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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, 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, 4
 
 
|2\10
|Reb, Solb, Lab
141; 5, 1.5
|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, 4
 
 
|2\11
|'''Re, Sol, La'''
126; 3, 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, 7
 
 
| 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, 9'''
|'''5\18'''
'''193; 1, 1, 4, 1.5'''
 
 
|'''2\7'''
|5\10, 352.941
 
 
'''200'''
|7\13, 381.818
 
 
|'''5\17'''
|-
'''206; 1, 8, 1.5'''
 
 
|'''3\10'''
|Mib, Lab, Sib
'''211; 1, 3, 4'''
|7\15, 323.077
 
 
|'''4\13'''
|5\11, 315.789
 
 
'''218.{{Overline|18}}'''
|8\18, 309.677
|-
 
 
|Re#, La#
|7\17, 289.655
 
 
|G#
|4\10, 282.353
 
 
|1#
|5\13, 272.727
|1#
|5\15
230; 1.3
 
 
|4\11
|-
252; 1, 1, 1.4
 
 
|7\18
|Mi, La, Si
270; 1, 30
|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, 16
 
 
| 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, 3.75
 
 
|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, 1.2
 
 
| 5\13
|-
 
 
272.{{Overline|72}}
|Fab, Sibb, Dob
|10\15, 461.538
 
 
|-
|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, 3
 
 
|6\11
|-
378; 1, 18
 
 
|10\18
|'''Fa, Sib, Do'''
387; 10, 3
|'''11\15,''' '''507.692'''
 
 
|4\7
|'''8\11,''' '''505.263'''
 
 
400
|'''13\18,''' '''503.226'''
 
 
|10\17
|'''5\7, 500'''
413; 1, 3, 1.2
 
 
| 6\10
|'''12\17,''' '''496.552'''
423; 1, 1, 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; 1.9375
 
 
|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, 2.4
 
 
|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, 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, 2.4
 
 
|5\10
!'''18\18,''' '''696.774'''
352; 1, 16
 
 
|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, 2, 4'''
 
 
|'''8\11'''
Cents
'''505; 3.8'''
!Notation
!Supersoft
 
 
|'''13\18'''
! Soft
'''503; 4, 2, 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, 5.5
 
 
|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, 1.375
| 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, 4.8
|-
 
 
|11\10
|'''G'''
|'''4\15,''' '''184.615'''
 
 
776; 2, 8
|'''3\11,''' '''189.474'''
|15\13
|'''5\18,''' '''193.548'''
 
 
818.{{Overline|18}}
|'''2\7,''' '''200'''
 
 
|-
|'''5\17,''' '''206.897'''
 
 
|Dob, Solb
|'''3\10,''' '''211.765'''
| Hb
|4b, 4c
|4f
| 14\15
646; 6.5
|16\18
619; 2, 1, 4.5
| 6\7
600
|14\17
579; 3.{{Overline|2}}
|8\10
564; 1, 2.4
|10\13
 
 
545.{{Overline|45}}
|'''4\13,''' '''218.182'''
 
 
|-
|-
 
 
!Do, Sol
|G#
|5\15, 230.769
 
 
! H
|4\11, 252.632
 
 
!4
|7\18, 270.968
!4
!'''15\15'''
 
 
'''692; 3, 4'''
| rowspan="2" |3\7, 300
 
 
!'''11\11'''
| 8\17, 331.034
'''694; 1, 2.8'''
 
 
!'''18\18'''
|5\10, 352.941
 
 
'''696; 1, 3, 2, 3'''
|7\13, 381.818
 
 
!'''7\7'''
|-
'''700'''
 
 
!'''17\17'''
|Ab, Æ
|7\15, 323.077
 
 
'''703; 2, 2, 6'''
|5\11, 315.789
 
 
!'''10\10'''
|8\18, 309.677
 
 
'''705; 1, 7.5'''
|7\17, 289.655
 
 
!'''13\13'''
|4\10, 282.353
 
 
'''709.'''{{Overline|09}}
|5\13, 272.727
 
 
|-
|-
 
 
|Do#, Sol#
|A
| 8\15, 369.231
 
 
|Η#
|6\11, 378.947
| 4#
|4#
|16\15
 
 
738; 2, 6
|10\18, 387.097
 
 
| 12\11
| 4\7, 400
 
 
757; 1, 8.5
|10\17, 413.793
 
 
|20\18
|6\10, 423.529
 
 
774; 5, 6
|8\13, 436.364
 
 
| rowspan="2" |8\8
|-
 
 
800
|A#
| 9\15, 415.385
 
 
|20\17
| rowspan="2" |7\11, 442.105
 
 
827; 1, 1, 2.4
|12\18, 464.516
 
 
|12\10
|5\7, 500
 
 
847; 17
|13\17, 537.069
 
 
| 16\13
|8\10, 564.706
 
 
872.{{Overline|72}}
|11\13, 600
 
 
|-
|-
 
 
|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, 3
|'''Bb, Be'''
|'''11\15,''' '''507.692'''
 
 
|19\17
|'''8\11,''' '''505.263'''
 
 
786; 4, 1.2
|'''13\18,''' '''503.226'''
 
 
|11\10
|'''5\7, 500'''
 
 
776; 2, 8
|'''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'''
 
 
|'''5'''
|9\11, 568.421
|'''5'''
 
 
|'''19\15'''
|15\18, 580.645
 
 
'''876; 1, 12'''
|6\7, 600
 
 
|'''14\11'''
| 15\17, 620.690
 
 
'''884; 4.75'''
|9\10, 635.294
 
 
|'''23\18'''
|12\13, 654.545
 
 
'''890; 3.1'''
|-
| B#
| 13\15, 600
 
 
|'''9\5'''
| rowspan="2" |10\11, 631.579
 
 
'''900'''
|17\18, 658.064
 
 
|'''22\17'''
|7\7, 700
 
 
'''910; 2.9'''
|18\17, 744.828
 
 
|'''13\10'''
|11\10, 776.471
 
 
'''917; 1, 1, 1.2'''
|15\13, 818.182
 
 
|'''17\13'''
|-
|Hb, He
'''927.{{Overline|27}}'''
|14\15, 646.154
| 16\18, 619.355
|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
|12\11, 757.895
 
 
|25\17
|20\18, 774.194
 
 
1034; 2, 14
| rowspan="2" |8\8, 800
 
 
|15\10
|20\17, 827.586
 
 
1058; 1, 4, 1.5
|12\10, 847.059
 
 
|20\13
|16\13, 872.727
1090.{{Overline|90}}
 
 
|-
|-
 
 
|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, 1.5
|'''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, 4
|'''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, 6
| rowspan="2" |10\7, 1000
 
 
|17\11
|25\17, 1034.483
 
 
1073; 1, 2, 6
|15\10, 1058.824
 
 
|28\18
|20\13, 1090.909
 
 
1083; 1, 6.75
|-
|11\7
1100
 
 
|27\17
| Db, De
|22\15, 1015.385
 
 
1117; 4, 7
|16\11, 1010.526
 
 
|16\10
|26\18, 1006.452
 
 
1129; 2, 2, 3
|24\17, 993.103
 
 
|21\9
|14\10, 988.235
 
 
1145.{{Overline|45}}
|18\13, 981.818
 
 
|-
|-
 
 
|Mi#, Si#
|D
|23\15, 1061.538
 
 
|D#
|17\11, 1073.684
 
 
|6#
|28\18, 1083.871
| 6#
|24\15
 
 
1107; 1, 2, 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, 2, 4
|-
 
 
|12\7
|D#
|24\15, 1107.923
1200
 
 
| 30\17
| rowspan="2" |18\11, 1136.842
 
 
1241; 2, 1, 1.75
|30\18, 1161.29
 
 
| 18\10
|12\7, 1200
 
 
1270; 1.7
|30\17, 1241.379
 
 
|24\13
|18\10, 1270.588
 
 
1309.{{Overline|09}}
|24\13, 1309.091
 
 
|-
|-
 
 
|Fab, Dob
|Ebb, Ëe
|25\15, 1153.846
 
 
|Ebb
|29\18, 1122.581
 
 
|7b, 7c
|11\7, 1100
|7f
|25\15
 
 
1153; 1, 5.5
|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, 1.5
|'''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'''
'''1200'''
 
