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{{Infobox MOS
'''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.


| 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 4 main ways to notate the angel scale. One method uses a simple sesquitave (fifth) repeating notation consisting of 4 naturals (eg. Do Re Mi Fa, Sol La Si Do). Given that 1-5/4-5/3 is fifth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate angel scales as repeating at the double, triple or quadruple sesquitave (major ninth, thirteenth or seventeenth i. e. ~pentave), 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] or an ~pentave which is the Mixolydian mode of Hextone[12L 4s]. Since there are exactly 8 naturals in double sesquitave notation, 12 in triple sesquitave notation and 16 in quadruple sesquitave notation, letters A-H (FGABHCDEF) or dozenal or hex digits (0123456789XE0 or D1234567FGACD with flats written C molle or 0123456789ABCDEF0 or G123456789ABCDEFG with flats written F 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 31: Line 17:
Cents
Cents
 
 
! colspan="4" |Notation
! Notation
 
 
!Supersoft
!Supersoft
Line 50: Line 36:
 
 
!Diatonic
!Diatonic
!Napoli
!Bijou
!Hextone
!~15edf
!~15edf
 
 
Line 71: Line 52:
|-
|-
 
 
|Do#, Sol#
|Do#, Fa#, Sol#
|1\15, 46.154
 
 
|F#
|1\11, 63.158
 
 
|0#, D#
|2\18, 77.419
|0#, G#
|1\15
 
 
46.153…
| rowspan="2" | 1\7, 100
 
 
|1\11
|3\17, 124.138
 
 
63.157…
|2\10, 141.176
 
 
|2\18
|3\13, 163.636
 
 
77.419…
|-
 
 
| rowspan="2" |1\7
|Reb, Solb, Lab
|3\15, 138.462
 
 
100
|2\11. 126.316
 
 
|3\17
|3\18, 116.129
 
 
124.137…
|2\17, 82.759
 
 
|2\10
|1\10, 70.588
141.176…
 
 
|3\13
|1\13, 54.545
163.{{Overline|63}}
 
 
|-
|-
 
 
|Reb, Lab
|'''Re, Sol, La'''
|'''4\15,''' '''184.615'''
 
 
|Gb
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
 
 
|1b, 1c
|'''2\7,''' '''200'''
|1f
|3\15
 
 
138.461…
|'''5\17,''' '''206.897'''
 
 
|2\11
|'''3\10,''' '''211.765'''
 
 
126.315…
|'''4\13,''' '''218.182'''
 
 
|3\18
|-
 
 
116.129…
|Re#, Sol#, La#
|5\15, 230.769
 
 
|2\17
|4\11, 252.632
 
 
82.758…
|7\18, 270.968
 
 
|1\10
| rowspan="2" | 3\7, 300
 
 
70.588…
|8\17, 331.034
 
 
|1\13
|5\10, 352.941
 
 
54.{{Overline|54}}
|7\13, 381.818
 
 
|-
|-
 
 
|'''Re, La'''
|Mib, Lab, Sib
|7\15, 323.077
 
 
|'''G'''
|5\11, 315.789
 
 
|'''1'''
|8\18, 309.677
|'''1'''
 
 
|'''4\15'''
|7\17, 289.655
 
 
'''184.615…'''
|4\10, 282.353
 
 
|'''3\11'''
|5\13, 272.727
 
 
'''189.473…'''
|-
|'''5\18'''
 
 
'''193.548…'''
|Mi, La, Si
|8\15, 369.231
 
 
|'''2\7'''
|6\11, 378.947
 
 
'''200'''
|10\18, 387.097
 
 
|'''5\17'''
|4\7, 400
 
 
'''206.896…'''
|10\17, 413.793
 
 
|'''3\10'''
|6\10, 423.529
 
 
'''211.764…'''
|8\13, 436.364
|'''4\13'''
'''218.{{Overline|18}}'''
 
 
|-
|-
 
 
|Re#, La#
|Mi#, La#, Si#
|9\15, 415.385
 
 
|G#
| rowspan="2" | 7\11, 442.105
 
 
|1#
|12\18, 464.516
|1#
|5\15
 
 
230.769…
|5\7, 500
 
 
|4\11
|13\17, 537.069
 
 
252.631…
|8\10, 564.706
 
 
|7\18
|11\13, 600
 
 
270.967…
|-
 
 
| rowspan="2" |3\7
|Fab, Sibb, Dob
|10\15, 461.538
 
 
300
|11\18, 425.806
 
 
|8\17
|4\7, 400
 
 
331.034…
|9\17, 372.414
 
 
|5\10
|5\10, 352.941
 
 
352.941…
|6\13, 327.273
 
 
|7\13
|-
 
 
381.{{Overline|81}}
|'''Fa, Sib, Do'''
|'''11\15,''' '''507.692'''
 
