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Revision as of 00:01, 15 July 2022 (edit)
'''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.
Moremajorthanmajor (talk | contribs)
 
(Undo revision 93402 by Moremajorthanmajor ([[User talk:Moremajorthanmajor|talk])
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).
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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.  
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−
'''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]].
{{Infobox MOS
+
#REDIRECT [[Angel/Tuning specifications]]
−
| Name = Diatonic
−
| 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. P
−
−
[[Basic]] diatonic is in [[7edf]], which is a very good fifth-based equal tuning similar to [[12edo]].
−
==Notation==
==Notation==
   
   
−
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.
There are 3 main ways to notate the diatonic 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.
 
−
{| class="wikitable"
{| class="wikitable"
−
|+
|+
−
Cents
Cents
−
! Notation
! colspan="3" |Notation
−
!Supersoft
!Supersoft
−
!Soft
!Soft
−
!Semisoft
!Semisoft
−
!Basic
!Basic
−
!Semihard
!Semihard
−
!Hard
!Hard
−
!Superhard
!Superhard
−
|-
|-
−
!Diatonic
!Diatonic
!~15edf
−
!Napoli
−
!Bijou
−
!~15edf
−
!~11edf
!~11edf
−
!~18edf
!~18edf
−
!~7edf
!~7edf
−
!~17edf
!~17edf
−
!~10edf
!~10edf
−
!~13edf
!~13edf
|-
|Do#, Fa#, Sol#
|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
|-
|Reb, Solb, Lab
|3\15, 138.462
|2\11. 126.316
|3\18, 116.129
|2\17, 82.759
|1\10, 70.588
|1\13, 54.545
|-
|'''Re, Sol, La'''
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
   
   
−
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|-
|Re#, Sol#, La#
|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
|-
|Mib, Lab, Sib
|7\15, 323.077
|5\11, 315.789
|8\18, 309.677
|7\17, 289.655
|4\10, 282.353
|5\13, 272.727
|-
|Mi, La, Si
|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
|-
|Mi#, La#, Si#
|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
|-
|Fab, Sibb, Dob
|10\15, 461.538
|11\18, 425.806
|4\7, 400
|9\17, 372.414
|5\10, 352.941
|6\13, 327.273
|-
|'''Fa, Sib, Do'''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|Fa#, Si, Do#
|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
|-
|Fax, Si#, Dox
|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
|-
|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
|-
!Do, Fa, Sol
!'''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'''
|}
{| class="wikitable"
|+
Cents
!Notation
!Supersoft
! Soft
!Semisoft
!Basic
!Semihard
! Hard
! Superhard
|-
!Napoli
! ~15edf
! ~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
|-
| Gb, Ge
|3\15, 138.462
| 2\11. 126.316
|3\18, 116.129
|2\17, 82.759
|1\10, 70.588
|1\13, 54.545
|-
|'''G'''
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
   
   
−
|'''5\18,''' '''193.548'''
|Do#, Sol#
|'''2\7,''' '''200'''
−
|F#
|'''5\17,''' '''206.897'''
−
|'''3\10,''' '''211.765'''
|0#, D#
|'''4\13,''' '''218.182'''
−
|1\15
−
46.153…
−
|1\11
−
63.157…
−
|2\18
−
77.419…
−
| rowspan="2" |1\7
−
100
−
|3\17
−
124.137…
−
|2\10
−
141.176…
−
|3\13
−
163.{{Overline|63}}
−
|-
|-
−
|G#
|Reb, Lab
|5\15, 230.769
−
|4\11, 252.632
|Gb
|7\18, 270.968
−
|1b, 1c
| rowspan="2" |3\7, 300
−
| 8\17, 331.034
|3\15
|5\10, 352.941
−
138.461…
|7\13, 381.818
−
|-
|2\11
|Ab, Æ
−
|7\15, 323.077
126.315…
|5\11, 315.789
−
|3\18
|8\18, 309.677
−
|7\17, 289.655
116.129…
|4\10, 282.353
−
|2\17
|5\13, 272.727
−
|-
82.758…
|A
−
| 8\15, 369.231
|1\10
|6\11, 378.947
−
70.588…
|10\18, 387.097
−
| 4\7, 400
|1\13
|10\17, 413.793
−
54.{{Overline|54}}
|6\10, 423.529
−
|8\13, 436.364
|-
|A#
| 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
|-
|Bbb, Bee
|10\15, 461.538
|11\18, 425.806
|4\7, 400
|9\17, 372.414
| 5\10, 352.941
|6\13, 327.273
|-
|'''Bb, Be'''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|-
−
|B
|'''Re, La'''
|12\15, 553.846
−
|9\11, 568.421
|'''G'''
|15\18, 580.645
−
|'''1'''
|6\7, 600
−
| 15\17, 620.690
|'''4\15'''
|9\10, 635.294
−
'''184.615…'''
|12\13, 654.545
−
|-
|'''3\11'''
| B#
| 13\15, 600
−
'''189.473…'''
| rowspan="2" |10\11, 631.579
−
|17\18, 658.064
|'''5\18'''
|7\7, 700
−
'''193.548…'''
|18\17, 744.828
−
|11\10, 776.471
|'''2\7'''
|15\13, 818.182
−
'''200'''
|-
|Hb, He
−
|14\15, 646.154
|'''5\17'''
| 16\18, 619.355
|6\7, 600
−
|14\17, 579.310
'''206.896…'''
|8\10, 564.706
|10\13, 545.455
−
|'''3\10'''
|-
−
! H
'''211.764…'''
!'''15\15,''' '''692.308'''
−
!'''11\11,''' '''694.737'''
|'''4\13'''
!'''18\18,''' '''696.774'''
−
'''218.{{Overline|18}}'''
! 7\7, 700
−
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
|-
|Η#
|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
|-
|Cb, Ce
|18\15, 830.769
|13\11, 821.053
|21\18, 812.903
|19\17, 786.207
|11\10, 776.471
|14\13, 763.63
|-
|'''C'''
|'''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'''
|-
|-
−
|C#
|Re#, La#
|20\15, 923.077
−
|15\11, 947.368
|G#
|25\18, 967.742
−
|1#
| rowspan="2" |10\7, 1000
−
|25\17, 1034.483
|5\15
|15\10, 1058.824
−
230.769…
|20\13, 1090.909
−
|4\11
−
252.631…
−
|7\18
−
270.967…
−
| rowspan="2" |3\7
−
300
−
|8\17
−
331.034…
−
|5\10
−
352.941…
−
|7\13
−
381.{{Overline|81}}
−
|-
|-
−
| Db, De
|Mib, Sib
|22\15, 1015.385
−
|16\11, 1010.526
|Ab
|26\18, 1006.452
−
|2b, 2c
|24\17, 993.103
−
|14\10, 988.235
|7\15
|18\13, 981.818
−
323.076…
−
|5\11
−
315.789…
−
|8\18
−
309.677…
−
|7\17
−
289.655…
−
|4\10
−
282.352…
−
|5\13
−
272.{{Overline|72}}
−
|-
|-
−
|D
|Mi, Si
|23\15, 1061.538
−
|17\11, 1073.684
|A
|28\18, 1083.871
−
|2
|11\7, 1100
−
|27\17, 1117.241
|8\15
|16\10, 1129.412
−
369.230…
|21\9, 1145.455
−
|-
|6\11
|D#
−
|24\15, 1107.923
378.947…
| rowspan="2" |18\11, 1136.842
−
|10\18
|30\18, 1161.29
−
|12\7, 1200
387.096…
|30\17, 1241.379
−
|4\7
|18\10, 1270.588
−
|24\13, 1309.091
400
|-
−
|10\17
|Ebb, Ëe
|25\15, 1153.846
−
413.793…
|29\18, 1122.581
−
|11\7, 1100
|6\10
|26\17, 1075.862
−
423.529…
|15\10, 1058.824
−
| 19\13, 1036.364
|8\13
|-
−
436.{{Overline|36}}
|'''Eb, Ë'''
|'''26\15,''' '''1200'''
−
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|E
|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
|-
|-
−
|E#
|Mi#, Si#
|28\15, 1292.308
−
| rowspan="2" |21\11, 1326.318
|A#
|35\18, 1354.834
−
|2#
|14\7, 1400
−
|35\17, 1448.275
|9\15
| 21\10, 1482.353
−
415.384…
|28\13, 1527.273
−
|-
| rowspan="2" |7\11
| Fb, Fe
−
|29\15, 1338.462
442.105…
|34\18, 1316.129
−
|12\18
|13\7, 1300
−
|31\17, 1282.759
464.516…
|18\10, 1270.588
−
|5\7
|23\13, 1254.545
−
500
−
|13\17
−
537.931…
−
|8\10
−
564.705…
−
|11\13
−
600
−
|-
|-
−
!F
|Fab, Dob
!30\15, 1384.615
−
!22\11, 1389.473
|Bbb
!36\18, 1393.548
−
|3bb, 3cc
!14\7, 1400
−
!34\17, 1406.897
|10\15
!20\10, 1411.765
−
461.538…
!26\13, 1418.182
|}
−
 
