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'''3L 1s<perfect fifth>''' is constructed by repeating the fifth-spanning pattern LLLs of the ordinary diatonic mos ([[5L 2s]]) at the equave of 3/2. The so-called "Super Ultra Hyper Mega Meta Lydian" is one mode of this mos.
{{Infobox MOS


| Name = Diatonic/Angel
The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 1s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). The generator range is 171.4 to 240 cents, placing it near the [[9/8|diatonic major second]], usually representing a major second of some type. The dark (chroma-negative) generator is, however, its fifth complement (480 to 514.3 cents).  
| Equave = 3/2
| nLargeSteps = 3
| nSmallSteps = 1
| Equalized = 2
| Paucitonic = 1
 
| Pattern = LLLs
}}'''3L 1s<3/2>''', is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 1s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]).  
The generator range is 171.4 to 240 cents, placing it near the [[9/8|diatonic major second]], usually representing a major second of some type. The dark (chroma-negative) generator is, however, its fifth complement (480 to 514.3 cents).  
   
   
In the fifth-repeating version of the diatonic scale, each tone has a 3/2 perfect fifth above it. The scale has two major chords and two minor chords.  
In the fifth-repeating version of the diatonic scale, each tone has a 3/2 perfect fifth above it. The scale has two major chords and two minor chords.  


[[Basic]] Angel is in [[7edf]], which is a very good fifth-based equal tuning similar to [[12edo]].
'''Angel''' is a proposed name for this mos. [[Basic]] Angel is in [[7edf]], which is a very good fifth-based equal tuning similar to [[12edo]].
 
 
==Notation==
==Notation==
   
   
There are 3 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 diatonic scales as repeating at the double or triple sesquitave (major ninth or thirteenth), 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] or a major thirteenth which is the Dorian mode of Bijou[9L 3s]. Since there are exactly 8 naturals in double sesquitave notation and 12 in triple sesquitave notation, letters A-H (FGABHCDEF) or dozenal digits (0123456789XE0 or D1234567FGACD with flats written C molle) may be used.
There are 6 main ways to notate the angel scale. One method uses a simple sesquitave (fifth) repeating notation consisting of 4 naturals (eg. Do Re Mi Fa, Fa Sol La Si, Sol La Si Do). Given that 1-5/4-5/3 is fifth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate angel scales as repeating at the double, triple, quadruple, quintuple or sextuple sesquitave (major ninth, thirteenth, seventeenth i. e. ~pentave or twenty-first or augmented twenty-fifth), however it does make navigating the [[Generator|genchain]] harder. This way, 5/3 is its own pitch class, distinct from 10/9. Notating this way produces a major ninth which is the Aeolian mode of Napoli[6L 2s], a major thirteenth which is the Dorian mode of Bijou[9L 3s], an ~pentave which is the Mixolydian mode of Hextone[12L 4s], a major twenty-first which is the Ionian mode of Guidotonic[15L 5s] or an augmented twenty-fifth which is the Lydian mode of Subdozenal[18L 6s]. Since there are exactly 8 naturals in double sesquitave notation, 12 in triple sesquitave notation, 16 in quadruple sesquitave notation, 20 in quintuple sesquitave notation and 24 in sextuple sesquitave notation, letters A-H (FGABHCDEF), dozenal or hex digits (0123456789XE0 or D1234567FGACD with flats written C molle or 0123456789ABCDEF0 or G123456789ABCDEFG with flats written F molle), the Guidonian names with F as the lowest ut or letters except I and O may be used.
 
{| class="wikitable"
{| class="wikitable"
 
 
Line 35: Line 17:
Cents
Cents
 
 
! colspan="3" |Notation
! Notation
 
 
!Supersoft
!Supersoft
Line 54: Line 36:
 
 
!Diatonic
!Diatonic
!Napoli
!Bijou
!~15edf
!~15edf
 
 
Line 75: Line 52:
|-
|-
 
 
|Do#, Sol#
|Do#, Fa#, Sol#
|1\15, 46.154
 
 
|F#
|1\11, 63.158
 
 
|0#, D#
|2\18, 77.419
 
 
|1\15
| rowspan="2" | 1\7, 100
 
 
46.153…
|3\17, 124.138
 
 
|1\11
|2\10, 141.176
 
 
63.157…
|3\13, 163.636
 
 
|2\18
|-
 
 
77.419…
|Reb, Solb, Lab
|3\15, 138.462
 
 
| rowspan="2" |1\7
|2\11. 126.316
 
 
100
|3\18, 116.129
 
 
|3\17
|2\17, 82.759
 
 
124.137…
|1\10, 70.588
 
 
|2\10
|1\13, 54.545
141.176…
 
 
|3\13
|-
 
 
163.{{Overline|63}}
|'''Re, Sol, La'''
|'''4\15,''' '''184.615'''
 
 
|-
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
 
 
|Reb, Lab
|'''2\7,''' '''200'''
 
 
|Gb
|'''5\17,''' '''206.897'''
 
 
|1b, 1c
|'''3\10,''' '''211.765'''
 
 
|3\15
|'''4\13,''' '''218.182'''
 
 
138.461…
|-
 
 
|2\11
|Re#, Sol#, La#
|5\15, 230.769
 
 
126.315…
|4\11, 252.632
 
 
|3\18
|7\18, 270.968
 
 
116.129…
| rowspan="2" | 3\7, 300
 
 
|2\17
|8\17, 331.034
 
 
82.758…
|5\10, 352.941
 
 
|1\10
|7\13, 381.818
 
 
70.588…
|-
 
 
|1\13
|Mib, Lab, Sib
|7\15, 323.077
 
 
54.{{Overline|54}}
|5\11, 315.789
 
 
|-
|8\18, 309.677
 
 
|'''Re, La'''
|7\17, 289.655
 
 
|'''G'''
|4\10, 282.353
 
 
|'''1'''
|5\13, 272.727
 
 
|'''4\15'''
|-
 
 
'''184.615…'''
|Mi, La, Si
|8\15, 369.231
 
 
|'''3\11'''
|6\11, 378.947
 
 
'''189.473…'''
|10\18, 387.097
|'''5\18'''
 
 
'''193.548…'''
|4\7, 400
 
 
|'''2\7'''
|10\17, 413.793
 
 
'''200'''
|6\10, 423.529
 
 
|'''5\17'''
|8\13, 436.364
 
 
'''206.896…'''
|-
 
 
|'''3\10'''
|Mi#, La#, Si#
|9\15, 415.385
 
 
'''211.764…'''
| rowspan="2" | 7\11, 442.105
 
 
|'''4\13'''
|12\18, 464.516
 
 
'''218.{{Overline|18}}'''
|5\7, 500
 
 
|-
|13\17, 537.069
 
 
|Re#, La#
|8\10, 564.706
 
 
|G#
|11\13, 600
 
 
|1#
|-
 
 
|5\15
|Fab, Sibb, Dob
|10\15, 461.538
 
 
230.769…
|11\18, 425.806
 
 
|4\11
|4\7, 400
 
 
252.631…
|9\17, 372.414
 
 
|7\18
|5\10, 352.941
 
 
270.967…
|6\13, 327.273
 
 
| rowspan="2" |3\7
|-
 
 
300
|'''Fa, Sib, Do'''
|'''11\15,''' '''507.692'''
 
 
|8\17
|'''8\11,''' '''505.263'''
 
 
331.034…
|'''13\18,''' '''503.226'''
 
 
|5\10
|'''5\7, 500'''
 
 
352.941…
|'''12\17,''' '''496.552'''
 
 
|7\13
|'''7\10,''' '''494.118'''
 
 
381.{{Overline|81}}
|'''9\13,''' '''490.909'''
 
 
|-
|-
 
 
|Mib, Sib
|Fa#, Si, Do#
|12\15, 553.846
 
 
|Ab
|9\11, 568.421
 
 
|2b, 2c
|15\18, 580.645
 
 
|7\15
|6\7, 600
 
 
323.076…
|15\17, 620.690
 
 
|5\11
|9\10, 635.294
 
 
315.789…
|12\13, 654.545
 
 
|8\18
|-
|Fax, Si#, Dox
|13\15, 600
 
 
309.677…
| rowspan="2" | 10\11, 631.579
 
 
|7\17
|17\18, 658.064
 
 
289.655…
|7\7, 700
 
 
|4\10
|18\17, 744.828
 
 
282.352…
|11\10, 776.471
 
 
|5\13
|15\13, 818.182
 
 
272.{{Overline|72}}
|-
|Dob, Fab, Solb
|14\15, 646.154
|16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
 
 
|-
|-
 
 
|Mi, Si
!Do, Fa, Sol
!'''15\15,''' '''692.308'''
 
 
|A
!'''11\11,''' '''694.737'''
 
 
|2
!'''18\18,''' '''696.774'''
 
 
|8\15
!7\7, 700
 
 
369.230…
!'''17\17,''' '''703.448'''
 
 
|6\11
!'''10\10,''' '''705.882'''
 
 
378.947…
!'''13\13,''' '''709.091'''
 
 
|10\18
|}
 
 
387.096…
{| class="wikitable"
 
 
|4\7
|+
 
 
400
Cents
!Notation
!Supersoft
 
 
|10\17
! Soft
 
 
413.793…
!Semisoft
 
 
|6\10
!Basic
 
 
423.529…
!Semihard
 
 
|8\13
! Hard
 
 
436.{{Overline|36}}
! Superhard
 
 
|-
|-
 
 
|Mi#, Si#
!Napoli
! ~15edf
 
 
|A#
! ~11edf
 
 
|2#
!~18edf
 
 
|9\15
!~7edf
 
 
415.384…
!~17edf
 
 
| rowspan="2" |7\11
!~10edf
 
 
442.105…
!~13edf
 
 
|12\18
|-
 
 
464.516…
|F#
|1\15, 46.154
 
 
|5\7
|1\11, 63.158
 
 
500
| 2\18, 77.419
 
 
|13\17
| rowspan="2" |1\7, 100
 
 
537.931…
|3\17, 124.138
 
 
|8\10
| 2\10, 141.176
 
 
564.705…
|3\13, 163.636
 
 
|11\13
|-
 
 
600
| Gb, Ge
|3\15, 138.462
 
 
|-
| 2\11. 126.316
 
 
|Fab, Dob
|3\18, 116.129
 
 
|Bbb
|2\17, 82.759
 
 
|3b, 3c
|1\10, 70.588
 
 
|10\15
|1\13, 54.545
 
 
461.538…
|-
 
 
|11\18
|'''G'''
|'''4\15,''' '''184.615'''
 
 
425.806…
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
 
 
|4\7
|'''2\7,''' '''200'''
 
 
400
|'''5\17,''' '''206.897'''
 
 
|9\17
|'''3\10,''' '''211.765'''
 
 
372.413…
|'''4\13,''' '''218.182'''
 
 
|5\10
|-
 
 
352.941…
|G#
|5\15, 230.769
|4\11, 252.632
 
 
|6\13
|7\18, 270.968
 
 
327.{{Overline|27}}
| rowspan="2" |3\7, 300
 
 
|-
| 8\17, 331.034
 
 
|'''Fa, Do'''
|5\10, 352.941
 
 
|'''Bb'''
|7\13, 381.818
 
 
|'''3'''
|-
 
 
|'''11\15'''
|Ab, Æ
|7\15, 323.077
 
 
'''507.692…'''
|5\11, 315.789
 
 
|'''8\11'''
|8\18, 309.677
 
 
'''505.263…'''
|7\17, 289.655
 
 
|'''13\18'''
|4\10, 282.353
 
 
'''503.225…'''
|5\13, 272.727
 
 
|'''5\7'''
|-
 
 
'''500'''
|A
| 8\15, 369.231
 
 
|'''12\17'''
|6\11, 378.947
 
 
'''496.551…'''
|10\18, 387.097
 
 
|'''7\10'''
| 4\7, 400
 
 
'''494.117…'''
|10\17, 413.793
 
 
|'''9\13'''
|6\10, 423.529
 
 
'''490.{{Overline|90}}'''
|8\13, 436.364
 
 
|-
|-
 
 
|Fa#, Do#
|A#
| 9\15, 415.385
 
 
|B
| rowspan="2" |7\11, 442.105
 
 
|3#
|12\18, 464.516
 
 
|12\15
|5\7, 500
 
 
553.846…
|13\17, 537.069
 
 
|9\11
|8\10, 564.706
568.421…
 
 
|15\18
|11\13, 600
 
 
580.645…
|-
 
 
|6\7
|Bbb, Bee
|10\15, 461.538
 
 
600
|11\18, 425.806
 
 
|15\17
|4\7, 400
 
 
620.689…
|9\17, 372.414
 
 
|9\10
| 5\10, 352.941
 
 
635.294…
|6\13, 327.273
 
 
|12\13
|-
 
 
654.{{Overline|54}}
|'''Bb, Be'''
|'''11\15,''' '''507.692'''
 
 
|-
|'''8\11,''' '''505.263'''
|Fax, Dox
|'''13\18,''' '''503.226'''
 
 
|B#
|'''5\7, 500'''
 
 
|3x
|'''12\17,''' '''496.552'''
 
 
|13\15
|'''7\10,''' '''494.118'''
 