 
|-
|'''8\11,''' '''505.263'''
 
 
|Mib, Sib
|'''13\18,''' '''503.226'''
 
 
|Ab
|'''5\7, 500'''
 
 
|2b, 2c
|'''12\17,''' '''496.552'''
|2f
|7\15
 
 
323.076…
|'''7\10,''' '''494.118'''
 
 
|5\11
|'''9\13,''' '''490.909'''
 
 
315.789…
|-
 
 
|8\18
|Fa#, Si, Do#
|12\15, 553.846
 
 
309.677…
|9\11, 568.421
 
 
|7\17
|15\18, 580.645
 
 
289.655…
|6\7, 600
 
 
|4\10
|15\17, 620.690
 
 
282.352…
|9\10, 635.294
 
 
|5\13
|12\13, 654.545
272.{{Overline|72}}
 
 
|-
|-
|Fax, Si#, Dox
|13\15, 600
 
 
|Mi, Si
| rowspan="2" | 10\11, 631.579
 
 
|A
|17\18, 658.064
 
 
|2
|7\7, 700
|2
|8\15
 
 
369.230…
|18\17, 744.828
 
 
|6\11
|11\10, 776.471
 
 
378.947…
|15\13, 818.182
 
 
|10\18
|-
 
 
387.096…
|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
 
 
|4\7
|-
 
 
400
!Do, Fa, Sol
!'''15\15,''' '''692.308'''
 
 
|10\17
!'''11\11,''' '''694.737'''
 
 
413.793…
!'''18\18,''' '''696.774'''
 
 
|6\10
!7\7, 700
 
 
423.529…
!'''17\17,''' '''703.448'''
 
 
|8\13
!'''10\10,''' '''705.882'''
 
 
436.{{Overline|36}}
!'''13\13,''' '''709.091'''
 
 
|-
|}
 
 
|Mi#, Si#
{| class="wikitable"
 
 
|A#
|+
 
 
|2#
Cents
|2#
!Notation
|9\15
!Supersoft
 
 
415.384…
! Soft
 
 
| rowspan="2" |7\11
!Semisoft
 
 
442.105…
!Basic
 
 
|12\18
!Semihard
 
 
464.516…
! Hard
 
 
|5\7
! Superhard
 
 
500
|-
 
 
|13\17
!Napoli
! ~15edf
 
 
537.931…
! ~11edf
 
 
|8\10
!~18edf
!~7edf
 
 
564.705…
!~17edf
 
 
|11\13
!~10edf
 
 
600
!~13edf
 
 
|-
|-
 
 
|Fab, Dob
|F#
|1\15, 46.154
 
 
|Bbb
|1\11, 63.158
 
 
|3b, 3c
| 2\18, 77.419
|3f
|10\15
 
 
461.538…
| rowspan="2" |1\7, 100
 
 
|11\18
|3\17, 124.138
 
 
425.806…
| 2\10, 141.176
 
 
|4\7
|3\13, 163.636
 
 
400
|-
 
 
|9\17
| Gb, Ge
|3\15, 138.462
 
 
372.413…
| 2\11. 126.316
 
 
|5\10
|3\18, 116.129
 
 
352.941…
|2\17, 82.759
 
 
|6\13
|1\10, 70.588
 
 
327.{{Overline|27}}
|1\13, 54.545
 
 
|-
|-
 
 
|'''Fa, Do'''
|'''G'''
|'''4\15,''' '''184.615'''
 
 
|'''Bb'''
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
 
 
|'''3'''
|'''2\7,''' '''200'''
|'''3'''
 
 
|'''11\15'''
|'''5\17,''' '''206.897'''
 
 
'''507.692…'''
|'''3\10,''' '''211.765'''
 
 
|'''8\11'''
|'''4\13,''' '''218.182'''
 