 
|'''29\17'''
| rowspan="2" |21\11, 1326.318
 
 
'''1200'''
|35\18, 1354.834
 
 
|'''17\10'''
|14\7, 1400
 
 
'''1200'''
|35\17, 1448.275
 
 
|'''22\13'''
| 21\10, 1482.353
 
 
'''1200'''
|28\13, 1527.273
 
 
|-
|-
 
 
| Fa#, Do#
| Fb, Fe
|29\15, 1338.462
 
 
|E
|34\18, 1316.129
 
 
|7#
|13\7, 1300
|7#
|27\15
 
 
1246; 6.5
|31\17, 1282.759
 
 
| 20\11
|18\10, 1270.588
 
 
1263; 6, 3
|23\13, 1254.545
 
 
|33\18
|-
 
 
1277; 2, 2.6
!F
!30\15, 1384.615
 
 
|13\7
!22\11, 1389.473
 
 
1300
!36\18, 1393.548
 
 
|32\17
!14\7, 1400
 
 
1324; 7, 4
!34\17, 1406.897
 
 
|19\10
!20\10, 1411.765
1341; 5, 1.5
|25\13
1363.{{Overline|63}}
 
 
!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#
|Fax, Dox
|1\15, 46.154
|1\11, 63.158
|E#
|2\18, 77.419
| rowspan="2" |1\7, 100
| 7x
|3\17, 124.138
|7x
|2\10, 141.176
|28\15
|3\13, 163.636
|-
1292; 3, 4
|1b, 1c
|3\15, 138.462
| rowspan="2" |21\11
| 2\11. 126.316
|3\18, 116.129
1326; 3, 6
|2\17, 82.759
|1\10, 70.588
|35\18
|1\13, 54.545
|-
1354; 1, 5.2
|'''1'''
|'''4\15,''' '''184.615'''
| 14\7
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
1400
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|35\17
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
1448; 3.625
|-
|1#
|21\10
|5\15, 230.769
|4\11, 252.632
1482; 2, 1.2
|7\18, 270.968
| rowspan="2" |3\7, 300
| 28\13
|8\17, 331.034
|5\10, 352.941
1527.{{Overline|27}}
|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
|Dob, Solb
|8\15, 369.231
|6\11, 378.947
|Fb
|10\18, 387.097
|4\7, 400
|8b, Fc
|10\17, 413.793
|8f
|6\10, 423.529
|29\15
|8\13, 436.364
|-
1338; 2, 6
|2#
| 9\15, 415.385
|34\18
| rowspan="2" |7\11, 442.105
|12\18, 464.516
1316; 7.75
|5\7, 500
|13\17, 537.069
|13\7
|8\10, 564.706
|11\13, 600
1300
|-
|3b, 3c
|31\17
| 10\15, 461.538
| 11\18, 425.806
1282; 1, 3, 7
|4\7, 400
|9\17, 372.414
|18\10
|5\10, 352.941
|6\13, 327.273
1270; 1.7
|-
|'''3'''
| 23\13
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
1254.{{Overline|54}}
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''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
!30\15
|15\13, 818.182
|-
1384; 1.625
|4b, 4c
|14\15, 646.154
!22\11
|16\18, 619.355
|6\7, 600
1389; 2, 9
|14\17, 579.310
|8\10, 564.706
! 36\18
|10\13, 545.455
|-
1393; 1, 1, 4, 1.5
!4
!'''15\15,''' '''692.308'''
!14\7
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
1400
!7\7, 700
!'''17\17,''' '''703.448'''
! 34\17
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
1406; 1, 8, 1.5
|-
|4#
!20\10
| 16\15, 738.462
|12\11, 757.895
1411; 1, 3, 4
|20\18, 774.194
| rowspan="2" |8\8, 800
!26\13
|20\17, 827.586
|12\10, 847.059
1418.{{Overline|18}}
| 16\13, 872.727
|-
|5b, 5c
|18\15, 830.769
|13\11, 821.053
|21\18, 812.903
|19\17, 786.207
|11\10, 776.471
|14\13, 763.63
|-
|-
|'''5'''
|Do#, Sol#
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
|F#
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
|8#, F#
|'''22\17,''' '''910.345'''
|8#
|'''13\10,''' '''917.647'''
|31\15
|'''17\13,''' '''927.273'''
1430; 1.3
|23\11
1452; 1, 1, 1.4
|38\18
1470; 1, 30
| rowspan="2" |15\7
1500
|37\17
1531; 29
|22\10
1552; 1, 16
|29\13
1581.{{Overline|81}}
|-
|-
|5#
|Reb, Lab
|20\15, 923.077
|15\11, 947.368
|Gb
|25\18, 967.742
| rowspan="2" |10\7, 1000
|9b, Gc
|25\17, 1034.483
| 9f
|15\10, 1058.824
|33\15
|20\13, 1090.909
1523; 13
|24\11
1515; 1, 3.75
|39\18
1509; 1, 2.1
|36\17
1489; 1, 1.9
|21\10
1482; 2, 1.2
|27\13
1472.{{Overline|72}}
|-
|-
|6b, 6c
|'''Re, La'''
|22\15, 1015.385
|16\11, 1010.526
|'''G'''
|26\18, 1006.452
|24\17, 993.103
|'''9, G'''
|14\10, 988.235
| 9
|18\13, 981.818
|'''34\15'''
|-
|6
'''1569; 4, 3'''
|23\15, 1061.538
|17\11, 1073.684
|'''25\11'''
| 28\18, 1083.871
|11\7, 1100
'''1578; 1, 18'''
|27\17, 1117.241
|16\10, 1129.412
|'''41\18'''
|21\9, 1145.455
|-
'''1587; 10, 3'''
|6#
|24\15, 1107.923
|'''16\7'''
| rowspan="2" |18\11, 1136.842
|30\18, 1161.290
'''1600'''
|12\7, 1200
|30\17, 1241.379
|'''39\17'''
|18\10, 1270.588
|24\13, 1309.091
'''1613; 1, 3, 1.2'''
|-
| 7b, 7c
|'''23\10'''
|25\15, 1153.846
|29\18, 1122.581
'''1623; 1, 1, 8'''
|11\7, 1100
|26\17, 1075.862
|'''30\13'''
|15\10, 1058.824
|19\13, 1036.364
'''1636.{{Overline|36}}'''
|-
|'''7'''
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|7#
|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
|-
|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
!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
|-
|8#, F#
|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
|-
|9b, Gc
|33\15, 1523.077
|24\11, 1515.789
|39\18, 1509.677
|36\17, 1489.655
|21\10, 1482.759
|27\13, 1472.273
|-
|'''9, G'''
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.364'''
|-
|-
|Re#, La#
|G#
|9#, G#
|9#, G#
| 9#
|35\15, 1615.385
|35\15
|26\11, 1642.105
|43\18, 1664.516
1615; 2.6
| rowspan="2" |17\7, 1700
|42\17, 1737.069
|26\11
|25\10, 1764.706
|33\13, 1800
1642; 9.5
|43\18
1664; 1, 6.75
| rowspan="2" |17\7
1700
|42\17
1737; 14.5
|25\10
1764; 1, 2.4
|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, 2, 4
|41\17, 1696.552
|24\10, 1694.118
|27\11
|31\13, 1690.909
1705; 3.8
|44\18
1703; 4, 2, 3
|41\17
1696; 1.8125
|24\10
1694; 8.5
|31\13
1690.{{Overline|90}}
|-
|-
| Mi, Si
|A
|X, A
|X, A
|A
|38\15, 1753.846
| 38\15
|28\11, 1768.421
|46\18, 1780.645
1753; 1, 5.5
|18\7, 1800
|44\17, 1820.690
|28\11
|26\10, 1835.294
|34\13, 1854.545
1768; 2.375
|-
|X#, A#
|46\18
|39\15, 1800
| rowspan="2" |29\11, 1831.579
1780; 1.55
|48\18, 1858.064
|19\7, 1900
| 18\7
|47\17, 1944.828
|28\10, 1976.471
1800
|37\13, 2018.182
|-
|44\17
|Ebb, Ccc
|40\15, 1846.154
1820; 1.45
|47\18, 1819.355
|18\7, 1800
|26\10
|43\17, 1779.310
|25\10, 1764.706
1835; 3.4
|32\13, 1745.545
|-
|34\13
|'''Eb, Cc'''
|'''41\15,''' '''1892.308'''
1854.{{Overline|54}}
|'''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
|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
| 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, 1. 375
!Supersoft
!Soft
|48\18
!Semisoft
! Basic
1858; 15.5
!Semihard
!Hard
|19\7
!Superhard
1900
|47\17
1944; 1, 4.8
|28\10
1976; 2, 8
|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, 1, 4.5
| 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, 4.5
|3\18, 116.129
|2\17, 82.759
| 25\10
|1\10, 70.588
|1\13, 54.545
1764; 1, 2.4
|-
|'''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#
|'''Fa, Do'''
|5\15, 230.769
|4\11, 252.632
|'''Bb'''
|7\18, 270.968
| rowspan="2" |3\7, 300
|'''Eb, Cc'''
|8\17, 331.034
|'''B'''
|5\10, 352.941
|'''41\15'''
|7\13, 381.818
|-
'''1892; 3, 4'''
|2f
|7\15, 323.077
|'''30\11'''
|5\11, 315.789
|8\18, 309.677
'''1894; 1, 2.8'''
|7\17, 289.655
|4\10, 282.353
|'''49\18'''
|5\13, 272.727
|-
'''1896; 1, 3, 2, 3'''
|2
|8\15, 369.231
|'''19\7'''
|6\11, 378.947
|10\18, 387.097
'''1900'''
| 4\7, 400
|10\17, 413.793
|'''46\17'''
|6\10, 423.529
|8\13, 436.364
'''1903; 2, 6'''
|-
|2#
|'''27\10'''
|9\15, 415.385
| rowspan="2" |7\11, 442.105
'''1905; 1, 7.5'''
|12\18, 464.516
|5\7, 500
|'''35\13'''
|13\17, 537.069
|8\10, 564.706
'''1909.{{Overline|09}}'''
|11\13, 600
|-
|-
|3f
|Fa#, Do#
| 10\15, 461.538
|11\18, 425.806
| B
|4\7, 400
|9\17, 372.414
| E, C
|5\10, 352.941
| B#
|6\13, 327.273
|42\15
|-
|'''3'''
1938; 2, 6
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
| 31\11
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
1957; 1, 8.5
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|51\18
|'''9\13,''' '''490.909'''
|-
1974; 5, 6
|3#
|12\15, 553.846
|20\7
|9\11, 568.421
|15\18, 580.645
2000
|6\7, 600
|15\17, 620.690
|49\17
|9\10, 635.294
|12\13, 654.545
2027; 1, 1, 2.4
|-
| 3x
| 29\10
|13\15, 600
| rowspan="2" | 10\11, 631.579
2047; 17
|17\18, 658.064
|7\7, 700
|38\13
|18\17, 744.828
|11\10, 776.471
2072.{{Overline|72}}
|15\13, 818.182
|-
|4f
| 14\15, 646.154
|16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
|-
!4
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
!7\7, 700
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
|-
|-
| 4#
|Fax, Dox
|16\15, 738.462
|12\11, 757.895
|B#
|20\18, 774.194
| rowspan="2" |8\8, 800
|Ex, Cx
|20\17, 827.586
|Bx
|12\10, 847.059
|43\15
|16\13, 872.727
|-
1984; 1.625
|5
|18\15, 830.769
| rowspan="2" |32\11
|13\11, 821.053
|21\18, 812.903
2021; 19
|19\17, 786.207
| 11\10, 776.471
|53\18
|14\13, 763.63
|-
2051; 1, 1, 1, 1.4