|11\18
{| class="wikitable"
|+Cents
−
! Notation
425.806…
!Supersoft
!Soft
−
!Semisoft
|4\7
!Basic
!Semihard
−
!Hard
400
! Superhard
|-
−
!Bijou
|9\17
!~15edf
!~11edf
−
!~18edf
372.413…
!~7edf
!~17edf
−
!~10edf
|5\10
!~13edf
−
352.941…
−
|6\13
−
327.{{Overline|27}}
−
|-
|-
|0#, D#
−
|1\15, 46.154
|'''Fa, Do'''
|1\11, 63.158
|2\18, 77.419
−
| rowspan="2" |1\7, 100
|'''Bb'''
|3\17, 124.138
|2\10, 141.176
−
|3\13, 163.636
|'''3b, 3c'''
−
|'''11\15'''
−
'''507.692…'''
−
|'''8\11'''
−
'''505.263…'''
−
|'''13\18'''
−
'''503.225…'''
−
|'''5\7'''
−
'''500'''
−
|'''12\17'''
−
'''496.551…'''
−
|'''7\10'''
−
'''494.117…'''
−
|'''9\13'''
−
'''490.{{Overline|90}}'''
−
|-
|-
|1b, 1c
−
|3\15, 138.462
|Fa#, Do#
| 2\11. 126.316
|3\18, 116.129
−
|2\17, 82.759
|B
|1\10, 70.588
|1\13, 54.545
−
|-
|3
|'''1'''
|'''4\15,''' '''184.615'''
−
|'''3\11,''' '''189.474'''
|12\15
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
−
|'''5\17,''' '''206.897'''
553.846…
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
−
|-
|9\11
|1#
|5\15, 230.769
−
|4\11, 252.632
568.421…
|7\18, 270.968
| rowspan="2" |3\7, 300
−
|8\17, 331.034
|15\18
|5\10, 352.941
|7\13, 381.818
−
|-
580.645…
|2b, 2c
|7\15, 323.077
−
|5\11, 315.789
|6\7
| 8\18, 309.677
| 7\17, 289.655
−
|4\10, 282.353
600
|5\13, 272.727
|-
−
|2
|15\17
|8\15, 369.231
|6\11, 378.947
−
|10\18, 387.097
620.689…
|4\7, 400
|10\17, 413.793
−
|6\10, 423.529
|9\10
|8\13, 436.364
|-
−
|2#
635.294…
| 9\15, 415.385
| rowspan="2" |7\11, 442.105
−
|12\18, 464.516
|12\13
|5\7, 500
|13\17, 537.069
−
|8\10, 564.706
654.{{Overline|54}}
|11\13, 600
|-
−
|3b, 3c
| 10\15, 461.538
| 11\18, 425.806
|4\7, 400
|9\17, 372.414
|5\10, 352.941
|6\13, 327.273
|-
|'''3'''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|-
−
|Fax, Dox
−
|B#
−
|3#
|3#
|12\15, 553.846
−
|9\11, 568.421
|13\15
|15\18, 580.645
|6\7, 600
−
|15\17, 620.690
600
|9\10, 635.294
|12\13, 654.545
−
|-
| rowspan="2" |10\11
|3x
|13\15, 600
−
| rowspan="2" |10\11, 631.579
631.578…
|17\18, 658.064
|7\7, 700
−
|18\17, 744.828
|17\18
|11\10, 776.471
|15\13, 818.182
−
658.064…
−
|7\7
−
700
−
|18\17
−
744.827…
−
|11\10
−
776.470…
−
|15\13
−
818.{{Overline|18}}
−
|-
|-
−
|Dob, Solb
−
|Hb
−
|4b, 4c
|4b, 4c
|14\15, 646.154
−
|16\18, 619.355
|14\15
|6\7, 600
|14\17, 579.310
−
|8\10, 564.706
646.153…
|10\13, 545.455
−
|16\18
−
619.354…
−
|6\7
−
600
−
|14\17
−
579.310…
−
|8\10
−
564.705…
−
|10\13
−
545.{{Overline|45}}
−
|-
|-
−
!Do, Sol
−
!H
−
!4
!4
!'''15\15,''' '''692.308'''
−
!'''11\11,''' '''694.737'''
!'''15\15'''
!'''18\18,''' '''696.774'''
!7\7, 700
−
!'''17\17,''' '''703.448'''
'''692.307…'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
−
|-
!'''11\11'''
|4#
| 16\15, 738.462
−
|12\11, 757.895
'''694.736…'''
|20\18, 774.194
| rowspan="2" |8\8, 800
−
|20\17, 827.586
!'''18\18'''
|12\10, 847.059
| 16\13, 872.727
−
|-
'''696.774…'''
|5b, 5c
|18\15, 830.769
−
|13\11, 821.053
!'''7\7'''
|21\18, 812.903
|19\17, 786.207
−
|11\10, 776.471
'''700'''
|14\13, 763.63
|-
−
|'''5'''
!'''17\17'''
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
−
|'''23\18,''' '''890.323'''
'''703.448…'''
|'''9\5,''' '''900'''
|'''22\17,''' '''910.345'''
−
|'''13\10,''' '''917.647'''
!'''10\10'''
|'''17\13,''' '''927.273'''
|-
−
|5#
'''705.882…'''
|20\15, 923.077
|15\11, 947.368
−
|25\18, 967.742
!'''13\13'''
| rowspan="2" |10\7, 1000
|25\17, 1034.483
−
|15\10, 1058.824
'''709.'''{{Overline|09}}
|20\13, 1090.909
−
|-
|-
|6b, 6c
−
|22\15, 1015.385
|Do#, Sol#
|16\11, 1010.526
|26\18, 1006.452
−
|24\17, 993.103
|Η#
|14\10, 988.235
|18\13, 981.818
−
|4#
−
|16\15
−
738.461…
−
|12\11
−
757.894…
−
|20\18
−
774.193…
−
| rowspan="2" |8\8
−
800
−
|20\17
−
827.586…
−
|12\10
−
847.058…
−
|16\13
−
872.{{Overline|72}}
−
|-
|-
|6
−
|23\15, 1061.538
|Reb, Lab
|17\11, 1073.684
| 28\18, 1083.871
−
|11\7, 1100
|Cb
|27\17, 1117.241
|16\10, 1129.412
−
|21\9, 1145.455
|5b, 5c
|-
|6#
−
|24\15, 1107.923
|18\15
| rowspan="2" |18\11, 1136.842
|30\18, 1161.290
−
|12\7, 1200
830.769…
|30\17, 1241.379
|18\10, 1270.588
−
|24\13, 1309.091
|13\11
|-
| 7b, 7c
−
|25\15, 1153.846
821.052…
|29\18, 1122.581
|11\7, 1100
−
|26\17, 1075.862
|21\18
|15\10, 1058.824
|19\13, 1036.364
−
|-
812.903…
|'''7'''
|'''26\15,''' '''1200'''
−
|'''19\11,''' '''1200'''
|19\17
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
−
|'''29\17,''' '''1200'''
786.206…
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
−
|-
|11\10
|7#
|27\15, 1246.154
−
|20\11, 1263.158
776.470…
|33\18, 1277.419
|13\7, 1300
−
|32\17, 1324.138
|14\13
|19\10, 1341.176
|25\13, 1363.636
−
|-
763.{{Overline|63}}
|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
|'''Re, La'''
|34\18, 1316.129
|13\7, 1300
−
|31\17, 1282.759
|'''C'''
|18\10, 1270.588
|23\13, 1254.545
−
|-
|'''5'''
!8, F
!30\15, 1384.615
−
!22\11, 1389.473
|'''19\18'''
!36\18, 1393.548
!14\7, 1400
−
!34\17, 1406.897
'''876.923…'''
!20\10, 1411.765
!26\13, 1418.182
−
|-
|'''14\11'''
|8#, F#
|31\15, 1430.769
−
|23\11, 1452.632
'''884.210…'''
|38\18, 1470.968
| rowspan="2" |15\7, 1500
−
|37\17, 1531.034
|'''23\18'''
|22\10, 1552.941
|29\13, 1581.818
−
|-
'''890.322…'''
|9b, Gc
|33\15, 1523.077
−
|24\11, 1515.789
|'''9\5'''
|39\18, 1509.677
|36\17, 1489.655
−
|21\10, 1482.759
'''900'''
|27\13, 1472.273
|-
−
|'''9, G'''
|'''22\17'''
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
−
|'''41\18,''' '''1587.097'''
'''910.344…'''
|'''16\7,''' '''1600'''
|'''39\17,''' '''1613.793'''
−
|'''23\10,''' '''1623.529'''
|'''13\10'''
|'''30\13,''' '''1636.364'''
−
'''917.647…'''
−
|'''17\13'''
−
'''927.{{Overline|27}}'''
−
|-
|-
|9#, G#
−
|35\15, 1615.385
|Re#, La#
|26\11, 1642.105
|43\18, 1664.516
−
| rowspan="2" |17\7, 1700
|C#
|42\17, 1737.069
|25\10, 1764.706
−
|33\13, 1800
|5#
−
|20\15
−
923.076…
−
|15\11
−
947.368…
−
|25\18
−
967.741…
−
| rowspan="2" |10\7
−
1000
−
|25\17
−
1034.482…
−
|15\10
−
1058.823…
−
|20\13
−
1090.{{Overline|90}}
−
|-
|-
|Xb, Ac
−
|37\15, 1707.692
|Mib, Sib
|27\11, 1705.263
|44\18, 1703.226
−
|41\17, 1696.552
|Db
|24\10, 1694.118
|31\13, 1690.909
−
|6b, 6c
−
|22\15
−
1015.384…
−
|16\11
−
1010.526…
−
|26\18
−
1006.451…
−
|24\17
−
993.103…
−
|14\10
−
988.235…
−
|18\13
−
981.{{Overline|81}}
−
|-
|-
|X, A
−
|38\15, 1753.846
|Mi, Si
|28\11, 1768.421
|46\18, 1780.645
−
|18\7, 1800
|D
|44\17, 1820.690
|26\10, 1835.294
−
|34\13, 1854.545
|6
|-
|X#, A#
−
|39\15, 1800
|23\15
| rowspan="2" |29\11, 1831.579
|48\18, 1858.064
−
|19\7, 1900
1061.538…
|47\17, 1944.828
|28\10, 1976.471
−
|37\13, 2018.182
|17\11
|-
|Ebb, Ccc
−
|40\15, 1846.154
1073.684…
|47\18, 1819.355
|18\7, 1800
−
|43\17, 1779.310
|28\18
|25\10, 1764.706
|32\13, 1745.545
−
|-
1083.870…
|'''Eb, Cc'''
|'''41\15,''' '''1892.308'''
−
|'''30\11,''' '''1894.737'''
|11\7
|'''49\18,''' '''1896.774'''
|'''19\7, 1900'''
−
|'''46\17,''' '''1903.448'''
1100
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
−
|27\17
−
1117.241…
−
|16\10
−
1129.411…
−
|21\9
−
1145.{{Overline|45}}
−
|-
|-
|E, C
−
|42\15, 1938.462
|Mi#, Si#
|31\11, 1957.895
|51\18, 1974.194
−
|20\7, 2000
|D#
|49\17, 2027.586
|29\10, 2047.059
−
|38\13, 2072.727
|6#
|-
|Ex, Cx
−
|43\15, 1984.615
|24\15
| rowspan="2" |32\11, 2021.053
|53\18, 2051.612
−
|21\7, 2100
1107.692…
|52\17, 2151.725
|31\10, 2188.235
−
|41\13, 2236.364
| rowspan="2" |18\11
|-
|0b, Dc
−
|44\15, 2030.769
1136.842…
|52\18, 2012.903
|20\7, 2000
−
|48\17, 1986.207
|30\18
|28\10, 1976.471
|36\13, 1963.636
−
1161.290…
−
|12\7
−
1200
−
|30\17
−
1241.379…
−
|18\10
−
1270.588…
−
|24\13
−
1309.{{Overline|09}}
−
|-
|-
! 0, D
−
!45\15, 2076.923
|Fab, Dob
!33\11, 2084.211
!54\18, 2090.323
−
!21\7, 2100
|Ebb
!51\17, 2110.345
!30\10, 2117.647
−
!39\13, 2127.273
|7bb, 7cc
|}
 