 
'''505.263…'''
|-
 
 
|'''13\18'''
|G#
|5\15, 230.769
 
 
'''503.225…'''
|4\11, 252.632
 
 
|'''5\7'''
|7\18, 270.968
 
 
'''500'''
| rowspan="2" |3\7, 300
 
 
|'''12\17'''
| 8\17, 331.034
 
 
'''496.551…'''
|5\10, 352.941
 
 
|'''7\10'''
|7\13, 381.818
 
 
'''494.117…'''
|-
 
 
|'''9\13'''
|Ab, Æ
|7\15, 323.077
 
 
'''490.{{Overline|90}}'''
|5\11, 315.789
 
 
|-
|8\18, 309.677
 
 
|Fa#, Do#
|7\17, 289.655
 
 
|B
|4\10, 282.353
 
 
|3#
|5\13, 272.727
|3#
|12\15
 
 
553.846…
|-
 
 
|9\11
|A
| 8\15, 369.231
568.421…
 
 
|15\18
|6\11, 378.947
 
 
580.645…
|10\18, 387.097
 
 
|6\7
| 4\7, 400
 
 
600
|10\17, 413.793
 
 
|15\17
|6\10, 423.529
 
 
620.689…
|8\13, 436.364
 
 
|9\10
|-
 
 
635.294…
|A#
| 9\15, 415.385
 
 
|12\13
| rowspan="2" |7\11, 442.105
 
 
654.{{Overline|54}}
|12\18, 464.516
 
 
|-
|5\7, 500
|Fax, Dox
 
 
|B#
|13\17, 537.069
 
 
|3x
|8\10, 564.706
|3x
|13\15
 
 
600
|11\13, 600
 
 
| rowspan="2" |10\11
|-
 
 
631.578…
|Bbb, Bee
|10\15, 461.538
 
 
|17\18
|11\18, 425.806
 
 
658.064…
|4\7, 400
 
 
|7\7
|9\17, 372.414
 
 
700
| 5\10, 352.941
 
 
|18\17
|6\13, 327.273
 
 
744.827…
|-
 
 
|11\10
|'''Bb, Be'''
|'''11\15,''' '''507.692'''
 
 
776.470…
|'''8\11,''' '''505.263'''
 
 
|15\13
|'''13\18,''' '''503.226'''
 
 
818.{{Overline|18}}
|'''5\7, 500'''
 
 
|-
|'''12\17,''' '''496.552'''
 
 
|Dob, Solb
|'''7\10,''' '''494.118'''
|Hb
| 4b, 4c
|4f
|14\15
646.153…
|16\18
619.354…
|6\7
600
|14\17
579.310…
|8\10
564.705…
|10\13
 
 
545.{{Overline|45}}
|'''9\13,''' '''490.909'''
 
 
|-
|-
 
 
!Do, Sol
|B
|12\15, 553.846
 
 
!H
|9\11, 568.421
 
 
!4
|15\18, 580.645
!4
!'''15\15'''
 
 
'''692.307…'''
|6\7, 600
 
 
!'''11\11'''
| 15\17, 620.690
'''694.736…'''
 
 
!'''18\18'''
|9\10, 635.294
 
 
'''696.774…'''
|12\13, 654.545
 
 
!'''7\7'''
|-
| B#
| 13\15, 600
 
 
'''700'''
| rowspan="2" |10\11, 631.579
 
 
!'''17\17'''
|17\18, 658.064
 
 
'''703.448…'''
|7\7, 700
 
 
!'''10\10'''
|18\17, 744.828
 
 
'''705.882…'''
|11\10, 776.471
 
 
!'''13\13'''
|15\13, 818.182
 
 
'''709.'''{{Overline|09}}
|-
|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
!'''15\15,''' '''692.308'''
 
 
|Η#
!'''11\11,''' '''694.737'''
 
 
|4#
!'''18\18,''' '''696.774'''
|4#
|16\15
 
 
738.461…
! 7\7, 700
 
 
|12\11
!'''17\17,''' '''703.448'''
 
 
757.894…
!'''10\10,''' '''705.882'''
 
 
| 20\18
!'''13\13,''' '''709.091'''
 
 
774.193…
|-
 
 
| rowspan="2" | 8\8
|Η#
|16\15, 738.462
800
 
 
|20\17
|12\11, 757.895
 
 
827.586…
|20\18, 774.194
 
 
|12\10
| rowspan="2" |8\8, 800
 
 
847.058…
|20\17, 827.586
 
 
| 16\13
|12\10, 847.059
 
 
872.{{Overline|72}}
|16\13, 872.727
 
 
|-
|-
 
 
|Reb, Lab
|Cb, Ce
|18\15, 830.769
 
 
|Cb
|13\11, 821.053
 
 
|5b, 5c
|21\18, 812.903
|5
|18\15
 
 
830.769…
|19\17, 786.207
 
 
|13\11
|11\10, 776.471
 
 
821.052…
|14\13, 763.63
 
 
| 21\18
|-
 
 
812.903…
|'''C'''
|'''19\15,''' '''876.923'''
 
 
| 19\17
|'''14\11,''' '''884.211'''
 
