182
 
 
'''917; 1.{{Overline|54}}'''
|-
|Hb, He
|'''17\13'''
|14\15, 646.154
| 16\18, 619.355
'''927.{{Overline|27}}'''
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
 
 
|-
|-
 
 
|Re#, La#
! H
!'''15\15,''' '''692.308'''
 
 
| C#
!'''11\11,''' '''694.737'''
 
 
| 5#
!'''18\18,''' '''696.774'''
|5#
|20\15
 
 
923: 13
! 7\7, 700
 
 
| 15\11
!'''17\17,''' '''703.448'''
 
 
947; 2, 1.4
!'''10\10,''' '''705.882'''
 
 
|25\18
!'''13\13,''' '''709.091'''
 
 
967; 1, 2.875
|-
 
 
| rowspan="2" |10\7
|Η#
|16\15, 738.462
1000
 
 
|25\17
|12\11, 757.895
 
 
1034; 2, 14
|20\18, 774.194
 
 
|15\10
| rowspan="2" |8\8, 800
 
 
1058; 1, 4.{{Overline|6}}
|20\17, 827.586
 
 
|20\13
|12\10, 847.059
 
 
1090.{{Overline|90}}
|16\13, 872.727
 
 
|-
|-
 
 
|Mib, Sib
|Cb, Ce
|18\15, 830.769
 
 
|Db
|13\11, 821.053
 
 
|6b, 6c
|21\18, 812.903
|6f
| 22\15
 
 
1015; 2.6
|19\17, 786.207
 
 
|16\11
|11\10, 776.471
 
 
1010; 1.9
|14\13, 763.63
 
 
|26\18
|-
 
 
1006; 2, 4.{{Overline|6}}
|'''C'''
|'''19\15,''' '''876.923'''
 
 
|24\17
|'''14\11,''' '''884.211'''
 
 
993; 9.{{Overline|6}}
|'''23\18,''' '''890.323'''
 
 
|14\10
|'''9\5,''' '''900'''
 
 
988; 4.25
|'''22\17,''' '''910.345'''
 
 
|18\13
|'''13\10,''' '''917.647'''
 
 
981.{{Overline|81}}
|'''17\13,''' '''927.273'''
 
 
|-
|-
 
 
|Mi, Si
|C#
|20\15, 923.077
 
 
|D
|15\11, 947.368
 
 
|6
|25\18, 967.742
|6
|23\15
 
 
1061; 1, 1.1{{Overline|6}}
| rowspan="2" |10\7, 1000
 
 
|17\11
|25\17, 1034.483
 
 
1073; 1, 2.1{{Overline|6}}
|15\10, 1058.824
 
 
|28\18
|20\13, 1090.909
 
 
1083; 1.{{Overline|148}}
|-
 
 
|11\7
| Db, De
|22\15, 1015.385
 
 
1100
|16\11, 1010.526
 
 
|27\17
|26\18, 1006.452
 
 
1117; 4, 7
|24\17, 993.103
 
 
|16\10
|14\10, 988.235
 
 
1129; 2, 2.{{Overline|3}}
|18\13, 981.818
|21\9
1145.{{Overline|45}}
 
 
|-
|-
 
 
|Mi#, Si#
|D
|23\15, 1061.538
 
 
|D#
|17\11, 1073.684
 
 
|6#
|28\18, 1083.871
| 6#
|24\15
 
 
1107; 1.{{Overline|4}}
|11\7, 1100
 
 
| rowspan="2" |18\11
|27\17, 1117.241
 
 
1136; 1.1875
|16\10, 1129.412
 
 
|30\18
|21\9, 1145.455
 
 
1161; 3.{{Overline|4}}
|-
 
 
|12\7
|D#
|24\15, 1107.923
 
 
1200
| rowspan="2" |18\11, 1136.842
 
 
| 30\17
|30\18, 1161.29
 
 
1241; 2.{{Overline|63}}
|12\7, 1200
 
 
| 18\10
|30\17, 1241.379
 
 
1270; 1.7
|18\10, 1270.588
 
 
|24\13
|24\13, 1309.091
1309.{{Overline|09}}
 
 
|-
|-
 
 
|Fab, Dob
|Ebb, Ëe
|25\15, 1153.846
 
 
|Ebb
|29\18, 1122.581
 
 
|7b, 7c
|11\7, 1100
|7f
|25\15
 
 
1153; 1.{{Overline|18}}
|26\17, 1075.862
 
 
| 29\18
|15\10, 1058.824
 
 
1121; 1, 1, 2.6
| 19\13, 1036.364
 
 
| 11\7
|-
 
 
1100
|'''Eb, Ë'''
|'''26\15,''' '''1200'''
 
 
| 26\17
|'''19\11,''' '''1200'''
 
 
1075; 1.16
|'''31\18,''' '''1200'''
 
 
|15\10
|'''12\7, 1200'''
 
 
1058; 1, 4.{{Overline|6}}
|'''29\17,''' '''1200'''
 
 
|19\13
|'''17\10,''' '''1200'''
 
 
1036.{{Overline|36}}
|'''22\13,''' '''1200'''
 
 
|-
|-
 
 
|'''Fa, Do'''
|E
|27\15, 1246.154
 
 
|'''Eb'''
|20\11, 1263.158
 
 
|'''7'''
|33\18, 1277.419
|'''7'''
 
 
|'''26\15'''
|13\7, 1300
 
 
'''1200'''
|32\17, 1324.138
 
 
|'''19\11'''
|19\10, 1341.176
 
 
'''1200'''
|25\13, 1363.636
 
 
|'''31\18'''
|-
 
 
'''1200'''
|E#
|28\15, 1292.308
 
 
|'''12\7'''
| rowspan="2" |21\11, 1326.318
 
 
'''1200'''
|35\18, 1354.834
 
 
|'''29\17'''
|14\7, 1400
 
 
'''1200'''
|35\17, 1448.275
 
 
|'''17\10'''
| 21\10, 1482.353
 
 
'''1200'''
|28\13, 1527.273
 
 
|'''22\13'''
|-
 
 
'''1200'''
| Fb, Fe
|29\15, 1338.462
 
 
|-
|34\18, 1316.129
 
 
| Fa#, Do#
|13\7, 1300
 
 
|E
|31\17, 1282.759
|7#
|7#
|27\15
1246; 6.5
| 20\11
1263; 6.{{Overline|3}}
|33\18
1277; 2, 2.6
|13\7
 
 
1300
|18\10, 1270.588
 
 
|32\17
|23\13, 1254.545
1324; 7.25
|19\10
1341; 5.{{Overline|6}}
|25\13
1363.{{Overline|63}}
 
 
|-
|-
 
 
|Fax, Dox
!F
!30\15, 1384.615
 
 
|E#
!22\11, 1389.473
 
 
| 7x
!36\18, 1393.548
|7x
|28\15
 
 
1292; 3.25
!14\7, 1400
 
 
| rowspan="2" |21\11
!34\17, 1406.897
 
 
1326; 3.1{{Overline|6}}
!20\10, 1411.765
|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}}
 