 
600
|'''9\13,''' '''490.909'''
 
 
| rowspan="2" |10\11
|-
 
 
631.578…
|B
|12\15, 553.846
 
 
|17\18
|9\11, 568.421
 
 
658.064…
|15\18, 580.645
 
 
|7\7
|6\7, 600
 
 
700
| 15\17, 620.690
 
 
|18\17
|9\10, 635.294
 
 
744.827…
|12\13, 654.545
 
 
|11\10
|-
| B#
| 13\15, 600
 
 
776.470…
| rowspan="2" |10\11, 631.579
 
 
|15\13
|17\18, 658.064
 
 
818.{{Overline|18}}
|7\7, 700
 
 
|-
|18\17, 744.828
 
 
|Dob, Solb
|11\10, 776.471
|Hb
| 4b, 4c
|14\15
646.153…
|16\18
619.354…
|6\7
600
|14\17
579.310…
|8\10
564.705…
|10\13
 
 
545.{{Overline|45}}
|15\13, 818.182
 
 
|-
|-
|Hb, He
|14\15, 646.154
| 16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
 
 
!Do, Sol
|-
 
 
!H
! H
!'''15\15,''' '''692.308'''
 
 
!4
!'''11\11,''' '''694.737'''
 
 
!'''15\15'''
!'''18\18,''' '''696.774'''
 
 
'''692.307…'''
! 7\7, 700
 
 
!'''11\11'''
!'''17\17,''' '''703.448'''
'''694.736…'''
 
 
!'''18\18'''
!'''10\10,''' '''705.882'''
 
 
'''696.774…'''
!'''13\13,''' '''709.091'''
 
 
!'''7\7'''
|-
 
 
'''700'''
|Η#
|16\15, 738.462
 
 
!'''17\17'''
|12\11, 757.895
 
 
'''703.448…'''
|20\18, 774.194
 
 
!'''10\10'''
| rowspan="2" |8\8, 800
 
 
'''705.882…'''
|20\17, 827.586
 
 
!'''13\13'''
|12\10, 847.059
 
 
'''709.'''{{Overline|09}}
|16\13, 872.727
 
 
|-
|-
 
 
|Do#, Sol#
|Cb, Ce
|18\15, 830.769
 
 
|Η#
|13\11, 821.053
 
 
|4#
|21\18, 812.903
 
 
|16\15
|19\17, 786.207
 
 
738.461…
|11\10, 776.471
 
 
|12\11
|14\13, 763.63
 
 
757.894…
|-
 
 
| 20\18
|'''C'''
|'''19\15,''' '''876.923'''
 
 
774.193…
|'''14\11,''' '''884.211'''
 
 
| rowspan="2" | 8\8
|'''23\18,''' '''890.323'''
 
 
800
|'''9\5,''' '''900'''
 
 
|20\17
|'''22\17,''' '''910.345'''
 
 
827.586…
|'''13\10,''' '''917.647'''
 
 
|12\10
|'''17\13,''' '''927.273'''
 
 
847.058…
|-
 
 
| 16\13
|C#
|20\15, 923.077
 
 
872.{{Overline|72}}
|15\11, 947.368
 
 
|-
|25\18, 967.742
 
 
|Reb, Lab
| rowspan="2" |10\7, 1000
 
 
|Cb
|25\17, 1034.483
 
 
|5b, 5c
|15\10, 1058.824
 
 
|18\15
|20\13, 1090.909
 
 
830.769…
|-
|13\11
821.052…
 
 
| 21\18
| Db, De
|22\15, 1015.385
 
 
812.903…
|16\11, 1010.526
 
 
| 19\17
|26\18, 1006.452
 
 
786.206…
|24\17, 993.103
 
 
| 11\10
|14\10, 988.235
 
 
776.470…
|18\13, 981.818
| 14\13
763.{{Overline|63}}
 
 
|-
|-
 
 
|'''Re, La'''
|D
|23\15, 1061.538
|'''C'''
|'''5'''
 
 
|'''19\18'''
|17\11, 1073.684
 
 
'''876.923…'''
|28\18, 1083.871
 
 
|'''14\11'''
|11\7, 1100
 
 
'''884.210…'''
|27\17, 1117.241
 
 
|'''23\18'''
|16\10, 1129.412
 
 
'''890.322…'''
|21\9, 1145.455
 
 
|'''9\5'''
|-
 
 
'''900'''
|D#
|24\15, 1107.923
 
 
|'''22\17'''
| rowspan="2" |18\11, 1136.842
 
 
'''910.344…'''
|30\18, 1161.29
 
 
|'''13\10'''
|12\7, 1200
 
 
'''917.647…'''
|30\17, 1241.379
 
 
|'''17\13'''
|18\10, 1270.588
 
 
'''927.{{Overline|27}}'''
|24\13, 1309.091
 
 
|-
|-
 
 
| Re#, La#
|Ebb, Ëe
|25\15, 1153.846
 
 
|C#
|29\18, 1122.581
 
 
| 5#
|11\7, 1100
 
 
|20\15
|26\17, 1075.862
 
 
923.076…
|15\10, 1058.824
 
 
|15\11
| 19\13, 1036.364
 
 
947.368…
|-
 
 
|25\18
|'''Eb, Ë'''
|'''26\15,''' '''1200'''
 
 
967.741…
|'''19\11,''' '''1200'''
 
 
| rowspan="2" |10\7
|'''31\18,''' '''1200'''
 
 
1000
|'''12\7, 1200'''
 
 
|25\17
|'''29\17,''' '''1200'''
 
 
1034.482…
|'''17\10,''' '''1200'''
 
 
| 15\10
|'''22\13,''' '''1200'''
1058.823…
|20\13
1090.{{Overline|90}}
 
 
|-
|-
 
 
|Mib, Sib
|E
|27\15, 1246.154
 
 
|Db
|20\11, 1263.158
 
 
|6b, 6c
|33\18, 1277.419
 
 
|22\15
|13\7, 1300
 
 
1015.384…
|32\17, 1324.138
 
 
|16\11
|19\10, 1341.176
 
 
1010.526…
|25\13, 1363.636
 
 
| 26\18
|-
 
 
1006.451…
|E#
|28\15, 1292.308
 
 
|24\17
| rowspan="2" |21\11, 1326.318
 
 
993.103…
|35\18, 1354.834
 
 
|14\10
|14\7, 1400
 
 
988.235…
|35\17, 1448.275
 
 
|18\13
| 21\10, 1482.353
 
 
981.{{Overline|81}}
|28\13, 1527.273
 
 
|-
|-
 
 
|Mi, Si
| Fb, Fe
|29\15, 1338.462
 
 
|D
|34\18, 1316.129
 
 
|6
|13\7, 1300
 
 
|23\15
|31\17, 1282.759
 
 
1061.538…
|18\10, 1270.588
 
 
|17\11
|23\13, 1254.545
 
 
1073.684…
|-
 
 
| 28\18
!F
!30\15, 1384.615
 
 
1083.870…
!22\11, 1389.473
 
 
|11\7
!36\18, 1393.548
 
 
1100
!14\7, 1400
 
 
| 27\17
!34\17, 1406.897
 
 
1117.241…
!20\10, 1411.765
| 16\10
1129.411…
| 21\9
1145.{{Overline|45}}
 
 
!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#
|Mi#, Si#
|1\15, 46.154
|1\11, 63.158
| D#
|2\18, 77.419
| rowspan="2" |1\7, 100
|6#
|3\17, 124.138
|2\10, 141.176
| 24\15
|3\13, 163.636
|-
1107.692…
|1b, 1c
|3\15, 138.462
| rowspan="2" | 18\11
| 2\11. 126.316
|3\18, 116.129
1136.842…
|2\17, 82.759
|1\10, 70.588
|30\18
|1\13, 54.545
|-
1161.290…
|'''1'''
|'''4\15,''' '''184.615'''
| 12\7
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
1200
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|30\17
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
1241.379…
|-
|1#
|18\10
|5\15, 230.769
|4\11, 252.632
1270.588…
|7\18, 270.968
| rowspan="2" |3\7, 300
|24\13
|8\17, 331.034
|5\10, 352.941
1309.{{Overline|09}}
|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
|Fab, Dob
|8\15, 369.231
|6\11, 378.947
|Ebb
|10\18, 387.097
|4\7, 400
|7b, 7c
|10\17, 413.793
|6\10, 423.529
|25\15
|8\13, 436.364
|-
1153.846…
|2#
| 9\15, 415.385
|29\18
| rowspan="2" |7\11, 442.105
|12\18, 464.516
1122.580…
|5\7, 500
|13\17, 537.069
| 11\7
|8\10, 564.706
|11\13, 600
1100
|-
|3b, 3c
|26\17
| 10\15, 461.538
| 11\18, 425.806
1075.862…
|4\7, 400
|9\17, 372.414
|15\10
|5\10, 352.941
|6\13, 327.273
1058.823…
|-
|'''3'''
|19\13
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
1036.{{Overline|36}}
|'''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
|'''Fa, Do'''
|13\15, 600
| rowspan="2" |10\11, 631.579
|'''Eb'''
|17\18, 658.064
|7\7, 700
|'''7'''
|18\17, 744.828
|11\10, 776.471
|'''26\15'''
|15\13, 818.182
|-
'''1200'''
|4b, 4c
|14\15, 646.154
|'''19\11'''
|16\18, 619.355
|6\7, 600
'''1200'''
|14\17, 579.310
|8\10, 564.706
|'''31\18'''
|10\13, 545.455
|-
'''1200'''
!4
!'''15\15,''' '''692.308'''
|'''12\7'''
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
'''1200'''
!7\7, 700
!'''17\17,''' '''703.448'''
|'''29\17'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
'''1200'''
|-
|4#
|'''17\10'''
| 16\15, 738.462
|12\11, 757.895
'''1200'''
|20\18, 774.194
| rowspan="2" |8\8, 800
|'''22\13'''
|20\17, 827.586
|12\10, 847.059
'''1200'''
| 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'''
|Fa#, Do#
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
| E
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
|7#
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|27\15
|'''17\13,''' '''927.273'''
|-
1246.153…
|5#
|20\15, 923.077
|20\11
|15\11, 947.368
|25\18, 967.742
1263.157…
| rowspan="2" |10\7, 1000
|25\17, 1034.483
| 33\18
|15\10, 1058.824
|20\13, 1090.909
1277.419…
|-
|6b, 6c
|13\7
|22\15, 1015.385
|16\11, 1010.526
1300
|26\18, 1006.452
|24\17, 993.103
|32\17
|14\10, 988.235
|18\13, 981.818
1324.137…
|-
|6
|19\10
|23\15, 1061.538
|17\11, 1073.684
1341.176…
| 28\18, 1083.871
|11\7, 1100
|25\13
|27\17, 1117.241
|16\10, 1129.412
1363.{{Overline|63}}
|21\9, 1145.455
|-
|6#
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
|30\18, 1161.290
|12\7, 1200
|30\17, 1241.379
|18\10, 1270.588
|24\13, 1309.091
|-
|-
| 7b, 7c
|Fax, Dox
|25\15, 1153.846
|29\18, 1122.581
|E#
|11\7, 1100
|26\17, 1075.862
|7x
|15\10, 1058.824
|19\13, 1036.364
|28\15
|-
|'''7'''
1292.307…
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
| rowspan="2" |21\11
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
1326.315…
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
|35\18
|'''22\13,''' '''1200'''
|-
1354.838…
|7#
|27\15, 1246.154
| 14\7
|20\11, 1263.158
|33\18, 1277.419
1400
|13\7, 1300
|32\17, 1324.138
|35\17
|19\10, 1341.176
|25\13, 1363.636
1448.275…
|-
|7x
|21\10
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
1482.352…
|35\18, 1354.834
|14\7, 1400
|28\13
|35\17, 1448.275
|21\10, 1482.353
1527.{{Overline|27}}
|28\13, 1527.273
|-
|-
|Dob, Solb
|Fb
|8b, Fc
|8b, Fc
|29\15, 1338.462
|29\15
|34\18, 1316.129
|13\7, 1300
1338.461…
|31\17, 1282.759
|18\10, 1270.588
|34\18
|23\13, 1254.545
|-
1316.129…
!8, F
!30\15, 1384.615
|13\7
!22\11, 1389.473
!36\18, 1393.548
1300
!14\7, 1400
!34\17, 1406.897
|31\17
!20\10, 1411.765
!26\13, 1418.182
1282.758…
|-
|8#, F#
|18\10
|31\15, 1430.769
|23\11, 1452.632
1270.588…
|38\18, 1470.968
| rowspan="2" |15\7, 1500
| 23\18
|37\17, 1531.034
|22\10, 1552.941
1254.{{Overline|54}}
|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'''
|-
|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
|-
|-
|Xb, Ac
!Do, Sol
|37\15, 1707.692
|27\11, 1705.263
!F
|44\18, 1703.226
|41\17, 1696.552
! 8, F
|24\10, 1694.118
|31\13, 1690.909
! 30\15
|-
|X, A
1384.615…
|38\15, 1753.846
|28\11, 1768.421
! 22\11
|46\18, 1780.645
|18\7, 1800
1389.473…
|44\17, 1820.690
|26\10, 1835.294
!36\18
|34\13, 1854.545
|-
1393.548…
|X#, A#
|39\15, 1800
!14\7
| rowspan="2" |29\11, 1831.579
|48\18, 1858.064
1400
|19\7, 1900
|47\17, 1944.828
! 34\17
|28\10, 1976.471
|37\13, 2018.182
1406.896…
|-
|Ebb, Ccc
! 20\10
|40\15, 1846.154
|47\18, 1819.355
1411.764…
|18\7, 1800
|43\17, 1779.310
!26\13
|25\10, 1764.706
|32\13, 1745.545
1418.{{Overline|18}}
|-
|'''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
|Do#, Sol#
|42\15, 1938.462
|31\11, 1957.895
|F#
|51\18, 1974.194
|20\7, 2000
|8#, F#
|49\17, 2027.586
|29\10, 2047.059
|31\15
|38\13, 2072.727
|-
1430.769…
|Ex, Cx
|43\15, 1984.615
| 23\11
| rowspan="2" |32\11, 2021.053
|53\18, 2051.612
1452.631…
|21\7, 2100
|52\17, 2151.725
|38\18
|31\10, 2188.235
|41\13, 2236.364
1470.967…
|-
|0b, Dc
| rowspan="2" |15\7
|44\15, 2030.769
|52\18, 2012.903
1500
|20\7, 2000
|48\17, 1986.207
| 37\17
|28\10, 1976.471
|36\13, 1963.636
1531.034…
| 22\10
1552.941…
|29\13
1581.{{Overline|81}}
|-
|-
! 0, D
| Reb, Lab
!45\15, 2076.923
!33\11, 2084.211
|Gb
!54\18, 2090.323
!21\7, 2100
|9b, Gc
!51\17, 2110.345
!30\10, 2117.647
|33\15
!39\13, 2127.273
|}
1523.076…
 