 
786.206…
|'''23\18,''' '''890.323'''
 
 
| 11\10
|'''9\5,''' '''900'''
 
 
776.470…
|'''22\17,''' '''910.345'''
 
 
| 14\13
|'''13\10,''' '''917.647'''
 
 
763.{{Overline|63}}
|'''17\13,''' '''927.273'''
 
 
|-
|-
 
 
|'''Re, La'''
|C#
|20\15, 923.077
 
 
|'''C'''
|15\11, 947.368
 
 
|'''5'''
|25\18, 967.742
|'''5'''
 
 
|'''19\18'''
| rowspan="2" |10\7, 1000
 
 
'''876.923…'''
|25\17, 1034.483
 
 
|'''14\11'''
|15\10, 1058.824
 
 
'''884.210…'''
|20\13, 1090.909
 
 
|'''23\18'''
|-
 
 
'''890.322…'''
| Db, De
|22\15, 1015.385
 
 
|'''9\5'''
|16\11, 1010.526
 
 
'''900'''
|26\18, 1006.452
 
 
|'''22\17'''
|24\17, 993.103
 
 
'''910.344…'''
|14\10, 988.235
 
 
|'''13\10'''
|18\13, 981.818
'''917.647…'''
|'''17\13'''
'''927.{{Overline|27}}'''
 
 
|-
|-
 
 
| Re#, La#
|D
|23\15, 1061.538
 
 
|C#
|17\11, 1073.684
 
 
| 5#
|28\18, 1083.871
|5#
|20\15
 
 
923.076…
|11\7, 1100
 
 
|15\11
|27\17, 1117.241
 
 
947.368…
|16\10, 1129.412
 
 
|25\18
|21\9, 1145.455
 
 
967.741…
|-
 
 
| rowspan="2" |10\7
|D#
|24\15, 1107.923
 
 
1000
| rowspan="2" |18\11, 1136.842
 
 
|25\17
|30\18, 1161.29
 
 
1034.482…
|12\7, 1200
 
 
| 15\10
|30\17, 1241.379
 
 
1058.823…
|18\10, 1270.588
 
 
|20\13
|24\13, 1309.091
1090.{{Overline|90}}
 
 
|-
|-
 
 
|Mib, Sib
|Ebb, Ëe
|25\15, 1153.846
 
 
|Db
|29\18, 1122.581
 
 
|6b, 6c
|11\7, 1100
|6f
|22\15
 
 
1015.384…
|26\17, 1075.862
 
 
|16\11
|15\10, 1058.824
 
 
1010.526…
| 19\13, 1036.364
 
 
| 26\18
|-
 
 
1006.451…
|'''Eb, Ë'''
|'''26\15,''' '''1200'''
 
 
|24\17
|'''19\11,''' '''1200'''
 
 
993.103…
|'''31\18,''' '''1200'''
 
 
|14\10
|'''12\7, 1200'''
 
 
988.235…
|'''29\17,''' '''1200'''
 
 
|18\13
|'''17\10,''' '''1200'''
 
 
981.{{Overline|81}}
|'''22\13,''' '''1200'''
 
 
|-
|-
 
 
|Mi, Si
|E
|27\15, 1246.154
 
 
|D
|20\11, 1263.158
 
 
|6
|33\18, 1277.419
|6
|23\15
 
 
1061.538…
|13\7, 1300
 
 
|17\11
|32\17, 1324.138
 
 
1073.684…
|19\10, 1341.176
 
 
| 28\18
|25\13, 1363.636
 
 
1083.870…
|-
 
 
|11\7
|E#
|28\15, 1292.308
1100
 
 
| 27\17
| rowspan="2" |21\11, 1326.318
 
 
1117.241…
|35\18, 1354.834
 
 
| 16\10
|14\7, 1400
 
 
1129.411…
|35\17, 1448.275
 
 
| 21\9
| 21\10, 1482.353
 
 
1145.{{Overline|45}}
|28\13, 1527.273
 
 
|-
|-
 
 
|Mi#, Si#
| Fb, Fe
|29\15, 1338.462
| D#
|6#
|6#
| 24\15
1107.692…
| rowspan="2" | 18\11
1136.842…
 