 
!26\13, 1418.182
|}
{| class="wikitable"
|+Cents
! Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
! Superhard
|-
!Bijou
!~15edf
!~11edf
!~18edf
!~7edf
!~17edf
!~10edf
!~13edf
|-
|-
|0#, D#
|Dob, Solb
|1\15, 46.154
|1\11, 63.158
|Fb
|2\18, 77.419
| rowspan="2" |1\7, 100
|8b, Fc
|3\17, 124.138
|8f
|2\10, 141.176
|29\15
|3\13, 163.636
|-
1338; 2.1{{Overline|6}}
|1b, 1c
|3\15, 138.462
|34\18
| 2\11. 126.316
|3\18, 116.129
1316; 7.75
|2\17, 82.759
|1\10, 70.588
|13\7
|1\13, 54.545
|-
1300
|'''1'''
|'''4\15,''' '''184.615'''
|31\17
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
1282; 1.3{{Overline|18}}
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|18\10
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
1270; 1.7
|-
|1#
| 23\13
|5\15, 230.769
|4\11, 252.632
1254.{{Overline|54}}
|7\18, 270.968
| rowspan="2" |3\7, 300
|8\17, 331.034
|5\10, 352.941
|7\13, 381.818
|-
|2b, 2c
|7\15, 323.077
|5\11, 315.789
| 8\18, 309.677
| 7\17, 289.655
|4\10, 282.353
|5\13, 272.727
|-
|-
|2
!Do, Sol
|8\15, 369.231
|6\11, 378.947
!F
|10\18, 387.097
|4\7, 400
!8, F
|10\17, 413.793
!8
|6\10, 423.529
!30\15
|8\13, 436.364
|-
1384; 1.625
|2#
| 9\15, 415.385
!22\11
| rowspan="2" |7\11, 442.105
|12\18, 464.516
1389; 2.{{Overline|1}}
|5\7, 500
|13\17, 537.069
! 36\18
|8\10, 564.706
|11\13, 600
1393; 1, 1, 4.{{Overline|6}}
|-
|3b, 3c
!14\7
| 10\15, 461.538
| 11\18, 425.806
1400
|4\7, 400
|9\17, 372.414
! 34\17
|5\10, 352.941
|6\13, 327.273
1406; 1, 8.{{Overline|6}}
|-
|'''3'''
!20\10
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
1411; 1, 3.25
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
!26\13
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
1418.{{Overline|18}}
|'''9\13,''' '''490.909'''
|-
|3#
|12\15, 553.846
|9\11, 568.421
|15\18, 580.645
|6\7, 600
|15\17, 620.690
|9\10, 635.294
|12\13, 654.545
|-
|-
|3x
|Do#, Sol#
|13\15, 600
| rowspan="2" |10\11, 631.579
|F#
|17\18, 658.064
|7\7, 700
|8#, F#
|18\17, 744.828
|8#
|11\10, 776.471
|31\15
|15\13, 818.182
|-
1430; 1.3
|4b, 4c
|14\15, 646.154
|23\11
|16\18, 619.355
|6\7, 600
1452; 1.58{{Overline|3}}
|14\17, 579.310
|8\10, 564.706
|38\18
|10\13, 545.455
|-
1470; 1.0{{Overline|3}}
!4
!'''15\15,''' '''692.308'''
| rowspan="2" |15\7
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
1500
!7\7, 700
!'''17\17,''' '''703.448'''
|37\17
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
1531; 29
|-
|4#
|22\10
| 16\15, 738.462
|12\11, 757.895
1552; 1.0625
|20\18, 774.194
| rowspan="2" |8\8, 800
|29\13
|20\17, 827.586
|12\10, 847.059
1581.{{Overline|81}}
| 16\13, 872.727
|-
|-
|5b, 5c
|Reb, Lab
|18\15, 830.769
|13\11, 821.053
|Gb
|21\18, 812.903
|19\17, 786.207
|9b, Gc
|11\10, 776.471
| 9f
|14\13, 763.63
|33\15
|-
|'''5'''
1523; 13
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
|24\11
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
1515; 1.2{{Overline|6}}
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|39\18
|'''17\13,''' '''927.273'''
|-
1509; 1, 2.1
|5#
|20\15, 923.077
|36\17
|15\11, 947.368
|25\18, 967.742
1489; 1, 1.9
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|21\10
|15\10, 1058.824
|20\13, 1090.909
1482; 2.8{{Overline|3}}
|-
|6b, 6c
|27\13
|22\15, 1015.385
|16\11, 1010.526
1472.{{Overline|72}}
|26\18, 1006.452
|24\17, 993.103
|14\10, 988.235
|18\13, 981.818
|-
|6
|23\15, 1061.538
|17\11, 1073.684
| 28\18, 1083.871
|11\7, 1100
|27\17, 1117.241
|16\10, 1129.412
|21\9, 1145.455
|-
|-
|6#
|'''Re, La'''
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
|'''G'''
|30\18, 1161.290
|12\7, 1200
|'''9, G'''
|30\17, 1241.379
| 9
|18\10, 1270.588
|'''34\15'''
|24\13, 1309.091
|-
'''1569; 4.{{Overline|3}}'''
| 7b, 7c
|25\15, 1153.846
|'''25\11'''
|29\18, 1122.581
|11\7, 1100
'''1578; 1.0{{Overline|5}}'''
|26\17, 1075.862
|15\10, 1058.824
|'''41\18'''
|19\13, 1036.364
|-
'''1587; 10.{{Overline|3}}'''
|'''7'''
|'''26\15,''' '''1200'''
|'''16\7'''
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
'''1600'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|'''39\17'''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
'''1613; 1, 3.8{{Overline|3}}'''
|-
|7#
|'''23\10'''
|27\15, 1246.154
|20\11, 1263.158
'''1623; 1.{{Overline|8}}'''
|33\18, 1277.419
|13\7, 1300
|'''30\13'''
|32\17, 1324.138
|19\10, 1341.176
'''1636.{{Overline|36}}'''
|25\13, 1363.636
|-
|7x
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
|35\18, 1354.834
|14\7, 1400
|35\17, 1448.275
|21\10, 1482.353
|28\13, 1527.273
|-
|8b, Fc
|29\15, 1338.462
|34\18, 1316.129
|13\7, 1300
|31\17, 1282.759
|18\10, 1270.588
|23\13, 1254.545
|-
|-
!8, F
|Re#, La#
!30\15, 1384.615
!22\11, 1389.473
|G#
!36\18, 1393.548
!14\7, 1400
|9#, G#
!34\17, 1406.897
| 9#
!20\10, 1411.765
|35\15
!26\13, 1418.182
|-
1615; 2.6
|8#, F#
|31\15, 1430.769
|26\11
|23\11, 1452.632
|38\18, 1470.968
1642; 9.5
| rowspan="2" |15\7, 1500
|37\17, 1531.034
|43\18
|22\10, 1552.941
|29\13, 1581.818
1664; 1.0625
|-
|9b, Gc
| rowspan="2" |17\7
|33\15, 1523.077
|24\11, 1515.789
1700
|39\18, 1509.677
|36\17, 1489.655
|42\17
|21\10, 1482.759
|27\13, 1472.273
1737; 14.5
|-
|'''9, G'''
|25\10
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
1764; 1.41{{Overline|6}}
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
|33\13
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
1800
|'''30\13,''' '''1636.364'''
|-
|9#, G#
|35\15, 1615.385
|26\11, 1642.105
|43\18, 1664.516
| rowspan="2" |17\7, 1700
|42\17, 1737.069
|25\10, 1764.706
|33\13, 1800
|-
|-
|Mib, Sib
|Ab
|Xb, Ac
|Xb, Ac
|Af
|37\15, 1707.692
| 37\15
|27\11, 1705.263
|44\18, 1703.226
1707; 1.{{Overline|4}}
|41\17, 1696.552
|24\10, 1694.118
|27\11
|31\13, 1690.909
|-
1705; 3.8
|X, A
|38\15, 1753.846
|44\18
|28\11, 1768.421
|46\18, 1780.645
1703; 4, 2.{{Overline|3}}
|18\7, 1800
|44\17, 1820.690
|41\17
|26\10, 1835.294
|34\13, 1854.545
1696; 1.8125
|-
|X#, A#
|24\10
|39\15, 1800
| rowspan="2" |29\11, 1831.579
1694; 8.5
|48\18, 1858.064
|19\7, 1900
|31\13
|47\17, 1944.828
|28\10, 1976.471
1690.{{Overline|90}}
|37\13, 2018.182
|-
|Ebb, Ccc
|40\15, 1846.154
|47\18, 1819.355
|18\7, 1800
|43\17, 1779.310
|25\10, 1764.706
|32\13, 1745.545
|-
|'''Eb, Cc'''
|'''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'''
|-
|E, C
|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
|-
|-
|Ex, Cx
| Mi, Si
|43\15, 1984.615
| rowspan="2" |32\11, 2021.053
|A
|53\18, 2051.612
|21\7, 2100
|X, A
|52\17, 2151.725
|A
|31\10, 2188.235
| 38\15
|41\13, 2236.364
|-
1753; 1.{{Overline|18}}
|0b, Dc
|44\15, 2030.769
|28\11
|52\18, 2012.903
|20\7, 2000
1768; 2.375
|48\17, 1986.207
|28\10, 1976.471
|46\18
|36\13, 1963.636
1780; 1.55
| 18\7
1800
|44\17
1820; 1.45
|26\10
1835; 3.4
|34\13
1854.{{Overline|54}}
|-
|-
! 0, D
| Mi#, Si#
!45\15, 2076.923
!33\11, 2084.211
|A#
!54\18, 2090.323
!21\7, 2100
|X#, A#
!51\17, 2110.345
|A#
!30\10, 2117.647
|39\15
!39\13, 2127.273
|}
1800
 