{| class="wikitable"
|24\11
|+Cents
!Notation
1515.789…
!Supersoft
!Soft
| 39\18
!Semisoft
! Basic
1509.677…
!Semihard
!Hard
|36\17
!Superhard
1489.655…
|21\10
1482.352…
|27\13
1472.{{Overline|72}}
|-
|-
!Hextone
|'''Re, La'''
!~15edf
!~11edf
|'''G'''
!~18edf
!~7edf
|'''9, G'''
!~17edf
!~10edf
|'''34\15'''
!~13edf
|-
'''1569.230…'''
|0#, G#
|1\15, 46.154
|'''25\11'''
|1\11, 63.158
|2\18, 77.419
'''1578.947…'''
| rowspan="2" |1\7, 100
|3\17, 124.138
|'''41\18'''
|2\10, 141.176
|3\13, 163.636
'''1587.096…'''
|-
| 1f
|'''16\7'''
|3\15, 138.462
|2\11. 126.316
'''1600'''
|3\18, 116.129
|2\17, 82.759
|'''39\17'''
|1\10, 70.588
|1\13, 54.545
'''1613.793…'''
|-
|'''1'''
|'''23\10'''
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
'''1623.529…'''
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|'''30\13'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
'''1636.{{Overline|36}}'''
|'''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
|Re#, La#
|7\15, 323.077
|5\11, 315.789
|G#
|8\18, 309.677
|7\17, 289.655
|9#, G#
|4\10, 282.353
|5\13, 272.727
|35\15
|-
|2
1615.384…
|8\15, 369.231
|6\11, 378.947
|26\11
|10\18, 387.097
| 4\7, 400
1642.105…
|10\17, 413.793
|6\10, 423.529
| 43\18
|8\13, 436.364
|-
1664.516…
|2#
|9\15, 415.385
| rowspan="2" | 17\7
| rowspan="2" |7\11, 442.105
|12\18, 464.516
1700
|5\7, 500
|13\17, 537.069
|42\17
|8\10, 564.706
|11\13, 600
1737.931…
|-
|3f
|25\10
| 10\15, 461.538
|11\18, 425.806
1764.705…
|4\7, 400
|9\17, 372.414
|33\13
|5\10, 352.941
|6\13, 327.273
1800
|-
|-
|'''3'''
|Mib, Sib
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|Ab
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|Xb, Ac
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|37\15
|'''9\13,''' '''490.909'''
|-
1707.692…
|3#
|12\15, 553.846
|27\11
|9\11, 568.421
|15\18, 580.645
1705.263…
|6\7, 600
|15\17, 620.690
|44\18
|9\10, 635.294
|12\13, 654.545
1703.225…
|-
| 3x
|41\17
|13\15, 600
| rowspan="2" | 10\11, 631.579
1696.551…
|17\18, 658.064
|7\7, 700
|24\10
|18\17, 744.828
|11\10, 776.471
1694.117…
|15\13, 818.182
|-
|31\13
|4f
| 14\15, 646.154
1690.{{Overline|90}}
|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#
|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
|Mi, Si
|18\15, 830.769
|13\11, 821.053
|A
|21\18, 812.903
|19\17, 786.207
|X, A
| 11\10, 776.471
|14\13, 763.63
|38\15
|-
|'''5'''
1753.846…
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
|28\11
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
1768.421…
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|46\18
|'''17\13,''' '''927.273'''
|-
1780.645…
|5#
|20\15, 923.077
|18\7
|15\11, 947.368
| 25\18, 967.742
1800
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|44\17
|15\10, 1058.824
|20\13, 1090.909
1820.689…
|-
|6f
|26\10
|22\15, 1015.385
|16\11, 1010.526
1835.294…
|26\18, 1006.452
|24\17, 993.103
|34\13
|14\10, 988.235
|18\13, 981.818
1854.{{Overline|54}}
|-
|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#
|Mi#, Si#
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
| A#
|30\18, 1161.290
|12\7, 1200
|X#, A#
|30\17, 1241.379
|18\10, 1270.588
|39\15
|24\13, 1309.091
|-
1800
| 7f
|25\15, 1153.846
| rowspan="2" |29\11
|29\18, 1122.581
|11\7, 1100
1831.578…
|26\17, 1075.862
|15\10, 1058.824
|48\18
|19\13, 1036.364
|-
1858.064…
|'''7'''
|'''26\15,''' '''1200'''
|19\7
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
1900
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|47\17
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
1944.827…
|-
|7#
|28\10
|27\15, 1246.154
|20\11, 1263.158
1976.470…
|33\18, 1277.419
|13\7, 1300
| 37\13
|32\17, 1324.138
|19\10, 1341.176
2018.{{Overline|18}}
|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
|-
|8f
|29\15, 1338.462
| 34\18, 1316.129
|13\7, 1300
|31\17, 1282.759
|18\10, 1270.588
|23\13, 1254.545
|-
|-
! 8
|Fab, Dob
!30\15, 1384.615
!22\11, 1389.473
|Bbb
!36\18, 1393.548
!14\7, 1400
|Ebb, Ccc
!34\17, 1406.897
!20\10, 1411.765
|40\15
!26\13, 1418.182
|-
1846.153…
|8#
|31\15, 1430.769
|47\18
|23\11, 1452.632
| 38\18, 1470.968
1819.354…
| rowspan="2" |15\7, 1500
|37\17, 1531.034
| 18\7
|22\10, 1552.941
|29\13, 1581.818
1800
|-
|9f
|43\17
|33\15, 1523.077
|24\11, 1515.789
1779.310…
|39\18, 1509.677
| 36\17, 1489.655
|25\10
|21\10, 1482.759
|27\13, 1472.273
1764.705…
|-
|9
| 32\13
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
1745.{{Overline|45}}
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.364'''
|-
|9#
|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
|-
|Af
| 37\15, 1707.692
| 27\11, 1705.263
|44\18, 1703.226
|41\17, 1696.552
|24\10, 1694.118
|31\13, 1690.909
|-
|A
| 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
|-
|-
|A#
|'''Fa, Do'''
| 39\15, 1800
| rowspan="2" |29\11, 1831.579
|'''Bb'''
| 48\18, 1858.064
|19\7, 1900
|Eb, Cc
|47\17, 1944.828
|28\10, 1976.471
|'''41\15'''
|37\13, 2018.182
|-
'''1892.307…'''
|Ax
|40\15, 1846.154
|'''30\11'''
|47\18, 1819.355
|18\7, 1800
'''1894.736…'''
|43\17, 1779.310
|25\10, 1764.706
|'''49\18'''
|32\13, 1745.545
|-
'''1896.774…'''
|'''Bf'''
|'''41\15,''' '''1892.308'''
|'''19\7'''
|'''30\11,''' '''1894.737'''
|'''49\18,''' '''1896.774'''
'''1900'''
|'''19\7, 1900'''
|'''46\17,''' '''1903.448'''
|'''46\17'''
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
'''1903.448…'''
|-
|B
|'''27\10'''
|42\15, 1938.462
|31\11, 1957.895
'''1905.882…'''
|51\18, 1974.194
|20\7, 2000
|'''35\13'''
|49\17, 2027.586
| 29\10, 2047.059
'''1909.{{Overline|09}}'''
|38\13, 2072.727
|-
|B#
|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
|-
|Cf
|44\15, 2030.769
|52\18, 2012.903
|20\7, 2000
|48\17, 1986.207
|28\10, 1976.471
|36\13, 1963.636
|-
!C
!45\15, 2076.923
!33\11, 2084.211
!54\18, 2090.323
!21\7, 2100
!51\17, 2110.345
!30\10, 2117.647
!39\13, 2127.273
|-
|-
|C#
|Fa#, Do#
|46\15, 2123.077
|34\11, 2147.368
| B
|56\15, 2167.742
| rowspan="2" |22\7, 2200
|E, C
|54\17, 2234.483
|32\10, 2258.824
|42\15
|42\13, 2090.909
|-
1938.461…
|Df
|48\15, 2215.385
|31\11
|35\11, 2210.526
|57\15, 2206.452
1957.894…
|53\17, 2193.103
|31\10, 2188.235
| 51\18
|40\13, 2181.818
|-
1974.193…
|'''D'''
|'''49\15, 2261.538'''
|20\7
|'''36\11, 1073.684'''
|'''59\18, 2283.871'''
2000
|'''23\7, 2300'''
|'''56\17, 2317.241'''
|49\17
|'''33\10, 2329.412'''
|'''43\13,''' '''2345.455'''
2027.586…
|-
|D#
|29\10
|50\15, 2307.692
|37\11, 2336.842
1976.470…
|61\18, 2361.290
| rowspan="2" |24\7, 2400
|38\13
|59\17, 2441.379
|35\10, 2470.588
2072.{{Overline|72}}
|46\13, 2509.091
|-
|Ef
|52\15, 2400
|38\11, 2400
|62\18, 2400
|58\17, 2400
|34\10, 2400
| 44\13, 2400
|-
|E
|53\15, 2446.154
| 39\11, 2463.158
|64\18, 2477,419
|25\7, 2500
|61\17, 2524.138
|36\10, 2541.176
|47\13, 2563.636
|-
|E#
|54\15, 2492.308
| rowspan="2" |40\11, 2526.316
|66\18, 2554.838
|26\7, 2600
|64\17, 2648.275
|38\10, 2682.353
|50\13, 2727.273
|-
|-
|Fff
|Fax, Dox
| 55\15, 2538.462
| 65\18, 2516.129
|B#
|25\7, 2500
|60\17, 2482.759
|Ex, Cx
|35\10, 2470.588
|45\13, 2454.545
|43\15
|-
|'''Ff'''
1984.615…
|'''56\15, 2584.615'''
|'''41\11, 2589.474'''
| rowspan="2" |32\11
|'''67\18, 2593.548'''
|'''26\7, 2600'''
2021.052…
|'''63\17, 2606.897'''
|'''37\10, 2611.765'''
|53\18
|'''48\13,''' '''2618.182'''
|-
2051.612…
|F
|57\15, 2630.769
|21\7
|42\11, 2652.632
|69\18, 2670.968
2100
|27\7, 2700
|66\17, 2731.034
|52\17
|39\10, 2752.941
|51\13, 2781.818
2151.724…
|-
| F#
|31\10
| rowspan="2" |58\15, 2676.923
|43\11, 2715.789
2188.235…
|71\18, 2748.387
| 28\7, 2800
|41\13
|69\17, 2855.172
|41\10, 2894.118
2236.{{Overline|36}}
|54\13, 2945.455
|-
|0ff, Gff
|42\11, 2652.632
|68\18, 2632.258
|26\7, 2600
|62\17, 2565.517
|36\10, 2541.176
|46\13, 2509.091
|-
|0f, Gf
|59\15, 2723.077
|43\11, 2715.789
|70\18, 2709.677
|27\7, 2700
|65\17, 2689.552
|38\10, 2682.353
|49\13, 2672.273
|-
|-
!0, G
|Dob, Solb
!60\15, 2769.231
!44\11, 2778.947
|Hb
!72\18, 2787.097
!28\7, 2800
|0b, Dc
!68\17, 2813.793
!40\10, 2823.529
|44\15
!52\13, 2836.364
|}
2030.769…
 