|'''5'''
|'''19\15,''' '''876.923'''
|21\7
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
2100
|'''9\5,''' '''900'''
|'''22\17,''' '''910.345'''
|52\17
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
2151; 2.625
|-
|5#
| 31\10
|20\15, 923.077
|15\11, 947.368
2188; 4, 4
| 25\18, 967.742
| rowspan="2" |10\7, 1000
| 41\13
|25\17, 1034.483
|15\10, 1058.824
2236.{{Overline|36}}
|20\13, 1090.909
|-
|6f
|22\15, 1015.385
|16\11, 1010.526
|26\18, 1006.452
|24\17, 993.103
|14\10, 988.235
|18\13, 981.818
|-
|-
|6
| Dob, Solb
|23\15, 1061.538
|17\11, 1073.684
|Hb
|28\18, 1083.871
|11\7, 1100
|0b, Dc
|27\17, 1117.241
|Cf
|16\10, 1129.412
| 44\15
|21\9, 1145.455
|-
2030; 1.3
|6#
|24\15, 1107.923
|52\18
| rowspan="2" |18\11, 1136.842
|30\18, 1161.290
2012; 1, 9, 3
|12\7, 1200
|30\17, 1241.379
|20\7
|18\10, 1270.588
|24\13, 1309.091
2000
|48\17
1986; 4, 1.2
|28\10
1976; 2, 8
|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, 12
!33\11
2084; 4.75
!54\18
2090; 3.1
!21\7
2100
!51\17
2110; 2.9
!30\10
2117; 1, 1, 1.2
!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
| rowspan="2" |22\7
2200
|54\17
2234; 2, 14
| 32\10
2258; 1, 4, 1.5
|42\13
2090.{{Overline|90}}
|-
|-
|Reb, Lab
|7#
|Cb
|27\15, 1246.154
|1b, 1c
|20\11, 1263.158
|Df
|33\18, 1277.419
|48\15
|13\7, 1300
2215; 2.6
|32\17, 1324.138
|35\11
|19\10, 1341.176
2210; 1.9
|25\13, 1363.636
|57\18
2206; 2, 4, 1.5
|53\17
2193; 9.{{Overline|6}}
|31\10
2188; 4, 4
|40\13
2181.{{Overline|81}}
|-
|-
|'''Re, La'''
|7x
|'''C'''
|28\15, 1292.308
|'''1'''
| rowspan="2" |21\11, 1326.318
|'''D'''
|35\18, 1354.834
|'''49\15'''
|14\7, 1400
'''2261; 1, 1, 6'''
|35\17, 1448.275
|'''36\11'''
|21\10, 1482.353
'''2273; 1, 2, 6'''
|28\13, 1527.273
|'''59\18'''
'''2283; 1, 6.75'''
|'''23\7'''
'''2300'''
|'''56\17'''
'''2317; 4, 7'''
|'''33\10'''
'''2329; 2, 2, 3'''
|'''43\13'''
'''2245.{{Overline|45}}'''
|-
|-
|Re#, La#
|8f
|C#
|29\15, 1338.462
|1#
| 34\18, 1316.129
|D#
|13\7, 1300
|50\15
|31\17, 1282.759
2307; 1, 2, 4
|18\10, 1270.588
|37\11
|23\13, 1254.545
2336; 1, 5, 3
|61\18
2361; 3, 2, 4
| rowspan="2" |24\7
2400
|59\17
2441; 2, 1, 1.75
|35\10
2470; 1.7
| 46\13
2509.{{Overline|09}}
|-
|-
|Mib, Sib
! 8
|Db
!30\15, 1384.615
| 2b, 2c
!22\11, 1389.473
|Ef
!36\18, 1393.548
|52\15
!14\7, 1400
2400
!34\17, 1406.897
|38\11
!20\10, 1411.765
2400
!26\13, 1418.182
|62\18
2400
|58\17
2400
|34\10
2400
|44\13
2400
|-
|-
|Mi, Si
|8#
|D
|31\15, 1430.769
|2
|23\11, 1452.632
|E
| 38\18, 1470.968
|53\15
| rowspan="2" |15\7, 1500
2446; 6.5
|37\17, 1531.034
|39\11
|22\10, 1552.941
2463; 6, 3
|29\13, 1581.818
|64\18
2477; 2, 2.6
|25\7
2500
|61\17
2524; 7, 4
|36\10
2541; 5, 3
|47\13
2563.{{Overline|63}}
|-
|-
|Mi#, Si#
|9f
|D#
|33\15, 1523.077
|2#
|24\11, 1515.789
|E#
|39\18, 1509.677
|54\15
| 36\17, 1489.655
2492; 3, 4
|21\10, 1482.759
| rowspan="2" |40\11
|27\13, 1472.273
2526; 3, 6
|66\18
2554; 1, 5.2
|26\7
2600
|64\17
2648; 2.625
|38\10
2682; 2, 1.2
|50\13
2727.{{Overline|27}}
|-
|-
|Fab, Dob
|9
|Ebb
|'''34\15,''' '''1569.231'''
|3b, 3c
|'''25\11,''' '''1578.947'''
|Fff
|'''41\18,''' '''1587.097'''
|55\15
|'''16\7,''' '''1600'''
2538; 2, 1
|'''39\17,''' '''1613.793'''
|65\18
|'''23\10,''' '''1623.529'''
2516; 7.75
|'''30\13,''' '''1636.364'''
| 25\7
2500
|60\17
2482; 1, 3, 7
|35\10
2470; 1.7
|45\13
2454.{{Overline|54}}
|-
|-
|'''Fa, Do'''
|9#
|'''Eb'''
|35\15, 1615.385
|'''3'''
|26\11, 1642.105
|'''Ff'''
|43\18, 1664.516
|'''56\15'''
| rowspan="2" |17\7, 1700
'''2584; 1.625'''
|42\17, 1737.069
|'''41\11'''
|25\10, 1764.706
'''2589; 2, 9'''
|33\13, 1800
|'''67\18'''
'''2593; 1, 1, 4, 1.5'''
|'''26\7'''
'''2600'''
|'''63\17'''
'''2606; 1, 8, 1.5'''
|'''37\10'''
'''2611; 1, 3, 4'''
|'''48\13'''
'''2618.{{Overline|18}}'''
|-
|-
|Fa#, Do#
|Af
|E
| 37\15, 1707.692
|3#
| 27\11, 1705.263
|F
|44\18, 1703.226
|57\15
|41\17, 1696.552
2630; 1.3
|24\10, 1694.118
|42\11
|31\13, 1690.909
2652; 1, 1, 1.4
|-
|69\18
|A
2670; 1, 30
| 38\15, 1753.846
| 27\7
|28\11, 1768.421
2700
|46\18, 1780.645
|66\17
|18\7, 1800
2731; 29
|44\17, 1820.690
|39\10
|26\10, 1835.294
2752; 1, 16
|34\13, 1854.545
|51\13
|-
2781.{{Overline|81}}
|A#
| 39\15, 1800
| rowspan="2" |29\11, 1831.579
| 48\18, 1858.064
|19\7, 1900
|47\17, 1944.828
|28\10, 1976.471
|37\13, 2018.182
|-
|-
|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, 12
|25\10, 1764.706
| rowspan="2" |43\11
|32\13, 1745.545
2715; 1, 3.75
|71\18
2748; 2, 1, 1.4
|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, 1.2
|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; 4,3
|49\17, 2027.586
! 44\11
| 29\10, 2047.059
2778; 1, 18
|38\13, 2072.727
! 72\18
2787; 3.1
!28\7
2800
!68\17
2813; 1, 3, 1.2
! 40\10
2823; 1, 1, 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, 3
|28\10, 1976.471
|2\18
|36\13, 1963.636
77; 2, 2.6
| rowspan="2" |1\7
100
|3\17
124; 7, 4
|2\10
141; 5, 1.5
|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, 7
|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, 9'''
|54\17, 2234.483
|'''5\18'''
|32\10, 2258.824
'''193; 1, 1, 4, 1.5'''
|42\13, 2090.909
|'''2\7'''
'''200'''
|'''5\17'''
'''206; 1, 8, 1.5'''
|'''3\10'''
'''211; 1, 3, 4'''
|'''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, 1, 1.4
|31\10, 2188.235
|7\18
|40\13, 2181.818
270; 1, 30
| rowspan="2" |3\7
300
|8\17
331; 29
|5\10
352; 1, 16
|7\13
381.{{Overline|81}}
|-
|-
|A mib
|'''D'''
|Hb
|'''49\15, 2261.538'''
|7\15
|'''36\11, 1073.684'''
323; 13
|'''59\18, 2283.871'''
|5\11
|'''23\7, 2300'''
315; 1, 3.75
|'''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, 1.2
|5\13
272.{{Overline|72}}
|-
|-
|A mi
|D#
|H
|50\15, 2307.692
| 8\15
|37\11, 2336.842
369; 4, 3
|61\18, 2361.290
|6\11
| rowspan="2" |24\7, 2400
378; 1, 18
|59\17, 2441.379
|10\18
|35\10, 2470.588
387; 10, 3
|46\13, 2509.091
|4\7
400
| 10\17
413; 1, 3, 1.2
|6\10
423; 1, 1, 8
|8\13
436.{{Overline|36}}
|-
|-
|A mi#
|Ef
| H#
|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; 1, 13.5
|8\10
564; 1, 2.4
|11\13
600
|-
|-
|B fa utb
|E
|Jbb
|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
|47\13, 2563.636
400
|-
|9\17
|E#
372; 2, 2.4
|54\15, 2492.308
|5\10
| rowspan="2" |40\11, 2526.316
352; 1, 16
|66\18, 2554.838
| 6\13
|26\7, 2600
327.{{Overline|27}}
|64\17, 2648.275
|38\10, 2682.353
|50\13, 2727.273
|-
|-
|'''B fa ut'''
|Fff
|'''Jb'''
| 55\15, 2538.462
|'''11\15'''
| 65\18, 2516.129
'''507; 1, 2, 4'''
|25\7, 2500
|'''8\11'''
|60\17, 2482.759
'''505; 3.8'''
|35\10, 2470.588
|'''13\18'''
|45\13, 2454.545
'''503; 4, 2, 3'''
|'''5\7'''
'''500'''
|'''12\17'''
'''496; 1.8125'''
|'''7\10'''
'''494; 8.5'''
|'''9\13'''
'''490.{{Overline|90}}'''
|-
|-
|B fa ut#
|'''Ff'''
|J
|'''56\15, 2584.615'''
| 12\15
|'''41\11, 2589.474'''
553; 1, 5.5
|'''67\18, 2593.548'''
|9\11
|'''26\7, 2600'''
568; 2.375
|'''63\17, 2606.897'''
|15\18
|'''37\10, 2611.765'''
580; 1.55
|'''48\13,''' '''2618.182'''
| 6\7
600
|15\17
620; 1.45
|9\10
635; 3.4
|12\13
654.{{Overline|54}}
|-
|-
|B fa utx
|F
|J#
|57\15, 2630.769
|13\15
|42\11, 2652.632
|69\18, 2670.968
600
|27\7, 2700
| rowspan="2" |10\11
|66\17, 2731.034
|39\10, 2752.941
631; 1, 1.375
|51\13, 2781.818
|17\18
658; 15.5
|7\7
700
|18\17
744; 1, 4.8
|11\10
776; 2, 8
|15\13
818.{{Overline|18}}
|-
|-
|C sol reb
| F#
|Kb
| rowspan="2" |58\15, 2676.923
|14\15
|43\11, 2715.789
|71\18, 2748.387
646; 6.5
| 28\7, 2800
|16\18
|69\17, 2855.172
|41\10, 2894.118
619; 2, 1, 4.5
|54\13, 2945.455
|6\7
600
|14\17
579; 3.{{Overline|2}}
|8\10
564; 1, 2.4
|10\13
545.{{Overline|45}}
|-
|-
!C sol re
|0ff, Gff
!K
|42\11, 2652.632
!'''15\15'''
|68\18, 2632.258
|26\7, 2600
'''692; 3, 4'''
|62\17, 2565.517
!'''11\11'''
|36\10, 2541.176
|46\13, 2509.091
'''694; 1, 2.8'''
!'''18\18'''
'''696; 1, 3, 2, 3'''
!'''7\7'''
'''700'''
!'''17\17'''
'''703; 2, 2, 6'''
!'''10\10'''
'''705; 1, 7.5'''
!'''13\13'''
'''709.'''{{Overline|09}}
|-
|-
|C sol re#
|0f, Gf
| K#
|59\15, 2723.077
|16\15
|43\11, 2715.789
|70\18, 2709.677
738; 2, 6
|27\7, 2700
|12\11
|65\17, 2689.552
|38\10, 2682.353
757; 1, 8.5
|49\13, 2672.273
|20\18
774; 5, 6
| rowspan="2" |8\8
800
|20\17
827; 1, 1, 2.4
|12\10
847; 17
| 16\13
872.{{Overline|72}}
|-
|-
|D la mib
!0, G
|Lb
!60\15, 2769.231
|18\15
!44\11, 2778.947
!72\18, 2787.097
830; 1.3
!28\7, 2800
|13\11
!68\17, 2813.793
!40\10, 2823.529
821; 19
!52\13, 2836.364
|21\18
|}
 