{| class="wikitable"
| rowspan="2" |29\11
|+Cents
!Notation
1831; 1.{{Overline|72}}
!Supersoft
!Soft
|48\18
!Semisoft
! Basic
1858; 15.5
!Semihard
!Hard
|19\7
!Superhard
1900
|47\17
1944; 1.208{{Overline|3}}
|28\10
1976; 2.125
|37\13
2018.{{Overline|18}}
|-
|-
!Hextone
|Fab, Dob
!~15edf
!~11edf
|Bbb
!~18edf
!~7edf
|Ebb, Ccc
!~17edf
|Bf
!~10edf
|40\15
!~13edf
|-
1846; 6.5
|0#, G#
|1\15, 46.154
|47\18
|1\11, 63.158
|2\18, 77.419
1819; 2.{{Overline|81}}
| rowspan="2" |1\7, 100
|3\17, 124.138
|18\7
|2\10, 141.176
|3\13, 163.636
1800
|-
| 1f
|43\17
|3\15, 138.462
|2\11. 126.316
1779; 3.{{Overline|2}}
|3\18, 116.129
|2\17, 82.759
| 25\10
|1\10, 70.588
|1\13, 54.545
1764; 1.41{{Overline|6}}
|-
|'''1'''
|32\13
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
1745.{{Overline|45}}
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|1#
|5\15, 230.769
|4\11, 252.632
|7\18, 270.968
| rowspan="2" |3\7, 300
|8\17, 331.034
|5\10, 352.941
|7\13, 381.818
|-
|-
|2f
|'''Fa, Do'''
|7\15, 323.077
|5\11, 315.789
|'''Bb'''
|8\18, 309.677
|7\17, 289.655
|'''Eb, Cc'''
|4\10, 282.353
|'''B'''
|5\13, 272.727
|'''41\15'''
|-
|2
'''1892; 3.25'''
|8\15, 369.231
|6\11, 378.947
|'''30\11'''
|10\18, 387.097
| 4\7, 400
'''1894; 1, 2.8'''
|10\17, 413.793
|6\10, 423.529
|'''49\18'''
|8\13, 436.364
|-
'''1896; 1.291{{Overline|6}}'''
|2#
|9\15, 415.385
|'''19\7'''
| rowspan="2" |7\11, 442.105
|12\18, 464.516
'''1900'''
|5\7, 500
|13\17, 537.069
|'''46\17'''
|8\10, 564.706
|11\13, 600
'''1903; 2.1{{Overline|6}}'''
|-
|3f
|'''27\10'''
| 10\15, 461.538
|11\18, 425.806
'''1905; 1.1{{Overline|3}}'''
|4\7, 400
|9\17, 372.414
|'''35\13'''
|5\10, 352.941
|6\13, 327.273
'''1909.{{Overline|09}}'''
|-
|'''3'''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|-
|3#
|Fa#, Do#
|12\15, 553.846
|9\11, 568.421
| B
|15\18, 580.645
|6\7, 600
| E, C
|15\17, 620.690
| B#
|9\10, 635.294
|42\15
|12\13, 654.545
|-
1938; 2.1{{Overline|6}}
| 3x
|13\15, 600
| 31\11
| rowspan="2" | 10\11, 631.579
|17\18, 658.064
1957; 1, 8.5
|7\7, 700
|18\17, 744.828
|51\18
|11\10, 776.471
|15\13, 818.182
1974; 5.1{{Overline|6}}
|-
|4f
|20\7
| 14\15, 646.154
|16\18, 619.355
2000
|6\7, 600
|14\17, 579.310
|49\17
|8\10, 564.706
|10\13, 545.455
2027; 1, 1.41{{Overline|6}}
|-
!4
| 29\10
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
2047; 17
!'''18\18,''' '''696.774'''
!7\7, 700
|38\13
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
2072.{{Overline|72}}
!'''13\13,''' '''709.091'''
|-
| 4#
|16\15, 738.462
|12\11, 757.895
|20\18, 774.194
| rowspan="2" |8\8, 800
|20\17, 827.586
|12\10, 847.059
|16\13, 872.727
|-
|-
|5
|Fax, Dox
|18\15, 830.769
|13\11, 821.053
|B#
|21\18, 812.903
|19\17, 786.207
|Ex, Cx
| 11\10, 776.471
|Bx
|14\13, 763.63
|43\15
|-
|'''5'''
1984; 1.625
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
| rowspan="2" |32\11
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
2021; 19
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|53\18
|'''17\13,''' '''927.273'''
|-
2051; 1, 1, 1, 1.4
|5#
|20\15, 923.077
|21\7
|15\11, 947.368
| 25\18, 967.742
2100
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|52\17
|15\10, 1058.824
|20\13, 1090.909
2151; 2.625
|-
|6f
| 31\10
|22\15, 1015.385
|16\11, 1010.526
2188; 4.25
|26\18, 1006.452
|24\17, 993.103
| 41\13
|14\10, 988.235
|18\13, 981.818
2236.{{Overline|36}}
|-
|6
|23\15, 1061.538
|17\11, 1073.684
|28\18, 1083.871
|11\7, 1100
|27\17, 1117.241
|16\10, 1129.412
|21\9, 1145.455
|-
|-
|6#
| Dob, Solb
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
|Hb
|30\18, 1161.290
|12\7, 1200
|0b, Dc
|30\17, 1241.379
|Cf
|18\10, 1270.588
| 44\15
|24\13, 1309.091
2030; 1.3
|52\18
2012; 1, 9,{{Overline|3}}
|20\7
2000
|48\17
1986; 4.8{{Overline|3}}
|28\10
1976; 2.125
|36\13
1963.{{Overline|63}}
|-
|-
| 7f
!Do, Sol
|25\15, 1153.846
|29\18, 1122.581
!H
|11\7, 1100
|26\17, 1075.862
!0, D
|15\10, 1058.824
! C
|19\13, 1036.364
! 45\15
2076; 1.08'''{{Overline|3}}'''
!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}}
|-
|-
|Do#, Sol#
|'''7'''
|Η#
|'''26\15,''' '''1200'''
|0#, D#
|'''19\11,''' '''1200'''
|C#
|'''31\18,''' '''1200'''
|46\15
|'''12\7, 1200'''
2123; 13
|'''29\17,''' '''1200'''
|34\11
|'''17\10,''' '''1200'''
2147; 2, 1.4
|'''22\13,''' '''1200'''
|56\18
|-
2167; 1, 2.875
|7#
| rowspan="2" |22\7
|27\15, 1246.154
2200
|20\11, 1263.158
|54\17
|33\18, 1277.419
2234; 2, 14
|13\7, 1300
| 32\10
|32\17, 1324.138
2258; 1, 4.{{Overline|6}}
|19\10, 1341.176
|42\13
|25\13, 1363.636
2090.{{Overline|90}}
|-
|-
|Reb, Lab
|7x
|Cb
|28\15, 1292.308
|1b, 1c
| rowspan="2" |21\11, 1326.318
|Df
|35\18, 1354.834
|48\15
|14\7, 1400
2215; 2.6
|35\17, 1448.275
|35\11
|21\10, 1482.353
2210; 1.9
|28\13, 1527.273
|57\18
2206; 2, 4.{{Overline|6}}
|53\17
2193; 9.{{Overline|6}}
|31\10
2188; 4.25
|40\13
2181.{{Overline|81}}
|-
|-
|'''Re, La'''
|8f
|'''C'''
|29\15, 1338.462
|'''1'''
| 34\18, 1316.129
|'''D'''
|13\7, 1300
|'''49\15'''
|31\17, 1282.759
'''2261; 1, 1.1{{Overline|6}}'''
|18\10, 1270.588
|'''36\11'''
|23\13, 1254.545
'''2273; 1, 2.1{{Overline|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}}'''
|-
|-
|Re#, La#
! 8
|C#
!30\15, 1384.615
|1#
!22\11, 1389.473
|D#
!36\18, 1393.548
|50\15
!14\7, 1400
2307; 1.{{Overline|4}}
!34\17, 1406.897
|37\11
!20\10, 1411.765
2336; 1.1875
!26\13, 1418.182
|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}}
|-
|-
|Mib, Sib
|8#
|Db
|31\15, 1430.769
| 2b, 2c
|23\11, 1452.632
|Ef
| 38\18, 1470.968
|52\15
| rowspan="2" |15\7, 1500
2400
|37\17, 1531.034
|38\11
|22\10, 1552.941
2400
|29\13, 1581.818
|62\18
2400
|58\17
2400
|34\10
2400
|44\13
2400
|-
|-
|Mi, Si
|9f
|D
|33\15, 1523.077
|2
|24\11, 1515.789
|E
|39\18, 1509.677
|53\15
| 36\17, 1489.655
2446; 6.5
|21\10, 1482.759
|39\11
|27\13, 1472.273
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}}
|-
|-
|Mi#, Si#
|9
|D#
|'''34\15,''' '''1569.231'''
|2#
|'''25\11,''' '''1578.947'''
|E#
|'''41\18,''' '''1587.097'''
|54\15
|'''16\7,''' '''1600'''
2492; 3.25
|'''39\17,''' '''1613.793'''
| rowspan="2" |40\11
|'''23\10,''' '''1623.529'''
2526; 3.1
|'''30\13,''' '''1636.364'''
|66\18
2554; 1, 5.2
|26\7
2600
|64\17
2648; 2.625
|38\10
2682; 2.8{{Overline|3}}
|50\13
2727.{{Overline|27}}
|-
|-
|Fab, Dob
|9#
|Ebb
|35\15, 1615.385
|3b, 3c
|26\11, 1642.105
|Fff
|43\18, 1664.516
|55\15
| rowspan="2" |17\7, 1700
2538; 2.1{{Overline|6}}
|42\17, 1737.069
|65\18
|25\10, 1764.706
2516; 7.75
|33\13, 1800
| 25\7
2500
|60\17
2482; 1.3{{Overline|18}}
|35\10
2470; 1.7
|45\13
2454.{{Overline|54}}
|-
|-
|'''Fa, Do'''
|Af
|'''Eb'''
| 37\15, 1707.692
|'''3'''
| 27\11, 1705.263
|'''Ff'''
|44\18, 1703.226
|'''56\15'''
|41\17, 1696.552
'''2584; 1.625'''
|24\10, 1694.118
|'''41\11'''
|31\13, 1690.909
'''2589; 2.{{Overline|1}}'''
|-
|'''67\18'''
|A
'''2593; 1, 1, 4.{{Overline|6}}'''
| 38\15, 1753.846
|'''26\7'''
|28\11, 1768.421
'''2600'''
|46\18, 1780.645
|'''63\17'''
|18\7, 1800
'''2606; 1, 8.{{Overline|6}}'''
|44\17, 1820.690
|'''37\10'''
|26\10, 1835.294
'''2611; 1, 3.25'''
|34\13, 1854.545
|'''48\13'''
'''2618.{{Overline|18}}'''
|-
|-
|Fa#, Do#
|A#
|E
| 39\15, 1800
|3#
| rowspan="2" |29\11, 1831.579
|F
| 48\18, 1858.064
|57\15
|19\7, 1900
2630; 1.3
|47\17, 1944.828
|42\11
|28\10, 1976.471
2652; 1.58{{Overline|3}}
|37\13, 2018.182
|69\18
2670; 1.0{{Overline|3}}
| 27\7
2700
|66\17
2731; 29
|39\10
2752; 1.0625
|51\13
2781.{{Overline|81}}
|-
|-
|Fax, Dox
|Ax
|E#
|40\15, 1846.154
|3x
|47\18, 1819.355
|F#
|18\7, 1800
|58\15
|43\17, 1779.310
2676; 1.08{{Overline|3}}
|25\10, 1764.706
| rowspan="2" |43\11
|32\13, 1745.545
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}}
|-
|-
|Dob, Solb
|'''Bf'''
|Fb
|'''41\15,''' '''1892.308'''
|4b, 4c
|'''30\11,''' '''1894.737'''
|0f, Gf
|'''49\18,''' '''1896.774'''
|59\15
|'''19\7, 1900'''
2723; 13
|'''46\17,''' '''1903.448'''
|70\18
|'''27\10,''' '''1905.882'''
2709; 1, 2.1
|'''35\13,''' '''1909.091'''
|27\7
2700
|65\17
2689; 1, 1.9
|38\10
2682; 2.8{{Overline|3}}
|49\13
2672.{{Overline|72}}
|-
|-
!Do, Sol
|B
!F
|42\15, 1938.462
!4
|31\11, 1957.895
!0, G
|51\18, 1974.194
! 60\15
|20\7, 2000
2769; 4.'''{{Overline|3}}'''
|49\17, 2027.586
! 44\11
| 29\10, 2047.059
2778; 1.0{{Overline|5}}
|38\13, 2072.727
! 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
|B#
!Subdozenal
|43\15, 1984.615
!~15edf
| rowspan="2" |32\11, 2021.053
!~11edf
|53\18, 2051.612
!~18edf
|21\7, 2100
!~7edf
|52\17, 2151.725
! ~17edf
|31\10, 2188.235
!~10edf
|41\13, 2236.364
! ~13edf
|-
|-
|F ut#
|Cf
|F#
|44\15, 2030.769
|1\15
|52\18, 2012.903
46; 6.5
|20\7, 2000
|1\11
|48\17, 1986.207
63: 6.{{Overline|3}}
|28\10, 1976.471
|2\18
|36\13, 1963.636
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
!C
| Gb
!45\15, 2076.923
|3\15
!33\11, 2084.211
138; 3, 4
!54\18, 2090.323
|2\11
!21\7, 2100
126; 3, 6
!51\17, 2110.345
|3\18
!30\10, 2117.647
116; 7.75
!39\13, 2127.273
|2\17
82; 1.3{{Overline|18}}
|1\10
70; 1.7
|1\13
54.{{Overline|54}}
|-
|-
|'''G re'''
|C#
|'''G'''
|46\15, 2123.077
|'''4\15'''
|34\11, 2147.368
'''184; 1.625'''
|56\15, 2167.742
|'''3\11'''
| rowspan="2" |22\7, 2200
'''189; 2.{{Overline|1}}'''
|54\17, 2234.483
|'''5\18'''
|32\10, 2258.824
'''193; 1, 1, 4.{{Overline|6}}'''
|42\13, 2090.909
|'''2\7'''
'''200'''
|'''5\17'''
'''206; 1, 8.{{Overline|6}}'''
|'''3\10'''
'''211; 1, 3.25'''
|'''4\13'''
'''218.{{Overline|18}}'''
|-
|-
|G re
|Df
|G#
|48\15, 2215.385
| 5\15
|35\11, 2210.526
230; 1.3
|57\15, 2206.452
|4\11
|53\17, 2193.103
252; 1.58{{Overline|3}}
|31\10, 2188.235
|7\18
|40\13, 2181.818
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
|'''D'''
|Ab
|'''49\15, 2261.538'''
|7\15
|'''36\11, 1073.684'''
323; 13
|'''59\18, 2283.871'''
|5\11
|'''23\7, 2300'''
315; 1.2{{Overline|6}}
|'''56\17, 2317.241'''
| 8\18
|'''33\10, 2329.412'''
309; 1, 2.1
|'''43\13,''' '''2345.455'''
|7\17
289; 1, 1.9
|4\10
282; 2.8{{Overline|3}}
|5\13
272.{{Overline|72}}
|-
|-
|A mi
|D#
|A
|50\15, 2307.692
| 8\15
|37\11, 2336.842
369; 4.{{Overline|3}}
|61\18, 2361.290
|6\11
| rowspan="2" |24\7, 2400
378; 1.0{{Overline|5}}
|59\17, 2441.379
|10\18
|35\10, 2470.588
387; 10.{{Overline|3}}
|46\13, 2509.091
|4\7
400
| 10\17
413; 1, 3.8{{Overline|3}}
|6\10
423; 1.{{Overline|8}}
|8\13
436.{{Overline|36}}
|-
|-
|A mi#
|Ef
| A#
|52\15, 2400
|9\15
|38\11, 2400
415; 2.6
|62\18, 2400
| rowspan="2" |7\11
|58\17, 2400
442; 9.5
|34\10, 2400
| 12\18
| 44\13, 2400
464; 1.9375
|5\7
500
| 13\17
537; 14.5
|8\10
564; 1.41{{Overline|6}}
|11\13
600
|-
|-
|B fa utb
|E
|Bbb
|53\15, 2446.154
|10\15
| 39\11, 2463.158
461; 1, 1, 6
|64\18, 2477,419
|11\18
|25\7, 2500
425; 1.24
|61\17, 2524.138
|4\7
|36\10, 2541.176
400
|47\13, 2563.636
|9\17
372; 2.41{{Overline|6}}
|5\10
352; 1, 16
| 6\13
327.{{Overline|27}}
|-
|-
|'''B fa ut'''
|E#
|'''Bb'''
|54\15, 2492.308
|'''11\15'''
| rowspan="2" |40\11, 2526.316
'''507; 1.{{Overline|4}}'''
|66\18, 2554.838
|'''8\11'''
|26\7, 2600
'''505; 3.8'''
|64\17, 2648.275
|'''13\18'''
|38\10, 2682.353
'''503; 4, 2.{{Overline|3}}'''
|50\13, 2727.273
|'''5\7'''
'''500'''
|'''12\17'''
'''496; 1.8125'''
|'''7\10'''
'''494; 8.5'''
|'''9\13'''
'''490.{{Overline|90}}'''
|-
|-
|B fa ut#
|Fff
|B
| 55\15, 2538.462
| 12\15
| 65\18, 2516.129
553; 1.{{Overline|18}}
|25\7, 2500
|9\11
|60\17, 2482.759
568; 2.375
|35\10, 2470.588
|15\18
|45\13, 2454.545
580; 1.55
| 6\7
600
|15\17
620; 1.45
|9\10
635; 3.4
|12\13
654.{{Overline|54}}
|-
|-
|B fa utx
|'''Ff'''
|B#
|'''56\15, 2584.615'''
|13\15
|'''41\11, 2589.474'''
600
|'''67\18, 2593.548'''
| rowspan="2" |10\11
|'''26\7, 2600'''
631; 1.{{Overline|72}}
|'''63\17, 2606.897'''
|17\18
|'''37\10, 2611.765'''
658; 15.5
|'''48\13,''' '''2618.182'''
|7\7
700
|18\17
744; 1.208{{Overline|3}}
|11\10
776; 2, 8
|15\13
818.{{Overline|18}}
|-
|-
|C sol reb
|F
|Hb
|57\15, 2630.769
|14\15
|42\11, 2652.632
646; 6.5
|69\18, 2670.968
|16\18
|27\7, 2700
619; 2.{{Overline|81}}
|66\17, 2731.034
|6\7
|39\10, 2752.941
600
|51\13, 2781.818
|14\17
579; 3.{{Overline|2}}
|8\10
564; 1.41{{Overline|6}}
|10\13
545.{{Overline|45}}
|-
|-
!C sol re
| F#
!H
| rowspan="2" |58\15, 2676.923
!'''15\15'''
|43\11, 2715.789
'''692; 3.25'''
|71\18, 2748.387
!'''11\11'''
| 28\7, 2800
'''694; 1, 2.8'''
|69\17, 2855.172
!'''18\18'''
|41\10, 2894.118
'''696; 1.291'''{{Overline|6}}
|54\13, 2945.455
!'''7\7'''
'''700'''
!'''17\17'''
'''703; 2, 2, 6'''
!'''10\10'''
'''705; 1.1'''{{Overline|3}}
!'''13\13'''
'''709.'''{{Overline|09}}
|-
|-
|C sol re#
|0ff, Gff
| Η#
|42\11, 2652.632
|16\15
|68\18, 2632.258
738; 2.1{{Overline|6}}
|26\7, 2600
|12\11
|62\17, 2565.517
757; 1, 8.5
|36\10, 2541.176
|20\18
|46\13, 2509.091
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
|0f, Gf
|Cb
|59\15, 2723.077
|18\15
|43\11, 2715.789
830; 1.3
|70\18, 2709.677
|13\11
|27\7, 2700
821; 19
|65\17, 2689.552
|21\18
|38\10, 2682.353
812; 1, 9.{{Overline|3}}
|49\13, 2672.273
|19\17
786; 4.8{{Overline|3}}
|11\10
776; 2, 8
|14\13
763.{{Overline|63}}
|-
|-
|'''D la mi'''
!0, G
|'''C'''
!60\15, 2769.231
|'''19\15'''
!44\11, 2778.947
'''876; 1, 12'''
!72\18, 2787.097
|'''14\11'''
!28\7, 2800
'''884; 4.75'''
!68\17, 2813.793
|'''23\18'''
!40\10, 2823.529
'''890; 3.1'''
!52\13, 2836.364
|'''9\5'''
|}
'''900'''
 