{| class="wikitable"
|52\18
|+Cents
!Notation
2012.903…
!Supersoft
!Soft
|20\7
! Semisoft
! Basic
2000
!Semihard
!Hard
|48\17
!Superhard
1986.206…
|28\10
1967.470…
|36\13
1963.{{Overline|63}}
|-
|-
!Guidotonic
!Do, Sol
!~15edf
!~11edf
!H
!~18edf
!~7edf
!0, D
!~17edf
!~10edf
!45\15
!~13edf
|-
2076.923…
|F ut#
|1\15, 46.154
!33\11
|1\11, 63.158
|2\18, 77.419
2084.210…
| rowspan="2" |1\7, 100
|3\17, 124.138
!54\18
|2\10, 141.176
|3\13, 163.636
2090.322…
|-
|G reb
!21\7
|3\15, 138.462
|2\11. 126.316
2100
|3\18, 116.129
|2\17, 82.759
!51\17
|1\10, 70.588
|1\13, 54.545
2110.344…
|-
|'''G re'''
!30\10
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
2117.647…
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
!39\13
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
2127.{{Overline|27}}
|'''4\13,''' '''218.182'''
|}
{| class="wikitable"
|+Relative cents
! colspan="3" | Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
|-
! Diatonic
|G re#
!Napoli
|5\15, 230.769
! Bijou
|4\11, 252.632
!~15edf
|7\18, 270.968
!~11edf
| rowspan="2" |3\7, 300
!~18edf
|8\17, 331.034
!~7edf
|5\10, 352.941
!~17edf
|7\13, 381.818
!~10edf
|-
!~13edf
|A mib
|7\15, 323.077
|5\11, 315.789
|8\18, 309.677
|7\17, 289.655
|4\10, 282.353
|5\13, 272.727
|-
|A mi
|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
|-
| A mi#
|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
|-
|-
|Do#, Sol#
|B fa utb
|F#
|10\15, 461.538
|0#, D#
|11\18, 425.806
|1\15
|4\7, 400
|9\17, 372.414
''46.{{Overline|6}}''
|5\10, 352.941
|1\11
|6\13, 327.273
''63.{{Overline|63}}''
|2\18
''77.7̄''
| rowspan="2" |1\7
''100''
| 3\17
''123.529…''
| 2\10
''140''
|3\13
''161.538…''
|-
|-
|Reb, Lab
|'''B fa ut'''
| Gb
|'''11\15,''' '''507.692'''
|1b, 1c
|'''8\11,''' '''505.263'''
|3\15
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
''140''
|'''12\17,''' '''496.552'''
|2\11
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
''127.{{Overline|27}}''
|3\18
''116.{{Overline|6}}''
| 2\17
''82.352…''
|1\10
''70''
|1\13
''53.846…''
|-
|-
|'''Re, La'''
|B fa ut#
|'''G'''
|12\15, 553.846
|'''1'''
|9\11, 568.421
|'''4\15'''
|15\18, 580.645
|6\7, 600
'''''186.{{Overline|6}}'''''
|15\17, 620.690
|'''3\11'''
|9\10, 635.294
|12\13, 654.545
'''''190.{{Overline|90}}'''''
|-
|'''5\18'''
|B fa utx
| 13\15, 600
'''''194.{{Overline|4}}'''''
| rowspan="2" |10\11, 631.579
|'''2\7'''
|17\18, 658.064
|7\7, 700
'''''200'''''
|18\17, 744.828
|'''5\17'''
|11\10, 776.471
|15\13, 818.182
'''''205.882…'''''
|-
|'''3\10'''
|C sol re utb
| 14\15, 646.154
'''''210'''''
|16\18, 619.355
|'''4\13'''
|6\7, 600
|14\17, 579.310
'''''215.384…'''''
|8\10, 564.706
|10\13, 545.455
|-
!C sol re ut
!'''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'''
|-
|-
|Re#, La#
|C sol re ut#
| G#
|16\15, 738.462
| 1#
|12\11, 757.895
|5\15
|20\18, 774.194
| rowspan="2" |8\8, 800
''233.{{Overline|3}}''
|20\17, 827.586
|4\11
|12\10, 847.059
|16\13, 872.727
''254.{{Overline|54}}''
|7\18
''272.2̄''
| rowspan="2" |3\7
''300''
|8\17
''329.411…''
|5\10
''350''
|7\13
''376.923…''
|-
|-
|Mib, Sib
|D la mi reb
|Ab
|18\15, 830.769
|2b, 2c
|13\11, 821.053
|7\15
|21\18, 812.903
|19\17, 786.207
''326.{{Overline|6}}''
|11\10, 776.471
|5\11
|14\13, 763.63
''318.{{Overline|18}}''
| 8\18
''311.{{Overline|1}}''
|7\17
''288.235…''
| 4\10
''280''
|5\13
''269.230…''
|-
|-
|Mi, Si
|'''D la mi re'''
|A
|'''19\15,''' '''876.923'''
| 2
|'''14\11,''' '''884.211'''
|8\15
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
''373.{{Overline|3}}''
|'''22\17,''' '''910.345'''
|6\11
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
''381.{{Overline|81}}''
|-
|10\18
|D la mi re#
|20\15, 923.077
''388.{{Overline|8}}''
| rowspan="2" |15\11, 947.368
|4\7
|25\18, 967.742
|10\7, 1000
''400''
|25\17, 1034.483
|10\17
|15\10, 1058.824
|20\13, 1090.909
''411.764…''
|-
|6\10
|E fa utb
|21\15, 969.231
''420''
|24\18, 929.032
|8\13
| 9\5, 900
|21\17, 868.966
''430.769…''
|12\10, 847.059
|15\13, 818.182
|-
|E fa ut
| 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
|-
|-
|Mi#, Si#
|E si mi re
|A#
|23\15, 1061.538
|2#
|17\11, 1073.684
|9\15
|28\18, 1083.871
|11\7, 1100
''420''
|27\17, 1117.241
| rowspan="2" |7\11
|16\10, 1129.412
|21\9, 1145.455
''445.{{Overline|45}}''
|12\18
''466.{{Overline|6}}''
|5\7
''500''
|13\17
''535.294…''
|8\10
''560''
|11\13
''592.307…''
|-
|-
|Fab, Dob
| E si mi re#
|Bbb
|24\15, 1107.923
|3b, 3c
| rowspan="2" |18\11, 1136.842
|10\15
|30\18, 1161.29
|12\7, 1200
''466.{{Overline|6}}''
|30\17, 1241.379
|11\18
| 18\10, 1270.588
|24\13, 1309.091
''427.{{Overline|7}}''
|4\7
''400''
|9\17
''370.588…''
|5\10
''350''
|6\13
''323.076.…''
|-
|-
|'''Fa, Do'''
|F sol fa ut reb
|'''Bb'''
|25\15, 1153.846
|'''3'''
|29\18, 1122.581
|'''11\15'''
|11\7, 1100
|26\17, 1075.862
'''''513.{{Overline|3}}'''''
|15\10, 1058.824
|'''8\11'''
|19\13, 1036.364
|-
'''''509.{{Overline|09}}'''''
|'''F sol fa ut re'''
|'''13\18'''
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
'''''505.{{Overline|5}}'''''
|'''31\18,''' '''1200'''
|'''5\7'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
'''''500'''''
|'''17\10,''' '''1200'''
|'''12\17'''
|'''22\13,''' '''1200'''
|-
'''''494.117…'''''
|F sol fa ut re#
|'''7\10'''
|27\15, 1246.154
|20\11, 1263.158
'''''490'''''
|33\18, 1277.419
|'''9\13'''
|13\7, 1300
|32\17, 1324.138
'''''484.615…'''''
| 19\10, 1341.176
| 25\13, 1363.636
|-
|F sol fa ut rex
|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
|-
|-
|Fa#, Do#
|G la sol re mib
| B
| 29\15, 1338.462
|3#
|34\18, 1316.129
|12\15
| 13\7, 1300
|31\17, 1282.759
''560''
|18\10, 1270.588
|9\11
|23\13, 1254.545
''572.{{Overline|72}}''
| 15\18
''583.{{Overline|3}}''
|6\7
''600''
|15\17
''617.647…''
|9\10
''630''
|12\13
''646.153…''
|-
|-
| Fax, Dox
!G la sol re mi
|B#
!30\15, 1384.615
|3x
!22\11, 1389.473
|13\15
!36\18, 1393.548
!14\7, 1400
''606. {{Overline|6}}''
!34\17, 1406.897
| rowspan="2" |10\11
!20\10, 1411.765
!26\13, 1418.182
''636.{{Overline|36}}''
|17\18
''661.{{Overline|1}}''
|7\7
''700''
|18\17
''741.176…''
|11\10
''770''
|15\13
''807.692…''
|-
|-
|Dob, Solb
|G la sol re mi#
|Hb
|31\15, 1430.769
|4b, 4c
|23\11, 1452.632
|14\15
|38\18, 1470.968
| rowspan="2" |15\7, 1500
''653.{{Overline|3}}''
|37\17, 1531.034
|16\18
|22\10, 1552.941
|29\13, 1581.818
''622.{{Overline|2}}''
|-
|6\7
|A si la mi fab
|33\15, 1523.077
''600''
| 24\11, 1515.789
| 14\17
|39\18, 1509.677
|36\17, 1489.655
''576.470…''
|21\10, 1482.759
| 8\10
| 27\13, 1472.273
|-
''560''
|'''A si la mi fa'''
|10\13
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
''538.461…''
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''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
|-
|-
!Do, Sol
|B sol fa utb
!H
|36\61, 1661.538
!4
|42\18, 1625.806
! colspan="7" |''700''
|16\7, 1600
|38\29, 1572.414
|22\10, 1552.941
|28\13, 1527.273
|-
|-
|Do#, Sol#
|B sol fa ut
|Η#
|37\15, 1707.692
|4#
|27\11, 1705.263
|16\15
| 44\18, 1703.226
| 17\7, 1700
''746.{{Overline|6}}''
|41\17, 1696.552
|12\11
|24\10, 1694.118
|31\13, 1690.909
''763.{{Overline|63}}''
|20\18
''777.{{Overline|7}}''
| rowspan="2" |8\7
''800''
|20\17
''823.529…''
|12\10
''840''
|16\13
''861.538…''
|-
|-
|Reb, Lab
|B si
|Cb
|38\15, 1753.846
|5b, 5c
| 28\11, 1768.421
|18\15
|46\18, 1780.645
|18\7, 1800
''840''
|44\17, 1820.690
|13\11
|26\10, 1835.294
|34\13, 1854.545
''827.{{Overline|27}}''
|21\18
''816.{{Overline|6}}''
| 19\17
''782.352…''
|11\10
''770''
|14\13
''753.846…''
|-
|-
|'''Re, La'''
|B si
|'''C'''
|39\15, 1800
|'''5'''
| rowspan="2" |29\11, 1831.579
|'''19\15'''
|48\18, 1858.064
|19\7, 1900
'''''886.{{Overline|6}}'''''
|47\17, 1944.828
|'''14\11'''
|28\10, 1976.471
|37\13, 2018.182
'''''890.{{Overline|90}}'''''
|-
|'''23\18'''
|C la sol re utb
|40\15, 1846.154
'''''894.{{Overline|4}}'''''
|47\18, 1819.355
|'''9\7'''
| 18\7, 1800
| 43\17, 1779.310
'''''900'''''
|25\10, 1764.706
|'''22\17'''
|32\13, 1745.545
|-
'''''905.882…'''''
|'''C la sol re ut'''
|'''13\10'''
|'''41\15,''' '''1892.308'''
|'''30\11,''' '''1894.737'''
'''''910'''''
|'''49\18,''' '''1896.774'''
|'''17\13'''
|'''19\7, 1900'''
|'''46\17,''' '''1903.448'''
'''''915.384…'''''
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
|-
|-
| Re#, La#