−
{| class="wikitable"
|25\15
|+Cents
!Notation
−
!Supersoft
1153.846…
!Soft
!Semisoft
−
! Basic
|29\18
!Semihard
!Hard
−
!Superhard
1122.580…
|-
!Hextone
−
!~15edf
|11\7
!~11edf
!~18edf
−
!~7edf
1100
!~17edf
!~10edf
−
!~13edf
|26\17
|-
|0#, G#
−
|1\15, 46.154
1075.862…
|1\11, 63.158
|2\18, 77.419
−
| rowspan="2" |1\7, 100
|15\10
|3\17, 124.138
|2\10, 141.176
−
|3\13, 163.636
1058.823…
−
|19\13
−
1036.{{Overline|36}}
−
|-
|-
| 1f
−
|3\15, 138.462
|'''Fa, Do'''
|2\11. 126.316
|3\18, 116.129
−
|2\17, 82.759
|'''Eb'''
|1\10, 70.588
|1\13, 54.545
−
|'''7b, 7c'''
−
|'''26\15'''
−
'''1200'''
−
|'''19\11'''
−
'''1200'''
−
|'''31\18'''
−
'''1200'''
−
|'''12\7'''
−
'''1200'''
−
|'''29\17'''
−
'''1200'''
−
|'''17\10'''
−
'''1200'''
−
|'''22\13'''
−
'''1200'''
−
|-
|-
|'''1'''
−
|'''4\15,''' '''184.615'''
|Fa#, Do#
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
−
|'''2\7,''' '''200'''
|E
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
−
|'''4\13,''' '''218.182'''
|7
−
|27\15
−
1246.153…
−
|20\11
−
1263.157…
−
|33\18
−
1277.419…
−
|13\7
−
1300
−
|32\17
−
1324.137…
−
|19\10
−
1341.176…
−
|25\13
−
1363.{{Overline|63}}
−
|-
|-
|1#
−
|5\15, 230.769
|Fax, Dox
|4\11, 252.632
|7\18, 270.968
−
| rowspan="2" |3\7, 300
|E#
|8\17, 331.034
|5\10, 352.941
−
|7\13, 381.818
|7#
|-
|2f
−
|7\15, 323.077
|28\15
|5\11, 315.789
|8\18, 309.677
−
|7\17, 289.655
1292.307…
|4\10, 282.353
|5\13, 272.727
−
|-
| rowspan="2" |21\11
|2
|8\15, 369.231
−
|6\11, 378.947
1326.315…
|10\18, 387.097
| 4\7, 400
−
|10\17, 413.793
|35\18
|6\10, 423.529
|8\13, 436.364
−
|-
1354.838…
|2#
|9\15, 415.385
−
| rowspan="2" |7\11, 442.105
|14\7
|12\18, 464.516
|5\7, 500
−
|13\17, 537.069
1400
|8\10, 564.706
|11\13, 600
−
|-
|35\17
|3f
| 10\15, 461.538
−
|11\18, 425.806
1448.275…
|4\7, 400
|9\17, 372.414
−
|5\10, 352.941
|21\10
|6\13, 327.273
−
1482.352…
−
|28\13
−
1527.{{Overline|27}}
−
|-
|-
|'''3'''
−
|'''11\15,''' '''507.692'''
|Dob, Solb
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
−
|'''5\7, 500'''
|Fb
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
−
|'''9\13,''' '''490.909'''
|8b, Fc
|-
|3#
−
|12\15, 553.846
|29\15
|9\11, 568.421
|15\18, 580.645
−
|6\7, 600
1338.461…
|15\17, 620.690
|9\10, 635.294
−
|12\13, 654.545
|34\18
|-
| 3x
−
|13\15, 600
1316.129…
| rowspan="2" | 10\11, 631.579
|17\18, 658.064
−
|7\7, 700
|13\7
|18\17, 744.828
|11\10, 776.471
−
|15\13, 818.182
1300
|-
|4f
−
| 14\15, 646.154
|31\17
|16\18, 619.355
|6\7, 600
−
|14\17, 579.310
1282.758…
|8\10, 564.706
|10\13, 545.455
−
|-
|18\10
!4
!'''15\15,''' '''692.308'''
−
!'''11\11,''' '''694.737'''
1270.588…
!'''18\18,''' '''696.774'''
!7\7, 700
−
!'''17\17,''' '''703.448'''
|23\18
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
−
|-
1254.{{Overline|54}}
| 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
|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'''
−
|'''19\15,''' '''876.923'''
!Do, Sol
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
−
|'''9\5,''' '''900'''
!F
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
−
|'''17\13,''' '''927.273'''
!8, F
|-
|5#
−
|20\15, 923.077
!30\15
|15\11, 947.368
| 25\18, 967.742
−
| rowspan="2" |10\7, 1000
1384.615…
|25\17, 1034.483
|15\10, 1058.824
−
|20\13, 1090.909
!22\11
|-
|6f
−
|22\15, 1015.385
1389.473…
|16\11, 1010.526
|26\18, 1006.452
−
|24\17, 993.103
!36\18
|14\10, 988.235
|18\13, 981.818
−
|-
1393.548…
|6
|23\15, 1061.538
−
|17\11, 1073.684
!14\7
|28\18, 1083.871
|11\7, 1100
−
|27\17, 1117.241
1400
|16\10, 1129.412
|21\9, 1145.455
−
|-
!34\17
|6#
|24\15, 1107.923
−
| rowspan="2" |18\11, 1136.842
1406.896…
|30\18, 1161.290
|12\7, 1200
−
|30\17, 1241.379
!20\10
|18\10, 1270.588
|24\13, 1309.091
−
|-
1411.764…
| 7f
|25\15, 1153.846
−
|29\18, 1122.581
!26\9
|11\7, 1100
|26\17, 1075.862
−
|15\10, 1058.824
1418.{{Overline|18}}
|19\13, 1036.364
|-
−
|'''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
|Do#, Sol#
|20\11, 1263.158
|33\18, 1277.419
−
|13\7, 1300
|F#
|32\17, 1324.138
|19\10, 1341.176
−
|25\13, 1363.636
|8#, F#
|-
|7x
−
|28\15, 1292.308
|31\15
| rowspan="2" |21\11, 1326.318
|35\18, 1354.834
−
|14\7, 1400
1430.769…
|35\17, 1448.275
|21\10, 1482.353
−
|28\13, 1527.273
|23\11
|-
|8f
−
|29\15, 1338.462
1452.631…
| 34\18, 1316.129
|13\7, 1300
−
|31\17, 1282.759
|38\18
|18\10, 1270.588
|23\13, 1254.545
−
1470.967…
−
| rowspan="2" |15\7
−
1500
−
|37\17
−
1531.034…
−
|22\10
−
1552.941…
−
|29\13
−
1581.{{Overline|81}}
−
|-
|-
! 8
−
!30\15, 1384.615
|Reb, Lab
!22\11, 1389.473
!36\18, 1393.548
−
!14\7, 1400
|Gb
!34\17, 1406.897
!20\10, 1411.765
−
!26\13, 1418.182
|9b, Gc
−
|33\15
−
1523.076…
−
|24\11
−
1515.789…
−
|39\18
−
1509.677…
−
|36\17
−
1489.655…
−
|21\10
−
1482.352…
−
|27\13
−
1472.{{Overline|72}}
−
|-
|-
|8#
−
|31\15, 1430.769
|'''Re, La'''
|23\11, 1452.632
| 38\18, 1470.968
−
| rowspan="2" |15\7, 1500
|'''G'''
|37\17, 1531.034
|22\10, 1552.941
−
|29\13, 1581.818
|'''9, G'''
|-
|9f
−
|33\15, 1523.077
|'''34\15'''
|24\11, 1515.789
|39\18, 1509.677
−
| 36\17, 1489.655
'''1569.230…'''
|21\10, 1482.759
|27\13, 1472.273
−
|-
|'''25\11'''
|9
|'''34\15,''' '''1569.231'''
−
|'''25\11,''' '''1578.947'''
'''1578.947…'''
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
−
|'''39\17,''' '''1613.793'''
|'''41\18'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.364'''
−
|-
'''1587.096…'''
|9#
|35\15, 1615.385
−
|26\11, 1642.105
|'''16\7'''
|43\18, 1664.516
| rowspan="2" |17\7, 1700
−
|42\17, 1737.069
'''1600'''
|25\10, 1764.706
|33\13, 1800
−
|-
|'''39\17'''
|Af
| 37\15, 1707.692
−
| 27\11, 1705.263
'''1613.793…'''
|44\18, 1703.226
|41\17, 1696.552
−
|24\10, 1694.118
|'''23\10'''
|31\13, 1690.909
|-
−
|A
'''1623.529…'''
| 38\15, 1753.846
|28\11, 1768.421
−
|46\18, 1780.645
|'''30\13'''
|18\7, 1800
|44\17, 1820.690
−
|26\10, 1835.294
'''1636.{{Overline|36}}'''
|34\13, 1854.545
−
|-
|-
|A#
−
| 39\15, 1800
|Re#, La#
| rowspan="2" |29\11, 1831.579
| 48\18, 1858.064
−
|19\7, 1900
|G#
|47\17, 1944.828
|28\10, 1976.471
−
|37\13, 2018.182
|9#, G#
|-
|Ax
−
|40\15, 1846.154
|35\15
|47\18, 1819.355
|18\7, 1800
−
|43\17, 1779.310
1615.384…
|25\10, 1764.706
|32\13, 1745.545
−
|-
|26\11
|'''Bf'''
|'''41\15,''' '''1892.308'''
−
|'''30\11,''' '''1894.737'''
1642.105…
|'''49\18,''' '''1896.774'''
|'''19\7, 1900'''
−
|'''46\17,''' '''1903.448'''
|43\18
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
−
|-
1664.516…
|B
|42\15, 1938.462
−
|31\11, 1957.895
| rowspan="2" |17\7
|51\18, 1974.194
|20\7, 2000
−
|49\17, 2027.586
1700
| 29\10, 2047.059
|38\13, 2072.727
−
|-
|42\17
|B#
|43\15, 1984.615
−
| rowspan="2" |32\11, 2021.053
1737.931…
|53\18, 2051.612
|21\7, 2100
−
|52\17, 2151.725
|25\10
|31\10, 2188.235
|41\13, 2236.364
−
|-
1764.705…
|Cf
|44\15, 2030.769
−
|52\18, 2012.903
|33\13
|20\7, 2000
|48\17, 1986.207
−
|28\10, 1976.471
1800
|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#
−
|46\15, 2123.077
|Mib, Sib
|34\11, 2147.368
|56\15, 2167.742
−
| rowspan="2" |22\7, 2200
|Ab
|54\17, 2234.483
|32\10, 2258.824
−
|42\13, 2090.909
|Xb, Ac
|-
|Df
−
|48\15, 2215.385
|37\15
|35\11, 2210.526
|57\15, 2206.452
−
|53\17, 2193.103
1707.692…
|31\10, 2188.235
|40\13, 2181.818
−
|27\11
−
1705.263…
−
|44\18
−
1703.225…
−
|41\17
−
1696.551…
−
|24\10
−
1694.117…
−
|31\13
−
1690.{{Overline|90}}
−
|-
|-
|'''D'''
−
|'''49\15, 2261.538'''
|Mi, Si
|'''36\11, 1073.684'''
|'''59\18, 2283.871'''
−
|'''23\7, 2300'''
|A
|'''56\17, 2317.241'''
|'''33\10, 2329.412'''
−
|'''43\13,''' '''2345.455'''
|X, A
−
|38\15
−
1753.846…
−
|28\11
−
1768.421…
−
|46\18
−
1780.645…
−
|18\7
−
1800
−
|44\17
−
1820.689…
−
|26\10
−
1835.294…
−
|34\13
−
1854.{{Overline|54}}
−
|-
|-
|D#
−
|50\15, 2307.692
|Mi#, Si#
|37\11, 2336.842
|61\18, 2361.290
−
| rowspan="2" |24\7, 2400
|A#
|59\17, 2441.379
|35\10, 2470.588
−
|46\13, 2509.091
|X#, A#
|-
|Ef
−
|52\15, 2400
|39\15
|38\11, 2400
|62\18, 2400
−
|58\17, 2400
1800
|34\10, 2400
| 44\13, 2400
−
|-
| rowspan="2" |29\11
|E
|53\15, 2446.154
−
| 39\11, 2463.158
1831.578…
|64\18, 2477,419
|25\7, 2500
−
|61\17, 2524.138
|48\18
|36\10, 2541.176
|47\13, 2563.636
−
|-
1858.064…
|E#
|54\15, 2492.308
−
| rowspan="2" |40\11, 2526.316
|19\7
|66\18, 2554.838
|26\7, 2600
−
|64\17, 2648.275
1900
|38\10, 2682.353
|50\13, 2727.273
−
|47\17
−
1944.827…
−
|28\10
−
1976.470…
−
|37\13
−
2018.{{Overline|18}}
−
|-
|-
|Fff
−
| 55\15, 2538.462
|Fab, Dob
| 65\18, 2516.129
|25\7, 2500
−
|60\17, 2482.759
|Bbb
|35\10, 2470.588
|45\13, 2454.545
−
|-
|Ebb, Ccc
|'''Ff'''
|'''56\15, 2584.615'''
−
|'''41\11, 2589.474'''
|40\15
|'''67\18, 2593.548'''
|'''26\7, 2600'''
−
|'''63\17, 2606.897'''
1846.153…
|'''37\10, 2611.765'''
|'''48\13,''' '''2618.182'''
−
|47\18
−
1819.354…
−
|18\7
−
1800
−
|43\17
−
1779.310…
−
|25\10
−
1764.705…
−
|32\13
−
1745.{{Overline|45}}
−
|-
|-
|F
−
|57\15, 2630.769
|'''Fa, Do'''
|42\11, 2652.632
|69\18, 2670.968
−
|27\7, 2700
|'''Bb'''
|66\17, 2731.034
|39\10, 2752.941
−
|51\13, 2781.818
|Eb, Cc
−
|'''41\15'''
−
'''1892.307…'''
−
|'''30\11'''
−
'''1894.736…'''
−
|'''49\18'''
−
'''1896.774…'''
−
|'''19\7'''
−
'''1900'''
−
|'''46\17'''
−
'''1903.448…'''
−
|'''27\10'''
−
'''1905.882…'''
−
|'''35\13'''
−
'''1909.{{Overline|09}}'''
−
|-
|-
| F#
−
| rowspan="2" |58\15, 2676.923
|Fa#, Do#
|43\11, 2715.789
|71\18, 2748.387
−
| 28\7, 2800
|B
|69\17, 2855.172
|41\10, 2894.118
−
|54\13, 2945.455
|E, C
|-
|0ff, Gff
−
|42\11, 2652.632
|42\15
|68\18, 2632.258
|26\7, 2600
−
|62\17, 2565.517
1938.461…
|36\10, 2541.176
|46\13, 2509.091
−
|-
|31\11
|0f, Gf
|59\15, 2723.077
−
|43\11, 2715.789
1957.894…
|70\18, 2709.677
|27\7, 2700
−
|65\17, 2689.552
|51\18
|38\10, 2682.353
|49\13, 2672.273
−
1974.193…
−
|20\7
−
2000
−
|49\17
−
2027.586…
−
|29\10
−
1976.470…
−
|38\13
−
2072.{{Overline|72}}
−
|-
|-
!0, G
−
!60\15, 2769.231
|Fax, Dox
!44\11, 2778.947
!72\18, 2787.097
−
!28\7, 2800
|B#
!68\17, 2813.793
!40\10, 2823.529
−
!52\13, 2836.364
|Ex, Cx
|}
 