812; 1, 9, 3
{| class="wikitable"
|19\17
|+Cents
!Notation
786; 4, 1.2
!Supersoft
|11\10
!Soft
776; 2, 8
! Semisoft
|14\13
! Basic
763.{{Overline|63}}
!Semihard
!Hard
!Superhard
|-
|-
|'''D la mi'''
!Guidotonic
|'''L'''
!~15edf
|'''19\15'''
!~11edf
!~18edf
'''876; 1, 12'''
!~7edf
|'''14\11'''
!~17edf
!~10edf
'''884; 4.75'''
!~13edf
|'''23\18'''
'''890; 3.1'''
|'''9\5'''
'''900'''
|'''22\17'''
'''910; 2.9'''
|'''13\10'''
'''917; 1, 1, 1.2'''
|'''17\13'''
'''927.{{Overline|27}}'''
|-
|-
|D la mi#
|F ut#
|L#
|1\15, 46.154
|20\15
|1\11, 63.158
|2\18, 77.419
923: 13
| rowspan="2" |1\7, 100
|15\11
|3\17, 124.138
|2\10, 141.176
947; 2, 1.4
|3\13, 163.636
|25\18
967; 1, 2.875
| rowspan="2" |10\7
1000
|25\17
1034; 2, 14
|15\10
1058; 1, 4, 1.5
|20\13
1090.{{Overline|90}}
|-
|-
|E fa utb
|G reb
|Mb
|3\15, 138.462
|22\15
|2\11. 126.316
|3\18, 116.129
1015; 2.6
|2\17, 82.759
|16\11
|1\10, 70.588
|1\13, 54.545
1010; 1.9
|26\18
1006; 2, 4, 1.5
|24\17
993; 9.{{Overline|6}}
|14\10
988; 4, 4
|18\13
981.{{Overline|81}}
|-
|-
|E fa ut
|'''G re'''
|M
|'''4\15,''' '''184.615'''
|23\15
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
1061; 1, 1, 6
|'''2\7,''' '''200'''
|17\11
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
1073; 1, 2, 6
|'''4\13,''' '''218.182'''
|28\18
1083; 1, 6.75
|11\7
1100
|27\17
1117; 4, 7
|16\10
1129; 2, 2, 3
|21\9
1145.{{Overline|45}}
|-
|-
|E fa ut#
|G re#
|M#
|5\15, 230.769
|24\15
|4\11, 252.632
|7\18, 270.968
1107; 1, 2, 4
| rowspan="2" |3\7, 300
| rowspan="2" |18\11
|8\17, 331.034
|5\10, 352.941
1136; 1.1875
|7\13, 381.818
|30\18
1161; 3, 2, 4
|12\7
1200
|30\17
1241; 2, 1, 1.75
|18\10
1270; 1.7
| 24\13
1309.{{Overline|09}}
|-
|-
|F sol re utb
|A mib
|Nbb
|7\15, 323.077
|25\15
|5\11, 315.789
|8\18, 309.677
1153; 1, 5.5
|7\17, 289.655
|29\18
|4\10, 282.353
|5\13, 272.727
1121; 1, 1, 2.6
|11\7
1100
|26\17
1075; 1.16
|15\10
1058; 1, 4, 1.5
|19\13
1036.{{Overline|36}}
|-
|-
|'''F sol re ut'''
|A mi
|'''Nb'''
|8\15, 369.231
|'''26\15'''
| 6\11, 378.947
|10\18, 387.097
'''1200'''
|4\7, 400
|'''19\11'''
|10\17, 413.793
|6\10, 423.529
'''1200'''
|8\13, 436.364
|'''31\18'''
'''1200'''
|'''12\7'''
'''1200'''
|'''29\17'''
'''1200'''
|'''17\10'''
'''1200'''
|'''22\13'''
'''1200'''
|-
|-
|F sol re ut#
| A mi#
|N
|9\15, 415.385
|27\15
| rowspan="2" |7\11, 442.105
|12\18, 464.516
1246; 6.5
|5\7, 500
|20\11
|13\17, 537.069
|8\10, 564.706
1263; 6, 3
|11\13, 600
|33\18
1277; 2, 2.6
|13\7
1300
|32\17
1324; 7, 4
| 19\10
1341; 5, 1.5
|25\13
1363.{{Overline|63}}
|-
|-
|F sol re utx
|B fa utb
| N#
|10\15, 461.538
|28\15
|11\18, 425.806
|4\7, 400
1292; 3, 4
|9\17, 372.414
| rowspan="2" |21\11
|5\10, 352.941
|6\13, 327.273
1326; 3, 6
|35\18
1354; 1, 5.2
|14\7
1400
|35\17
1448; 3.625
|21\10
1482; 2, 1.2
|28\13
1527.{{Overline|27}}
|-
|-
|G la mi reb
|'''B fa ut'''
| Pb
|'''11\15,''' '''507.692'''
| 29\15
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
1338; 2, 6
|'''5\7, 500'''
|34\18
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
1316; 7.75
|'''9\13,''' '''490.909'''
|13\7
1300
|31\17
1282; 1, 3, 7
|18\10
1270; 1.7
|23\13
1254.{{Overline|54}}
|-
|-
!G la mi re
|B fa ut#
!P
|12\15, 553.846
!30\15
|9\11, 568.421
|15\18, 580.645
1384; 1.625
|6\7, 600
! 22\11
|15\17, 620.690
|9\10, 635.294
1389; 2, 9
|12\13, 654.545
!36\18
1393; 1, 1, 4, 1.5
!14\7
1400
!34\17
1406; 1, 8, 1.5
!20\10
1411; 1, 3, 4
!26\13
1418.{{Overline|18}}
|-
|-
|G la mi re#
|B fa utx
|P#
| 13\15, 600
|31\15
| rowspan="2" |10\11, 631.579
|17\18, 658.064
1430; 1.3
|7\7, 700
| rowspan="2" |23\11
|18\17, 744.828
|11\10, 776.471
1452; 1, 1, 1.4
|15\13, 818.182
|38\18
1470; 1, 30
|15\7
1500
|37\17
1531; 29
|22\10
1552; 1, 16
|29\13
1581.{{Overline|81}}
|-
|-
|A fab
|C sol re utb
|Qbb
| 14\15, 646.154
|32\15
|16\18, 619.355
1476; 1, 12
|6\7, 600
|37\18
|14\17, 579.310
1432; 3.875
|8\10, 564.706
|14\7
|10\13, 545.455
1400
|33\17
1365; 1, 1, 14
|19\10
1341; 5, 1.5
|24\13
1309.{{Overline|09}}
|-
|-
|A fa
!C sol re ut
|Qb
!'''15\15,''' '''692.308'''
|33\15
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
1523; 13
!7\7, 700
|24\11
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
1515; 1, 3.75
!'''13\13,''' '''709.091'''
|39\18
1509; 1, 2.1
|15\7
1500
|36\17
1489; 1, 1.9
|21\10
1482; 2, 1.2
|27\13
1472.{{Overline|72}}
|-
|-
|'''A mi'''
|C sol re ut#
|'''Q'''
|16\15, 738.462
|'''34\15'''
|12\11, 757.895
|20\18, 774.194
'''1569; 4, 3'''
| rowspan="2" |8\8, 800
|'''25\11'''
|20\17, 827.586
|12\10, 847.059
'''1578; 1, 18'''
|16\13, 872.727
|'''41\18'''
|-
|D la mi reb
'''1587; 10, 3'''
|18\15, 830.769
|'''16\7'''
|13\11, 821.053
|21\18, 812.903
'''1600'''
|19\17, 786.207
|'''39\17'''
|11\10, 776.471
|14\13, 763.63
'''1613; 1, 3, 1.2'''
|-
|'''23\10'''
|'''D la mi re'''
|'''19\15,''' '''876.923'''
'''1623; 1, 1, 8'''
|'''14\11,''' '''884.211'''
|'''30\13'''
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
'''1636.{{Overline|36}}'''
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
|-
|-
|A mi#
|D la mi re#
|Q#
|20\15, 923.077
|35\15
| rowspan="2" |15\11, 947.368
|25\18, 967.742
1615; 2.6
|10\7, 1000
|26\11
|25\17, 1034.483
|15\10, 1058.824
1642; 9.5
|20\13, 1090.909
| 43\18
1664; 1, 6.75
| rowspan="2" |17\7
1700
|42\17
1737; 1, 13.5
|25\10
1764; 1, 2.4
| 33\13
1800
|-
|-
|B sol fa utb  
|E fa utb
|Rb
|21\15, 969.231
|37\15
|24\18, 929.032
| 9\5, 900
1707; 1, 2, 4
|21\17, 868.966
|27\11
|12\10, 847.059
|15\13, 818.182
1705; 3.8
|44\18
1703; 4, 2, 3
|41\17
1696; 1.8125
|24\10
1694; 8.5
|31\13
1690.{{Overline|90}}
|-
|-
| B sol fa ut
|E fa ut
|R
| 22\15, 1015.385
| 38\15
|16\11, 1010.526
|26\18, 1006.452
1753; 1, 5.5
|10\7, 1000
|28\11
|24\17, 993.103
|14\10, 988.235
1768; 2.375
|18\13, 981.818
|46\18
|-
|E si mi re
1780; 1.55
|23\15, 1061.538
| 18\7
|17\11, 1073.684
|28\18, 1083.871
1800
|11\7, 1100
|44\17
|27\17, 1117.241
|16\10, 1129.412
1820; 1.45
|21\9, 1145.455
|26\10
1835; 3.4
|34\13
1854.{{Overline|54}}
|-
|-
|B sol fa ut#
| E si mi re#
|R#
|24\15, 1107.923
| 39\15
| rowspan="2" |18\11, 1136.842
|30\18, 1161.29
1800
|12\7, 1200
| rowspan="2" |29\11
|30\17, 1241.379
| 18\10, 1270.588
1831; 1, 1.375
|24\13, 1309.091
|48\18
1858; 15.5
|19\7
1900
| 47\17
1944; 1, 4.8
|28\10
1976; 2, 8
|37\13
2018.{{Overline|18}}
|-
|-
|C la sol reb
|F sol fa ut reb
|Sbb
|25\15, 1153.846
| 40\15
|29\18, 1122.581
|11\7, 1100
1846; 6.5
|26\17, 1075.862
| 47\18
|15\10, 1058.824
|19\13, 1036.364
1819; 2, 1, 4.5
|18\7
1800
|43\17
1779; 3, 4.5
|25\10
1764; 1, 2.4
|32\13
1745.{{Overline|45}}
|-
|-
|'''C la sol re'''
|'''F sol fa ut re'''
|'''Sb'''
|'''26\15,''' '''1200'''
|'''41\15'''
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
'''1892; 3, 4'''
|'''12\7, 1200'''
|'''30\11'''
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
'''1894; 1, 2.8'''
|'''22\13,''' '''1200'''
|'''49\18'''
'''1896; 1, 3, 2, 3'''
|'''19\7'''
'''1900'''
|'''46\17'''
'''1903; 2, 6'''
|'''27\10'''
'''1905; 1, 7.5'''
|'''35\13'''
'''1909.{{Overline|09}}'''
|-
|-
| C la sol re#
|F sol fa ut re#
| S#
|27\15, 1246.154
| 42\15
|20\11, 1263.158
|33\18, 1277.419
1938; 2, 6
|13\7, 1300
|31\11
|32\17, 1324.138
| 19\10, 1341.176
1957; 1, 8.5
| 25\13, 1363.636
|51\18
|-
|F sol fa ut rex
1974; 5, 6
|28\15, 1292.308
| 20\7
| rowspan="2" |21\11, 1326.318
|35\18, 1354.834
2000
| 14\7, 1400
|49\17
|35\17, 1448.275
|21\10, 1482.353
2027; 1, 1, 2.4
|28\13, 1527.273
|29\10
|-
|G la sol re mib
2047; 17
| 29\15, 1338.462
|38\13
|34\18, 1316.129
| 13\7, 1300
2072.{{Overline|72}}
|31\17, 1282.759
|18\10, 1270.588
|23\13, 1254.545
|-
!G la sol re mi
!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
|-
|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
|-
|-
|C la sol rex
|A si la mi fab
|Sx
|33\15, 1523.077
|43\15
| 24\11, 1515.789
|39\18, 1509.677
1984; 1.625
|36\17, 1489.655
| rowspan="2" |32\11
|21\10, 1482.759
| 27\13, 1472.273
2021; 19
|53\18
2051; 1, 1, 1, 1.4
| 21\7
2100
|52\17
2151; 2.625
|31\10
2188; 4, 4
|41\13
2236.{{Overline|36}}
|-
|-
|D la mib
|'''A si la mi fa'''
| Tb
|'''34\15,''' '''1569.231'''
|44\15
|'''25\11,''' '''1578.947'''
|'''41\18,''' '''1587.097'''
2030; 1.3
|'''16\7,''' '''1600'''
|52\18
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
2012; 1, 9, 3
|'''30\13,''' '''1636.364'''
|20\7
2000
|48\17
1986; 4, 1.2
|28\10
1976; 2, 8
|36\13
1963.{{Overline|63}}
|-
|-
!D la mi
|A si la mi fa#
!T
| 35\15, 1615.385
!45\15
| rowspan="2" |26\11, 1642.105
|43\18, 1664.516
2076; 1, 12
|17\7, 1700
!33\11
|42\17, 1737.069
| 25\10, 1764.706
2084; 4.75
|33\13, 1800
!54\18
|-
|B sol fa utb
2090; 3.1
|36\61, 1661.538
! 21\7
|42\18, 1625.806
|16\7, 1600
2100
|38\29, 1572.414
!51\17
|22\10, 1552.941
|28\13, 1527.273
2110; 2.9
!30\10
2117; 1, 1, 1.2
! 39\13
2127.{{Overline|27}}
|-
|-
|D la mib
|B sol fa ut
|T#
|37\15, 1707.692
|46\15
|27\11, 1705.263
2123; 13
| 44\18, 1703.226
|34\11
| 17\7, 1700
2147; 2, 1.4
|41\17, 1696.552
| 56\18
|24\10, 1694.118
2167; 1, 2.875
|31\13, 1690.909
| rowspan="2" |22\7
2200
| 54\17
2234; 2, 14
| 32\10
2258; 1, 4, 1.5
|42\13
2090.{{Overline|90}}
|-
|-
|E fa utb
|B si
|Ub
|38\15, 1753.846
|48\15
| 28\11, 1768.421
2215; 2.6
|46\18, 1780.645
|35\11
|18\7, 1800
2210; 1.9
|44\17, 1820.690
|57\18
|26\10, 1835.294
2206; 2, 4, 1.5
|34\13, 1854.545
|53\17
2193; 9.{{Overline|6}}
|31\10
2188; 4, 4
|40\13
2181.{{Overline|81}}
|-
|-
|'''E fa ut'''
|B si
|'''U'''
|39\15, 1800
|'''49\15'''
| rowspan="2" |29\11, 1831.579
'''2261; 1, 1, 6'''
|48\18, 1858.064
|'''36\11'''
|19\7, 1900
'''2273; 1, 2, 6'''
|47\17, 1944.828
|'''59\18'''
|28\10, 1976.471
'''2283; 1, 6.75'''
|37\13, 2018.182
|'''23\7'''
'''2300'''
|'''56\17'''
'''2317; 4, 7'''
|'''33\10'''
'''2329; 2, 2, 3'''
|'''43\13'''
'''2245.{{Overline|45}}'''
|-
|-
|E fa ut#
|C la sol re utb
|U
|40\15, 1846.154
|50\15
|47\18, 1819.355
2307; 1, 2, 4
| 18\7, 1800
|37\11
| 43\17, 1779.310
2336; 1, 5, 3
|25\10, 1764.706
|61\18
|32\13, 1745.545
2361; 3, 2, 4
| rowspan="2" |24\7
2400
|59\17
2441; 2, 1, 1.75
|35\10
2470; 1.7
|46\13
2509.{{Overline|09}}
|-
|-
|F sol re utb
|'''C la sol re ut'''
|Vb
|'''41\15,''' '''1892.308'''