|C la sol re ut#
|C#
|42\15, 1938.462
|5#
|31\11, 1957.895
|20\15
|51\18, 1974.194
|20\7, 2000
''933.{{Overline|3}}''
|49\17, 2027.586
|15\11
| 29\10, 2047.059
|38\13, 2072.727
''954.{{Overline|54}}''
|25\18
''972.{{Overline|2}}''
| rowspan="2" | 10\7
''1000''
|25\17
''1029.411…''
|15\10
''1050''
|20\13
''1076.923…''
|-
|-
|Mib, Sib
|C la sol re utx
|Db
| rowspan="2" |43\15, 1984.615
|6b, 6c
|32\11, 2021.053
|22\15
|53\18, 2051.612
|21\7, 2100
''1026.{{Overline|6}}''
|52\17, 2151.725
|16\11
|31\10, 2188.235
|41\13, 2236.364
''1018.{{Overline|18}}''
|26\18
''1011. {{Overline|1}}''
|24\17
''988.235…''
|14\10
''980''
|18\13
''969.230…''
|-
|-
|Mi, Si
|D fa la mi reb
|D
|31\11, 1957.895
|6
|50\18, 1935.484
| 23\15
|19\7, 1900
|45\17, 1862.069
''1073.{{Overline|3}}''
|26\10, 1835.294
|17\11
|33\13, 1800
|-
''1081.{{Overline|81}}''
|D fa la mi re
|28\18
|44\15, 2030.769
|32\11, 2021.053
''1088.{{Overline|8}}''
|52\18, 2012.903
|11\7
|20\7, 2000
|48\17, 1986.207
''1100''
|28\10, 1976.471
|27\17
|36\13, 1963.636
|-
''1111.764…''
!D si la mi re
|16\10
!45\15, 2076.923
!33\11, 2084.211
''1120''
!54\18, 2090.323
|21\13
!21\7, 2100
! 51\17, 2110.345
''1130.769…''
!30\10, 2117.647
!39\13, 2127.273
|-
|D si la mi re#
|46\15, 2123.077
| rowspan="2" |34\11, 2147.368
|56\18, 2167.742
|22\7, 2200
|54\17, 2234.483
| 32\10, 2258.824
|42\13, 2090.909
|-
|-
|Mi#, Si#
|E fab
| D#
|47\26, 2169.231
|6#
|55\16, 2129.032
|24\15
|21\7, 2100
|50\17, 2068.966
''1120''
|29\10, 2047.059
| rowspan="2" | 18\11
|37\13, 2018.182
''1145.{{Overline|45}}''
|30\18
''1166.{{Overline|6}}''
|12\7
''1200''
| 30\17
''1235.294…''
|18\10
''1260''
|24\13
''1292.307…''
|-
|-
| Fab, Dob
|E fa
| Ebb
|48\15, 2215.385
| 7b, 7c
|35\11, 2210.526
|25\15
|57\18, 2206.452
|23\7, 2300
''1166.{{Overline|6}}''
|53\17, 2193.103
|29\18
|31\10, 2188.235
|40\13, 2181.818
''1127.{{Overline|7}}''
|11\7
''1100''
|26\17
''1070.588…''
|15\10
''1050''
|19\13
''1023.076…''
|-
|-
|'''Fa, Do'''
|E si mi
|'''Eb'''
|49\15, 2261.538
|'''7'''
|36\11, 1073.684
|'''26\15'''
|59\18, 2283.871
|24\7, 2400
'''''1213.{{Overline|3}}'''''
|56\17, 2317.241
|'''19\11'''
|33\10, 2329.412
|43\13, 2345.455
'''''1209.{{Overline|09}}'''''
|-
|'''31\18'''
|E si mi#
|50\15, 2307.692
'''''1205.{{Overline|5}}'''''
| rowspan="2" |37\11, 2336.842
|'''12\7'''
|61\18, 2361.290
| rowspan="2" |23\7, 2300
'''''1200'''''
| 59\17, 2441.379
|'''29\17'''
|35\10, 2470.588
|46\13, 2509.091
'''''1194.117…'''''
|-
|'''17\10'''
|F sol fa utb
|51\15, 2353.846
'''''1190'''''
|60\18, 2322.581
|'''22\13'''
|55\17, 2275.862
|32\10, 2258.824
'''''1184.615…'''''
|41\13, 2236.364
|-
|-
|Fa#, Do#
|F sol fa ut
|E
|52\15, 2400
|7#
|38\11, 2400
|27\15
|62\18, 2400
|24\7, 2400
''1260''
|58\17, 2400
|20\11
|34\10, 2400
|44\13, 2400
''1272.{{Overline|72}}''
| 33\18
''1283.{{Overline|3}}''
|13\7
''1300''
|32\17
''1317.647…''
|19\10
''1330''
| 25\13
''1346.153…''
|-
|-
|Fax, Dox
|F sol fa ut#
|E#
|53\15, 2446.154
|7x
|39\11, 2463.158
|28\15
|64\18, 2477,419
| rowspan="2" |25\7, 2500
''1306.{{Overline|6}}''
|61\17, 2524.138
| rowspan="2" |21\11
|36\10, 2541.176
|47\13, 2563.636
''1336.{{Overline|36}}''
|35\18
''1361.{{Overline|1}}''
|14\7
''1400''
|35\17
''1441.176…''
|21\10
''1470''
|28\13
''1507.692…''
|-
|-
|Dob, Solb
|G la sol reb
|Fb
|55\15, 2538.462
|8b, Fc
|40\11, 2526.316
|29\15
|65\18, 2516.129
|60\17, 2482.759
''1333.{{Overline|3}}''
|35\10, 2470.588
|34\18
|45\13, 2454.545
|-
''1322.{{Overline|2}}''
|'''G la sol re'''
|13\7
|'''56\15, 2584.615'''
|'''41\11, 2589.474'''
''1300''
|'''67\18, 2593.548'''
|31\17
|'''26\7, 2600'''
|'''63\17, 2606.897'''
''1276.470…''
|'''37\10, 2611.765'''
|18\10
|'''48\13,''' '''2618.182'''
|-
''1260''
|G la sol re#
|23\13
|57\15, 2630.769
|42\11, 2652.632
''1238.461…''
|69\18, 2670.968
| rowspan="2" |27\7, 2700
|66\17, 2731.034
|39\10, 2752.941
|51\13, 2781.818
|-
|-
!Do, Sol
|A si la mib
!F
|59\15, 2723.077
!8, F
|43\11, 2715.789
! colspan="7" |''1400''
|70\18, 2709.677
|65\17, 2689.552
|38\10, 2682.353
|49\13, 2672.273
|-
|-
|Do#, Sol#
!A si la mi
|F#
!60\15, 2769.231
|8#, F#
!44\11, 2778.947
|31\15
!72\18, 2787.097
!28\7, 2800
''1446.{{Overline|6}}''
!68\17, 2813.793
|23\11
!40\10, 2823.529
!52\13, 2836.364
''1463.{{Overline|63}}''
|38\18
''1477.7̄''
| rowspan="2" |15\7
''1500''
|37\17
''1523.529…''
|22\10
''1540''
| 29\13
''1561.538…''
|-
|-
|Reb, Lab
|A si la mi#
|Gb
|61\15, 2815.385
| 9b, Gc
| rowspan="2" |45\11, 2842.105
|33\15
| 74\18, 2864.516
|29\7, 2900
''1540''
|71\17, 2937.069
|24\11
|42\10, 2964.706
|55\13, 3000
''1527.{{Overline|27}}''
|39\18
''1516.{{Overline|6}}''
| 36\17
''1482.352…''
|21\10
''1470''
|27\13
''1453.846…''
|-
|-
|'''Re, La'''
|B fab
|'''G'''
|62\15, 2861.538
|'''9, G'''
|73\18, 2825.806
|'''34\15'''
| 28\7, 2800
|67\17, 2772.414
'''''1586.{{Overline|6}}'''''
|39\10, 2752.941
|'''25\11'''
|50\13, 2727.273
|-
'''''1590.{{Overline|90}}'''''
|B fa
|'''41\18'''
|63\15, 2907.692
|46\11, 2905.263
'''''1594.{{Overline|4}}'''''
|75\18, 2903.226
|'''16\7'''
|29\7, 2900
|70\17, 2896.552
'''''1600'''''
|41\10, 2894.118
|'''39\17'''
|53\13, 2890.909
|-
'''''1605.882…'''''
|'''B si'''
|'''23\10'''
|'''64\15, 2953.846'''
|'''47\11, 2968.421'''
'''''1610'''''
|'''77\18, 2980.645'''
|'''30\13'''
|'''30\7, 3000'''
|'''73\17, 3020.690'''
'''''1615.384…'''''
|'''43\10, 3035.294'''
|'''56\13, 3054.545'''
|-
|-
|Re#, La#
|B si#
|G#
|65\15, 3000
|9#, G#
|48\11, 3031.579
|35\15
|79\18, 3058.064
| rowspan="2" |31\7, 3100
''1633.{{Overline|3}}''
|76\17, 3144.828
|26\11
|45\10, 3176.471
|59\13, 3218.182
''1654.{{Overline|54}}''
|43\18
''1672.{{Overline|2}}''
| rowspan="2" |17\7
''1700''
|42\17
''1729.411…''
|25\10
''1750''
|33\13
''1776.923…''
|-
|-
|Mib, Sib
|C solb
| Ab
|67\15, 3092.308
|Xb, Ac
|49\11, 3094.737
|37\15
|80\18, 3096.774
|75\17, 3103.448
''1726.{{Overline|6}}''
|44\10, 3105.882
| 27\11
|57\13, 3109.091
''1718.{{Overline|18}}''
|44\18
''1711.{{Overline|1}}''
|41\17
''1688.235…''
| 24\10
''1680''
|31\13
''1669.230…''
|-
|-
|Mi, Si
|C sol
|A
|68\15, 3138.462
|X, A
|50\11, 3157.895
|38\15
| 82\18, 3174.194
|32\7, 3200
''1773.{{Overline|3}}''
|78\17, 3227.586
|28\11
| 46\10, 3247.059
|60\13, 3272.273
''1781.{{Overline|81}}''
|-
|46\18
|C sol#
| 69\15, 3184.615
''1788.{{Overline|8}}''
| rowspan="2" |51\11, 3221.053
|18\7
|84\18, 3251.612
|33\7, 3300
''1800''
|81\17, 3351.725
| 44\17
|48\10, 3388.235
|63\13, 3436.364
''1811.764…''
|-
|26\10
|D labb
|70\15, 3230.769
''1820''
|83\18, 3212.903
|34\13
|32\7, 3200
|77\17, 3186.207
''1830.769…''
|45\10, 3176.471
|58\13, 3163.636
|-
|-
|Mi#, Si#
|'''D lab'''
|A#
|'''71\15,''' '''3276.923'''
|X#, A#
|'''52\11,''' '''3284.211'''
|39\15
|'''85\18,''' '''3290.323'''
|'''33\7, 3300'''
''1820''
|'''80\17,''' '''3310.345'''
| rowspan="2" |29\11
|'''47\10,''' '''3317.647'''
|'''61\13,''' '''3327.{{Overline|27}}'''
''1845.{{Overline|45}}''
|48\18
''1866.{{Overline|6}}''
|19\7
''1900''
|47\17
''1935.294…''
|28\10
''1960''
| 37\13
''1992.307…''
|-
|-
|Fab, Dob
|D la
|Bbb
|72\15, 3323.077
|Ebb, Ccc
|53\11, 3347.368
|40\15
|87\18, 3367.742
|34\7, 3400
''1866.{{Overline|6}}''
|83\17, 3434.583
|47\18
|49\10, 3458.824
|64\13, 3490.909
''1827.{{Overline|7}}''
|18\7
''1800''
|43\17
''1770.588…''
|25\10
''1750''
|32\13
''1723.076…''
|-
|-
|'''Fa, Do'''
|D la#
|'''Bb'''
|73\15, 3369.231
|Eb, Cc
| rowspan="2" |54\11, 3410.625
|'''41\15'''
|89\18, 3445.162
|35\7, 3500
'''''1913.{{Overline|3}}'''''
|86\17, 3558.621
|'''30\11'''
|51\10, 3600
|67\13, 3654.545
'''''1909.{{Overline|09}}'''''
|'''49\18'''
'''''1905.{{Overline|5}}'''''
|'''19\7'''
'''''1900'''''
|'''46\17'''
'''''1894.117…'''''
|'''27\10'''
'''''1890'''''
|'''35\13'''
'''''1884.615…'''''
|-
|-
|Fa#, Do#
|F utb
|B
|74\15, 3415.385
|E, C
|88\18, 3406.452
| 42\15
|34\7, 3400
|82\17, 3393.103
''1960''
|48\10, 3388.235
|31\11
|62\13, 3381.818
''1972.{{Overline|72}}''
|51\18
''1983.{{Overline|3}}''
|20\7
''2000''
|49\17
''2017.647…''
|29\10
''2030''
|38\13
''2046.153…''
|-
|-
|Fax, Dox
!F ut
|B#
!75\15, 3461.538
|Ex, Cx
!55\11, 3473.684
|43\15
!90\18, 3483.871
!35\7, 3500
''2006.{{Overline|6}}''
!85\17, 3517.241
| rowspan="2" |32\11
!50\10, 3529.412
!65\13, 3545.455
''2036.{{Overline|36}}''
|}
|53\18
 