−
{| class="wikitable"
|43\15
|+Cents
!Notation
−
!Supersoft
1984.615…
!Soft
! Semisoft
−
! Basic
| rowspan="2" |32\11
!Semihard
!Hard
−
!Superhard
2021.052…
−
|53\18
−
2051.612…
−
|21\7
−
2100
−
|52\17
−
2151.724…
−
|31\10
−
2188.235…
−
|41\13
−
2236.{{Overline|36}}
−
|-
|-
!Guidotonic
−
!~15edf
|Dob, Solb
!~11edf
!~18edf
−
!~7edf
|Hb
!~17edf
!~10edf
−
!~13edf
|0b, Dc
|-
|F ut#
−
|1\15, 46.154
|44\15
|1\11, 63.158
|2\18, 77.419
−
| rowspan="2" |1\7, 100
2030.769…
|3\17, 124.138
|2\10, 141.176
−
|3\13, 163.636
|52\18
|-
|G reb
−
|3\15, 138.462
2012.903…
|2\11. 126.316
|3\18, 116.129
−
|2\17, 82.759
|20\7
|1\10, 70.588
|1\13, 54.545
−
|-
2000
|'''G re'''
|'''4\15,''' '''184.615'''
−
|'''3\11,''' '''189.474'''
|48\17
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
−
|'''5\17,''' '''206.897'''
1986.206…
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
−
|-
|28\10
|G re#
|5\15, 230.769
−
|4\11, 252.632
1967.470…
|7\18, 270.968
| rowspan="2" |3\7, 300
−
|8\17, 331.034
|36\13
|5\10, 352.941
|7\13, 381.818
−
|-
1963.{{Overline|63}}
|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
|-
|B fa utb
|10\15, 461.538
|11\18, 425.806
|4\7, 400
|9\17, 372.414
|5\10, 352.941
|6\13, 327.273
|-
|'''B fa ut'''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|B fa ut#
|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
|-
|-
|B fa utx
−
| 13\15, 600
!Do, Sol
| rowspan="2" |10\11, 631.579
|17\18, 658.064
−
|7\7, 700
!H
|18\17, 744.828
|11\10, 776.471
−
|15\13, 818.182
!0, D
|-
|C sol re utb
−
| 14\15, 646.154
!45\15
|16\18, 619.355
|6\7, 600
−
|14\17, 579.310
2076.923…
|8\10, 564.706
|10\13, 545.455
−
|-
!33\11
!C sol re ut
!'''15\15,''' '''692.308'''
−
!'''11\11,''' '''694.737'''
2084.210…
!'''18\18,''' '''696.774'''
!7\7, 700
−
!'''17\17,''' '''703.448'''
!54\18
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
−
2090.322…
−
!21\7
−
2100
−
!51\17
−
2110.344…
−
!30\10
−
2117.647…
−
!39\13
−
2127.{{Overline|27}}
−
|}
−
{| class="wikitable"
−
|+Relative cents
−
! colspan="3" |Notation
−
!Supersoft
−
!Soft
−
!Semisoft
−
!Basic
−
!Semihard
−
!Hard
−
!Superhard
−
|-
|-
|C sol re ut#
−
|16\15, 738.462
!Diatonic
|12\11, 757.895
|20\18, 774.194
−
| rowspan="2" |8\8, 800
!Napoli
|20\17, 827.586
|12\10, 847.059
−
|16\13, 872.727
!Bijou
|-
|D la mi reb
−
|18\15, 830.769
!~15edf
|13\11, 821.053
|21\18, 812.903
−
|19\17, 786.207
!~11edf
|11\10, 776.471
|14\13, 763.63
−
|-
!~18edf
|'''D la mi re'''
|'''19\15,''' '''876.923'''
−
|'''14\11,''' '''884.211'''
!~7edf
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
−
|'''22\17,''' '''910.345'''
!~17edf
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
−
|-
!~10edf
|D la mi re#
|20\15, 923.077
−
| rowspan="2" |15\11, 947.368
!~13edf
|25\18, 967.742
|10\7, 1000
−
|25\17, 1034.483
|15\10, 1058.824
|20\13, 1090.909
|-
|E fa utb
|21\15, 969.231
|24\18, 929.032
| 9\5, 900
|21\17, 868.966
|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
|-
|E si mi re
|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
|-
|-
| E si mi re#
−
|24\15, 1107.923
|Do#, Sol#
| rowspan="2" |18\11, 1136.842
|30\18, 1161.29
−
|12\7, 1200
|F#
|30\17, 1241.379
| 18\10, 1270.588
−
|24\13, 1309.091
|0#, D#
|-
|F sol fa ut reb
−
|25\15, 1153.846
|1\15
|29\18, 1122.581
|11\7, 1100
−
|26\17, 1075.862
''46.{{Overline|6}}''
|15\10, 1058.824
|19\13, 1036.364
−
|-
|1\11
|'''F sol fa ut re'''
|'''26\15,''' '''1200'''
−
|'''19\11,''' '''1200'''
''63.{{Overline|63}}''
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
−
|'''29\17,''' '''1200'''
|2\18
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
−
|-
''77.7̄''
|F sol fa ut re#
|27\15, 1246.154
−
|20\11, 1263.158
| rowspan="2" |1\7
|33\18, 1277.419
|13\7, 1300
−
|32\17, 1324.138
''100''
| 19\10, 1341.176
| 25\13, 1363.636
−
|-
|3\17
|F sol fa ut rex
|28\15, 1292.308
−
| rowspan="2" |21\11, 1326.318
''123.529…''
|35\18, 1354.834
| 14\7, 1400
−
|35\17, 1448.275
|2\10
|21\10, 1482.353
|28\13, 1527.273
−
|-
''140''
|G la sol re mib
| 29\15, 1338.462
−
|34\18, 1316.129
|3\13
| 13\7, 1300
|31\17, 1282.759
−
|18\10, 1270.588
''161.538…''
|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
|-
|A si la mi fab
|33\15, 1523.077
| 24\11, 1515.789
|39\18, 1509.677
|36\17, 1489.655
|21\10, 1482.759
| 27\13, 1472.273
|-
|-
|'''A si la mi fa'''
−
|'''34\15,''' '''1569.231'''
|Reb, Lab
|'''25\11,''' '''1578.947'''
|'''41\18,''' '''1587.097'''
−
|'''16\7,''' '''1600'''
|Gb
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
−
|'''30\13,''' '''1636.364'''
|1b, 1c
|-
|A si la mi fa#
−
| 35\15, 1615.385
|3\15
| rowspan="2" |26\11, 1642.105
|43\18, 1664.516
−
|17\7, 1700
''140''
|42\17, 1737.069
| 25\10, 1764.706
−
|33\13, 1800
|2\11
−
''127.{{Overline|27}}''
−
|3\18
−
''116.{{Overline|6}}''
−
|2\17
−
''82.352…''
−
|1\10
−
''70''
−
|1\13
−
''53.846…''
−
|-
|-
|B sol fa utb
−
|36\61, 1661.538
|'''Re, La'''
|42\18, 1625.806
|16\7, 1600
−
|38\29, 1572.414
|'''G'''
|22\10, 1552.941
|28\13, 1527.273
−
|'''1'''
−
|'''4\15'''
−
'''''186.{{Overline|6}}'''''
−
|'''3\11'''
−
'''''190.{{Overline|90}}'''''
−
|'''5\18'''
−
'''''194.{{Overline|4}}'''''
−
|'''2\7'''
−
'''''200'''''
−
|'''5\17'''
−
'''''205.882…'''''
−
|'''3\10'''
−
'''''210'''''
−
|'''4\13'''
−
'''''215.384…'''''
−
|-
|-
|B sol fa ut
−
|37\15, 1707.692
|Re#, La#
|27\11, 1705.263
| 44\18, 1703.226
−
| 17\7, 1700
|G#
|41\17, 1696.552
|24\10, 1694.118
−
|31\13, 1690.909
|1#
|-
|B si
−
|38\15, 1753.846
|5\15
| 28\11, 1768.421
|46\18, 1780.645
−
|18\7, 1800
''233.{{Overline|3}}''
|44\17, 1820.690
|26\10, 1835.294
−
|34\13, 1854.545
|4\11
|-
|B si
−
|39\15, 1800
''254.{{Overline|54}}''
| rowspan="2" |29\11, 1831.579
|48\18, 1858.064
−
|19\7, 1900
|7\18
|47\17, 1944.828
|28\10, 1976.471
−
|37\13, 2018.182
''272.2̄''
|-
|C la sol re utb
−
|40\15, 1846.154
| rowspan="2" |3\7
|47\18, 1819.355
| 18\7, 1800
−
| 43\17, 1779.310
''300''
|25\10, 1764.706
|32\13, 1745.545
−
|-
|8\17
|'''C la sol re ut'''
|'''41\15,''' '''1892.308'''
−
|'''30\11,''' '''1894.737'''
''329.411…''
|'''49\18,''' '''1896.774'''
|'''19\7, 1900'''
−
|'''46\17,''' '''1903.448'''
|5\10
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
−
|-
''350''
|C la sol re ut#
|42\15, 1938.462
−
|31\11, 1957.895
|7\13
|51\18, 1974.194
|20\7, 2000
−
|49\17, 2027.586
''376.923…''
| 29\10, 2047.059
|38\13, 2072.727
−
|-
|C la sol re utx
| rowspan="2" |43\15, 1984.615
|32\11, 2021.053
|53\18, 2051.612
|21\7, 2100
|52\17, 2151.725
|31\10, 2188.235
|41\13, 2236.364
|-
|-
|D fa la mi reb
−
|31\11, 1957.895
|Mib, Sib
|50\18, 1935.484
|19\7, 1900
−
|45\17, 1862.069
|Ab
|26\10, 1835.294
|33\13, 1800
−
|2b, 2c
−
|7\15
−
''326.{{Overline|6}}''
−
|5\11
−
''318.{{Overline|18}}''
−
|8\18
−
''311.{{Overline|1}}''
−
|7\17
−
''288.235…''
−
|4\10
−
''280''
−
|5\13
−
''269.230…''
−
|-
|-
|D fa la mi re
−
|44\15, 2030.769
|Mi, Si
|32\11, 2021.053
|52\18, 2012.903
−
|20\7, 2000
|A
|48\17, 1986.207
|28\10, 1976.471
−
|36\13, 1963.636
|2
−
|8\15
−
''373.{{Overline|3}}''
−
|6\11
−
''381.{{Overline|81}}''
−
|10\18
−
''388.{{Overline|8}}''
−
|4\7
−
''400''
−
|10\17
−
''411.764…''
−
|6\10
−
''420''
−
|8\13
−
''430.769…''
−
|-
|-
!D si la mi re
−
!45\15, 2076.923
|Mi#, Si#
!33\11, 2084.211
!54\18, 2090.323
−
!21\7, 2100
|A#
! 51\17, 2110.345
!30\10, 2117.647
−
!39\13, 2127.273
|2#
|-
|D si la mi re#
−
|46\15, 2123.077
|9\15
| rowspan="2" |34\11, 2147.368
|56\18, 2167.742
−
|22\7, 2200
''420''
|54\17, 2234.483
| 32\10, 2258.824
−
|42\13, 2090.909
| rowspan="2" |7\11
|-
|E fab
−
|47\26, 2169.231
''445.{{Overline|45}}''
|55\16, 2129.032
|21\7, 2100
−
|50\17, 2068.966
|12\18
|29\10, 2047.059
|37\13, 2018.182
−
|-
''466.{{Overline|6}}''
|E fa
|48\15, 2215.385
−
|35\11, 2210.526
|5\7
|57\18, 2206.452
|23\7, 2300
−
|53\17, 2193.103
''500''
|31\10, 2188.235
|40\13, 2181.818
−
|-
|13\17
|E si mi
|49\15, 2261.538
−
|36\11, 1073.684
''535.294…''
|59\18, 2283.871
|24\7, 2400
−
|56\17, 2317.241
|8\10
|33\10, 2329.412
|43\13, 2345.455
−
|-
''560''
|E si mi#
|50\15, 2307.692
−
| rowspan="2" |37\11, 2336.842
|11\13
|61\18, 2361.290
| rowspan="2" |23\7, 2300
−
| 59\17, 2441.379
''592.307…''
|35\10, 2470.588
|46\13, 2509.091
−
|-
|F sol fa utb
|51\15, 2353.846
|60\18, 2322.581
|55\17, 2275.862
|32\10, 2258.824
|41\13, 2236.364
|-
|-
|F sol fa ut
−
|52\15, 2400
|Fab, Dob
|38\11, 2400
|62\18, 2400
−
|24\7, 2400
|Bbb
|58\17, 2400
|34\10, 2400
−
|44\13, 2400
|3bb, 3cc
|-
|F sol fa ut#
−
|53\15, 2446.154
|10\15
|39\11, 2463.158
|64\18, 2477,419
−
| rowspan="2" |25\7, 2500
''466.{{Overline|6}}''
|61\17, 2524.138
|36\10, 2541.176
−
|47\13, 2563.636
|11\18
−
''427.{{Overline|7}}''
−
|4\7
−
''400''
−
|9\17
−
''370.588…''
−
|5\10
−
''350''
−
|6\13
−
''323.076.…''
−
|-
|-
|G la sol reb
−
|55\15, 2538.462
|'''Fa, Do'''
|40\11, 2526.316
|65\18, 2516.129
−
|60\17, 2482.759
|'''Bb'''
|35\10, 2470.588
|45\13, 2454.545
−
|'''3b, 3c'''
−
|'''11\15'''
−
'''''513.{{Overline|3}}'''''
−
|'''8\11'''
−
'''''509.{{Overline|09}}'''''
−
|'''13\18'''
−
'''''505.{{Overline|5}}'''''
−
|'''5\7'''
−
'''''500'''''
−
|'''12\17'''
−
'''''494.117…'''''
−
|'''7\10'''
−
'''''490'''''
−
|'''9\13'''
−
'''''484.615…'''''
−
|-
|-
|'''G la sol re'''
−
|'''56\15, 2584.615'''
|Fa#, Do#
|'''41\11, 2589.474'''
|'''67\18, 2593.548'''
−
|'''26\7, 2600'''
|B
|'''63\17, 2606.897'''
|'''37\10, 2611.765'''
−
|'''48\13,''' '''2618.182'''
|3
|-
|G la sol re#
−
|57\15, 2630.769
|12\15
|42\11, 2652.632
|69\18, 2670.968
−
| rowspan="2" |27\7, 2700
''560''
|66\17, 2731.034
|39\10, 2752.941
−
|51\13, 2781.818
|9\11
|-
|A si la mib
−
|59\15, 2723.077
''572.{{Overline|72}}''
|43\11, 2715.789
|70\18, 2709.677
−
|65\17, 2689.552
|15\18
|38\10, 2682.353
|49\13, 2672.273
−
|-
''583.{{Overline|3}}''
!A si la mi
!60\15, 2769.231
−
!44\11, 2778.947
|6\7
!72\18, 2787.097
!28\7, 2800
−
!68\17, 2813.793
''600''
!40\10, 2823.529
!52\13, 2836.364
−
|-
|15\17
|A si la mi#
|61\15, 2815.385
−
| rowspan="2" |45\11, 2842.105
''617.647…''
| 74\18, 2864.516
|29\7, 2900
−
|71\17, 2937.069
|9\10
|42\10, 2964.706
|55\13, 3000
−
|-
''630''
|B fab
|62\15, 2861.538
−
|73\18, 2825.806
|12\13
| 28\7, 2800
|67\17, 2772.414
−
|39\10, 2752.941
''646.153…''
|50\13, 2727.273
|-
−
|B fa
|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
|-
|-
|'''B si'''
−
|'''64\15, 2953.846'''
|Fax, Dox
|'''47\11, 2968.421'''
|'''77\18, 2980.645'''
−
|'''30\7, 3000'''
|B#
|'''73\17, 3020.690'''
|'''43\10, 3035.294'''
−
|'''56\13, 3054.545'''
|3#
|-
|B si#
−
|65\15, 3000
|13\15
|48\11, 3031.579
|79\18, 3058.064
−
| rowspan="2" |31\7, 3100
''606. {{Overline|6}}''
|76\17, 3144.828
|45\10, 3176.471
−
|59\13, 3218.182
| rowspan="2" |10\11
−
''636.{{Overline|36}}''
−
|17\18
−
''661.{{Overline|1}}''
−
|7\7
−
''700''
−
|18\17
−
''741.176…''
−
|11\10
−
''770''
−
|15\13
−
''807.692…''
−
|-
|-
|C solb
−
|67\15, 3092.308
|Dob, Solb
|49\11, 3094.737
|80\18, 3096.774
−
|75\17, 3103.448
|Hb
|44\10, 3105.882
|57\13, 3109.091
−
|4b, 4c
−
|14\15
−
''653.{{Overline|3}}''
−
|16\18
−
''622.{{Overline|2}}''
−
|6\7
−
''600''
−
|14\17
−
''576.470…''
−
|8\10
−
''560''
−
|10\13
−
''538.461…''
−
|-
|-
|C sol
−
|68\15, 3138.462
!Do, Sol
|50\11, 3157.895
| 82\18, 3174.194
−
|32\7, 3200
!H
|78\17, 3227.586
| 46\10, 3247.059
−
|60\13, 3272.273
!4
|-
|C sol#
−
| 69\15, 3184.615
! colspan="7" |''700''
| rowspan="2" |51\11, 3221.053
|84\18, 3251.612
−
|33\7, 3300
|81\17, 3351.725
|48\10, 3388.235
|63\13, 3436.364
|-
|D labb
|70\15, 3230.769
|83\18, 3212.903
|32\7, 3200
|77\17, 3186.207
|45\10, 3176.471
|58\13, 3163.636
|-
|'''D lab'''
|'''71\15,''' '''3276.923'''
|'''52\11,''' '''3284.211'''
|'''85\18,''' '''3290.323'''
|'''33\7, 3300'''
|'''80\17,''' '''3310.345'''
|'''47\10,''' '''3317.647'''
|'''61\13,''' '''3327.{{Overline|27}}'''
|-
|-
|D la
−
|72\15, 3323.077
|Do#, Sol#
|53\11, 3347.368
|87\18, 3367.742
−
|34\7, 3400
|Η#
|83\17, 3434.583
|49\10, 3458.824
−
|64\13, 3490.909
|4#
−
|16\15
−
''746.{{Overline|6}}''
−
|12\11
−
''763.{{Overline|63}}''
−
|20\18
−
''777.{{Overline|7}}''
−
| rowspan="2" |8\7
−
''800''
−
|20\17
−
''823.529…''
−
|12\10
−
''840''
−
|16\13
−
''861.538…''
−
|-
|-
|D la#
−
|73\15, 3369.231
|Reb, Lab
| rowspan="2" |54\11, 3410.625
|89\18, 3445.162
−
|35\7, 3500
|Cb
|86\17, 3558.621
|51\10, 3600
−
|67\13, 3654.545
|5b, 5c
|-
|F utb
−
|74\15, 3415.385
|18\15
|88\18, 3406.452
|34\7, 3400
−
|82\17, 3393.103
''840''
|48\10, 3388.235
|62\13, 3381.818
−
|13\11
−
''827.{{Overline|27}}''
−
|21\18
−
''816.{{Overline|6}}''
−
|19\17
−
''782.352…''
−
|11\10
−
''770''
−
|14\13
−
''753.846…''
−
|-
|-
!F ut
−
!75\15, 3461.538
|'''Re, La'''
!55\11, 3473.684
!90\18, 3483.871
−
!35\7, 3500
|'''C'''
!85\17, 3517.241
!50\10, 3529.412
−
!65\13, 3545.455
|'''5'''
|}
 