|'''22\17'''
{| class="wikitable"
'''910; 2.9'''
|+Cents
|'''13\10'''
!Notation
'''917; 1.{{Overline|54}}'''
!Supersoft
|'''17\13'''
!Soft
'''927.{{Overline|27}}'''
! Semisoft
! Basic
!Semihard
!Hard
!Superhard
|-
|-
|D la mib
!Guidotonic
|C#
!~15edf
|20\15
!~11edf
923: 13
!~18edf
|15\11
!~7edf
947; 2, 1.4
!~17edf
|25\18
!~10edf
967; 1, 2.875
!~13edf
| 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
|F ut#
|Db
|1\15, 46.154
|22\15
|1\11, 63.158
1015; 2.6
|2\18, 77.419
|16\11
| rowspan="2" |1\7, 100
1010; 1.9
|3\17, 124.138
|26\18
|2\10, 141.176
1006; 2, 4.{{Overline|6}}
|3\13, 163.636
|24\17
993; 9.{{Overline|6}}
|14\10
988; 4, 4
|18\13
981.{{Overline|81}}
|-
|-
|E fa ut
|G reb
|D
|3\15, 138.462
|23\15
|2\11. 126.316
1061; 1, 1, 6
|3\18, 116.129
|17\11
|2\17, 82.759
1073; 1, 2, 6
|1\10, 70.588
|28\18
|1\13, 54.545
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#
|'''G re'''
|D#
|'''4\15,''' '''184.615'''
|24\15
|'''3\11,''' '''189.474'''
1107; 1.{{Overline|4}}
|'''5\18,''' '''193.548'''
| rowspan="2" |18\11
|'''2\7,''' '''200'''
1136; 1.1875
|'''5\17,''' '''206.897'''
|30\18
|'''3\10,''' '''211.765'''
1161; 3.{{Overline|4}}
|'''4\13,''' '''218.182'''
|12\7
1200
|30\17
1241; 2.{{Overline|63}}
|18\10
1270; 1.7
| 24\13
1309.{{Overline|09}}
|-
|-
|F sol re utb
|G re#
|Ebb
|5\15, 230.769
|25\15
|4\11, 252.632
1153; 1.{{Overline|18}}
|7\18, 270.968
|29\18
| rowspan="2" |3\7, 300
1121; 1, 1, 2.6
|8\17, 331.034
|11\7
|5\10, 352.941
1100
|7\13, 381.818
|26\17
1075; 1.16
|15\10
1058; 1, 4.{{Overline|6}}
|19\13
1036.{{Overline|36}}
|-
|-
|'''F sol re ut'''
|A mib
|'''Eb'''
|7\15, 323.077
|'''26\15'''
|5\11, 315.789
'''1200'''
|8\18, 309.677
|'''19\11'''
|7\17, 289.655
'''1200'''
|4\10, 282.353
|'''31\18'''
|5\13, 272.727
'''1200'''
|'''12\7'''
'''1200'''
|'''29\17'''
'''1200'''
|'''17\10'''
'''1200'''
|'''22\13'''
'''1200'''
|-
|-
|F sol re ut#
|A mi
|E
|8\15, 369.231
|27\15
| 6\11, 378.947
1246; 6.5
|10\18, 387.097
|20\11
|4\7, 400
1263; 6.{{Overline|3}}
|10\17, 413.793
|33\18
|6\10, 423.529
1277; 2, 2.6
|8\13, 436.364
|13\7
1300
|32\17
1324; 7.25
| 19\10
1341; 5.{{Overline|6}}
|25\13
1363.{{Overline|63}}
|-
|-
|F sol re utx
| A mi#
| E#
|9\15, 415.385
|28\15
| rowspan="2" |7\11, 442.105
1292; 3, 4
|12\18, 464.516
| rowspan="2" |21\11
|5\7, 500
1326; 3, 6
|13\17, 537.069
|35\18
|8\10, 564.706
1354; 1, 5.2
|11\13, 600
|14\7
1400
|35\17
1448; 3.625
|21\10
1482; 2.8{{Overline|3}}
|28\13
1527.{{Overline|27}}
|-
|-
|G la mi reb
|B fa utb
| Fb
|10\15, 461.538
| 29\15
|11\18, 425.806
1338; 2, 6
|4\7, 400
|34\18
|9\17, 372.414
1316; 7.75
|5\10, 352.941
|13\7
|6\13, 327.273
1300
|31\17
1282; 1.3{{Overline|18}}
|18\10
1270; 1.7
|23\13
1254.{{Overline|54}}
|-
|-
!G la mi re
|'''B fa ut'''
!F
|'''11\15,''' '''507.692'''
!30\15
|'''8\11,''' '''505.263'''
1384; 1.625
|'''13\18,''' '''503.226'''
! 22\11
|'''5\7, 500'''
1389; 2.{{Overline|1}}
|'''12\17,''' '''496.552'''
!36\18
|'''7\10,''' '''494.118'''
1393; 1, 1, 4.{{Overline|6}}
|'''9\13,''' '''490.909'''
!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#
|B fa ut#
|F#
|12\15, 553.846
|31\15
|9\11, 568.421
1430; 1.3
|15\18, 580.645
| rowspan="2" |23\11
|6\7, 600
1452; 1.58{{Overline|3}}
|15\17, 620.690
|38\18
|9\10, 635.294
1470; 1.0{{Overline|3}}
|12\13, 654.545
|15\7
1500
|37\17
1531; 29
|22\10
1552; 1, 16
|29\13
1581.{{Overline|81}}
|-
|-
|A fab
|B fa utx
|
| 13\15, 600
|32\15
| rowspan="2" |10\11, 631.579
1476; 1, 12
|17\18, 658.064
|37\18
|7\7, 700
1432; 3.875
|18\17, 744.828
|14\7
|11\10, 776.471
1400
|15\13, 818.182
|33\29
1365; 1.9{{Overline|3}}
|19\10
1341; 5.{{Overline|6}}
|24\13
1309.{{Overline|09}}
|-
|-
|A fa
|C sol re utb
|Gb
| 14\15, 646.154
|33\15
|16\18, 619.355
1523; 13
|6\7, 600
|24\11
|14\17, 579.310
1515; 1.2{{Overline|6}}
|8\10, 564.706
|39\18
|10\13, 545.455
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'''
!C sol re ut
|'''G'''
!'''15\15,''' '''692.308'''
|'''34\15'''
!'''11\11,''' '''694.737'''
'''1569; 4.{{Overline|3}}'''
!'''18\18,''' '''696.774'''
|'''25\11'''
!7\7, 700
'''1578; 1.0{{Overline|5}}'''
!'''17\17,''' '''703.448'''
|'''41\18'''
!'''10\10,''' '''705.882'''
'''1587; 10.{{Overline|3}}'''
!'''13\13,''' '''709.091'''
|'''16\7'''
'''1600'''
|'''39\17'''
'''1613; 1, 3.8{{Overline|3}}'''
|'''23\10'''
'''1623; 1.{{Overline|8}}'''
|'''30\13'''
'''1636.{{Overline|36}}'''
|-
|-
|A mi#
|C sol re ut#
|G#
|16\15, 738.462
|35\15
|12\11, 757.895
1615; 2.6
|20\18, 774.194
|26\11
| rowspan="2" |8\8, 800
1642; 9.5
|20\17, 827.586
| 43\18
|12\10, 847.059
1664; 1.9375
|16\13, 872.727
| rowspan="2" |17\7
1700
|42\17
1737; 14.5
|25\10
1764; 1.41{{Overline|6}}
| 33\13
1800
|-
|-
|B sol fa utb
|D la mi reb
|Ab
|18\15, 830.769
|37\15
|13\11, 821.053
1707; 1.{{Overline|4}}
|21\18, 812.903
|27\11
|19\17, 786.207
1705; 3.8
|11\10, 776.471
|44\18
|14\13, 763.63
1703; 4, 2.{{Overline|3}}
|41\17
1696; 1.8125
|24\10
1694; 8.5
|31\13
1690.{{Overline|90}}
|-
|-
| B sol fa ut
|'''D la mi re'''
|A
|'''19\15,''' '''876.923'''
| 38\15
|'''14\11,''' '''884.211'''
1753; 1.{{Overline|18}}
|'''23\18,''' '''890.323'''
|28\11
|'''9\5,''' '''900'''
1768; 2.375
|'''22\17,''' '''910.345'''
|46\18
|'''13\10,''' '''917.647'''
1780; 1.55
|'''17\13,''' '''927.273'''
| 18\7
1800
|44\17
1820; 1.45
|26\10
1835; 3.4
|34\13
1854.{{Overline|54}}
|-
|-
|B sol fa ut#
|D la mi re#
|A#
|20\15, 923.077
| 39\15
| rowspan="2" |15\11, 947.368
1800
|25\18, 967.742
| rowspan="2" |29\11
|10\7, 1000
1831; 1.{{Overline|72}}
|25\17, 1034.483
|48\18
|15\10, 1058.824
1858; 15.5
|20\13, 1090.909
|19\7
1900
| 47\17
1944; 1.208{{Overline|3}}
|28\10
1976; 2, 8
|37\13
2018.{{Overline|18}}
|-
|-
|C la sol reb
|E fa utb
|Bbb
|21\15, 969.231
| 40\15
|24\18, 929.032
1846; 6.5
| 9\5, 900
| 47\18
|21\17, 868.966
1819; 2.{{Overline|81}}
|12\10, 847.059
|18\7
|15\13, 818.182
1800
|43\17
1779; 3.{{Overline|2}}
|25\10
1764; 1.41{{Overline|6}}
|32\13
1745.{{Overline|45}}
|-
|-
|'''C la sol re'''
|E fa ut
|'''Bb'''
| 22\15, 1015.385
|'''41\15'''
|16\11, 1010.526
'''1892; 3, 4'''
|26\18, 1006.452
|'''30\11'''
|10\7, 1000
'''1894; 1, 2.8'''
|24\17, 993.103
|'''49\18'''
|14\10, 988.235
'''1896; 1.291{{Overline|6}}'''
|18\13, 981.818
|'''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#
|E si mi re
| B
|23\15, 1061.538
| 42\15
|17\11, 1073.684
1938; 2, 6
|28\18, 1083.871
|31\11
|11\7, 1100
1957; 1, 8.5
|27\17, 1117.241
|51\18
|16\10, 1129.412
1974; 5, 6
|21\9, 1145.455
| 20\7
2000
|49\17
2027; 1, 1.41{{Overline|6}}
|29\10
2047; 17
|38\13
2072.{{Overline|72}}
|-
|-
|C la sol rex
| E si mi re#
|B#
|24\15, 1107.923
|43\15
| rowspan="2" |18\11, 1136.842
1984; 1.625
|30\18, 1161.29
| rowspan="2" |32\11
|12\7, 1200
2021; 19
|30\17, 1241.379
|53\18
| 18\10, 1270.588
2051; 1, 1, 1, 1.4
|24\13, 1309.091
| 21\7
2100
|52\17
2151; 1, 2.625
|31\10
2188; 4.25
|41\13
2236.{{Overline|36}}
|-
|-
|D la mib
|F sol fa ut reb
| Hb
|25\15, 1153.846
|44\15
|29\18, 1122.581
2030; 1.3
|11\7, 1100
|52\18
|26\17, 1075.862
2012; 1, 9.{{Overline|3}}
|15\10, 1058.824
|20\7
|19\13, 1036.364
2000
|48\17
1986; 4.8{{Overline|3}}
|28\10
1976; 2, 8
|36\13
1963.{{Overline|63}}
|-
|-
!D la mi
|'''F sol fa ut re'''
!H
|'''26\15,''' '''1200'''
!45\15
|'''19\11,''' '''1200'''
2076; 1, 12
|'''31\18,''' '''1200'''
!33\11
|'''12\7, 1200'''
2084; 4.75
|'''29\17,''' '''1200'''
!54\18
|'''17\10,''' '''1200'''
2090; 3.1
|'''22\13,''' '''1200'''
! 21\7
2100
!51\17
2110; 2.9
!30\10
2117; 1.{{Overline|54}}
! 39\13
2127.{{Overline|27}}
|-
|-
|D la mib
|F sol fa ut re#
|Η#
|27\15, 1246.154
|46\15
|20\11, 1263.158
2123; 13
|33\18, 1277.419
|34\11
|13\7, 1300
2147; 2, 1.4
|32\17, 1324.138
| 56\18
| 19\10, 1341.176
2167; 1, 2.875
| 25\13, 1363.636
| 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
|F sol fa ut rex
|Cb
|28\15, 1292.308
|48\15
| rowspan="2" |21\11, 1326.318
2215; 2.6
|35\18, 1354.834
|35\11
| 14\7, 1400
2210; 1.9
|35\17, 1448.275
|57\18
|21\10, 1482.353
2206; 2, 4.{{Overline|6}}
|28\13, 1527.273
|53\17
2193; 9.{{Overline|6}}
|31\10
2188; 4, 4
|40\13
2181.{{Overline|81}}
|-
|-
|'''E fa ut'''
|G la sol re mib
|'''C'''
| 29\15, 1338.462
|'''49\15'''
|34\18, 1316.129
'''2261; 1, 1, 6'''
| 13\7, 1300
|'''36\11'''
|31\17, 1282.759
'''2273; 1, 2, 6'''
|18\10, 1270.588
|'''59\18'''
|23\13, 1254.545
'''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#
!G la sol re mi
|C#
!30\15, 1384.615
|50\15
!22\11, 1389.473
2307; 1.{{Overline|4}}
!36\18, 1393.548
|37\11
!14\7, 1400
2336; 1.1875
!34\17, 1406.897
|61\18
!20\10, 1411.765
2361; 3.{{Overline|4}}
!26\13, 1418.182
| 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
|G la sol re mi#
|Db
|31\15, 1430.769
|52\15
|23\11, 1452.632
2400
|38\18, 1470.968
|38\11
| rowspan="2" |15\7, 1500
2400
|37\17, 1531.034
|62\18
|22\10, 1552.941
2400
|29\13, 1581.818
|58\17
2400
|34\10
2400
|44\13
2400
|-
|-
|F sol re ut
|A si la mi fab
|D
|33\15, 1523.077
|53\15
| 24\11, 1515.789
2446; 6.5
|39\18, 1509.677
|39\11