{| class="wikitable"
''2061. {{Overline|1}}''
|+Cents
|21\7
!Notation
!Supersoft
''2100''
!Soft
|52\17
! Semisoft
!Basic
''2141.176…''
!Semihard
|31\10
!Hard
!Superhard
''2170''
|-
|41\13
!Subdozenal
!~15edf
''2207.692…''
!~11edf
!~18edf
!~7edf
!~17edf
!~10edf
!~13edf
|-
|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
|-
|-
| Dob, Solb
|Gb, Ge
|Hb
|3\15, 138.462
|0b, Dc
|2\11. 126.316
|44\15
|3\18, 116.129
|2\17, 82.759
''2053.{{Overline|3}}''
|1\10, 70.588
|52\18
|1\13, 54.545
''2022.{{Overline|2}}''
|20\7
''2000''
|48\17
''1976.470…''
|28\10
''1960''
| 36\13
1938.615…
|-
|-
!Do, Sol
|'''G'''
!H
|'''4\15,''' '''184.615'''
!0, D
|'''3\11,''' '''189.474'''
! colspan="7" |2100
|'''5\18,''' '''193.548'''
|}
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
==Intervals==
|'''3\10,''' '''211.765'''
{| class="wikitable"
|'''4\13,''' '''218.182'''
!Generators
|-
! Sesquitave notation
|G#
!Interval category name
|5\15, 230.769
!Generators
|4\11, 252.632
!Notation of 3/2 inverse
|7\18, 270.968
!Interval category name
| 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
|-
|-
| colspan="6" |The 4-note MOS has the following intervals (from some root):
|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
|-
|-
|0
|H#
|Do, Sol
|9\15, 415.385
|perfect unison
| rowspan="2" |7\11, 442.105
|0
|12\18, 464.516
|Do, Sol
|5\7, 500
|sesquitave (just fifth)
|13\17, 537.069
|8\10, 564.706
|11\13, 600
|-
|-
|1
|Jbb, Jee
|Fa, Do
|10\15, 461.538
|perfect fourth
|11\18, 425.806
| -1
|4\7, 400
|Re, La
|9\17, 372.414
|perfect second
|5\10, 352.941
|6\13, 327.273
|-
|-
|2
|'''Jb, Je'''
|Mib, Sib
|'''11\15,''' '''507.692'''
|minor third
|'''8\11,''' '''505.263'''
| -2
|'''13\18,''' '''503.226'''
|Mi, Si
|'''5\7, 500'''
|major third
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|-
|3
|J
|Reb, Lab
|12\15, 553.846
|diminished second
|9\11, 568.421
| -3
|15\18, 580.645
|Fa#, Do#
|6\7, 600
|augmented fourth
|15\17, 620.690
|9\10, 635.294
|12\13, 654.545
|-
|-
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|J#
|13\15, 600
| rowspan="2" |10\11, 631.579
|17\18, 658.064
|7\7, 700
|18\17, 744.828
|11\10, 776.471
|15\13, 818.182
|-
|-
|4
|Kb, Ke
|Dob, Solb
|14\15, 646.154
|diminished sesquitave
|16\18, 619.355
| -4
|6\7, 600
| Do#, Sol#
|14\17, 579.310
|augmented unison (chroma)
|8\10, 564.706
|10\13, 545.455
|-
!K
!'''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'''
|-
|K#
|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
|-
|Lb, Le
|18\15, 830.769
|13\11, 821.053
|21\18, 812.903
|19\17, 786.207
|11\10, 776.471
|14\13, 763.63
|-
|'''L'''
|'''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
|-
|-
|5
|Nbb, Nee
|Fab, Dob
|25\15, 1153.846
|diminished fourth
|29\18, 1122.581
| -5
|11\7, 1100
|Re#, La#
|26\17, 1075.862
|augmented second
|15\10, 1058.824
|19\13, 1036.364
|-
|-
|6
|'''Nb, Ne'''
| Mibb, Sibb
|'''26\15,''' '''1200'''
|diminished third
|'''19\11,''' '''1200'''
| -6
|'''31\18,''' '''1200'''
|Mi#, Si#
|'''12\7, 1200'''
|augmented third
|'''29\17,''' '''1200'''
|}
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
==Genchain==
|-
|N
The generator chain for this scale is as follows:
|27\15, 1246.154
{| class="wikitable"
|20\11, 1263.158
|Mibb
|33\18, 1277.419
|13\7, 1300
Sibb
|32\17, 1324.138
|Fab
|19\10, 1341.176
|25\13, 1363.636
Dob
|-
|Dob
|N#
|28\15, 1292.308
Solb
| rowspan="2" |21\11, 1326.318
|Reb
|35\18, 1354.834
|14\7, 1400
Lab
|35\17, 1448.275
|Mib
|21\10, 1482.353
|28\13, 1527.273
Sib
|-
|Fa
|Pb, Pe
|29\15, 1338.462
Do
|34\18, 1316.129
|Do
|13\7, 1300
|31\17, 1282.759
Sol
|18\10, 1270.588
|Re
|23\13, 1254.545
|-
La
!P
|Mi
!30\15, 1384.615
!22\11, 1389.473
Si
!36\18, 1393.548
|Fa#
!14\7, 1400
!34\17, 1406.897
Do#
!20\10, 1411.765
|Do#
!26\13, 1418.182
|-
Sol#
|P#
|Re#
|31\15, 1430.769
|23\11, 1452.632
La#
|38\18, 1470.968
|Mi#
| rowspan="2" |15\7, 1500
|37\17, 1531.034
Si#
|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
|-
|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
|-
|R#
|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
|-
|Sb, Se
|40\15, 1846.154
|47\18, 1819.355
|18\7, 1800
|43\17, 1779.310
|25\10, 1764.706
|32\13, 1745.545
|-
|'''S'''
|'''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'''
|-
|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
|-
|-
|d3
|Sx
|d4
|43\15, 1984.615
|d5
| rowspan="2" |32\11, 2021.053
|d2
|53\18, 2051.612
| m3
|21\7, 2100
|P4
|52\17, 2151.725
|P1
|31\10, 2188.235
|P2
|41\13, 2236.364
|M3
|A4
| A1
|A2
|A3
|}
==Modes==
The mode names are based on the species of fifth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
|-
|-
!name
|Tb, Te
!pattern
|44\15, 2030.769
!notation
|52\18, 2012.903
!2nd
|20\7, 2000
!3rd
|48\17, 1986.207
!4th
|28\10, 1976.471
|36\13, 1963.636
|-
|-
|Lydian
!T
|LLLs
!45\15, 2076.923
|<nowiki>3|0</nowiki>
!33\11, 2084.211
|P
!54\18, 2090.323
|M
!21\7, 2100
| A
!51\17, 2110.345
!30\10, 2117.647
!39\13, 2127.273
|-
|T#
|46\15, 2123.077
| rowspan="2" |34\11, 2147.368
|56\18, 2167.742
|22\7, 2200
|54\17, 2234.483
|32\10, 2258.824
|42\13, 2090.909
|-
|Ub, Üe
|47\26, 2169.231
|55\16, 2129.032
|21\7, 2100
|50\17, 2068.966
|29\10, 2047.059
|37\13, 2018.182
|-
|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#
|50\15, 2307.692
| rowspan="2" |37\11, 2336.842
|61\18, 2361.290
| rowspan="2" |23\7, 2300
|59\17, 2441.379
|35\10, 2470.588
|46\13, 2509.091
|-
|Vb, Ve
|51\15, 2353.846
|60\18, 2322.581
|55\17, 2275.862
|32\10, 2258.824
|41\13, 2236.364
|-
|-
|Major
|V
|LLsL
|52\15, 2400
|<nowiki>2|1</nowiki>
|38\11, 2400
|P
|62\18, 2400
|M
|24\7, 2400
|P
|58\17, 2400
|34\10, 2400
|44\13, 2400
|-
|-
| Minor
|V#
|LLsL
|53\15, 2446.154
|<nowiki>1|2</nowiki>
|39\11, 2463.158
| P
|64\18, 2477,419
|m
| rowspan="2" |25\7, 2500
|P
|61\17, 2524.138
|36\10, 2541.176
|47\13, 2563.636
|-
|-
|Phrygian
|Wb, We
|sLLL
|55\15, 2538.462
|<nowiki>0|3</nowiki>
|40\11, 2526.316
|d
|65\18, 2516.129
|m
|60\17, 2482.759
| P
|35\10, 2470.588
|}
|45\13, 2454.545
==Temperaments==
The most basic rank-2 temperament interpretation of diatonic 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'''===
[[Subgroup]]: 3/2.6/5.8/5
[[Comma]] list: [[81/80]]
 