−
{| class="wikitable"
|'''19\15'''
|+Cents
!Notation
−
!Supersoft
'''''886.{{Overline|6}}'''''
!Soft
! Semisoft
−
!Basic
|'''14\11'''
!Semihard
!Hard
−
!Superhard
'''''890.{{Overline|90}}'''''
|-
!Subdozenal
−
!~15edf
|'''23\18'''
!~11edf
!~18edf
−
!~7edf
'''''894.{{Overline|4}}'''''
!~17edf
!~10edf
−
!~13edf
|'''9\7'''
−
'''''900'''''
−
|'''22\17'''
−
'''''905.882…'''''
−
|'''13\10'''
−
'''''910'''''
−
|'''17\13'''
−
'''''915.384…'''''
−
|-
|-
|F#
−
|1\15, 46.154
|Re#, La#
|1\11, 63.158
|2\18, 77.419
−
| rowspan="2" |1\7, 100
|C#
|3\17, 124.138
|2\10, 141.176
−
|3\13, 163.636
|5#
|-
|Gb, Ge
−
|3\15, 138.462
|20\15
|2\11. 126.316
|3\18, 116.129
−
|2\17, 82.759
''933.{{Overline|3}}''
|1\10, 70.588
|1\13, 54.545
−
|15\11
−
''954.{{Overline|54}}''
−
|25\18
−
''972.{{Overline|2}}''
−
| rowspan="2" |10\7
−
''1000''
−
|25\17
−
''1029.411…''
−
|15\10
−
''1050''
−
|20\13
−
''1076.923…''
−
|-
|-
|'''G'''
−
|'''4\15,''' '''184.615'''
|Mib, Sib
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
−
|'''2\7,''' '''200'''
|Db
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
−
|'''4\13,''' '''218.182'''
|6b, 6c
−
|22\15
−
''1026.{{Overline|6}}''
−
|16\11
−
''1018.{{Overline|18}}''
−
|26\18
−
''1011. {{Overline|1}}''
−
|24\17
−
''988.235…''
−
|14\10
−
''980''
−
|18\13
−
''969.230…''
−
|-
|-
|G#
−
|5\15, 230.769
|Mi, Si
|4\11, 252.632
|7\18, 270.968
−
| rowspan="2" |3\7, 300
|D
|8\17, 331.034
|5\10, 352.941
−
|7\13, 381.818
|6
|-
|Hb, He
−
|7\15, 323.077
|23\15
|5\11, 315.789
|8\18, 309.677
−
|7\17, 289.655
''1073.{{Overline|3}}''
|4\10, 282.353
|5\13, 272.727
−
|-
|17\11
|H
|8\15, 369.231
−
|6\11, 378.947
''1081.{{Overline|81}}''
|10\18, 387.097
|4\7, 400
−
|10\17, 413.793
|28\18
|6\10, 423.529
|8\13, 436.364
−
|-
''1088.{{Overline|8}}''
|H#
|9\15, 415.385
−
| rowspan="2" |7\11, 442.105
|11\7
|12\18, 464.516
|5\7, 500
−
|13\17, 537.069
''1100''
|8\10, 564.706
|11\13, 600
−
|-
|27\17
|Jbb, Jee
|10\15, 461.538
−
|11\18, 425.806
''1111.764…''
|4\7, 400
|9\17, 372.414
−
|5\10, 352.941
|16\10
|6\13, 327.273
|-
−
|'''Jb, Je'''
''1120''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
−
|'''13\18,''' '''503.226'''
|21\13
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
−
|'''7\10,''' '''494.118'''
''1130.769…''
|'''9\13,''' '''490.909'''
|-
−
|J
|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
|-
|-
|J#
−
|13\15, 600
|Mi#, Si#
| rowspan="2" |10\11, 631.579
|17\18, 658.064
−
|7\7, 700
|D#
|18\17, 744.828
|11\10, 776.471
−
|15\13, 818.182
|6#
−
|24\15
−
''1120''
−
| rowspan="2" |18\11
−
''1145.{{Overline|45}}''
−
|30\18
−
''1166.{{Overline|6}}''
−
|12\7
−
''1200''
−
|30\17
−
''1235.294…''
−
|18\10
−
''1260''
−
|24\13
−
''1292.307…''
−
|-
|-
|Kb, Ke
−
|14\15, 646.154
|Fab, Dob
|16\18, 619.355
|6\7, 600
−
|14\17, 579.310
|Ebb
|8\10, 564.706
|10\13, 545.455
−
|7bb, 7cc
−
|25\15
−
''1166.{{Overline|6}}''
−
|29\18
−
''1127.{{Overline|7}}''
−
|11\7
−
''1100''
−
|26\17
−
''1070.588…''
−
|15\10
−
''1050''
−
|19\13
−
''1023.076…''
−
|-
|-
!K
−
!'''15\15,''' '''692.308'''
|'''Fa, Do'''
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
−
!7\7, 700
|'''Eb'''
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
−
!'''13\13,''' '''709.091'''
|'''7b, 7c'''
|-
|K#
−
|16\15, 738.462
|'''26\15'''
|12\11, 757.895
|20\18, 774.194
−
| rowspan="2" |8\8, 800
'''''1213.{{Overline|3}}'''''
|20\17, 827.586
|12\10, 847.059
−
|16\13, 872.727
|'''19\11'''
|-
|Lb, Le
−
|18\15, 830.769
'''''1209.{{Overline|09}}'''''
|13\11, 821.053
|21\18, 812.903
−
|19\17, 786.207
|'''31\18'''
|11\10, 776.471
|14\13, 763.63
−
|-
'''''1205.{{Overline|5}}'''''
|'''L'''
|'''19\15,''' '''876.923'''
−
|'''14\11,''' '''884.211'''
|'''12\7'''
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
−
|'''22\17,''' '''910.345'''
'''''1200'''''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
−
|-
|'''29\17'''
|L#
|20\15, 923.077
−
| rowspan="2" |15\11, 947.368
'''''1194.117…'''''
|25\18, 967.742
|10\7, 1000
−
|25\17, 1034.483
|'''17\10'''
|15\10, 1058.824
|20\13, 1090.909
−
|-
'''''1190'''''
|Mbb, Mee
|21\15, 969.231
−
|24\18, 929.032
|'''22\13'''
|9\5, 900
|21\17, 868.966
−
|12\10, 847.059
'''''1184.615…'''''
|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
|Fa#, Do#
|17\11, 1073.684
|28\18, 1083.871
−
|11\7, 1100
|E
|27\17, 1117.241
|16\10, 1129.412
−
|21\9, 1145.455
|7
|-
|M#
−
|24\15, 1107.923
|27\15
| rowspan="2" |18\11, 1136.842
|30\18, 1161.29
−
|12\7, 1200
''1260''
|30\17, 1241.379
|18\10, 1270.588
−
|24\13, 1309.091
|20\11
|-
|Nbb, Nee
−
|25\15, 1153.846
''1272.{{Overline|72}}''
|29\18, 1122.581
|11\7, 1100
−
|26\17, 1075.862
|33\18
|15\10, 1058.824
|19\13, 1036.364
−
|-
''1283.{{Overline|3}}''
|'''Nb, Ne'''
|'''26\15,''' '''1200'''
−
|'''19\11,''' '''1200'''
|13\7
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
−
|'''29\17,''' '''1200'''
''1300''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
−
|-
|32\17
|N
|27\15, 1246.154
−
|20\11, 1263.158
''1317.647…''
|33\18, 1277.419
|13\7, 1300
−
|32\17, 1324.138
|19\10
|19\10, 1341.176
|25\13, 1363.636
−
|-
''1330''
|N#
|28\15, 1292.308
−
| rowspan="2" |21\11, 1326.318
|25\13
|35\18, 1354.834
|14\7, 1400
−
|35\17, 1448.275
''1346.153…''
|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'''
|Fax, Dox
|'''25\11,''' '''1578.947'''
|'''41\18,''' '''1587.097'''
−
|'''16\7,''' '''1600'''
|E#
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
−
|'''30\13,''' '''1636.364'''
|7#
|-
|Q#
−
|35\15, 1615.385
|28\15
| rowspan="2" |26\11, 1642.105
|43\18, 1664.516
−
|17\7, 1700
''1306.{{Overline|6}}''
|42\17, 1737.069
|25\10, 1764.706
−
|33\13, 1800
| rowspan="2" |21\11
−
''1336.{{Overline|36}}''
−
|35\18
−
''1361.{{Overline|1}}''
−
|14\7
−
''1400''
−
|35\17
−
''1441.176…''
−
|21\10
−
''1470''
−
|28\13
−
''1507.692…''
−
|-
|-
|Rb, Re
−
|36\61, 1661.538
|Dob, Solb
|42\18, 1625.806
|16\7, 1600
−
|38\29, 1572.414
|Fb
|22\10, 1552.941
|28\13, 1527.273
−
|8b, Fc
−
|29\15
−
''1333.{{Overline|3}}''
−
|34\18
−
''1322.{{Overline|2}}''
−
|13\7
−
''1300''
−
|31\17
−
''1276.470…''
−
|18\10
−
''1260''
−
|23\13
−
''1238.461…''
−
|-
|-
|R
−
|37\15, 1707.692
!Do, Sol
|27\11, 1705.263
|44\18, 1703.226
−
|17\7, 1700
!F
|41\17, 1696.552
|24\10, 1694.118
−
|31\13, 1690.909
!8, F
|-
|R#
−
|38\15, 1753.846
! colspan="7" |''1400''
|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'''
|Do#, Sol#
|'''30\11,''' '''1894.737'''
|'''49\18,''' '''1896.774'''
−
|'''19\7, 1900'''
|F#
|'''46\17,''' '''1903.448'''
|'''27\10,''' '''1905.882'''
−
|'''35\13,''' '''1909.091'''
|8#, F#
−
|31\15
−
''1446.{{Overline|6}}''
−
|23\11
−
''1463.{{Overline|63}}''
−
|38\18
−
''1477.7̄''
−
| rowspan="2" |15\7
−
''1500''
−
|37\17
−
''1523.529…''
−
|22\10
−
''1540''
−
|29\13
−
''1561.538…''
−
|-
|-
|S#
−
|42\15, 1938.462
|Reb, Lab
|31\11, 1957.895
|51\18, 1974.194
−
|20\7, 2000
|Gb
|49\17, 2027.586
|29\10, 2047.059
−
|38\13, 2072.727
|9b, Gc
|-
|Sx
−
|43\15, 1984.615
|33\15
| rowspan="2" |32\11, 2021.053
|53\18, 2051.612
−
|21\7, 2100
''1540''
|52\17, 2151.725
|31\10, 2188.235
−
|41\13, 2236.364
|24\11
|-
|Tb, Te
−
|44\15, 2030.769
''1527.{{Overline|27}}''
|52\18, 2012.903
|20\7, 2000
−
|48\17, 1986.207
|39\18
|28\10, 1976.471
|36\13, 1963.636
−
|-
''1516.{{Overline|6}}''
!T
!45\15, 2076.923
−
!33\11, 2084.211
|36\17
!54\18, 2090.323
!21\7, 2100
−
!51\17, 2110.345
''1482.352…''
!30\10, 2117.647
!39\13, 2127.273
−
|-
|21\10
|T#
|46\15, 2123.077
−
| rowspan="2" |34\11, 2147.368
''1470''
|56\18, 2167.742
|22\7, 2200
−
|54\17, 2234.483
|27\13
|32\10, 2258.824
|42\13, 2090.909
−
|-
''1453.846…''
|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
|'''Re, La'''
|60\18, 2322.581
|55\17, 2275.862
−
|32\10, 2258.824
|'''G'''
|41\13, 2236.364
|-
−
|V
|'''9, G'''