|36\17, 1489.655
2463; 6.{{Overline|3}}
|21\10, 1482.759
|64\18
| 27\13, 1472.273
2477; 2, 2.6
|-
|25\7
|'''A si la mi fa'''
2500
|'''34\15,''' '''1569.231'''
|61\17
|'''25\11,''' '''1578.947'''
2524; 7.25
|'''41\18,''' '''1587.097'''
|36\10
|'''16\7,''' '''1600'''
2541; 5.{{Overline|6}}
|'''39\17,''' '''1613.793'''
| 47\13
|'''23\10,''' '''1623.529'''
2563.{{Overline|63}}
|'''30\13,''' '''1636.364'''
|-
|A si la mi fa#
| 35\15, 1615.385
| rowspan="2" |26\11, 1642.105
|43\18, 1664.516
|17\7, 1700
|42\17, 1737.069
| 25\10, 1764.706
|33\13, 1800
|-
|B sol fa utb
|36\61, 1661.538
|42\18, 1625.806
|16\7, 1600
|38\29, 1572.414
|22\10, 1552.941
|28\13, 1527.273
|-
|B sol fa ut
|37\15, 1707.692
|27\11, 1705.263
| 44\18, 1703.226
| 17\7, 1700
|41\17, 1696.552
|24\10, 1694.118
|31\13, 1690.909
|-
|-
|F sol re ut#
|B si
|D#
|38\15, 1753.846
|54\15
| 28\11, 1768.421
2492; 3, 4
|46\18, 1780.645
| rowspan="2" |40\11
|18\7, 1800
2526; 3.1
|44\17, 1820.690
| 66\18
|26\10, 1835.294
2554; 1, 5.2
|34\13, 1854.545
|26\7
2600
|64\17
2648; 3.625
|38\10
2682; 2.8{{Overline|3}}
|50\13
2727.{{Overline|27}}
|-
|-
|G la mi reb
|B si
|Ebb
|39\15, 1800
|55\15
| rowspan="2" |29\11, 1831.579
2538; 2, 6
|48\18, 1858.064
|65\18
|19\7, 1900
2516; 7.75
|47\17, 1944.828
| 25\7
|28\10, 1976.471
2500
|37\13, 2018.182
|60\17
2482; 1.3{{Overline|18}}
|35\10
2470; 1.7
|45\13
2454.{{Overline|54}}
|-
|-
|'''G la mi re'''
|C la sol re utb
|'''Eb'''
|40\15, 1846.154
|'''56\15'''
|47\18, 1819.355
'''2584; 1.625'''
| 18\7, 1800
|'''41\11'''
| 43\17, 1779.310
'''2589; 2.{{Overline|1}}'''
|25\10, 1764.706
|'''67\18'''
|32\13, 1745.545
'''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#
|'''C la sol re ut'''
|E
|'''41\15,''' '''1892.308'''
|57\15
|'''30\11,''' '''1894.737'''
2630; 1.3
|'''49\18,''' '''1896.774'''
|42\11
|'''19\7, 1900'''
2652; 1.58{{Overline|3}}
|'''46\17,''' '''1903.448'''
|69\18
|'''27\10,''' '''1905.882'''
2670; 1.0{{Overline|3}}
|'''35\13,''' '''1909.091'''
| 27\7
2700
|66\17
2731; 29
|39\10
2752; 1, 16
|51\13
2781.{{Overline|81}}
|-
|-
|G la mi rex
|C la sol re ut#
|E#
|42\15, 1938.462
| rowspan="2" | 58\15
|31\11, 1957.895
2676; 1, 12
|51\18, 1974.194
|43\11
|20\7, 2000
2715; 1.2{{Overline|6}}
|49\17, 2027.586
|71\18
| 29\10, 2047.059
2748; 2.58{{Overline|3}}
|38\13, 2072.727
|28\7
2800
|69\17
2855; 4.8
|41\10
2894; 8.5
|54\13
2945.{{Overline|45}}
|-
|-
|A fab
|C la sol re utx
|
| rowspan="2" |43\15, 1984.615
|42\11
|32\11, 2021.053
2652; 1.58{{Overline|3}}
|53\18, 2051.612
|68\18
|21\7, 2100
2632; 3.875
|52\17, 2151.725
|26\7
|31\10, 2188.235
2600
|41\13, 2236.364
|62\17
2565; 1.9{{Overline|3}}
|36\10
2541; 5.{{Overline|6}}
|46\13
2509.{{Overline|09}}
|-
|-
|A fa
|D fa la mi reb
|Fb
|31\11, 1957.895
|59\15
|50\18, 1935.484
2723; 13
|19\7, 1900
|43\11
|45\17, 1862.069
2715; 1.2{{Overline|6}}
|26\10, 1835.294
|70\18
|33\13, 1800
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
|D fa la mi re
!F
|44\15, 2030.769
!60\15
|32\11, 2021.053
2769; 4.'''{{Overline|3}}'''
|52\18, 2012.903
!44\11
|20\7, 2000
2778; 1.0{{Overline|5}}
|48\17, 1986.207
!72\18
|28\10, 1976.471
2787; 3.1
|36\13, 1963.636
!28\7
2800
!68\17
2813; 1, 3.8{{Overline|3}}
!40\10
2823; 1.{{Overline|8}}
!52\13
2836.{{Overline|36}}
|-
|-
|A mi#
!D si la mi re
|
!45\15, 2076.923
|61\15
!33\11, 2084.211
2815; 2.6
!54\18, 2090.323
|45\11
!21\7, 2100
2842; 9.5
! 51\17, 2110.345
|74\18
!30\10, 2117.647
2864; 1.9375
!39\13, 2127.273
| rowspan="2" |29\7
2900
|71\17
2937; 14.5
|42\10
2964; 1.41{{Overline|6}}
|55\13
3000
|-
|-
|B sol fab
|D si la mi re#
|
|46\15, 2123.077
|63\15
| rowspan="2" |34\11, 2147.368
2907; 1.{{Overline|4}}
|56\18, 2167.742
|46\11
|22\7, 2200
2905; 3.8
|54\17, 2234.483
|75\18
| 32\10, 2258.824
2903; 4, 2.{{Overline|3}}
|42\13, 2090.909
|70\17
2896; 1.8125
|41\10
2894; 8.5
|53\13
2890.{{Overline|90}}
|-
|-
|'''B sol fa'''
|E fab
|
|47\26, 2169.231
|'''64\15'''
|55\16, 2129.032
'''2953; 1.{{Overline|18}}'''
|21\7, 2100
|'''47\11'''
|50\17, 2068.966
'''2968; 2.375'''
|29\10, 2047.059
|'''77\18'''
|37\13, 2018.182
'''2980; 1.55'''
|'''30\7'''
'''3000'''
|'''73\17'''
'''3020; 1.45'''
|'''43\10'''
'''3035; 3.4'''
|'''56\13'''
'''3054.{{Overline|54}}'''
|-
|-
|B sol fa#
|E fa
|
|48\15, 2215.385
|65\15
|35\11, 2210.526
3000
|57\18, 2206.452
|48\11
|23\7, 2300
3031; 1.{{Overline|72}}
|53\17, 2193.103
|79\18
|31\10, 2188.235
3058; 15.5
|40\13, 2181.818
| 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
|E si mi
|
|49\15, 2261.538
|67\15
|36\11, 1073.684
3092; 3, 4
|59\18, 2283.871
|49\11
|24\7, 2400
3094; 1, 2.8
|56\17, 2317.241
|80\18
|33\10, 2329.412
3096; 1.291{{Overline|6}}
|43\13, 2345.455
|75\17
3103; 2, 2, 6
|44\10
3105; 1.1{{Overline|3}}
|57\13
3109.{{Overline|09}}
|-
|-
|C la sol
|E si mi#
|
|50\15, 2307.692
|68\15
| rowspan="2" |37\11, 2336.842
3138; 2, 6
|61\18, 2361.290
|50\11
| rowspan="2" |23\7, 2300
3157; 1, 8.5
| 59\17, 2441.379
|82\18
|35\10, 2470.588
3174; 5, 6
|46\13, 2509.091
|32\7
3200
|78\17
3227; 1, 1.41{{Overline|6}}
|46\10
3247; 17
|60\13
3272.{{Overline|72}}
|-
|-
|C la sol#
|F sol fa utb
|
|51\15, 2353.846
|69\15
|60\18, 2322.581
3184; 1.625
|55\17, 2275.862
| rowspan="2" |51\11
|32\10, 2258.824
3221: 19
|41\13, 2236.364
|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
|F sol fa ut
|
|52\15, 2400
|70\15
|38\11, 2400
3230; 1.3
|62\18, 2400
|83\18
|24\7, 2400
3212;  1, 9.{{Overline|3}}
|58\17, 2400
|32\7
|34\10, 2400
3200
|44\13, 2400
|77\17
3186; 4.{{Overline|3}}
|45\10
3176: 2, 8
|58\13
3172.{{Overline|72}}
|-
|-
|'''D la'''
|F sol fa ut#
|
|53\15, 2446.154
|'''71\15'''
|39\11, 2463.158
'''3276; 1, 12'''
|64\18, 2477,419
|'''52\11'''
| rowspan="2" |25\7, 2500
'''3284; 4.75'''
|61\17, 2524.138
|'''85\18'''
|36\10, 2541.176
'''3290; 3.1'''
|47\13, 2563.636
|'''33\7'''
'''3300'''
|'''80\17'''
'''3310; 2.9'''
|'''47\10'''
'''3317; 1.5{{Overline|4}}'''
|'''61\13'''
'''3327.{{Overline|27}}'''
|-
|-
|D la#
|G la sol reb
|
|55\15, 2538.462
|72\15
|40\11, 2526.316
3323; 13
|65\18, 2516.129
|53\11
|60\17, 2482.759
3347; 2, 1.4
|35\10, 2470.588
|87\18
|45\13, 2454.545
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
|'''G la sol re'''
|
|'''56\15, 2584.615'''
|74\15
|'''41\11, 2589.474'''
3415; 2.6
|'''67\18, 2593.548'''
|54\15
|'''26\7, 2600'''
3410; 1.9
|'''63\17, 2606.897'''
|88\18
|'''37\10, 2611.765'''
3406; 2, 4.{{Overline|6}}
|'''48\13,''' '''2618.182'''
|82\17
3393; 9.{{Overline|6}}
|48\10
3388; 4, 4
|62\13
3381.{{Overline|81}}
|-
|-
!F ut
|G la sol re#
!
|57\15, 2630.769
!75\15
|42\11, 2652.632
3461;  1, 1, 6
|69\18, 2670.968
!55\11
| rowspan="2" |27\7, 2700
3473; 1, 2, 6
|66\17, 2731.034
!90\18
|39\10, 2752.941
3483; 1.'''{{Overline|148}}'''
|51\13, 2781.818
!35\7
3500
!85\17
3517; 4, 7
!50\10
3529; 2, 2.{{Overline|3}}q
!65\13
3545.{{Overline|45}}
|}
==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):
|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
|-
|-
|0
!A si la mi
|Do, Sol
!60\15, 2769.231
|perfect unison
!44\11, 2778.947
|0
!72\18, 2787.097
|Do, Sol
!28\7, 2800
|sesquitave (just fifth)
!68\17, 2813.793
!40\10, 2823.529
!52\13, 2836.364
|-
|-
|1
|A si la mi#
|Fa, Do
|61\15, 2815.385
|perfect fourth
| rowspan="2" |45\11, 2842.105
| -1
| 74\18, 2864.516
|Re, La
|29\7, 2900
|perfect second
|71\17, 2937.069
|42\10, 2964.706
|55\13, 3000
|-
|-
|2
|B fab
|Mib, Sib
|62\15, 2861.538
|minor third
|73\18, 2825.806
| -2
| 28\7, 2800
|Mi, Si
|67\17, 2772.414
|major third
|39\10, 2752.941
|50\13, 2727.273
|-
|-
| 3
|B fa
|Reb, Lab
|63\15, 2907.692
|diminished second
|46\11, 2905.263
| -3
|75\18, 2903.226
|Fa#, Do#
|29\7, 2900
|augmented fourth
|70\17, 2896.552
|41\10, 2894.118
|53\13, 2890.909
|-
|-
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|'''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'''
|-
|-
|4
|B si#
|Dob, Solb
|65\15, 3000
|diminished sesquitave
|48\11, 3031.579
| -4
|79\18, 3058.064
| Do#, Sol#
| rowspan="2" |31\7, 3100
|augmented unison (chroma)
|76\17, 3144.828
|45\10, 3176.471
|59\13, 3218.182
|-
|-
|5
|C solb
|Fab, Dob
|67\15, 3092.308
|diminished fourth
|49\11, 3094.737
| -5
|80\18, 3096.774
|Re#, La#
|75\17, 3103.448
|augmented second
|44\10, 3105.882
|57\13, 3109.091
|-
|C sol
|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
|-
|C sol#
| 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
|-
|D labb
|70\15, 3230.769
|83\18, 3212.903
|32\7, 3200
|77\17, 3186.207
|45\10, 3176.471
|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}}'''
|-
|D la
|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
|-
|D la#
|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
|-
|F utb
|74\15, 3415.385
|88\18, 3406.452
|34\7, 3400
|82\17, 3393.103
|48\10, 3388.235
|62\13, 3381.818
|-
|-
|6
!F ut
|Mibb, Sibb
!75\15, 3461.538
|diminished third
!55\11, 3473.684
| -6
!90\18, 3483.871
|Mi#, Si#
!35\7, 3500
|augmented third
!85\17, 3517.241
|}  
!50\10, 3529.412
!65\13, 3545.455
==Genchain==
|}
 