|52\15
|'''30\11,''' '''1894.737'''
2400
|'''49\18,''' '''1896.774'''
|38\11
|'''19\7, 1900'''
2400
|'''46\17,''' '''1903.448'''
|62\18
|'''27\10,''' '''1905.882'''
2400
|'''35\13,''' '''1909.091'''
|58\17
2400
|34\10
2400
|44\13
2400
|-
|-
|F sol re ut
|C la sol re ut#
|V
|42\15, 1938.462
|53\15
|31\11, 1957.895
2446; 6.5
|51\18, 1974.194
|39\11
|20\7, 2000
2463; 6, 3
|49\17, 2027.586
|64\18
| 29\10, 2047.059
2477; 2, 2.6
|38\13, 2072.727
|25\7
2500
|61\17
2524; 7, 4
|36\10
2541; 5, 3
| 47\13
2563.{{Overline|63}}
|-
|-
|F sol re ut#
|C la sol re utx
|V#
| rowspan="2" |43\15, 1984.615
|54\15
|32\11, 2021.053
2492; 3, 4
|53\18, 2051.612
| rowspan="2" |40\11
|21\7, 2100
2526; 3, 6
|52\17, 2151.725
| 66\18
|31\10, 2188.235
2554; 1, 5.2
|41\13, 2236.364
|26\7
2600
|64\17
2648; 2.625
|38\10
2682; 2, 1.2
|50\13
2727.{{Overline|27}}
|-
|-
|G la mi reb
|D fa la mi reb
|Wbb
|31\11, 1957.895
|55\15
|50\18, 1935.484
2538; 2, 1
|19\7, 1900
|65\18
|45\17, 1862.069
2516; 7.75
|26\10, 1835.294
| 25\7
|33\13, 1800
2500
|60\17
2482; 1, 3, 7
|35\10
2470; 1.7
|45\13
2454.{{Overline|54}}
|-
|-
|'''G la mi re'''
|D fa la mi re
|'''Wb'''
|44\15, 2030.769
|'''56\15'''
|32\11, 2021.053
'''2584; 1.625'''
|52\18, 2012.903
|'''41\11'''
|20\7, 2000
'''2589; 2, 9'''
|48\17, 1986.207
|'''67\18'''
|28\10, 1976.471
'''2593; 1, 1, 4, 1.5'''
|36\13, 1963.636
|'''26\7'''
'''2600'''
|'''63\17'''
'''2606; 1, 8, 1.5'''
|'''37\10'''
'''2611; 1, 3, 4'''
|'''48\13'''
'''2618.{{Overline|18}}'''
|-
|-
|G la mi re#
!D si la mi re
|W
!45\15, 2076.923
|57\15
!33\11, 2084.211
2630; 1.3
!54\18, 2090.323
|42\11
!21\7, 2100
2652; 1, 1, 1.4
! 51\17, 2110.345
|69\18
!30\10, 2117.647
2670; 1, 30
!39\13, 2127.273
| 27\7
2700
|66\17
2731; 29
|39\10
2752; 1, 16
|51\13
2781.{{Overline|81}}
|-
|-
|G la mi rex
|D si la mi re#
|W#
|46\15, 2123.077
| rowspan="2" | 58\15
| rowspan="2" |34\11, 2147.368
2676; 1, 12
|56\18, 2167.742
|43\11
|22\7, 2200
2715; 1, 3.75
|54\17, 2234.483
|71\18
| 32\10, 2258.824
2748; 2, 1, 1.4
|42\13, 2090.909
|28\7
2800
|69\17
2855; 5.8
|41\10
2894; 8.5
|54\13
2945.{{Overline|45}}
|-
|-
|A fab
|E fab
|Xbb
|47\26, 2169.231
|42\11
|55\16, 2129.032
2652; 1, 1, 1.4
|21\7, 2100
|68\18
|50\17, 2068.966
2632; 3.875
|29\10, 2047.059
|26\7
|37\13, 2018.182
2600
|62\17
2565; 1, 1, 14
|36\10
2541; 5, 1.5
|46\13
2509.{{Overline|09}}
|-
|-
|A fa
|E fa
|Xb
|48\15, 2215.385
|59\15
|35\11, 2210.526
2723; 13
|57\18, 2206.452
|43\11
|23\7, 2300
2715; 1, 3.75
|53\17, 2193.103
|70\18
|31\10, 2188.235
2709; 1, 2.1
|40\13, 2181.818
|27\7
2700
|65\17
2689; 1, 1.9
|38\10
2682; 2, 1.2
|49\13
2672.{{Overline|72}}
|-
|-
!A mi
|E si mi
!X
|49\15, 2261.538
!60\15
|36\11, 1073.684
2769; 4, 3
|59\18, 2283.871
!44\11
|24\7, 2400
2778; 1, 18
|56\17, 2317.241
!72\18
|33\10, 2329.412
2787; 3.1
|43\13, 2345.455
!28\7
2800
!68\17
2813; 1, 3, 1.2
!40\10
2823; 1, 1, 8
!52\13
2836.{{Overline|36}}
|-
|-
|A mi#
|E si mi#
|X#
|50\15, 2307.692
|61\15
| rowspan="2" |37\11, 2336.842
2815; 2.6
|61\18, 2361.290
|45\11
| rowspan="2" |23\7, 2300
2842; 9.5
| 59\17, 2441.379
|74\18
|35\10, 2470.588
2864; 1.9375
|46\13, 2509.091
| rowspan="2" |29\7
2900
|71\17
2937; 1, 13.5
|42\10
2964; 1, 2.4
|55\13
3000
|-
|-
|B sol fab
|F sol fa utb
|Yb
|51\15, 2353.846
|63\15
|60\18, 2322.581
2907; 1, 2, 4
|55\17, 2275.862
|46\11
|32\10, 2258.824
2905; 3.8
|41\13, 2236.364
|75\18
2903; 4, 2, 3
|70\17
2896; 1.8125
|41\10
2894; 8.5
|53\13
2890.{{Overline|90}}
|-
|-
|'''B sol fa'''
|F sol fa ut
|'''Y'''
|52\15, 2400
|'''64\15'''
|38\11, 2400
'''2953; 1, 5.5'''
|62\18, 2400
|'''47\11'''
|24\7, 2400
'''2968; 2.375'''
|58\17, 2400
|'''77\18'''
|34\10, 2400
'''2980; 1.55'''
|44\13, 2400
|'''30\7'''
'''3000'''
|'''73\17'''
'''3020; 1.45'''
|'''43\10'''
'''3035; 3.4'''
|'''56\13'''
'''3054.{{Overline|54}}'''
|-
|-
|B sol fa#
|F sol fa ut#
|Y#
|53\15, 2446.154
|65\15
|39\11, 2463.158
3000
|64\18, 2477,419
|48\11
| rowspan="2" |25\7, 2500
3031; 1, 1.375
|61\17, 2524.138
|79\18
|36\10, 2541.176
3058; 15.5
|47\13, 2563.636
| 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 la sol reb
|Zb
|55\15, 2538.462
|67\15
|40\11, 2526.316
3092; 3, 4
|65\18, 2516.129
|49\11
|60\17, 2482.759
3094; 1, 2.8
|35\10, 2470.588
|80\18
|45\13, 2454.545
3096; 1, 3, 2, 3
|75\17
3103; 2, 2, 6
|44\10
3105; 1, 7.5
|57\13
3109.{{Overline|09}}
|-
|-
|C la sol
|'''G la sol re'''
|Z
|'''56\15, 2584.615'''
|68\15
|'''41\11, 2589.474'''
3138; 2, 6
|'''67\18, 2593.548'''
|50\11
|'''26\7, 2600'''
3157; 1, 8.5
|'''63\17, 2606.897'''
|82\18
|'''37\10, 2611.765'''
3174; 5, 6
|'''48\13,''' '''2618.182'''
|32\7
3200
|78\17
3227; 1, 1, 2.4
|46\10
3247; 17
|60\13
3272.{{Overline|72}}
|-
|-
|C la sol#
|G la sol re#
|Z#
|57\15, 2630.769
|69\15
|42\11, 2652.632
3184; 1.625
|69\18, 2670.968
| rowspan="2" |51\11
| rowspan="2" |27\7, 2700
3221: 19
|66\17, 2731.034
|84\18
|39\10, 2752.941
3251; 1, 1, 1, 1.4
|51\13, 2781.818
|33\7
3300
|81\17
3351; 1, 2.625
|48\10
3388; 4, 4
|63\13
3436.{{Overline|36}}
|-
|-
|D labb
|A si la mib
|Ab
|59\15, 2723.077
|70\15
|43\11, 2715.789
3230; 1.3
|70\18, 2709.677
|83\18
|65\17, 2689.552
3212;  1, 9, 3
|38\10, 2682.353
|32\7
|49\13, 2672.273
3200
|77\17
3186; 4, 3
|45\10
3176: 2, 8
|58\13
3163.{{Overline|63}}
|-
|-
|'''D lab'''
!A si la mi
|'''A'''
!60\15, 2769.231
|'''71\15'''
!44\11, 2778.947
'''3276; 1, 12'''
!72\18, 2787.097
|'''52\11'''
!28\7, 2800
'''3284; 4.75'''
!68\17, 2813.793
|'''85\18'''
!40\10, 2823.529
'''3290; 3.1'''
!52\13, 2836.364
|'''33\7'''
'''3300'''
|'''80\17'''
'''3310; 2.9'''
|'''47\10'''
'''3317; 1, 1, 1.2'''
|'''61\13'''
'''3327.{{Overline|27}}'''
|-
|-
|D la
|A si la mi#
|A#
|61\15, 2815.385
|72\15
| rowspan="2" |45\11, 2842.105
3323; 13
| 74\18, 2864.516
|53\11
|29\7, 2900
3347; 2, 1.4
|71\17, 2937.069
|87\18
|42\10, 2964.706
3367; 1, 2.875
|55\13, 3000
|34\7
3400
|83\17
3434; 2, 14
|49\10
3458; 1, 4, 1.5
|64\13
3490.{{Overline|90}}
|-
|-
|D la#
|B fab
|Ax
|62\15, 2861.538
|73\15
|73\18, 2825.806
3369; 4, 3
| 28\7, 2800
| rowspan="2" |54\15
|67\17, 2772.414
3410; 1.9
|39\10, 2752.941
|89\18
|50\13, 2727.273
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
|Bb
|63\15, 2907.692
|74\15
|46\11, 2905.263
3415; 2.6
|75\18, 2903.226
|88\18
|29\7, 2900
3406; 2, 4, 1.5
|70\17, 2896.552
|34\7
|41\10, 2894.118
3400
|53\13, 2890.909
|82\17
3393; 9, 1.5
|48\10
3388; 4, 4
|62\13
3381.{{Overline|81}}
|-
|-
!F ut
|'''B si'''
!B
|'''64\15, 2953.846'''
!75\15
|'''47\11, 2968.421'''
3461; 1, 1, 6
|'''77\18, 2980.645'''
!55\11
|'''30\7, 3000'''
3473; 1, 2, 6
|'''73\17, 3020.690'''
!90\18
|'''43\10, 3035.294'''
3483; 1, 6.75
|'''56\13, 3054.545'''
!35\7
3500
!85\17
3517; 4, 7
!50\10
3529; 2, 2, 3
!65\13
3545.{{Overline|45}}
|-
|-
|F ut#
|B si#
|B#
|65\15, 3000
|76\15
|48\11, 3031.579
3507; 1, 2, 4
|79\18, 3058.064
|56\15
| rowspan="2" |31\7, 3100
3536; 1, 5, 3
|76\17, 3144.828
|92\18
|45\10, 3176.471
3561: 3, 2, 4
|59\13, 3218.182
| rowspan="2" |36\7
3600
|88\17
3641; 2, 1, 1.75
|52\10
3670; 1.7
|68\13
3709.{{Overline|09}}
|-
|-
|G reb
|C solb
|Cb
|67\15, 3092.308
|78\15
|49\11, 3094.737
3600
|80\18, 3096.774
|57\15
|75\17, 3103.448
3600
|44\10, 3105.882
|93\18
|57\13, 3109.091
3600
|87\17
3600
|51\10
3600
|66\13
3600
|-
|-
|'''G re'''
|C sol
|'''C'''
|68\15, 3138.462
|'''79\15'''
|50\11, 3157.895
'''3646; 6.5'''
| 82\18, 3174.194
|'''58\11'''
|32\7, 3200
'''3663; 6, 3'''
|78\17, 3227.586
|'''95\18'''
| 46\10, 3247.059
'''3677; 2, 2.6'''
|60\13, 3272.273
|'''37\7'''
'''3700'''
|'''90\17'''
'''3724; 7, 4'''
|'''53\17'''
'''3741; 5, 1.5'''
|'''69\13'''
'''3763.{{Overline|63}}'''
|-
|-
|G re#
|C sol#
|C#
| 69\15, 3184.615
|80\15
| rowspan="2" |51\11, 3221.053
3692; 4, 3
|84\18, 3251.612
|59\11
|33\7, 3300
3726; 3, 6
|81\17, 3351.725
|97\18
|48\10, 3388.235
3755; 5.2
|63\13, 3436.364
| rowspan="2" |38\7
3800
|93\17
3848; 3.625
|55\17
3882; 2, 1.2
|72\13
3927.{{Overline|27}}
|-
|-
|A mib
|D labb
|Db
|70\15, 3230.769
|82\15
|83\18, 3212.903
3784; 1.625
|32\7, 3200
|60\11
|77\17, 3186.207
3789; 2,9
|45\10, 3176.471
|98\18
|58\13, 3163.636
3793; 1, 1, 4, 1.5
|92\17
3806; 1, 8, 1.5
|54\17
3811; 1, 3, 4
|70\13
3818.{{Overline|18}}
|-
|-
|A mi
|'''D lab'''
|D
|'''71\15,''' '''3276.923'''
|83\15
|'''52\11,''' '''3284.211'''
3830, 1.3
|'''85\18,''' '''3290.323'''
|61\11
|'''33\7, 3300'''
3852; 1, 1, 1.4
|'''80\17,''' '''3310.345'''
|100\18
|'''47\10,''' '''3317.647'''
3870; 1, 30
|'''61\13,''' '''3327.{{Overline|27}}'''
|39\7
3900
|95\17
3931; 29
|56\17
3952; 1, 16
|73\13
3981.{{Overline|81}}
|-
|-
|A mi#
|D la
|D#
|72\15, 3323.077
|84\15
|53\11, 3347.368
3876; 1, 12
|87\18, 3367.742
| rowspan="2" |62\11
|34\7, 3400
3915; 1, 3.75
|83\17, 3434.583
|102\18
|49\10, 3458.824
3948; 2, 1, 1.4
|64\13, 3490.909
|40\7
4000
|98\17
4055; 5.8
|58\10
4094; 8.5
|76\13
4145.{{Overline|45}}
|-
|-
|B fa utb
|D la#
|Ebb
|73\15, 3369.231
|85\15
| rowspan="2" |54\11, 3410.625
3923; 13
|89\18, 3445.162
|101\18
|35\7, 3500
3909; 1, 2.1
|86\17, 3558.621
|39\7
|51\10, 3600
3900
|67\13, 3654.545
|94\17
3889; 1, 1.9
|55\10
3882; 2, 1.2
|71\13
3872.{{Overline|72}}
|-
|-
|'''B fa ut'''
|F utb
|'''Eb'''
|74\15, 3415.385
|'''86\15'''
|88\18, 3406.452
'''3969; 4, 3'''
|34\7, 3400
|'''63\11'''
|82\17, 3393.103
'''3978; 1, 3.75'''
|48\10, 3388.235
|'''103\18'''
|62\13, 3381.818
'''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#
!F ut
|E
!75\15, 3461.538
|87\15
!55\11, 3473.684
4015; 2.6
!90\18, 3483.871
|64\11
!35\7, 3500
4042; 9.5
!85\17, 3517.241
|105\18
!50\10, 3529.412
4064; 1.9375
!65\13, 3545.455
|41\7
4100
|100\17
4137; 1, 13.5
|59\10
4164; 1, 2.4
|77\13
4200
|-
|B fa utx
|E#
|88\15
4061; 1, 1, 6
| rowspan="2" |65\11
4105; 3.8
|107\18
4141; 1, 14.5
|42\7
4200
|103\17
4262; 14.5
|61\10
4305; 1, 7.5
|80\13
4363.{{Overline|63}}
|-
|C sol reb
|Fb
|89\15
4107; 1.3
|106\18
4103; 4, 2, 3
|41\7
4100
|99\17
4096; 1.8125
|58\10
4094; 8.5
|75\13
4090.{{Overline|90}}
|-
!C sol re
!F
!90\15
4153; 1, 5.5
!66\11
4168; 2.375
!108\18
4180; 1.55
!42\7
4200
!102\17
4220; 1.45
!60\10
4235; 3.4
!78\13
4254.{{Overline|54}}
|}
|}
==Intervals==
 