|52\15, 2400
|38\11, 2400
−
|62\18, 2400
|'''34\15'''
|24\7, 2400
|58\17, 2400
−
|34\10, 2400
'''''1586.{{Overline|6}}'''''
|44\13, 2400
|-
−
|V#
|'''25\11'''
|53\15, 2446.154
|39\11, 2463.158
−
|64\18, 2477,419
'''''1590.{{Overline|90}}'''''
| rowspan="2" |25\7, 2500
|61\17, 2524.138
−
|36\10, 2541.176
|'''41\18'''
|47\13, 2563.636
|-
−
|Wb, We
'''''1594.{{Overline|4}}'''''
|55\15, 2538.462
|40\11, 2526.316
−
|65\18, 2516.129
|'''16\7'''
|60\17, 2482.759
|35\10, 2470.588
−
|45\13, 2454.545
'''''1600'''''
|-
|'''Wb'''
−
|'''56\15, 2584.615'''
|'''39\17'''
|'''41\11, 2589.474'''
|'''67\18, 2593.548'''
−
|'''26\7, 2600'''
'''''1605.882…'''''
|'''63\17, 2606.897'''
|'''37\10, 2611.765'''
−
|'''48\13,''' '''2618.182'''
|'''23\10'''
|-
|W#
−
|57\15, 2630.769
'''''1610'''''
|42\11, 2652.632
|69\18, 2670.968
−
| rowspan="2" |27\7, 2700
|'''30\13'''
|66\17, 2731.034
|39\10, 2752.941
−
|51\13, 2781.818
'''''1615.384…'''''
|-
|Xb, Xe
−
|59\15, 2723.077
|43\11, 2715.789
|70\18, 2709.677
|65\17, 2689.552
|38\10, 2682.353
|49\13, 2672.273
|-
!X
!60\15, 2769.231
!44\11, 2778.947
!72\18, 2787.097
!28\7, 2800
!68\17, 2813.793
!40\10, 2823.529
!52\13, 2836.364
|-
|X#
|61\15, 2815.385
| rowspan="2" |45\11, 2842.105
|74\18, 2864.516
|29\7, 2900
|71\17, 2937.069
|42\10, 2964.706
|55\13, 3000
|-
|Ybb, Yee
|62\15, 2861.538
|73\18, 2825.806
|28\7, 2800
|67\17, 2772.414
|39\10, 2752.941
|50\13, 2727.273
|-
|Yb, Ye
|63\15, 2907.692
|46\11, 2905.263
|75\18, 2903.226
|29\7, 2900
|70\17, 2896.552
|41\10, 2894.118
|53\13, 2890.909
|-
|-
|'''Y'''
−
|'''64\15, 2953.846'''
|Re#, La#
|'''47\11, 2968.421'''
|'''77\18, 2980.645'''
−
|'''30\7, 3000'''
|G#
|'''73\17, 3020.690'''
|'''43\10, 3035.294'''
−
|'''56\13, 3054.545'''
|9#, G#
|-
|Y#
−
|65\15, 3000
|35\15
|48\11, 3031.579
|79\18, 3058.064
−
| rowspan="2" |31\7, 3100
''1633.{{Overline|3}}''
|76\17, 3144.828
|45\10, 3176.471
−
|59\13, 3218.182
|26\11
|-
|Zb. Ze
−
|67\15, 3092.308
''1654.{{Overline|54}}''
|49\11, 3094.737
|80\18, 3096.774
−
|75\17, 3103.448
|43\18
|44\10, 3105.882
|57\13, 3109.091
−
''1672.{{Overline|2}}''
−
| rowspan="2" |17\7
−
''1700''
−
|42\17
−
''1729.411…''
−
|25\10
−
''1750''
−
|33\13
−
''1776.923…''
−
|-
|-
|Z
−
|68\15, 3138.462
|Mib, Sib
|50\11, 3157.895
|82\18, 3174.194
−
|32\7, 3200
|Ab
|78\17, 3227.586
|46\10, 3247.059
−
|60\13, 3272.273
|Xb, Ac
−
|37\15
−
''1726.{{Overline|6}}''
−
|27\11
−
''1718.{{Overline|18}}''
−
|44\18
−
''1711.{{Overline|1}}''
−
|41\17
−
''1688.235…''
−
|24\10
−
''1680''
−
|31\13
−
''1669.230…''
−
|-
|-
|Z#
−
|69\15, 3184.615
|Mi, Si
| rowspan="2" |51\11, 3221.053
|84\18, 3251.612
−
|33\7, 3300
|A
|81\17, 3351.725
|48\10, 3388.235
−
|63\13, 3436.364
|X, A
|-
|Ab, Æ
−
|70\15, 3230.769
|38\15
|83\18, 3212.903
|32\7, 3200
−
|77\17, 3186.207
''1773.{{Overline|3}}''
|45\10, 3176.471
|58\13, 3163.636
−
|-
|28\11
|'''A'''
|'''71\15,''' '''3276.923'''
−
|'''52\11,''' '''3284.211'''
''1781.{{Overline|81}}''
|'''85\18,''' '''3290.323'''
|'''33\7, 3300'''
−
|'''80\17,''' '''3310.345'''
|46\18
|'''47\10,''' '''3317.647'''
|'''61\13,''' '''3327.{{Overline|27}}'''
−
''1788.{{Overline|8}}''
−
|18\7
−
''1800''
−
|44\17
−
''1811.764…''
−
|26\10
−
''1820''
−
|34\13
−
''1830.769…''
−
|-
|-
−
|Mi#, Si#
−
|A#
|A#
|72\15, 3323.077
−
|53\11, 3347.368
|X#, A#
|87\18, 3367.742
|34\7, 3400
−
|83\17, 3434.583
|39\15
|49\10, 3458.824
|64\13, 3490.909
−
|-
''1820''
|Ax
|73\15, 3369.231
−
| rowspan="2" |54\11, 3410.625
| rowspan="2" |29\11
|89\18, 3445.162
|35\7, 3500
−
|86\17, 3558.621
''1845.{{Overline|45}}''
|51\10, 3600
|67\13, 3654.545
−
|-
|48\18
|Bb, Be
|74\15, 3415.385
−
|88\18, 3406.452
''1866.{{Overline|6}}''
|34\7, 3400
|82\17, 3393.103
−
|48\10, 3388.235
|19\7
|62\13, 3381.818
|-
−
!B
''1900''
!75\15, 3461.538
!55\11, 3473.684
−
!90\18, 3483.871
|47\17
!35\7, 3500
!85\17, 3517.241
−
!50\10, 3529.412
''1935.294…''
!65\13, 3545.455
|-
−
|B#
|28\10
|76\15, 3507.692
|56\11, 3536.842
−
|92\18, 3561.290
''1960''
| rowspan="2" |36\7, 3600
|88\17, 3641.379
−
|52\10, 3670.588
|37\13
|68\13, 3709.091
−
''1992.307…''
−
|-
|-
|Cb, Ce
−
|78\15, 3600
|Fab, Dob
|57\11, 3600
|93\18, 3600
−
|87\17, 3600
|Bbb
|51\10, 3600
|66\13, 3600
−
|Ebb, Ccc
−
|40\15
−
''1866.{{Overline|6}}''
−
|47\18
−
''1827.{{Overline|7}}''
−
|18\7
−
''1800''
−
|43\17
−
''1770.588…''
−
|25\10
−
''1750''
−
|32\13
−
''1723.076…''
−
|-
|-
|'''C'''
−
|'''79\15,''' '''3646.154'''
|'''Fa, Do'''
|'''58\11,''' '''3663.158'''
|'''95\18,''' '''3677.419'''
−
|'''37\7,''' '''3700'''
|'''Bb'''
|'''90\17,''' '''3724.138'''
|'''53\10,''' '''3741.176'''
−
|'''69\13,''' '''3763.636'''
|Eb, Cc
|-
|C#
−
|80\15, 3692.308
|'''41\15'''
|59\11, 3726.316
|97\18, 3755.838
−
| rowspan="2" |38\7, 3800
'''''1913.{{Overline|3}}'''''
|93\17, 3848.275
|55\10, 3882.353
−
|72\13, 3927.273
|'''30\11'''
|-
|Db, De
−
|82\15, 3784.615
'''''1909.{{Overline|09}}'''''
|60\11, 3789.474
|98\18, 3793.548
−
|92\17, 3806.897
|'''49\18'''
|54\10, 3811.765
|70\13, 3818.182
−
|-
'''''1905.{{Overline|5}}'''''
|D
|83\15, 3830.769
−
|61\11, 3852.632
|'''19\7'''
|100\18, 3870.968
|39\7, 3900
−
|95\17, 3931.03$
'''''1900'''''
|56\10, 3952.941
|73\13, 3981.818
−
|'''46\17'''
−
'''''1894.117…'''''
−
|'''27\10'''
−
'''''1890'''''
−
|'''35\13'''
−
'''''1884.615…'''''
−
|-
|-
|D#
−
|84\15, 3876.923
|Fa#, Do#
| rowspan="2" |62\11, 3915.789
|102\18, 3948.387
−
|40\7, 4000
|B
|98\17, 4055.172
|58\10, 4094.118
−
|76\13, 4145.455
|E, C
|-
|Ebb, Ëe
−
|85\15, 3923.077
|42\15
|101\18, 3909.677
|39\7, 3900
−
|94\17, 3889.552
''1960''
|55\10, 3882.353
|71\13, 3872.727
−
|-
|31\11
|'''Eb, Ë'''
|'''86\15,''' '''3969.231'''
−
|'''63\11,''' '''3978.947'''
''1972.{{Overline|72}}''
|'''103\18,''' '''3987.097'''
|'''40\7, 4000'''
−
|'''97\17,''' '''4013.793'''
|51\18
|'''57\10,''' '''4023.529'''
|'''74\13,''' '''4036.364'''
−
|-
''1983.{{Overline|3}}''
|E
|87\15, 4015.385
−
|64\11, 4042.105
|20\7
|105\18, 4064.516
|41\7, 4100
−
|100\17, 4137.931
''2000''
|59\10, 4164.706
|77\13, 4200
−
|-
|49\17
|E#
|88\15, 4061.583
−
| rowspan="2" |65\11, 4105.263
''2017.647…''
|107\18, 4141.956
|42\7, 4200
−
|103\17, 4262.069
|29\10
|61\10, 4305.882
|80\13, 4363.636
−
|-
''2030''
|Fb, Fe
|89\15, 4107.692
−
|106\18, 4103.226
|38\13
|41\7, 4100
|99\17, 4096.552
−
|58\10, 4094.118
''2046.153…''
|75\13, 4090.909
−
|-
|-
!F
−
!90\15, 4153.846
|Fax, Dox
!66\11, 4168.421
!108\18, 4180.645
−
!42\7, 4200
|B#
!102\17, 4220.690
!60\10, 4235.294
−
!78\13, 4254.545
|Ex, Cx
|}
==Intervals==
−
{| class="wikitable"
|43\15
!Generators
!Sesquitave notation
−
!Interval category name
''2006.{{Overline|6}}''
!Generators
!Notation of 3/2 inverse
−
!Interval category name
| rowspan="2" |32\11
|-
| colspan="6" |The 4-note MOS has the following intervals (from some root):
−
''2036.{{Overline|36}}''
−
|53\18
−
''2061. {{Overline|1}}''
−
|21\7
−
''2100''
−
|52\17
−
''2141.176…''
−
|31\10
−
''2170''
−
|41\13
−
''2207.692…''
−
|-
|-
|0
−
|Do, Fa, Sol
|Dob, Solb
|perfect unison
|0
−
|Do, Fa, Sol
|Hb
|sesquitave (just fifth)
|-
−
|1
|0b, Dc
|Fa, Sib, Do
|perfect fourth
−
| -1
|44\15
|Re, Sol, La
|perfect second
−
|-
''2053.{{Overline|3}}''
|2
|Mib, Lab, Sib
−
|minor third
|52\18
| -2
|Mi, La, Si
−
|major third
''2022.{{Overline|2}}''
−
|20\7
−
''2000''
−
|48\17
−
''1976.470…''
−
|28\10
−
''1960''
−
|36\13
−
1938.615…
−
|-
|-
|3
|Reb, Solb, Lab
|diminished second
| -3
|Fa#, Si, Do#
|augmented fourth
|-
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|-
|4
|Dob, Fab, Solb
|diminished sesquitave
| -4
|Do#, Fa#, Sol#
|augmented unison (chroma)
|-
|5
|Fab, Sibb, Dob
|diminished fourth
| -5
|Re#, Sol#, La#
|augmented second
|-
|6
|Mibb, Labb, Sibb
|diminished third
| -6
|Mi#, La#, Si#
|augmented third
|}
==Genchain==
   