The generator chain for this scale is as follows:
{| class="wikitable"
{| class="wikitable"
|Mibb
|+Cents
!Notation
Sibb
!Supersoft
|Fab
!Soft
! Semisoft
Dob
!Basic
|Dob
!Semihard
!Hard
Solb
!Superhard
|Reb
|-
!Subdozenal
Lab
!~15edf
|Mib
!~11edf
!~18edf
Sib
!~7edf
|Fa
!~17edf
!~10edf
Do
!~13edf
|Do
Sol
|Re
La
|Mi
Si
|Fa#
Do#
|Do#
Sol#
|Re#
La#
|Mi#
Si#
|-
|-
|d3
|F#
|d4
|1\15, 46.154
|d5
|1\11, 63.158
|d2
|2\18, 77.419
|m3
| rowspan="2" |1\7, 100
|P4
|3\17, 124.138
|P1
|2\10, 141.176
|P2
|3\13, 163.636
|M3
|-
|A4
|Gb, Ge
|A1
|3\15, 138.462
|A2
|2\11. 126.316
|A3
|3\18, 116.129
|}
|2\17, 82.759
|1\10, 70.588
==Modes==
|1\13, 54.545
|-
The mode names are based on the species of fifth:
|'''G'''
{| class="wikitable"
|'''4\15,''' '''184.615'''
!Mode
|'''3\11,''' '''189.474'''
!Scale
|'''5\18,''' '''193.548'''
![[Modal UDP Notation|UDP]]
|'''2\7,''' '''200'''
! colspan="3" |Interval type
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|-
!name
|G#
!pattern
|5\15, 230.769
!notation
|4\11, 252.632
!2nd
|7\18, 270.968
!3rd
| rowspan="2" |3\7, 300
!4th
|8\17, 331.034
|5\10, 352.941
|7\13, 381.818
|-
|Hb, He
|7\15, 323.077
|5\11, 315.789
|8\18, 309.677
|7\17, 289.655
|4\10, 282.353
|5\13, 272.727
|-
|H
|8\15, 369.231
|6\11, 378.947
|10\18, 387.097
|4\7, 400
|10\17, 413.793
|6\10, 423.529
|8\13, 436.364
|-
|H#
|9\15, 415.385
| rowspan="2" |7\11, 442.105
|12\18, 464.516
|5\7, 500
|13\17, 537.069
|8\10, 564.706
|11\13, 600
|-
|-
|Lydian
|Jbb, Jee
|LLLs
|10\15, 461.538
|<nowiki>3|0</nowiki>
|11\18, 425.806
|P
|4\7, 400
|M
|9\17, 372.414
|A
|5\10, 352.941
|6\13, 327.273
|-
|-
|Major
|'''Jb, Je'''
|LLsL
|'''11\15,''' '''507.692'''
|<nowiki>2|1</nowiki>
|'''8\11,''' '''505.263'''
|P
|'''13\18,''' '''503.226'''
|M
|'''5\7, 500'''
|P
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|-
|Minor
|J
|LLsL
|12\15, 553.846
|<nowiki>1|2</nowiki>
|9\11, 568.421
|P
|15\18, 580.645
|m
|6\7, 600
| P
|15\17, 620.690
|9\10, 635.294
|12\13, 654.545
|-
|-
|Phrygian
|J#
| sLLL
|13\15, 600
|<nowiki>0|3</nowiki>
| rowspan="2" |10\11, 631.579
|d
|17\18, 658.064
|m
|7\7, 700
|P
|18\17, 744.828
|}
|11\10, 776.471
|15\13, 818.182
==Temperaments==
|-
|Kb, Ke
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.
|14\15, 646.154
==='''Napoli-Meantone'''===
|16\18, 619.355
|6\7, 600
[[Subgroup]]: 3/2.6/5.8/5
|14\17, 579.310
|8\10, 564.706
[[Comma]] list: [[81/80]]
|10\13, 545.455
 