{| class="wikitable"
{| class="wikitable"
!Generators
|+Cents
!Sesquitave notation
!Notation
!Interval category name
!Supersoft
!Generators
!Soft
!Notation of 3/2 inverse
! Semisoft
!Interval category name
!Basic
!Semihard
!Hard
!Superhard
|-
!Subdozenal
!~15edf
!~11edf
!~18edf
!~7edf
!~17edf
!~10edf
!~13edf
|-
|-
| colspan="6" |The 4-note MOS has the following intervals (from some root):
|F#
|1\15, 46.154
|1\11, 63.158
|2\18, 77.419
| rowspan="2" |1\7, 100
|3\17, 124.138
|2\10, 141.176
|3\13, 163.636
|-
|-
|0
|Gb, Ge
|Do, Sol
|3\15, 138.462
|perfect unison
|2\11. 126.316
|0
|3\18, 116.129
|Do, Sol
|2\17, 82.759
|sesquitave (just fifth)
|1\10, 70.588
|1\13, 54.545
|-
|-
|1
|'''G'''
|Fa, Do
|'''4\15,''' '''184.615'''
|perfect fourth
|'''3\11,''' '''189.474'''
| -1
|'''5\18,''' '''193.548'''
|Re, La
|'''2\7,''' '''200'''
|perfect second
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|G#
|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
|-
|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
|-
|-
|2
|H
|Mib, Sib
|8\15, 369.231
|minor third
|6\11, 378.947
| -2
|10\18, 387.097
|Mi, Si
|4\7, 400
|major third
|10\17, 413.793
|6\10, 423.529
|8\13, 436.364
|-
|-
| 3
|H#
|Reb, Lab
|9\15, 415.385
|diminished second
| rowspan="2" |7\11, 442.105
| -3
|12\18, 464.516
|Fa#, Do#
|5\7, 500
|augmented fourth
|13\17, 537.069
|8\10, 564.706
|11\13, 600
|-
|-
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|Jbb, Jee
|10\15, 461.538
|11\18, 425.806
|4\7, 400
|9\17, 372.414
|5\10, 352.941
|6\13, 327.273
|-
|-
|4
|'''Jb, Je'''
|Dob, Solb
|'''11\15,''' '''507.692'''
|diminished sesquitave
|'''8\11,''' '''505.263'''
| -4
|'''13\18,''' '''503.226'''
| Do#, Sol#
|'''5\7, 500'''
|augmented unison (chroma)
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|-
|5
|J
|Fab, Dob
|12\15, 553.846
|diminished fourth
|9\11, 568.421
| -5
|15\18, 580.645
|Re#, La#
|6\7, 600
|augmented second
|15\17, 620.690
|9\10, 635.294
|12\13, 654.545
|-
|-
|6
|J#
|Mibb, Sibb
|13\15, 600
|diminished third
| rowspan="2" |10\11, 631.579
| -6
|17\18, 658.064
|Mi#, Si#
|7\7, 700
|augmented third
|18\17, 744.828
|}
|11\10, 776.471
|15\13, 818.182
==Genchain==
|-
|Kb, Ke
The generator chain for this scale is as follows:
|14\15, 646.154
{| class="wikitable"
|16\18, 619.355
|Mibb
|6\7, 600
|14\17, 579.310
Sibb
|8\10, 564.706
|Fab
|10\13, 545.455
|-
Dob
!K
|Dob
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
Solb
!'''18\18,''' '''696.774'''
|Reb
!7\7, 700
!'''17\17,''' '''703.448'''
Lab
!'''10\10,''' '''705.882'''
|Mib
!'''13\13,''' '''709.091'''
|-
Sib
|K#
|Fa
|16\15, 738.462
|12\11, 757.895
Do
|20\18, 774.194
|Do
| rowspan="2" |8\8, 800
|20\17, 827.586
Sol
|12\10, 847.059
|Re
|16\13, 872.727
|-
La
|Lb, Le
|Mi
|18\15, 830.769
|13\11, 821.053
Si
|21\18, 812.903
|Fa#
|19\17, 786.207
|11\10, 776.471
Do#
|14\13, 763.63
|Do#
|-
|'''L'''
Sol#
|'''19\15,''' '''876.923'''
|Re#
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
La#
|'''9\5,''' '''900'''
|Mi#
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
Si#
|'''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
|-
|N#
|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
|-
|Pb, Pe
|29\15, 1338.462
|34\18, 1316.129
|13\7, 1300
|31\17, 1282.759
|18\10, 1270.588
|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#
|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
|-
|Qb, Qe
|33\15, 1523.077
|24\11, 1515.789
|39\18, 1509.677
|36\17, 1489.655
|21\10, 1482.759
|27\13, 1472.273
|-
|'''Q'''
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.364'''
|-
|Q#
|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
|-
|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
|-
|-
|d3
|R#
|d4
|38\15, 1753.846
|d5
|28\11, 1768.421
|d2
|46\18, 1780.645
|m3
|18\7, 1800
|P4
|44\17, 1820.690
|P1
|26\10, 1835.294
|P2
|34\13, 1854.545
|M3
|-
|A4
|R#
|A1
|39\15, 1800
|A2
| rowspan="2" |29\11, 1831.579
|A3
|48\18, 1858.064
|}
|19\7, 1900
|47\17, 1944.828
==Modes==
|28\10, 1976.471
|37\13, 2018.182
The mode names are based on the species of fifth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
|-
|-
!name
|Sb, Se
!pattern
|40\15, 1846.154
!notation
|47\18, 1819.355
!2nd
|18\7, 1800
!3rd
|43\17, 1779.310
!4th
|25\10, 1764.706
|32\13, 1745.545
|-
|-
|Lydian
|'''S'''
|LLLs
|'''41\15,''' '''1892.308'''
|<nowiki>3|0</nowiki>
|'''30\11,''' '''1894.737'''
|P
|'''49\18,''' '''1896.774'''
|M
|'''19\7, 1900'''
|A
|'''46\17,''' '''1903.448'''
|'''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
|44\15, 2030.769
|52\18, 2012.903
|20\7, 2000
|48\17, 1986.207
|28\10, 1976.471
|36\13, 1963.636
|-
|-
|Major
!T
|LLsL
!45\15, 2076.923
|<nowiki>2|1</nowiki>
!33\11, 2084.211
|P
!54\18, 2090.323
|M
!21\7, 2100
|P
!51\17, 2110.345
!30\10, 2117.647
!39\13, 2127.273
|-
|-
|Minor
|T#
|LLsL
|46\15, 2123.077
|<nowiki>1|2</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
|-
|-
|Phrygian
|Ub, Üe
| sLLL
|47\26, 2169.231
|<nowiki>0|3</nowiki>
|55\16, 2129.032
|d
|21\7, 2100
|m
|50\17, 2068.966
|P
|29\10, 2047.059
|}
|37\13, 2018.182
|-
==Temperaments==
|Ub, Ü
|48\15, 2215.385
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.
|35\11, 2210.526
==='''Napoli-Meantone'''===
|57\18, 2206.452
|23\7, 2300
[[Subgroup]]: 3/2.6/5.8/5
|53\17, 2193.103
|31\10, 2188.235
[[Comma]] list: [[81/80]]
|40\13, 2181.818
 