   
−
The generator chain for this scale is as follows:
!Do, Sol
−
!H
−
!0, D
−
! colspan="7" |2100
−
|}
−
−
==Intervals==
−
{| class="wikitable"
{| class="wikitable"
|Mibb
Labb
   
   
−
Sibb
!Generators
|Fab
Sibb
   
   
−
Dob
!Sesquitave notation
|Dob
Fab
   
   
−
Solb
!Interval category name
|Reb
Solb
   
   
−
Lab
!Generators
|Mib
Lab
   
   
−
Sib
!Notation of 3/2 inverse
|Fa
Sib
   
   
−
Do
!Interval category name
|Do
Fa
   
   
−
Sol
|-
|Re
Sol
   
   
−
La
| colspan="6" |The 4-note MOS has the following intervals (from some root):
|Mi
La
   
   
−
Si
|-
|Fa#
Si
   
   
−
Do#
|0
|Do#
Fa#
   
   
−
Sol#
|Do, Sol
|Re#
Sol#
   
   
−
La#
|perfect unison
|Mi#
La#
   
   
−
Si#
|0
−
|Do, Sol
−
|sesquitave (just fifth)
−
|-
|-
|d3
|d4
|d5
|d2
|m3
|P4
|P1
|P2
|M3
|A4
|A1
|A2
|A3
|}
==Modes==
   
   
−
The mode names are based on the species of fifth:
|1
{| class="wikitable"
!Mode
−
!Scale
|Fa, Do
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
−
|perfect fourth
−
| -1
−
|Re, La
−
|perfect second
−
|-
|-
!name
−
!pattern
|2
!notation
!2nd
−
!3rd
|Mib, Sib
!4th
−
|minor third
−
| -2
−
|Mi, Si
−
|major third
−
|-
|-
|Lydian
|LLLs
|<nowiki>3|0</nowiki>
|P
|M
|A
|-
|Major
|LLsL
|<nowiki>2|1</nowiki>
|P
|M
|P
|-
|Minor
|LsLL
|<nowiki>1|2</nowiki>
|P
|m
|P
|-
|Phrygian
|sLLL
|<nowiki>0|3</nowiki>
|d
|m
|P
|}
==Temperaments==
   
   
−
The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
|3
==='''Napoli-Meantone (Hex meantone)'''===
−
|Reb, Lab
   