|-
[[POL2]] generator: ~9/8 = 192.6406¢
!K
 
!'''15\15,''' '''692.308'''
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
!'''11\11,''' '''694.737'''
 
!'''18\18,''' '''696.774'''
[[Optimal ET sequence]]: ~(7edf, 11edf, 18edf)
!7\7, 700
==='''Napoli-Archy'''===
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
[[Subgroup]]: 3/2.7/6.14/9
!'''13\13,''' '''709.091'''
|-
[[Comma]] list: [[64/63]]
|K#
 
|16\15, 738.462
[[POL2]] generator: ~8/7 = 218.6371¢
|12\11, 757.895
 
|20\18, 774.194
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
| rowspan="2" |8\8, 800
 
|20\17, 827.586
[[Optimal ET sequence]]: ~(7edf, 10edf, 13edf, 16edf)
|12\10, 847.059
===Scale tree===
|16\13, 872.727
|-
The spectrum looks like this:
|Lb, Le
{| class="wikitable"
|18\15, 830.769
! colspan="3" |Generator
|13\11, 821.053
|21\18, 812.903
(bright)
|19\17, 786.207
!Cents<u><ref name=":03">Fractions repeating more than 4 digits written as continued fractions</ref></u>
|11\10, 776.471
!L
|14\13, 763.63
!s
|-
!L/s
|'''L'''
!Comments
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
|-
|L#
|20\15, 923.077
| rowspan="2" |15\11, 947.368
|25\18, 967.742
|10\7, 1000
|25\17, 1034.483
|15\10, 1058.824
|20\13, 1090.909
|-
|Mbb, Mee
|21\15, 969.231
|24\18, 929.032
|9\5, 900
|21\17, 868.966
|12\10, 847.059
|15\13, 818.182
|-
|Mb, Me
|22\15, 1015.385
|16\11, 1010.526
|26\18, 1006.452
|10\7, 1000
|24\17, 993.103
|14\10, 988.235
|18\13, 981.818
|-
|M
|23\15, 1061.538
|17\11, 1073.684
|28\18, 1083.871
|11\7, 1100
|27\17, 1117.241
|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
|25\15, 1153.846
|29\18, 1122.581
|11\7, 1100
|26\17, 1075.862
|15\10, 1058.824
|19\13, 1036.364
|-
|'''Nb, Ne'''
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|N
|27\15, 1246.154
|20\11, 1263.158
|33\18, 1277.419
|13\7, 1300
|32\17, 1324.138
|19\10, 1341.176
|25\13, 1363.636
|-
|-
|1\4
|N#
|
|28\15, 1292.308
|
| rowspan="2" |21\11, 1326.318
|<u>171; 2.{{Overline|3}}</u>
|35\18, 1354.834
|1
|14\7, 1400
|1
|35\17, 1448.275
|1.000
|21\10, 1482.353
|Equalised
|28\13, 1527.273
|-
|-
|6\23
|Pb, Pe
|
|29\15, 1338.462
|
|34\18, 1316.129
|<u>180</u>
|13\7, 1300
|6
|31\17, 1282.759
|5
|18\10, 1270.588
|1.200
|23\13, 1254.545
|
|-
!P
!30\15, 1384.615
!22\11, 1389.473
!36\18, 1393.548
!14\7, 1400
!34\17, 1406.897
!20\10, 1411.765
!26\13, 1418.182
|-
|-
|
|P#
|11\42
|31\15, 1430.769
|
|23\11, 1452.632
|<u>180; 1.21{{Overline|6}}</u>
|38\18, 1470.968
|11
| rowspan="2" |15\7, 1500
|9
|37\17, 1531.034
|1.222
|22\10, 1552.941
|
|29\13, 1581.818
|-
|-
|5\19
|Qb, Qe
|
|33\15, 1523.077
|
|24\11, 1515.789
|<u>181.{{Overline|81}}</u>
|39\18, 1509.677
|5
|36\17, 1489.655
|4
|21\10, 1482.759
|1.250
|27\13, 1472.273
|
|-
|-
|
|'''Q'''
|14\53
|'''34\15,''' '''1569.231'''
|
|'''25\11,''' '''1578.947'''
|<u>182; 1, 1.5</u>
|'''41\18,''' '''1587.097'''
|14
|'''16\7,''' '''1600'''
|11
|'''39\17,''' '''1613.793'''
|1.273
|'''23\10,''' '''1623.529'''
|
|'''30\13,''' '''1636.364'''
|-
|-
|
|Q#
|9\34
|35\15, 1615.385
|
| rowspan="2" |26\11, 1642.105
|<u>183; 19.{{Overline|6}}</u>
|43\18, 1664.516
|9
|17\7, 1700
|7
|42\17, 1737.069
|1.286
|25\10, 1764.706
|
|33\13, 1800
|-
|Rb, Re
|36\61, 1661.538
|42\18, 1625.806
|16\7, 1600
|38\29, 1572.414
|22\10, 1552.941
|28\13, 1527.273
|-
|R
|37\15, 1707.692
|27\11, 1705.263
|44\18, 1703.226
|17\7, 1700
|41\17, 1696.552
|24\10, 1694.118
|31\13, 1690.909
|-
|R#
|38\15, 1753.846
|28\11, 1768.421
|46\18, 1780.645
|18\7, 1800
|44\17, 1820.690
|26\10, 1835.294
|34\13, 1854.545
|-
|-
|4\15
|R#
|
|39\15, 1800
|
| rowspan="2" |29\11, 1831.579
|<u>184; 1.625</u>
|48\18, 1858.064
|4
|19\7, 1900
|3
|47\17, 1944.828
|1.333
|28\10, 1976.471
|
|37\13, 2018.182
|-
|-
|
|Sb, Se
|11\41
|40\15, 1846.154
|
|47\18, 1819.355
|<u>185, 1, 10.8{{Overline|3}}</u>
|18\7, 1800
|11
|43\17, 1779.310
|8
|25\10, 1764.706
|1.375
|32\13, 1745.545
|
|-
|-
|
|'''S'''
|7\26
|'''41\15,''' '''1892.308'''
|
|'''30\11,''' '''1894.737'''
|<u>186.{{Overline|6}}</u>
|'''49\18,''' '''1896.774'''
|7
|'''19\7, 1900'''
|5
|'''46\17,''' '''1903.448'''
|1.400
|'''27\10,''' '''1905.882'''
|
|'''35\13,''' '''1909.091'''
|-
|S#
|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
|-
|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
|10\37
|44\15, 2030.769
|
|52\18, 2012.903
|<u>187.5</u>
|20\7, 2000
| 10
|48\17, 1986.207
|7
|28\10, 1976.471
|1.429
|36\13, 1963.636
|
|-
|-
|
!T
|13\48
!45\15, 2076.923
|
!33\11, 2084.211
|<u>187; 1, 19.75</u>
!54\18, 2090.323
|13
!21\7, 2100
|9
!51\17, 2110.345
|1.444
!30\10, 2117.647
|
!39\13, 2127.273
|-
|-
|
|T#
|16\59
|46\15, 2123.077
|
| rowspan="2" |34\11, 2147.368
|<u>188; 4.25</u>
|56\18, 2167.742
|16
|22\7, 2200
|11
|54\17, 2234.483
| 1.455
|32\10, 2258.824
|
|42\13, 2090.909
|-
|-
|3\11
|Ub, Üe
|
|47\26, 2169.231
|
|55\16, 2129.032
|<u>189; 2.{{Overline|1}}</u>
|21\7, 2100
|3
|50\17, 2068.966
|2
|29\10, 2047.059
|1.500
|37\13, 2018.182
|Napoli-Meantone starts here
|-
|Ub, Ü
|48\15, 2215.385
|35\11, 2210.526
|57\18, 2206.452
|23\7, 2300
|53\17, 2193.103
|31\10, 2188.235
|40\13, 2181.818
|-
|U
|49\15, 2261.538
|36\11, 1073.684
|59\18, 2283.871
|24\7, 2400
|56\17, 2317.241
|33\10, 2329.412
|43\13, 2345.455
|-
|-
|
|U#
|17\62
|50\15, 2307.692
|
| rowspan="2" |37\11, 2336.842
|<u>190; 1, 1.{{Overline|12}}</u>
|61\18, 2361.290
|17
| rowspan="2" |23\7, 2300
|11
|59\17, 2441.379
|1.545
|35\10, 2470.588
|
|46\13, 2509.091
|-
|-
|
|Vb, Ve
|14\51
|51\15, 2353.846
|
|60\18, 2322.581
|<u>190.{{Overline|90}}</u>
|55\17, 2275.862
|14
|32\10, 2258.824
|9
|41\13, 2236.364
|1.556
|
|-
|-
|
|V
|11\40
|52\15, 2400
|
|38\11, 2400
|<u>191; 3, 2.{{Overline|3}}</u>
|62\18, 2400
|11
|24\7, 2400
|7
|58\17, 2400
|1.571
|34\10, 2400
|
|44\13, 2400
|-
|-
|
|V#
|8\29
|53\15, 2446.154
|
|39\11, 2463.158
|<u>192</u>
|64\18, 2477,419
|8
| rowspan="2" |25\7, 2500
|5
|61\17, 2524.138
|1.600
|36\10, 2541.176
|
|47\13, 2563.636
|-
|-
|
|Wb, We
|5\18
|55\15, 2538.462
|
|40\11, 2526.316
|<u>193; 1, 1, 4.{{Overline|6}}</u>
|65\18, 2516.129
|5
|60\17, 2482.759
|3
|35\10, 2470.588
|1.667
|45\13, 2454.545
|
|-
|-
|
|'''Wb'''
|
|'''56\15, 2584.615'''
|12\43
|'''41\11, 2589.474'''
|<u>194.{{Overline|594}}</u>
|'''67\18, 2593.548'''
|12
|'''26\7, 2600'''
|7
|'''63\17, 2606.897'''
|1.714
|'''37\10, 2611.765'''
|
|'''48\13,''' '''2618.182'''
|-
|-
|
|W#
|7\25
|57\15, 2630.769
|
|42\11, 2652.632
|<u>195; 2.8{{Overline|6}}</u>
|69\18, 2670.968
|7
| rowspan="2" |27\7, 2700
|4
|66\17, 2731.034
|1.750
|39\10, 2752.941
|
|51\13, 2781.818
|-
|-
|
|Xb, Xe
|9\32
|59\15, 2723.077
|
|43\11, 2715.789
|<u>196.{{Overline|36}}</u>
|70\18, 2709.677
|9
|65\17, 2689.552
|5
|38\10, 2682.353
|1.800
|49\13, 2672.273
|
|-
|-
|
!X
|11\39
!60\15, 2769.231
|
!44\11, 2778.947
|<u>197; 67</u>
!72\18, 2787.097
|11
!28\7, 2800
|6
!68\17, 2813.793
|1.833
!40\10, 2823.529
|
!52\13, 2836.364
|-
|-
|
|X#
|13\46
|61\15, 2815.385
|
| rowspan="2" |45\11, 2842.105
|<u>197; 2.{{Overline|135}}</u>
|74\18, 2864.516
| 13
|29\7, 2900
|7
|71\17, 2937.069
|1.857
|42\10, 2964.706
|
|55\13, 3000
|-
|-
|
|Ybb, Yee
|15\53
|62\15, 2861.538
|
|73\18, 2825.806
|<u>197; 1, 2, 1, 1.{{Overline|54}}</u>
|28\7, 2800
|15
|67\17, 2772.414
|8
|39\10, 2752.941
|1.875
|50\13, 2727.273
|
|-
|-
|
|Yb, Ye
|17\60
|63\15, 2907.692
|
|46\11, 2905.263
|<u>198; 17.1{{Overline|6}}</u>
|75\18, 2903.226
|17
|29\7, 2900
|9
|70\17, 2896.552
|1.889
|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
|19\67
|68\15, 3138.462
|
|50\11, 3157.895
|<u>198: 3, 1, 28</u>
|82\18, 3174.194
|19
|32\7, 3200
|10
|78\17, 3227.586
|1.900
|46\10, 3247.059
|
|60\13, 3272.273
|-
|-
|
|Z#
|21\74
|69\15, 3184.615
|
| rowspan="2" |51\11, 3221.053
|<u>198; 2.3{{Overline|518}}</u>
|84\18, 3251.612
|21
|33\7, 3300
|11
|81\17, 3351.725
|1.909
|48\10, 3388.235
|
|63\13, 3436.364
|-
|-
|
|Ab, Æ
|23\81
|70\15, 3230.769
|
|83\18, 3212.903
|<u>198; 1, 3, 1.7</u>
|32\7, 3200
|23
|77\17, 3186.207
|12
|45\10, 3176.471
|1.917
|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#
|25\88
|72\15, 3323.077
|
|53\11, 3347.368
|<u>198; 1, 2, 12.25</u>
|87\18, 3367.742
|25
|34\7, 3400
|13
|83\17, 3434.583
|1.923
|49\10, 3458.824
|
|64\13, 3490.909
|-
|-
|
|Ax
|27\95
|73\15, 3369.231
|
| rowspan="2" |54\11, 3410.625
|<u>198; 1, 3.{{Overline|405}}</u>
|89\18, 3445.162
|27
|35\7, 3500
|14
|86\17, 3558.621
|1.929
|51\10, 3600
|
|67\13, 3654.545
|-
|-
|
|Bb, Be
|29\102
|74\15, 3415.385
|
|88\18, 3406.452
|<u>198; 1, 1.1{{Overline|6}}</u>
|34\7, 3400
|29
|82\17, 3393.103
|15
|48\10, 3388.235
|1.933
|62\13, 3381.818
|
|-
|-
|2\7
!B
|
!75\15, 3461.538
|
!55\11, 3473.684
|<u>200</u>
!90\18, 3483.871
|2
!35\7, 3500
|1
!85\17, 3517.241
|2.000
!50\10, 3529.412
|Napoli-Meantone ends, Napoli-Pythagorean begins
!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
|17\59
|78\15, 3600
|
|57\11, 3600
|<u>201.{{Overline|9801}}</u>
|93\18, 3600
|17
|87\17, 3600
|8
|51\10, 3600
|2.125
|66\13, 3600
|
|-
|-
|
|'''C'''
|15\52
|'''79\15,''' '''3646.154'''
|
|'''58\11,''' '''3663.158'''
|<u>202; 4.0{{Overline|45}}</u>
|'''95\18,''' '''3677.419'''
|15
|'''37\7,''' '''3700'''
|7
|'''90\17,''' '''3724.138'''
|2.143
|'''53\10,''' '''3741.176'''
|
|'''69\13,''' '''3763.636'''
|-
|-
|
|C#
|13\45
|80\15, 3692.308
|
|59\11, 3726.316
|<u>202; 1, 1, 2.0{{Overline|6}}</u>
|97\18, 3755.838
|13
| rowspan="2" |38\7, 3800
|6
|93\17, 3848.275
|2.167
|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
|11\38
|83\15, 3830.769
|
|61\11, 3852.632
|<u>203; 13</u>
|100\18, 3870.968
|11
|39\7, 3900
|5
|95\17, 3931.03$
|2.200
|56\10, 3952.941
|
|73\13, 3981.818
|-
|-
|
|D#
|9\31
|84\15, 3876.923
|
| rowspan="2" |62\11, 3915.789
|<u>203; 1, 3.41{{Overline|6}}</u>
|102\18, 3948.387
|9
|40\7, 4000
|4
|98\17, 4055.172
|2.250
|58\10, 4094.118
|
|76\13, 4145.455
|-
|-
|
|Ebb, Ëe
| 7\24
|85\15, 3923.077
|
|101\18, 3909.677
|<u>204; 1. 7.2</u>
|39\7, 3900
| 7
|94\17, 3889.552
|3
|55\10, 3882.353
|2.333
|71\13, 3872.727
|
|-
|-
|
|'''Eb, Ë'''
|
|'''86\15,''' '''3969.231'''
|12\41
|'''63\11,''' '''3978.947'''
|<u>205; 1.4</u>
|'''103\18,''' '''3987.097'''
|12
|'''40\7, 4000'''
|5
|'''97\17,''' '''4013.793'''
|2.400
|'''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#
|5\17
|88\15, 4061.583
|
| rowspan="2" |65\11, 4105.263
|<u>206; 1, 8.{{Overline|6}}</u>
|107\18, 4141.956
|5
|42\7, 4200
|2
|103\17, 4262.069
|2.500
|61\10, 4305.882
|Napoli-Neogothic heartland is from here…
|80\13, 4363.636
|-
|-
|
|Fb, Fe
|
|89\15, 4107.692
|18\61
|106\18, 4103.226
|<u>207; 1.{{Overline|4}}</u>
|41\7, 4100
|18
|99\17, 4096.552
|7
|58\10, 4094.118
|2.571
|75\13, 4090.909
|
|-
|-
|
!F
|
!90\15, 4153.846
|13\44
!66\11, 4168.421
|<u>208</u>
!108\18, 4180.645
|13
!42\7, 4200
|5
!102\17, 4220.690
|2.600
!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):
|8\27
|
|<u>208; 1.4375</u>
|8
|3
|2.667
|…to here
|-
|-
|
|0
|11\37
|Do, Fa, Sol
|
|perfect unison
|<u>209; 1.{{Overline|90}}</u>
|0
|11
|Do, Fa, Sol
|4
|sesquitave (just fifth)
|2.750
|
|-
|-
|
|1
|14\47
|Fa, Sib, Do
|
|perfect fourth
|<u>210</u>
| -1
|14
|Re, Sol, La
|5
|perfect second
|2.800
|
|-
|-
|
|2
|17\57
|Mib, Lab, Sib
|
|minor third
|<u>210; 3.2{{Overline|3}}</u>
| -2
|17
|Mi, La, Si
|6
|major third
|2.833
|
|-
|-
|
|3
|20\67
|Reb, Solb, Lab
|
|diminished second
|<u>210; 1.9</u>
| -3
|20
|Fa#, Si, Do#
|7
|augmented fourth
|2.857
|
|-
|-
|
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|23\77
|
|<u>210; 1.4{{Overline|5}}</u>
|23
|8
|2.875
|
|-
|-
|3\10
|4
|
|Dob, Fab, Solb
|
|diminished sesquitave
|<u>211; 1, 3.25</u>
| -4
|3
|Do#, Fa#, Sol#
|1
|augmented unison (chroma)
|3.000
|Napoli-Pythagorean ends, Napoli-Archy begins
|-
|-
|
|5
|22\73
|Fab, Sibb, Dob
|
|diminished fourth
|<u>212; 1, 9.{{Overline|3}}</u>
| -5
|22
|Re#, Sol#, La#
|7
|augmented second
|3.143
|
|-
|-
|
|19\63
|
|<u>213; 11.{{Overline|8}}</u>
|19
|6
|6
|3.167
|Mibb, Labb, Sibb
|
|diminished third
|-
| -6
|
|Mi#, La#, Si#
|16\53
|augmented third
|
|}
|<u>213.{{Overline|3}}</u>
|16
==Genchain==
|5
|3.200
The generator chain for this scale is as follows:
|
{| class="wikitable"
|-
|Mibb
|
Labb
|13\43
|
Sibb
|<u>213; 1, 2.3{{Overline|18}}</u>
|Fab
|13
Sibb
|4
|3.250
Dob
|
|Dob
|-
Fab
|
|10\33
Solb
|
|Reb
|<u>214; 3.5</u>
Solb
|10
|3
Lab
|3.333
|Mib
|
Lab
|-
|
Sib
|7\23
|Fa
|
Sib
|<u>215; 2.6</u>
|7
Do
|2
|Do
|3.500
Fa
|
Sol
|Re
Sol
La
|Mi
La
Si
|Fa#
Si
Do#
|Do#
Fa#
Sol#
|Re#
Sol#
La#
|Mi#
La#
Si#
|-
|-
|
|d3
|11\36
|d4
|
|d5
|<u>216; 2.541{{Overline|6}}</u>
|d2
|11
|m3
|3
|P4
|3.667
|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
|15\49
!pattern
|
!notation
|<u>216; 1.152{{Overline|7}}</u>
!2nd
|15
!3rd
|4
!4th
| 3.750
|
|-
|-
|
|Lydian
|19\62
|LLLs
|
|<nowiki>3|0</nowiki>
|<u>217; 7</u>
|P
|19
|M
|5
|A
|3.800
|
|-
|-
|4\13
|Major
|
|LLsL
|
|<nowiki>2|1</nowiki>
|<u>218.{{Overline|18}}</u>
|P
|4
|M
|1
|P
|4.000
|
|-
|-
|
|Minor
|13\42
|LsLL
|
|<nowiki>1|2</nowiki>
|<u>219; 1, 2.55</u>
|P
|13
|m
|3
|P
|4.333
|
|-
|-
|
|Phrygian
|9\29
|sLLL
|
|<nowiki>0|3</nowiki>
|<u>220; 2.45</u>
|d
|9
|m
|2
|P
|4.500
|}
|
|-
==Temperaments==
|
|14\45
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)'''===
|<u>221; 19</u>
|14
[[Subgroup]]: 3/2.6/5.8/5 (5.2.3)
|3
|4.667
[[Comma]] list: [[81/80]]
|
 