[[POL2]] generator: ~9/8 = 192.6406
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Vals]]: {{val list|~(7edf, 11edf, 18edf)}}
==='''Napoli-Superpyth'''===
[[Subgroup]]: 3/2.7/6.14/9
[[Comma]] list: [[64/63]]
 
[[POL2]] generator: ~8/7 = 218.6371
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Vals]]: {{val list|~(7edf, 10edf, 13edf, 16edf)}}
===Scale tree===
The spectrum looks like this:
{| class="wikitable"
! colspan="3" rowspan="2" |Generator
(bright)
! colspan="2" |Cents
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |L/s
! rowspan="2" | Comments
|-
|-
!<u>Normalised</u>
|'''Wb'''
!''ed7\12''
|'''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'''
|-
|-
| 1\4
|W#
|
|57\15, 2630.769
|
|42\11, 2652.632
|<u>171.428…</u>
|69\18, 2670.968
|''175''
| rowspan="2" |27\7, 2700
|1
|66\17, 2731.034
|1
|39\10, 2752.941
|1.000
|51\13, 2781.818
|Equalised
|-
|-
|6\23
|Xb, Xe
|
|59\15, 2723.077
|
|43\11, 2715.789
|<u>180</u>
|70\18, 2709.677
|''182.608…''
|65\17, 2689.552
|6
|38\10, 2682.353
|5
|49\13, 2672.273
|1.200
|-
|
!X
!60\15, 2769.231
!44\11, 2778.947
!72\18, 2787.097
!28\7, 2800
!68\17, 2813.793
!40\10, 2823.529
!52\13, 2836.364
|-
|X#
|61\15, 2815.385
| rowspan="2" |45\11, 2842.105
|74\18, 2864.516
|29\7, 2900
|71\17, 2937.069
|42\10, 2964.706
|55\13, 3000
|-
|-
|
|Ybb, Yee
| 11\42
|62\15, 2861.538
|
|73\18, 2825.806
|<u>180.821…</u>
|28\7, 2800
|''183.{{Overline|3}}''
|67\17, 2772.414
|11
|39\10, 2752.941
|9
|50\13, 2727.273
|1.222
|
|-
|-
|5\19
|Yb, Ye
|
|63\15, 2907.692
|
|46\11, 2905.263
|<u>181.{{Overline|81}}</u>
|75\18, 2903.226
|''184.210…''
|29\7, 2900
|5
|70\17, 2896.552
|4
|41\10, 2894.118
|1.250
|53\13, 2890.909
|
|-
|-
|
|'''Y'''
|14\53
|'''64\15, 2953.846'''
|
|'''47\11, 2968.421'''
|<u>182.608…</u>
|'''77\18, 2980.645'''
|''184.905…''
|'''30\7, 3000'''
|14
|'''73\17, 3020.690'''
|11
|'''43\10, 3035.294'''
|1.273
|'''56\13, 3054.545'''
|
|-
|-
|
|Y#
|9\34
|65\15, 3000
|
|48\11, 3031.579
|<u>183.050…</u>
|79\18, 3058.064
|''185.294…''
| rowspan="2" |31\7, 3100
| 9
|76\17, 3144.828
|7
|45\10, 3176.471
|1.286
|59\13, 3218.182
|
|-
|-
|4\15
|Zb. Ze
|
|67\15, 3092.308
|
|49\11, 3094.737
|<u>184.615…</u>
|80\18, 3096.774
|''186.{{Overline|6}}''
|75\17, 3103.448
|4
|44\10, 3105.882
|3
|57\13, 3109.091
|1.333
|
|-
|-
|
|Z
|11\41
|68\15, 3138.462
|
|50\11, 3157.895
|<u>185.915…</u>
|82\18, 3174.194
|''187.804…''
|32\7, 3200
|11
|78\17, 3227.586
| 8
|46\10, 3247.059
|1.375
|60\13, 3272.273
|
|-
|-
|
|Z#
|7\26
|69\15, 3184.615
|
| rowspan="2" |51\11, 3221.053
|<u>186.{{Overline|6}}</u>
|84\18, 3251.612
|''188.461…''
|33\7, 3300
|7
|81\17, 3351.725
|5
|48\10, 3388.235
|1.400
|63\13, 3436.364
|
|-
|Ab, Æ
|70\15, 3230.769
|83\18, 3212.903
|32\7, 3200
|77\17, 3186.207
|45\10, 3176.471
|58\13, 3163.636
|-
|-
|
|'''A'''
|10\37
|'''71\15,''' '''3276.923'''
|
|'''52\11,''' '''3284.211'''
|<u>187.5</u>
|'''85\18,''' '''3290.323'''
|''189.{{Overline|189}}''
|'''33\7, 3300'''
|10
|'''80\17,''' '''3310.345'''
| 7
|'''47\10,''' '''3317.647'''
| 1.429
|'''61\13,''' '''3327.{{Overline|27}}'''
|
|-
|-
|
|A#
|13\48
|72\15, 3323.077
|
|53\11, 3347.368
|<u>187.951…</u>
|87\18, 3367.742
|''189.58{{Overline|3}}''
|34\7, 3400
|13
|83\17, 3434.583
|9
|49\10, 3458.824
|1.444
|64\13, 3490.909
|
|-
|-
|
|Ax
|16\59
|73\15, 3369.231
|
| rowspan="2" |54\11, 3410.625
|<u>188.235…</u>
|89\18, 3445.162
|''189.830…''
|35\7, 3500
|86\17, 3558.621
|16
|51\10, 3600
|11
|67\13, 3654.545
|1.4545
|
|-
|-
| 3\11
|Bb, Be
|  
|74\15, 3415.385
|
|88\18, 3406.452
|<u>189.473…</u>
|34\7, 3400
|''190.{{Overline|90}}''
|82\17, 3393.103
| 3
|48\10, 3388.235
|2
|62\13, 3381.818
|1.500
|Napoli-Meantone starts here
|-
|-
|
!B
|14\51
!75\15, 3461.538
|
!55\11, 3473.684
|<u>190.{{Overline|90}}</u>
!90\18, 3483.871
|''192.156…''
!35\7, 3500
|14
!85\17, 3517.241
| 9
!50\10, 3529.412
| 1.556
!65\13, 3545.455
|
|-
|-
|
|B#
|11\40
|76\15, 3507.692
|
|56\11, 3536.842
|<u>191.304…</u>
|92\18, 3561.290
|''192.5''
| rowspan="2" |36\7, 3600
|11
|88\17, 3641.379
| 7
|52\10, 3670.588
| 1.571
|68\13, 3709.091
|
|-
|Cb, Ce
|78\15, 3600
|57\11, 3600
|93\18, 3600
|87\17, 3600
|51\10, 3600
|66\13, 3600
|-
|'''C'''
|'''79\15,''' '''3646.154'''
|'''58\11,''' '''3663.158'''
|'''95\18,''' '''3677.419'''
|'''37\7,''' '''3700'''
|'''90\17,''' '''3724.138'''
|'''53\10,''' '''3741.176'''
|'''69\13,''' '''3763.636'''
|-
|-
|
|C#
|8\29
|80\15, 3692.308
|
|59\11, 3726.316
|<u>192</u>
|97\18, 3755.838
|''193.103…''
| rowspan="2" |38\7, 3800
| 8
|93\17, 3848.275
| 5
|55\10, 3882.353
|1.600
|72\13, 3927.273
|
|-
|-
|
|Db, De
|5\18
|82\15, 3784.615
|  
|60\11, 3789.474
|<u>193.548…</u>
|98\18, 3793.548
|''194.{{Overline|4}}''
|92\17, 3806.897
|5
|54\10, 3811.765
|3
|70\13, 3818.182
|1.667
|
|-
|-
|
|D
|
|83\15, 3830.769
|12\43
|61\11, 3852.632
|<u>194.{{Overline|594}}</u>
|100\18, 3870.968
|''195.348…''
|39\7, 3900
| 12
|95\17, 3931.03$
| 7
|56\10, 3952.941
|1.714
|73\13, 3981.818
|
|-
|-
|
|D#
|7\25
|84\15, 3876.923
|
| rowspan="2" |62\11, 3915.789
|<u>195.348…</u>
|102\18, 3948.387
|''196''
|40\7, 4000
|7
|98\17, 4055.172
|4
|58\10, 4094.118
|1.750
|76\13, 4145.455
|  
|-
|-
|  
|Ebb, Ëe
|9\32
|85\15, 3923.077
|
|101\18, 3909.677
|<u>196.{{Overline|36}}</u>
|39\7, 3900
|''196.875''
|94\17, 3889.552
|9
|55\10, 3882.353
|5
|71\13, 3872.727
|1.800
|
|-
|-
|
|'''Eb, Ë'''
|11\39
|'''86\15,''' '''3969.231'''
|
|'''63\11,''' '''3978.947'''
|<u>197.014…</u>
|'''103\18,''' '''3987.097'''
|''197.435…''
|'''40\7, 4000'''
|11
|'''97\17,''' '''4013.793'''
| 6
|'''57\10,''' '''4023.529'''
|1.833
|'''74\13,''' '''4036.364'''
|
|-
|-
|  
|E
|13\46
|87\15, 4015.385
|
|64\11, 4042.105
|<u>197.468…</u>
|105\18, 4064.516
|''197.826…''
|41\7, 4100
| 13
|100\17, 4137.931
| 7
|59\10, 4164.706
| 1.857
|77\13, 4200
|
|-
|-
|
|E#
|15\53
|88\15, 4061.583
|
| rowspan="2" |65\11, 4105.263
|<u>197.802…</u>
|107\18, 4141.956
|''198.113…''
|42\7, 4200
|15
|103\17, 4262.069
|8
|61\10, 4305.882
|1.875
|80\13, 4363.636
|
|-
|-
|
|Fb, Fe
| 17\60
|89\15, 4107.692
|  
|106\18, 4103.226
|<u>198.058…</u>
|41\7, 4100
|''198.{{Overline|3}}''
|99\17, 4096.552
|17
|58\10, 4094.118
| 9
|75\13, 4090.909
| 1.889
|
|-
|-
|
!F
|19\67
!90\15, 4153.846
|
!66\11, 4168.421
|<u>198.260…</u>
!108\18, 4180.645
|''198.507…''
!42\7, 4200
|19
!102\17, 4220.690
| 10
!60\10, 4235.294
|1.900
!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):
|21\74
|
|<u>198.425…</u>
| ''198.{{Overline |''198.''{{Overline|648}}
|21
| 11
|1.909
|  
|-
|-
|
|0
|23\81
|Do, Fa, Sol
|
|perfect unison
|<u>198.561…</u>
|0
|''198.765…''
|Do, Fa, Sol
|23
|sesquitave (just fifth)
|12
| 1.917
|
|-
|-
|
|1
| 25\88
|Fa, Sib, Do
|  
|perfect fourth
|<u>198.675…</u>
| -1
|''198.8{{Overline|63}}''
|Re, Sol, La
|25
|perfect second
| 13
|1.923
|
|-
|-
|
|2
|27\95
|Mib, Lab, Sib
|  
|minor third
|<u>198.773…</u>
| -2
|''198.947…''
|Mi, La, Si
|27
|major third
|14
|1.929
|
|-
|-
|
|3
|29\102
|Reb, Solb, Lab
|
|diminished second
|<u>198.857…</u>
| -3
|''199.019…''
|Fa#, Si, Do#
|29
|augmented fourth
|15
|1.933
|
|-
|-
|  
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
| 31\109
|
|<u>198.930…</u>
|''199.082…''
|31
|16
|1.9375
|
|-
|-
|
|4
|33\116
|Dob, Fab, Solb
|
|diminished sesquitave
|<u>198.994…</u>
| -4
|''199.137…''
|Do#, Fa#, Sol#
|33
|augmented unison (chroma)
|17
|1.941
|
|-
|-
|
|5
|35\123
|Fab, Sibb, Dob
|
|diminished fourth
|<u>199.052…</u>
| -5
|''199.186…''
|Re#, Sol#, La#
|35
|augmented second
|18
|1.944
|
|-
|-
|2\7
|6
|
|Mibb, Labb, Sibb
|
|diminished third
|<u>200</u>
| -6
|''200''
|Mi#, La#, Si#
|2
|augmented third
|1
|}
|2.000
| Napoli-Meantone ends, Napoli-Pythagorean begins
==Genchain==
|-
|
The generator chain for this scale is as follows:
|17\59
{| class="wikitable"
|
|Mibb
|<u>201.980…</u>
Labb
|''201.694…''
|17
Sibb
|8
|Fab
|2.125
Sibb
|
|-
Dob
|
|Dob
| 15\52
Fab
|
|<u>202.247…</u>
Solb
|''201.923…''
|Reb
|15
Solb
|7
|2.143
Lab
|
|Mib
|-
Lab
|
|13\45
Sib
|
|Fa
|<u>202.597…</u>
Sib
|''202.{{Overline|2}}''
|13
Do
|6
|Do
|2.167
Fa
|
|-
Sol
|
|Re
|11\38
Sol
|
|<u>203.076…</u>
La
|''202.631…''
|Mi
|11
La
|5
|2.200
Si
|
|Fa#
|-
Si
|
|9\31
Do#
|
|Do#
|<u>203.773…</u>
Fa#
|''203.225…''
|9
Sol#
|4
|Re#
| 2.250
Sol#
|
La#
|Mi#
La#
Si#
|-
|-
|
|d3
|7\24
|d4
|
|d5
|<u>204.878…</u>
|d2
|''204.1{{Overline|6}}''
|m3
| 7
|P4
|3
|P1
|2.333
|P2
|
|M3
|A4
|A1
|A2
|A3
|}  
==Modes==
The mode names are based on the species of fifth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
|-
|-
|
!name
|
!pattern
|12\41
!notation
|<u>205.714…</u>
!2nd
|''204.878…''
!3rd
|12
!4th
|5
|2.400
|
|-
|-
|
|Lydian
|5\17
|LLLs
|
|<nowiki>3|0</nowiki>
|<u>206.896…</u>
|P
|''205.882…''
|M
|5
|A
|2
|2.500
|Napoli-Neogothic heartland is from here…
|-
|-
|
|Major
|
|LLsL
|18\61
|<nowiki>2|1</nowiki>
|<u>207.692…</u>
|P
|''206.557…''
|M
|18
|P
|7
| 2.571
|
|-
|-
|
|Minor
|
|LsLL
|13\44
|<nowiki>1|2</nowiki>
|<u>208</u>
|P
|''206.{{Overline|81}}''
|m
|13
|P
| 5
| 2.600
|
|-
|-
|
|Phrygian
|8\27
|sLLL
|
|<nowiki>0|3</nowiki>
|<u>208.695…</u>
|d
|''207.{{Overline|407}}''
|m
| 8
|P
|3
|}
|2.667
|…to 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.
|11\37
==='''Napoli-Meantone (Hex meantone)'''===
|
|<u>209.523…</u>
[[Subgroup]]: 3/2.6/5.8/5 (5.2.3)
|''208.{{Overline|108}}''
|11
[[Comma]] list: [[81/80]]
|4
 