|-
[[POL2]] generator: ~9/8 = 192.6406¢
|U
 
|49\15, 2261.538
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
|36\11, 1073.684
 
|59\18, 2283.871
[[Optimal ET sequence]]: ~(7edf, 11edf, 18edf)
|24\7, 2400
==='''Napoli-Archy'''===
|56\17, 2317.241
|33\10, 2329.412
[[Subgroup]]: 3/2.7/6.14/9
|43\13, 2345.455
|-
[[Comma]] list: [[64/63]]
|U#
 
|50\15, 2307.692
[[POL2]] generator: ~8/7 = 218.6371¢
| rowspan="2" |37\11, 2336.842
 
|61\18, 2361.290
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
| rowspan="2" |23\7, 2300
 
|59\17, 2441.379
[[Optimal ET sequence]]: ~(7edf, 10edf, 13edf, 16edf)
|35\10, 2470.588
===Scale tree===
|46\13, 2509.091
|-
The spectrum looks like this:
|Vb, Ve
{| class="wikitable"
|51\15, 2353.846
! colspan="3" |Generator
|60\18, 2322.581
|55\17, 2275.862
(bright)
|32\10, 2258.824
!Cents<u><ref name=":03">Fractions repeating more than 4 digits written as continued fractions</ref></u>
|41\13, 2236.364
!L
|-
!s
|V
!L/s
|52\15, 2400
!Comments
|38\11, 2400
|62\18, 2400
|24\7, 2400
|58\17, 2400
|34\10, 2400
|44\13, 2400
|-
|V#
|53\15, 2446.154
|39\11, 2463.158
|64\18, 2477,419
| rowspan="2" |25\7, 2500
|61\17, 2524.138
|36\10, 2541.176
|47\13, 2563.636
|-
|Wb, We
|55\15, 2538.462
|40\11, 2526.316
|65\18, 2516.129
|60\17, 2482.759
|35\10, 2470.588
|45\13, 2454.545
|-
|'''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
|-
|-
|1\4
|X#
|
|61\15, 2815.385
|
| rowspan="2" |45\11, 2842.105
|<u>171; 2, 3</u>
|74\18, 2864.516
|1
|29\7, 2900
|1
|71\17, 2937.069
|1.000
|42\10, 2964.706
|Equalised
|55\13, 3000
|-
|-
|6\23
|Ybb, Yee
|
|62\15, 2861.538
|
|73\18, 2825.806
|<u>180</u>
|28\7, 2800
|6
|67\17, 2772.414
|5
|39\10, 2752.941
|1.200
|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'''
|11\42
|'''64\15, 2953.846'''
|
|'''47\11, 2968.421'''
|<u>180; 1, 4, 1.625</u>
|'''77\18, 2980.645'''
|11
|'''30\7, 3000'''
|9
|'''73\17, 3020.690'''
|1.222
|'''43\10, 3035.294'''
|
|'''56\13, 3054.545'''
|-
|-
|5\19
|Y#
|
|65\15, 3000
|
|48\11, 3031.579
|<u>181.{{Overline|81}}</u>
|79\18, 3058.064
|5
| rowspan="2" |31\7, 3100
|4
|76\17, 3144.828
|1.250
|45\10, 3176.471
|
|59\13, 3218.182
|-
|-
|
|Zb. Ze
|14\53
|67\15, 3092.308
|
|49\11, 3094.737
|<u>182; 1, 1.5</u>
|80\18, 3096.774
|14
|75\17, 3103.448
|11
|44\10, 3105.882
|1.273
|57\13, 3109.091
|
|-
|-
|
|Z
|9\34
|68\15, 3138.462
|
|50\11, 3157.895
|<u>183; 19, 1.5</u>
|82\18, 3174.194
|9
|32\7, 3200
|7
|78\17, 3227.586
|1.286
|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
|-
|-
|4\15
|Ab, Æ
|
|70\15, 3230.769
|
|83\18, 3212.903
|<u>184; 1.625</u>
|32\7, 3200
|4
|77\17, 3186.207
|3
|45\10, 3176.471
|1.333
|58\13, 3163.636
|
|-
|-
|
|'''A'''
|11\41
|'''71\15,''' '''3276.923'''
|
|'''52\11,''' '''3284.211'''
|<u>185, 1, 10, 1.2</u>
|'''85\18,''' '''3290.323'''
|11
|'''33\7, 3300'''
|8
|'''80\17,''' '''3310.345'''
|1.375
|'''47\10,''' '''3317.647'''
|
|'''61\13,''' '''3327.{{Overline|27}}'''
|-
|-
|
|A#
|7\26
|72\15, 3323.077
|
|53\11, 3347.368
|<u>186.{{Overline|6}}</u>
|87\18, 3367.742
|7
|34\7, 3400
|5
|83\17, 3434.583
|1.400
|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
|10\37
|74\15, 3415.385
|
|88\18, 3406.452
|<u>187.5</u>
|34\7, 3400
| 10
|82\17, 3393.103
|7
|48\10, 3388.235
|1.429
|62\13, 3381.818
|
|-
|-
|
!B
|13\48
!75\15, 3461.538
|
!55\11, 3473.684
|<u>187; 1, 19.75</u>
!90\18, 3483.871
|13
!35\7, 3500
|9
!85\17, 3517.241
|1.444
!50\10, 3529.412
|
!65\13, 3545.455
|-
|-
|
|B#
|16\59
|76\15, 3507.692
|
|56\11, 3536.842
|<u>188; 4, 4</u>
|92\18, 3561.290
|16
| rowspan="2" |36\7, 3600
|11
|88\17, 3641.379
| 1.455
|52\10, 3670.588
|
|68\13, 3709.091
|-
|-
|3\11
|Cb, Ce
|
|78\15, 3600
|
|57\11, 3600
|<u>189; 2, 9</u>
|93\18, 3600
|3
|87\17, 3600
|2
|51\10, 3600
|1.500
|66\13, 3600
|Napoli-Meantone starts here
|-
|'''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
|14\51
|82\15, 3784.615
|
|60\11, 3789.474
|<u>190.{{Overline|90}}</u>
|98\18, 3793.548
|14
|92\17, 3806.897
|9
|54\10, 3811.765
|1.556
|70\13, 3818.182
|
|-
|-
|
|D
|11\40
|83\15, 3830.769
|
|61\11, 3852.632
|<u>191; 3, 2, 3</u>
|100\18, 3870.968
|11
|39\7, 3900
|7
|95\17, 3931.03$
|1.571
|56\10, 3952.941
|
|73\13, 3981.818
|-
|-
|
|D#
|8\29
|84\15, 3876.923
|
| rowspan="2" |62\11, 3915.789
|<u>192</u>
|102\18, 3948.387
|8
|40\7, 4000
|5
|98\17, 4055.172
|1.600
|58\10, 4094.118
|
|76\13, 4145.455
|-
|-
|
|Ebb, Ëe
|5\18
|85\15, 3923.077
|
|101\18, 3909.677
|<u>193; 1, 1, 4, 1.5</u>
|39\7, 3900
|5
|94\17, 3889.552
|3
|55\10, 3882.353
|1.667
|71\13, 3872.727
|
|-
|-
|
|'''Eb, Ë'''
|
|'''86\15,''' '''3969.231'''
|12\43
|'''63\11,''' '''3978.947'''
|<u>194.{{Overline|594}}</u>
|'''103\18,''' '''3987.097'''
|12
|'''40\7, 4000'''
|7
|'''97\17,''' '''4013.793'''
|1.714
|'''57\10,''' '''4023.529'''
|
|'''74\13,''' '''4036.364'''
|-
|-
|
|E
|7\25
|87\15, 4015.385
|
|64\11, 4042.105
|<u>195; 2, 1, 6.5</u>
|105\18, 4064.516
|7
|41\7, 4100
|4
|100\17, 4137.931
|1.750
|59\10, 4164.706
|
|77\13, 4200
|-
|-
|
|E#
|9\32
|88\15, 4061.583
|
| rowspan="2" |65\11, 4105.263
|<u>196.{{Overline|36}}</u>
|107\18, 4141.956
|9
|42\7, 4200
|5
|103\17, 4262.069
|1.800
|61\10, 4305.882
|
|80\13, 4363.636
|-
|
|11\39
|
|<u>197; 67</u>
|11
|6
|1.833
|
|-
|-
|
|Fb, Fe
|13\46
|89\15, 4107.692
|
|106\18, 4103.226
|<u>197; 2, 7.4</u>
|41\7, 4100
| 13
|99\17, 4096.552
|7
|58\10, 4094.118
|1.857
|75\13, 4090.909
|
|-
|-
|
!F
|15\53
!90\15, 4153.846
|
!66\11, 4168.421
|<u>197; 1, 2, 1, 1, 1, 1.2</u>
!108\18, 4180.645
|15
!42\7, 4200
|8
!102\17, 4220.690
|1.875
!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
|17\60
|Do, Fa, Sol
|
|perfect unison
|<u>198; 17, 6</u>
|0
|17
|Do, Fa, Sol
|9
|sesquitave (just fifth)
|1.889
|
|-
|-
|
|1
|19\67
|Fa, Sib, Do
|
|perfect fourth
|<u>198: 3, 1, 28</u>
| -1
|19
|Re, Sol, La
|10
|perfect second
|1.900
|
|-
|-
|
|2
|21\74
|Mib, Lab, Sib
|
|minor third
|<u>198; 2, 2, 1.1875</u>
| -2
|21
|Mi, La, Si
|11
|major third
|1.909
|
|-
|-
|
|3
|23\81
|Reb, Solb, Lab
|
|diminished second
|<u>198; 1, 3, 1.7</u>
| -3
|23
|Fa#, Si, Do#
|12
|augmented fourth
|1.917
|
|-
|-
|
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|25\88
|-
|
|4
|<u>198; 1, 2, 12, 4</u>
|Dob, Fab, Solb
|25
|diminished sesquitave
|13
| -4
|1.923
|Do#, Fa#, Sol#
|
|augmented unison (chroma)
|-
|-
|
|5
|27\95
|Fab, Sibb, Dob
|
|diminished fourth
|<u>198; 1, 3, 2, 13</u>
| -5
|27
|Re#, Sol#, La#
|14
|augmented second
|1.929
|
|-
|-
|
|6
|29\102
|Mibb, Labb, Sibb
|
|diminished third
|<u>198; 1, 1, 6</u>
| -6
|29
|Mi#, La#, Si#
|15
|augmented third
|1.933
|}
|
|-
==Genchain==
|
|31\109
The generator chain for this scale is as follows:
|
{| class="wikitable"
|<u>198; 1, 13, 2.6</u>
|Mibb
|31
Labb
|16
|1.9375
Sibb
|
|Fab
|-
Sibb
|
|33\116
Dob
|
|Dob
|<u>198; 1, 198</u>
Fab
|33
|17
Solb
|1.941
|Reb
|
Solb
|-
|2\7
Lab
|
|Mib
|
Lab
|<u>200</u>
|2
Sib
|1
|Fa
|2.000
Sib
|Napoli-Meantone ends, Napoli-Pythagorean begins
|-
Do
|
|Do
|17\59
Fa
|
|<u>201.{{Overline|9801}}</u>
Sol
|17
|Re
|8
Sol
|2.125
|
La
|-
|Mi
|
La
|15\52
|
Si
|<u>202; 4, 22</u>
|Fa#
|15
Si
|7
|2.143
Do#
|
|Do#
Fa#
Sol#
|Re#
Sol#
La#
|Mi#
La#
Si#
|-
|-
|
|d3
|13\45
|d4
|
|d5
|<u>202; 1, 1, 2, 15</u>
|d2
|13
|m3
|6
|P4
|2.167
|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
|11\38
!pattern
|
!notation
|<u>203; 13</u>
!2nd
|11
!3rd
|5
!4th
|2.200
|
|-
|-
|
|Lydian
|9\31
|LLLs
|
|<nowiki>3|0</nowiki>
|<u>203; 1, 3, 2.4</u>
|P
|9
|M
|4
|A
|2.250
|
|-
|-
|
|Major
| 7\24
|LLsL
|
|<nowiki>2|1</nowiki>
|<u>204; 1. 7.2</u>
|P
| 7
|M
|3
|P
|2.333
|
|-
|-
|
|Minor
|
|LsLL
|12\41
|<nowiki>1|2</nowiki>
|<u>205; 1.4</u>
|P
|12
|m
|5
|P
|2.400
|
|-
|-
|
|Phrygian
|5\17
|sLLL
|
|<nowiki>0|3</nowiki>
|<u>206; 1, 8, 1.5</u>
|d
|5
|m
|2
|P
|2.500
|}
|Napoli-Neogothic heartland is from here…
|-
==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.
|18\61
==='''Napoli-Meantone (Hex meantone)'''===
|<u>207; 1, 2, 4</u>
|18
[[Subgroup]]: 3/2.6/5.8/5 (5.2.3)
|7
|2.571
[[Comma]] list: [[81/80]]
|
 