 
|30\18
|34\18, 1316.129
 
 
1161.290…
|13\7, 1300
 
 
| 12\7
|31\17, 1282.759
 
 
1200
|18\10, 1270.588
 
 
|30\17
|23\13, 1254.545
1241.379…
|18\10
1270.588…
|24\13
1309.{{Overline|09}}
 
 
|-
|-
 
 
|Fab, Dob
!F
!30\15, 1384.615
 
 
|Ebb
!22\11, 1389.473
 
 
|7b, 7c
!36\18, 1393.548
|7f
|25\15
 
 
1153.846…
!14\7, 1400
 
 
|29\18
!34\17, 1406.897
 
 
1122.580…
!20\10, 1411.765
| 11\7
1100
|26\17
1075.862…
|15\10
1058.823…
|19\13
1036.{{Overline|36}}
 
 
!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#
|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
|-
|-
|1b, 1c
|'''Fa, Do'''
|3\15, 138.462
| 2\11. 126.316
|'''Eb'''
|3\18, 116.129
|2\17, 82.759
|'''7'''
|1\10, 70.588
|'''7'''
|1\13, 54.545
|-
|'''26\15'''
|'''1'''
|'''4\15,''' '''184.615'''
'''1200'''
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
|'''19\11'''
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
'''1200'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|'''31\18'''
|-
|1#
'''1200'''
|5\15, 230.769
|4\11, 252.632
|'''12\7'''
|7\18, 270.968
| rowspan="2" |3\7, 300
'''1200'''
|8\17, 331.034
|5\10, 352.941
|'''29\17'''
|7\13, 381.818
|-
'''1200'''
|2b, 2c
|7\15, 323.077
|'''17\10'''
|5\11, 315.789
| 8\18, 309.677
'''1200'''
| 7\17, 289.655
|4\10, 282.353
|'''22\13'''
|5\13, 272.727
|-
'''1200'''
|2
|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
|-
|-
|2#
|Fa#, Do#
| 9\15, 415.385
| rowspan="2" |7\11, 442.105
| E
|12\18, 464.516
|5\7, 500
|7#
|13\17, 537.069
|7#
|8\10, 564.706
|27\15
|11\13, 600
|-
1246.153…
|3b, 3c
| 10\15, 461.538
|20\11
| 11\18, 425.806
|4\7, 400
1263.157…
|9\17, 372.414
|5\10, 352.941
| 33\18
|6\13, 327.273
|-
1277.419…
|'''3'''
|'''11\15,''' '''507.692'''
|13\7
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
1300
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|32\17
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
1324.137…
|-
|3#
|19\10
|12\15, 553.846
|9\11, 568.421
1341.176…
|15\18, 580.645
|6\7, 600
|25\13
|15\17, 620.690
|9\10, 635.294
1363.{{Overline|63}}
|12\13, 654.545
|-
|3x
|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
|-
|-
|4b, 4c
|Fax, Dox
|14\15, 646.154
|16\18, 619.355
|E#
|6\7, 600
|14\17, 579.310
|7x
|8\10, 564.706
|7x
|10\13, 545.455
|28\15
|-
!4
1292.307…
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
| rowspan="2" |21\11
!'''18\18,''' '''696.774'''
!7\7, 700
1326.315…
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
|35\18
!'''13\13,''' '''709.091'''
|-
1354.838…
|4#
| 16\15, 738.462
| 14\7
|12\11, 757.895
|20\18, 774.194
1400
| rowspan="2" |8\8, 800
|20\17, 827.586
|35\17
|12\10, 847.059
| 16\13, 872.727
1448.275…
|-
|5b, 5c
|21\10
|18\15, 830.769
|13\11, 821.053
1482.352…
|21\18, 812.903
|19\17, 786.207
|28\13
|11\10, 776.471
|14\13, 763.63
1527.{{Overline|27}}
|-
|-
|'''5'''
|Dob, Solb
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
|Fb
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
|8b, Fc
|'''22\17,''' '''910.345'''
|8f
|'''13\10,''' '''917.647'''
|29\15
|'''17\13,''' '''927.273'''
|-
1338.461…
|5#
|20\15, 923.077
|34\18
|15\11, 947.368
|25\18, 967.742
1316.129…
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|13\7
|15\10, 1058.824