|-
[[POL2]] generator: ~9/8 = 192.6406¢
|5\16
 
|
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
|
 
|<u>222.{{Overline|2}}</u>
[[Optimal ET sequence]]: *[[28ed5]], [[44ed5]], [[72ed5]] ≈ [[7edf]], [[11edf]], [[18edf]]
|5
==='''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
|5.000
|1.000
|Napoli-Archy ends
|Equalised
|-
|-
|6\23
|180.000
|6
|5
|1.200
|
|
|16\51
|-
|
|5\19
|<u>223; 3.{{Overline|90}}</u>
|181.818
|16
|5
|3
|4
|5.333
|1.250
|
|
|-
|-
|
|14\53
|11\35
|182.609
|
|14
|<u>223; 1, 2.6875</u>
|11
|11
|2
|1.273
|5.500
|
|
|-
|-
|9\34
|183.051
|9
|7
|1.286
|
|
|17\54
|-
|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
|
|
|<u>224; 5.7{{Overline|2}}</u>
|-
| 17
|13\48
|187.952
|13
|9
|1.444
|
|-
|16\59
|188.253
|16
|11
|1.455
|
|-
|3\11
|189.474
|3
|3
|5.667
|2
|
|1.500
|-
|Napoli-Meantone starts here
|6\19
|-
|
|14\51
|
|190.909
|<u>225</u>
|14
|6
|9
|1
|1.556
|6.000
|
|
|-
|-
|11\40
|1\3
|191.304
|
|11
|
|7
|<u>240</u>
|1.571
|1
|
|0
|-
|→ inf
|8\29
|Paucitonic
|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


==See also==
[[12L 4s (36/7-equivalent)]] - Hextone 1/4-comma archy
[[3L 1s (3/2-equivalent)]] - idealized tuning


[[6L 2s (20/9-equivalent)]] - Neapolitan 1/2-comma meantone
[[15L 5s (15/2-equivalent)]] - Guidotonic major 1/5-comma meantone


[[6L 2s (52/23-equivalent)]] - Neapolitan gentle temperament  
[[15L 5s (84/11-equivalent)]] - Guidotonic major gentle temperament


[[6L 2s (16/7-equivalent)]] - Neapolitan 1/2-comma archy
[[15L 5s (54/7-equivalent)]] - Guidotonic major 1/5-comma archy


[[9L 3s (10/3-equivalent)]] - Bijou 1/3-comma meantone
[[18L 6s (11/1-equivalent)]] - Subdozenal harmonic tuning


[[9L 3s (22/13-equivalent]]) - Bijou gentle temperament
[[18L 6s (56/5-equivalent)]] - Subdozenal low septimal (meantone) tuning


[[9L 3s (24/7-equivalent)]] - Bijou 1/3-comma archy
[[18L 6s (512/45-equivalent)]] - Subdozenal 1/6-comma meantone


[[12L 4s (5/1-equivalent)]] - Hex meantone
[[18L 6s (80/7-equivalent)]] - Subdozenal high septimal tuning


[[12L 4s (56/11-equivalent)]] - Hextone gentle temperament
[[18L 6s (128/11-equivalent)]] - Subdozenal subharmonic tuning


[[12L 4s (36/7-equivalent)]] - Hextone 1/4-comma archy<references />
[[18L 6s (11/1-equivalent)|18L 6s (12/1-equivalent)]] - Warped Pythagorean tuning
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