|-
[[POL2]] generator: ~9/8 = 192.6406¢
|
 
|8\27
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
|
 
|<u>208; 1, 5, 3</u>
[[Optimal ET sequence]]: *[[28ed5]], [[44ed5]], [[72ed5]] ≈ [[7edf]], [[11edf]], [[18edf]]
|8
==='''Napoli-Archy (Hex Archytas)'''===
|3
|2.667
[[Subgroup]]: 3/2.7/6.14/9 (36/7.2.3)
|…to here
[[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
|
|
|11\37
|-
|
|5\19
|<u>209; 1, 1.1</u>
|181.818
|11
|5
|4
|4
|2.750
|1.250
|
|
|-
|-
|
|14\53
|14\47
|182.609
|
|<u>210</u>
|14
|14
|5
|11
|2.800
|1.273
|
|
|-
|-
|3\10
|9\34
|183.051
|9
|7
|1.286
|
|
|-
|4\15
|184.615
|4
|3
|1.333
|
|
|<u>211; 1, 3, 4</u>
|3
|1
|3.000
|Napoli-Pythagorean ends, Napoli-Archy begins
|-
|-
|11\41
|185.915
|11
|8
|1.375
|
|
|22\73
|-
|
|7\26
|<u>212; 1, 9, 3</u>
|186.667
|22
|7
|7
|3.143
|5
|1.400
|
|
|-
|-
|10\37
|187.5
|10
|7
|1.429
|
|
|19\63
|-
|13\48
|187.952
|13
|9
|1.444
|
|
|<u>213; 11, 1, 8</u>
|-
|19
|16\59
|6
|188.253
|3.167
|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
|
|
|16\53
|-
|
|8\29
|<u>213.{{Overline|3}}</u>
|192.000
|16
|8
|5
|5
|3.200
|1.600
|
|
|-
|-
|5\18
|193.548
|5
|3
|1.667
|
|
|13\43
|-
|12\43
|194.595
|12
|7
|1.714
|
|
|<u>213; 1, 2, 3, 7</u>
|-
|13
|7\25
|195.348
|7
|4
|4
|3.250
|1.750
|
|
|-
|-
|9\32
|196.364
|9
|5
|1.800
|
|
|10\33
|-
|
|11\39
|<u>214; 3.5</u>
|197.015
|10
|11
|3
|6
|3.333
|1.833
|
|
|-
|-
|
|13\46
|7\23
|197.468
|
|13
|<u>215; 2.6</u>
|7
|7
|2
|1.857
|3.500
|
|
|-
|-
|15\53
|197.802
|15
|8
|1.875
|
|
|11\36
|-
|17\60
|198.058
|17
|9
|1.889
|
|
|<u>216; 2, 1, 1, 5.5</u>
|-
|11
|19\67
|3
|198.261
|3.667
|19
|10
|1.900
|
|
|-
|-
|21\74
|198.425
|21
|11
|1.909
|
|
|15\49
|-
|23\81
|198.561
|23
|12
|1.917
|
|
|<u>216; 1, 6, 1, 1.2</u>
|-
|15
|25\88
|4
|198.675
| 3.750
|25
|13
|1.923
|
|
|-
|-
|27\95
|198.773
|27
|14
|1.929
|
|
|19\62
|-
|
|29\102
|<u>217; 7</u>
|198.857
|19
|29
|5
|15
|3.800
|1.933
|
|
|-
|-
|4\13
|31\109
|
|198.930
|31
|16
|1.9375
|
|
|<u>218.{{Overline|18}}</u>
|-
|4
|33\116
|1
|198.995
|4.000
|33
|17
|1.941
|
|
|-
|-
|
|35\123
|13\42
|199.009
|
|35
|<u>219; 1, 2.55</u>
|18
|13
|1.944
|3
|4.333
|
|
|-
|-
|
|2\7
|9\29
|200
|
|<u>220; 2.45</u>
|9
|2
|2
|4.500
|1
|
|2.000
|-
|Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|17\59
|201.980
|17
|8
|2.125
|
|
|14\45
|-
|15\52
|202.247
|15
|7
|2.143
|
|
|<u>221; 19</u>
|-
|14
|13\45
|3
|202.597
|4.667
|13
|6
|2.167
|
|
|-
|-
|5\16
|11\38
|
|203.077
|
|11
|<u>222.{{Overline|2}}</u>
|5
|5
|1
|2.200
|5.000
|
|Napoli-Archy ends
|-
|-
|9\31
|203.774
|9
|4
|2.250
|
|
|16\51
|-
|
|7\24
|<u>223; 3, 1.1</u>
|204.878
|16
|7
|3
|3
|5.333
|2.333
|
|
|-
|-
|12\41
|205.714
|12
|5
|2.400
|
|
|11\35
|-
|
|5\17
|<u>223; 1, 2.6875</u>
|206.897
|11
|5
|2
|2
|5.500
|2.500
|
|Napoli-Neogothic heartland is from here…
|-
|-
|18\61
|207.693
|18
|7
|2.571
|
|-
|13\44
|208.000
|13
|5
|2.600
|
|
|17\54
|-
|
|8\27
|<u>224; 5, 1, 2.6</u>
|208.696
| 17
|8
|3
|3
|5.667
|2.667
|…to here
|-
|11\37
|209.524
|11
|4
|2.750
|
|
|-
|-
|6\19
|14\47
|210.000
|14
|5
|2.800
|
|
|
|-
|<u>225</u>
|3\10
|6
|211.765
|1
|3
|6.000
|1
|3.000
|Napoli-Pythagorean ends, Napoli-Archy begins
|-
|22\73
|212.903
|22
|7
|3.143
|
|
|-
|-
|1\3
|19\63
|213.084
|19
|6
|3.167
|
|
|-
|16\53
|213.333
|16
|5
|3.200
|
|
|<u>240</u>
|-
|1
|13\43
|0
|213.699
|→ inf
|13
|Paucitonic
|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


==See also==
[[12L 4s (56/11-equivalent)]] - Hextone gentle temperament
[[3L 1s (3/2-equivalent)]] - idealized tuning
 
 
[[12L 4s (36/7-equivalent)]] - Hextone 1/4-comma archy
[[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
 
[[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 (128/11-equivalent)]] - Subdozenal subharmonic 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
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