| 2.750
[[POL2]] generator: ~9/8 = 192.6406¢
|
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Optimal ET sequence]]: *[[28ed5]], [[44ed5]], [[72ed5]] ≈ [[7edf]], [[11edf]], [[18edf]]
==='''Napoli-Archy (Hex Archytas)'''===
[[Subgroup]]: 3/2.7/6.14/9 (36/7.2.3)
[[Comma]] list: [[64/63]]
 
[[POL2]] generator: ~8/7 = 218.6371¢
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Optimal ET sequence]]: *[[28ed36/7]], [[40ed36/7]], [[52ed36/7]] ≈ [[7edf]], [[10edf]], [[13edf]]
===Scale tree===
The spectrum looks like this:
{| class="wikitable"
!Generator
(bright)
!Cents
!L
!s
!L/s
!Comments
|-
|-
|
|1\4
|14\47
|171.429
|
|1
|<u>210</u>
|1
|''208.510…''
|1.000
| 14
|Equalised
| 5
|-
|2.800
|6\23
|180.000
|6
|5
|1.200
|
|
|-
|-
|
|5\19
|17\57
|181.818
|5
|4
|1.250
|
|
|<u>210.309…</u>
|''208.771…''
|17
|6
|2.833
|
|-
|-
|14\53
|182.609
|14
|11
|1.273
|
|
| 20\67
|-
|
|9\34
|<u>210.526…</u>
|183.051
|''208.955…''
|9
| 20
|7
|7
|2.857
|1.286
|
|
|-
|-
|4\15
|184.615
|4
|3
|1.333
|
|
| 23\77
|-
|
|11\41
|<u>210.687…</u>
|185.915
|''209.{{Overline|09}}''
|11
|23
|8
|8
|2.875
|1.375
|
|
|-
|-
|3\10
|7\26
|
|186.667
|7
|5
|1.400
|
|
|<u>211.764…</u>
|''210''
|3
| 1
|3.000
|Napoli-Pythagorean ends, Napoli-Superpyth begins
|-
|-
|
|10\37
|22\73
|187.5
|
|10
|<u>212.903…</u>
|''210.958…''
|22
|7
|7
|3.143
|1.429
|  
|
|-
|-
|
|13\48
|19\63
|187.952
|
|13
|<u>213.084…</u>
|9
|''211.{{Overline|1}}''
|1.444
|19
|6
|3.167
|
|
|-
|-
|
|16\59
|16\53
|188.253
|
|<u>213.{{Overline|3}}</u>
|''211.320…''
|16
|16
|5
|11
|3.200
|1.455
|
|
|-
|-
|
|3\11
|13\43
|189.474
|3
|2
|1.500
|Napoli-Meantone starts here
|-
|14\51
|190.909
|14
|9
|1.556
|
|
|<u>213.698…</u>
|-
|''211.627…''
|11\40
|13
|191.304
|4
|11
|3.250
|7
|1.571
|
|
|-
|-
|8\29
|192.000
|8
|5
|1.600
|
|
| 10\33
|-
|
|5\18
|<u>214.285…</u>
|193.548
|''212.{{Overline|12}}''
|5
|10
|3
|3
|3.333
|1.667
|
|
|-
|-
|12\43
|194.595
|12
|7
|1.714
|
|
|7\23
|-
|
|7\25
|<u>215.384…</u>
|195.348
|''213.043…''
|7
|7
|2
|4
|3.500
|1.750
|
|
|-
|-
|9\32
|196.364
|9
|5
|1.800
|
|
|11\36
|
|<u>216.393…</u>
|''213.{{Overline|3}}''
| 11
|3
|3.667
|
|-
|-
|11\39
|197.015
|11
|6
|1.833
|
|-
|13\46
|197.468
|13
|7
|1.857
|
|
|15\49
|-
|
|15\53
|<u>216.867…</u>
|197.802
|''214.285…''
|15
|15
|4
|8
|3.750
|1.875
|
|
|-
|-
|4\13
|17\60
|
|198.058
|
|17
|<u>218.{{Overline|18}}</u>
|9
|''215.385…''
|1.889
|4
|1
|4.000
|
|
|-
|-
|19\67
|198.261
|19
|10
|1.900
|
|
|13\42
|-
|21\74
|198.425
|21
|11
|1.909
|
|
|<u>219.718…</u>
|-
|''216.{{Overline|6}}''
|23\81
|13
|198.561
|3
|23
|4.333
|12
|1.917
|
|
|-
|-
|25\88
|198.675
|25
|13
|1.923
|
|
|9\29
|
|<u>220.408…</u>
|''217.241…''
|9
|2
|4.500
|
|-
|-
|
|27\95
|14\45
|198.773
|
|27
|<u>221.052…</u>
|14
|''217.{{Overline|7}}''
|1.929
|14
| 3
| 4.667
|
|
|-
|-
|5\16
|29\102
|
|198.857
|29
|15
|1.933
|
|
|<u>222.{{Overline|2}}</u>
|''218.75''
|5
| 1
|5.000
|Napoli-Superpyth ends
|-
|-
|
|31\109
|16\51
|198.930
|
|31
|<u>223.255…</u>
|''219.607…''
|16
|16
|3
|1.9375
|5.333
|
|
|-
|-
|33\116
|198.995
|33
|17
|1.941
|
|
|11\35
|-
|35\123
|199.009
|35
|18
|1.944
|
|
|<u>223.728…</u>
|-
|''220''
|2\7
|11
|200
|2
|2
|5.500
|1
|2.000
|Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|17\59
|201.980
|17
|8
|2.125
|
|
|-
|-
|
|15\52
|17\54
|202.247
|
|15
|<u>224.175…</u>
|7
|''220.{{Overline|370}}''
|2.143
| 17
| 3
|5.667
|
|
|-
|-
|6\19
|13\45
|
|202.597
|  
|13
|<u>225</u>
|''221.052…''
|6
|6
|1
|2.167
|6.000
|
|
|-
|-
|1\3
|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
|
|
|<u>240</u>
|-
|''233.{{Overline|3}}''
|5\17
|1
|206.897
|0
|5
|→ inf
|2
|Paucitonic
|2.500
|Napoli-Neogothic heartland is from here…
|-
|18\61
|207.693
|18
|7
|2.571
|
|-
|13\44
|208.000
|13
|5
|2.600
|
|-
|8\27
|208.696
|8
|3
|2.667
|…to here
|-
|11\37
|209.524
|11
|4
|2.750
|
|-
|14\47
|210.000
|14
|5
|2.800
|
|-
|3\10
|211.765
|3
|1
|3.000
|Napoli-Pythagorean ends, Napoli-Archy begins
|-
|22\73
|212.903
|22
|7
|3.143
|
|-
|19\63
|213.084
|19
|6
|3.167
|
|-
|16\53
|213.333
|16
|5
|3.200
|
|-
|13\43
|213.699
|13
|4
|3.250
|
|-
|10\33
|214.286
|10
|3
|3.333
|
|-
|7\23
|215.385
|7
|2
|3.500
|
|-
|11\36
|216.393
|11
|3
|3.667
|
|-
|15\49
|216.867
|15
|4
|3.750
|
|-
|19\62
|217.143
|19
|5
|3.800
|
|-
|4\13
|218.182
|4
|1
|4.000
|
|-
|13\42
|219.718
|13
|3
|4.333
|
|-
|9\29
|220.408
|9
|2
|4.500
|
|-
|14\45
|221.053
|14
|3
|4.667
|
|-
|5\16
|222.222
|5
|1
|5.000
|Napoli-Archy ends
|-
|11\35
|223.728
|11
|2
|5.500
|
|-
|17\54
|224.176
|17
|3
|5.667
|
|-
|6\19
|225.000
|6
|1
|6.000
|
|-
|1\3
|240.000
|1
|0
|→ inf
|Paucitonic
|}
|}
==See also==
[[3L 1s (3/2-equivalent)]] - idealized tuning
[[6L 2s (20/9-equivalent)]] - Neapolitan 1/2-comma meantone
[[6L 2s (88/39-equivalent)]] - Neapolitan gentle temperament
[[6L 2s (16/7-equivalent)]] - Neapolitan 1/2-comma archy
[[9L 3s (10/3-equivalent)]] - Bijou 1/3-comma meantone
[[9L 3s (44/13-equivalent)]] - Bijou gentle temperament
[[9L 3s (24/7-equivalent)]] - Bijou 1/3-comma archy
[[12L 4s (5/1-equivalent)]] - Hex meantone
[[12L 4s (56/11-equivalent)]] - Hextone gentle temperament
[[12L 4s (36/7-equivalent)]] - Hextone 1/4-comma archy
[[15L 5s (15/2-equivalent)]] - Guidotonic major 1/5-comma meantone
[[15L 5s (84/11-equivalent)]] - Guidotonic major gentle temperament
[[15L 5s (54/7-equivalent)]] - Guidotonic major 1/5-comma archy
[[18L 6s (11/1-equivalent)]] - Subdozenal harmonic tuning
[[18L 6s (56/5-equivalent)]] - Subdozenal low septimal (meantone) tuning
[[18L 6s (512/45-equivalent)]] - Subdozenal 1/6-comma meantone
[[18L 6s (80/7-equivalent)]] - Subdozenal high septimal tuning
[[18L 6s (128/11-equivalent)]] - Subdozenal subharmonic tuning
[[18L 6s (11/1-equivalent)|18L 6s (12/1-equivalent)]] - Warped Pythagorean tuning
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/3L_1s_(perfect_fifth-equivalent)"