   
−
[[Subgroup]]: 3/2.6/5.8/5 (5.2.3)
|diminished second
   
   
−
[[Comma]] list: [[81/80]]
| -3
 
[[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)
|Fa#, Do#
   
   
−
[[Comma]] list: [[64/63]]
|augmented fourth
 
[[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)
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
!Cents
!L
−
!s
!L/s
!Comments
|-
|1\4
|171.429
|1
|1
|1.000
|Equalised
|-
|-
|6\23
−
|180.000
|4
|6
|5
−
|1.200
|Dob, Solb
|
−
|diminished sesquitave
−
| -4
−
|Do#, Sol#
−
|augmented unison (chroma)
−
|-
|-
|5\19
−
|181.818
|5
|5
|4
−
|1.250
|Fab, Dob
|
|-
−
|14\53
|diminished fourth
|182.609
|14
−
|11
| -5
|1.273
|
−
|-
|Re#, La#
|9\34
|183.051
−
|9
|augmented second
|7
|1.286
−
|
|-
|-
|4\15
−
|184.615
|6
|4
|3
−
|1.333
|Mibb, Sibb
|
|-
−
|11\41
|diminished third
|185.915
|11
−
|8
| -6
|1.375
|
−
|-
|Mi#, Si#
|7\26
|186.667
−
|7
|augmented third
|5
|1.400
−
|
|}
|-
|10\37
−
|187.5
==Genchain==
|10
|7
−
|1.429
The generator chain for this scale is as follows:
|
|-
−
|13\48
{| class="wikitable"
|187.952
|13
−
|9
|Mibb
|1.444
|
−
|-
Sibb
|16\59
|188.253
−
|16
|Fab
|11
|1.455
−
|
Dob
−
|Dob
−
Solb
−
|Reb
−
Lab
−
|Mib
−
Sib
−
|Fa
−
Do
−
|Do
−
Sol
−
|Re
−
La
−
|Mi
−
Si
−
|Fa#
−
Do#
−
|Do#
−
Sol#
−
|Re#
−
La#
−
|Mi#
−
Si#
−
|-
|-
|3\11
−
|189.474
|d3
|3
|2
−
|1.500
|d4
|Napoli-Meantone starts here
|-
−
|14\51
|d6
|190.909
|14
−
|9
|d2
|1.556
|
−
|-
|m3
|11\40
|191.304
−
|11
|P4
|7
|1.571
−
|
|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
−
|-
|-
|8\29
−
|192.000
!name
|8
|5
−
|1.600
!pattern
|
|-
−
|5\18
!notation
|193.548
|5
−
|3
!2nd
|1.667
|
−
!3rd
−
!4th
−
|-
|-
|12\43
−
|194.595
|Lydian
|12
|7
−
|1.714
|LLLs
|
−
|<nowiki>3|0</nowiki>
−
|P
−
|M
−
|A
−
|-
|-
|7\25
−
|195.348
|Major
|7
|4
−
|1.750
|LLsL
|
−
|<nowiki>2|1</nowiki>
−
|P
−
|M
−
|P
−
|-
|-
|9\32
−
|196.364
|Minor
|9
|5
−
|1.800
|LLsL
|
|-
−
|11\39
|<nowiki>1|2</nowiki>
|197.015
|11
−
|6
|P
|1.833
|
−
|m
−
|P
−
|-
|-
|13\46
−
|197.468
|Phrygian
|13
|7
−
|1.857
|sLLL
|
|-
−
|15\53
|<nowiki>0|3</nowiki>
|197.802
|15
−
|8
|d
|1.875
|
−
|-
|m
|17\60
|198.058
−
|17
|P
|9
|1.889
−
|
|}
|-
|19\67
−
|198.261
==Temperaments==
|19
|10
−
|1.900
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.
|
|-
−
|21\74
==='''Napoli-Meantone'''===
|198.425
|21
−
|11
[[Subgroup]]: 3/2.6/5.8/5
|1.909
|
−
|-
|23\81
|198.561
−
|23
[[Comma]] list: [[81/80]]
|12
|1.917
−
|
−
[[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
−
|-
|-
|25\88
−
|198.675
!<u>Normalised</u>
|25
|13
−
|1.923
!''ed7\12''
|
−
|-
|-
|27\95
−
|198.773
|1\4
|27
|14
−
|1.929
|
|
|-
−
|29\102
|198.857
|29
|15
|1.933
|
|
−
|<u>171.428…</u>
−
|''175''
−
|1
−
|1
−
|1.000
−
|Equalised
−
|-
|-
|31\109
−
|198.930
|6\23
|31
|16
−
|1.9375
|
|
|-
−
|33\116
|198.995
|33
|17
|1.941
|
|
|-
−
|35\123
|<u>180</u>
|199.009
|35
−
|18
|''182.608…''
|1.944
−
|6
−
|5
−
|1.200
−
|
|
−
|-
|-
|2\7
−
|200
|2
|1
|2.000
|Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|17\59
|201.980
|17
|8
|2.125
|
|
|-
−
|15\52
|11\42
|202.247
|15
−
|7
|2.143
|
|-
|13\45
|202.597
|13
|6
|2.167
|
|
|-
−
|11\38
|<u>180.821…</u>
|203.077
−
|''183.{{Overline|3}}''
−
|11
|11
|5
−
|2.200
|
|-
|9\31
|203.774
|9
|9
|4
−
|2.250
|1.222
−
|
|
−
|-
|-
|7\24
−
|204.878
|5\19
|7
|3
−
|2.333
|
|
|-
−
|12\41
|205.714
|12
|5
|2.400
|
|
|-
−
|5\17
|<u>181.{{Overline|81}}</u>
|206.897
−
|''184.210…''
−
|5
|5
|2
−
|2.500
|4
|Napoli-Neogothic heartland is from here…
|-
−
|18\61
|1.250
|207.693
|18
−
|7
|2.571
|
|
−
|-
|-
|13\44
−
|208.000
|
|13
|5
−
|2.600
|14\53
−
|
|
|-
−
|8\27
|<u>182.608…</u>
|208.696
|8
−
|3
|''184.905…''
|2.667
|…to here
−
|-
|14
|11\37
|209.524
−
|11
|11
|4
−
|2.750
|1.273
−
|
|
−
|-
|-
|14\47
−
|210.000
|14
|5
|2.800
|
|
|-
−
|3\10
|9\34
|211.765
|3
−
|1
|
|3.000
|Napoli-Pythagorean ends, Napoli-Archy begins
−
|-
|<u>183.050…</u>
|22\73
|212.903
−
|22
|''185.294…''
−
|9
−
|7
|7
|3.143
−
|1.286
−
|
|
−
|-
|-
|19\63
−
|213.084
|4\15
|19
|6
−
|3.167
|
|
|-
−
|16\53
|213.333
|16
|5
|3.200
|
|
|-
−
|13\43
|<u>184.615…</u>
|213.699
|13
−
|''186.{{Overline|6}}''
−
|4
|4
|3.250
−
|
|-
|10\33
|214.286
|10
|3
|3
|3.333
−
|1.333
−
|
|
−
|-
|-
|7\23
−
|215.385
|7
|2
|3.500
|
|
|-
−
|11\36
|11\41
|216.393
|11
−
|
−
|<u>185.915…</u>
−
|''187.804…''
−
|11
−
|8
−
|1.375
−
|
−
|-
−
|
−
|7\26
−
|
−
|<u>186.{{Overline|6}}</u>
−
|''188.461…''
−
|7
−
|5
−
|1.400
−
|
−
|-
−
|
−
|10\37
−
|
−
|<u>187.5</u>
−
|''189.{{Overline|189}}''
−
|10
−
|7
−
|1.429
−
|
−
|-
−
|
−
|13\48
−
|
−
|<u>187.951…</u>
−
|''189.58{{Overline|3}}''
−
|13
−
|9
−
|1.444
−
|
−
|-
−
|
−
|16\59
−
|
−
|<u>188.235…</u>
−
|''189.830…''
−
|16
−
|11
−
|1.4545
−
|
−
|-
−
|3\11
−
|
−
|
−
|<u>189.473…</u>
−
|''190.{{Overline|90}}''
−
|3
−
|2
−
|1.500
−
|Napoli-Meantone starts here
−
|-
−
|
−
|17\62
−
|
−
|<u>190.654…</u>
−
|''191.935…''
−
|17
−
|11
−
|1.5455
−
|
−
|-
−
|
−
|14\51
−
|
−
|<u>190.{{Overline|90}}</u>
−
|''192.156…''
−
|14
−
|9
−
|1.556
−
|
−
|-
−
|
−
|11\40
−
|
−
|<u>191.304…</u>
−
|''192.5''
−
|11
−
|7
−
|1.571
−
|
−
|-
−
|
−
|8\29
−
|
−
|<u>192</u>
−
|''193.103…''
−
|8
−
|5
−
|1.600
−
|
−
|-
−
|
−
|5\18
−
|
−
|<u>193.548…</u>
−
|''194.{{Overline|4}}''
−
|5
−
|3
−
|1.667
−
|
−
|-
−
|
−
|
−
|12\43
−
|<u>194.{{Overline|594}}</u>
−
|''195.348…''
−
|12
−
|7
−
|1.714
−
|
−
|-
−
|
−
|7\25
−
|
−
|<u>195.348…</u>
−
|''196''
−
|7
−
|4
−
|1.750
−
|
−
|-
−
|
−
|9\32
−
|
−
|<u>196.{{Overline|36}}</u>
−
|''196.875''
−
|9
−
|5
−
|1.800
−
|
−
|-
−
|
−
|11\39
−
|
−
|<u>197.014…</u>
−
|''197.435…''
−
|11
−
|6
−
|1.833
−
|
−
|-
−
|
−
|13\46
−
|
−
|<u>197.468…</u>
−
|''197.826…''
−
|13
−
|7
−
|1.857
−
|
−
|-
−
|
−
|15\53
−
|
−
|<u>197.802…</u>
−
|''198.113…''
−
|15
−
|8
−
|1.875
−
|
−
|-
−
|
−
|17\60
−
|
−
|<u>198.058…</u>
−
|''198.{{Overline|3}}''
−
|17
−
|9
−
|1.889
−
|
−
|-
−
|
−
|19\67
−
|
−
|<u>198.260…</u>
−
|''198.507…''
−
|19
−
|10
−
|1.900
−
|
−
|-
−
|
−
|21\74
−
|
−
|<u>198.425…</u>
−
|''198.{{Overline|648}”''
−
|21
−
|11
−
|1.909
−
|
−
|-
−
|
−
|23\81
−
|
−
|<u>198.561…</u>
−
|''198.765…''
−
|23
−
|12
−
|1.917
−
|
−
|-
−
|
−
|25\88
−
|
−
|<u>198.675…</u>
−
|''198.8{{Overline|63}}''
−
|25
−
|13
−
|1.923
−
|
−
|-
−
|
−
|27\95
−
|
−
|<u>198.773…</u>
−
|''198.947…''
−
|27
−
|14
−
|1.929
−
|
−
|-
−
|
−
|29\102
−
|
−
|<u>198.857…</u>
−
|''199.019…''
−
|29
−
|15
−
|1.933
−
|
−
|-
−
|
−
|31\109
−
|
−
|<u>198.930…</u>
−
|''199.082…''
−
|31
−
|16
−
|1.9375
−
|
−
|-
−
|
−
|33\116
−
|
−
|<u>198.994…</u>
−
|''199.137…''
−
|33
−
|17
−
|1.941
−
|
−
|-
−
|
−
|35\123
−
|
−
|<u>199.052…</u>
−
|''199.186…''
−
|35
−
|18
−
|1.944
−
|
−
|-
−
|2\7
−
|
−
|
−
|<u>200</u>
−
|''200''
−
|2
−
|1
−
|2.000
−
|Napoli-Meantone ends, Napoli-Pythagorean begins
−
|-
−
|
−
|19\66
−
|
−
|<u>201.769…</u>
−
|''201.{{Overline|51}}''
−
|19
−
|9
−
|2.111
−
|
−
|-
−
|
−
|17\59
−
|
−
|<u>201.980…</u>
−
|''201.694…''
−
|17
−
|8
−
|2.125
−
|
−
|-
−
|
−
|15\52
−
|
−
|<u>202.247…</u>
−
|''201.923…''
−
|15
−
|7
−
|2.143
−
|
−
|-
−
|
−
|13\45
−
|
−
|<u>202.597…</u>
−
|''202.{{Overline|2}}''
−
|13
−
|6
−
|2.167
−
|
−
|-
−
|
−
|11\38
−
|
−
|<u>203.076…</u>
−
|''202.631…''
−
|11
−
|5
−
|2.200
−
|
−
|-
−
|
−
|9\31
−
|
−
|<u>203.773…</u>
−
|''203.225…''
−
|9
−
|4
−
|2.250
−
|
−
|-
−
|
−
|7\24
−
|
−
|<u>204.878…</u>
−
|''204.1{{Overline|6}}''
−
|7
−
|3
−
|2.333
−
|
−
|-
−
|
−
|
−
|12\41
−
|<u>205.714…</u>
−
|''204.878…''
−
|12
−
|5
−
|2.400
−
|
−
|-
−
|
−
|5\17
−
|
−
|<u>206.896…</u>
−
|''205.882…''
−
|5
−
|2
−
|2.500
−
|Napoli-Neogothic heartland is from here…
−
|-
−
|
−
|
−
|18\61
−
|<u>207.692…</u>
−
|''206.557…''
−
|18
−
|7
−
|2.571
−
|
−
|-
−
|
−
|
−
|13\44
−
|<u>208</u>
−
|''206.8̄1̄''
−
|13
−
|5
−
|2.600
−
|
−
|-
−
|
−
|8\27
−
|
−
|<u>208.695…</u>
−
|''207.4̄0̄7̄''
−
|8
−
|3
−
|2.667
−
|…to here
−
|-
−
|
−
|11\37
−
|
−
|<u>209.523…</u>
−
|''208.1̄0̄8̄''
−
|11
−
|4
−
|2.750
−
|
−
|-
−
|
−
|14\47
−
|
−
|<u>210</u>
−
|''208.510…''
−
|14
−
|5
−
|2.800
−
|
−
|-
−
|
−
|17\57
−
|
−
|<u>210.309…</u>
−
|''208.771…''
−
|17
−
|6
−
|2.833
−
|
−
|-
−
|
−
|20\67
−
|
−
|<u>210.526…</u>
−
|''208.955…''
−
|20
−
|7
−
|2.857
−
|
−
|-
−
|
−
|23\77
−
|
−
|<u>210.687…</u>
−
|''209.{{Overline|09}}''
−
|23
−
|8
−
|2.875
−
|
−
|-
−
|3\10
−
|
−
|
−
|<u>211.764…</u>
−
|''210''
−
|3
−
|1
−
|3.000
−
|Napoli-Pythagorean ends, Napoli-Superpyth begins
−
|-
−
|
−
|22\73
−
|
−
|<u>212.903…</u>
−
|''210.958…''
−
|22
−
|7
−
|3.143
−
|
−
|-
−
|
−
|19\63
−
|
−
|<u>213.084…</u>
−
|''211.{{Overline|1}}''
−
|19
−
|6
−
|3.167
−
|
−
|-
−
|
−
|16\53
−
|
−
|<u>213.{{Overline|3}}</u>
−
|''211.320…''
−
|16
−
|5
−
|3.200
−
|
−
|-
−
|
−
|13\43
−
|
−
|<u>213.698…</u>
−
|''211.627…''
−
|13
−
|4
−
|3.250
−
|
−
|-
−
|
−
|10\33
−
|
−
|<u>214.285…</u>
−
|''212.{{Overline|12}}''
−
|10
−
|3
|3
|3.667
−
|3.333
−
|
|
−
|-
|-
|15\49
−
|216.867
|
|15
|4
−
|3.750
|7\23
−
|
|
−
|<u>215.384…</u>
−
|''213.043…''
−
|7
−
|2
−
|3.500
−
|
−
|-
|-
|19\62
−
|217.143
|
|19
|5
−
|3.800
|11\36
−
|
−
|<u>216.393…</u>
−
|''213.{{Overline|3}}''
−
|11
−
|3
−
|3.667
−
|
−
|-
−
|
|
−
|15\49
−
|
−
|<u>216.867…</u>
−
|''214.285…''
−
|15
−
|4
−
|3.750
−
|
−
|-
|-
−
|4\13
|4\13
|218.182
−
|
−
|
−
|<u>218.{{Overline|18}}</u>
−
|''215.385…''
−
|4
|4
−
|1
|1
−
|4.000
|4.000
−
|
|
−
|-
|-
−
|
−
|13\42
|13\42
|219.718
−
|
−
|<u>219.718…</u>
−
|''216.{{Overline|6}}''
−
|13
|13
−
|3
|3
−
|4.333
|4.333
−
|
|
−
|-
|-
−
|
−
|9\29
|9\29
|220.408
−
|
−
|<u>220.408…</u>
−
|''217.241…''
−
|9
|9
−
|2
|2
−
|4.500
|4.500
−
|
|
−
|-
|-
−
|
−
|14\45
|14\45
|221.053
−
|
−
|<u>221.052…</u>
−
|''217.{{Overline|7}}''
−
|14
|14
−
|3
|3
−
|4.667
|4.667
−
|
|
−
|-
|-
−
|5\16
|5\16
|222.222
−
|
−
|
−
|<u>222.{{Overline|2}}</u>
−
|''218.75''
−
|5
|5
−
|1
|1
−
|5.000
|5.000
|Napoli-Archy ends
−
|Napoli-Superpyth ends
−
|-
−
|
−
|16\51
−
|
−
|<u>223.255…</u>
−
|''219.607…''
−
|16
−
|3
−
|5.333
−
|
−
|-
|-
−
|
−
|11\35
|11\35
|223.728
−
|
−
|<u>223.728…</u>
−
|''220''
−
|11
|11
−
|2
|2
−
|5.500
|5.500
−
|
|
−
|-
|-
−
|
−
|17\54
|17\54
|224.176
−
|
−
|<u>224.175…</u>
−
|''220.{{Overline|370}}''
−
|17
|17
−
|3
|3
−
|5.667
|5.667
−
|
|
−
|-
|-
−
|6\19
|6\19
|225.000
−
|
−
|
−
|<u>225</u>
−
|''221.052…''
−
|6
|6
−
|1
|1
−
|6.000
|6.000
−
|
|
−
|-
|-
−
|1\3
|1\3
|240.000
−
|
−
|
−
|<u>240</u>
−
|''233.{{Overline|3}}''
−
|1
|1
−
|0
|0
−
|→ inf
|→ inf
−
|Paucitonic
|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)"