|20\13, 1090.909
1300
|-
|6b, 6c
|31\17
|22\15, 1015.385
|16\11, 1010.526
1282.758…
|26\18, 1006.452
|24\17, 993.103
|18\10
|14\10, 988.235
|18\13, 981.818
1270.588…
|-
|6
| 23\13
|23\15, 1061.538
|17\11, 1073.684
1254.{{Overline|54}}
| 28\18, 1083.871
|11\7, 1100
|27\17, 1117.241
|16\10, 1129.412
|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
!Do, Sol
|25\15, 1153.846
|29\18, 1122.581
!F
|11\7, 1100
|26\17, 1075.862
! 8, F
|15\10, 1058.824
!8
|19\13, 1036.364
! 30\15
|-
|'''7'''
1384.615…
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
! 22\11
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
1389.473…
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
!36\18
|'''22\13,''' '''1200'''
|-
1393.548…
|7#
|27\15, 1246.154
!14\7
|20\11, 1263.158
|33\18, 1277.419
1400
|13\7, 1300
|32\17, 1324.138
! 34\17
|19\10, 1341.176
|25\13, 1363.636
1406.896…
|-
|7x
! 20\10
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
1411.764…
|35\18, 1354.834
|14\7, 1400
!26\13
|35\17, 1448.275
|21\10, 1482.353
1418.{{Overline|18}}
|28\13, 1527.273
|-
|8b, Fc
|29\15, 1338.462
|34\18, 1316.129
|13\7, 1300
|31\17, 1282.759
|18\10, 1270.588
|23\13, 1254.545
|-
!8, F
!30\15, 1384.615
!22\11, 1389.473
!36\18, 1393.548
!14\7, 1400
!34\17, 1406.897
!20\10, 1411.765
!26\13, 1418.182
|-
|-
|Do#, Sol#
|F#
|8#, F#
|8#, F#
|8#
|31\15, 1430.769
|31\15
|23\11, 1452.632
|38\18, 1470.968
1430.769…
| rowspan="2" |15\7, 1500
|37\17, 1531.034
| 23\11
|22\10, 1552.941
|29\13, 1581.818
1452.631…
|-
|9b, Gc
|38\18
|33\15, 1523.077
|24\11, 1515.789
1470.967…
|39\18, 1509.677
|36\17, 1489.655
| rowspan="2" |15\7
|21\10, 1482.759
|27\13, 1472.273
1500
|-
|'''9, G'''
| 37\17
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
1531.034…
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
| 22\10
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
1552.941…
|'''30\13,''' '''1636.364'''
|-
|29\13
|9#, G#
|35\15, 1615.385
1581.{{Overline|81}}
|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
|37\15, 1707.692
|27\11, 1705.263
|44\18, 1703.226
|41\17, 1696.552
|24\10, 1694.118
|31\13, 1690.909
|-
|-
|X, A
| Reb, Lab
|38\15, 1753.846
|28\11, 1768.421
|Gb
|46\18, 1780.645
|18\7, 1800
|9b, Gc
|44\17, 1820.690
|9f
|26\10, 1835.294
|33\15
|34\13, 1854.545
|-
1523.076…
|X#, A#
|39\15, 1800
|24\11
| rowspan="2" |29\11, 1831.579
|48\18, 1858.064
1515.789…
|19\7, 1900
|47\17, 1944.828
| 39\18
|28\10, 1976.471
|37\13, 2018.182
1509.677…
|-
|Ebb, Ccc
|36\17
|40\15, 1846.154
|47\18, 1819.355
1489.655…
|18\7, 1800
|43\17, 1779.310
|21\10
|25\10, 1764.706
|32\13, 1745.545
1482.352…
|-
|'''Eb, Cc'''
|27\13
|'''41\15,''' '''1892.308'''
|'''30\11,''' '''1894.737'''
1472.{{Overline|72}}
|'''49\18,''' '''1896.774'''
|'''19\7, 1900'''
|'''46\17,''' '''1903.448'''
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
|-
|E, C
|42\15, 1938.462
|31\11, 1957.895
|51\18, 1974.194
|20\7, 2000
|49\17, 2027.586
|29\10, 2047.059
|38\13, 2072.727
|-
|-
|Ex, Cx
|'''Re, La'''
|43\15, 1984.615
| rowspan="2" |32\11, 2021.053
|'''G'''
|53\18, 2051.612
|21\7, 2100
|'''9, G'''
|52\17, 2151.725
|9
|31\10, 2188.235
|'''34\15'''
|41\13, 2236.364
|-
'''1569.230…'''
|0b, Dc
|44\15, 2030.769
|'''25\11'''
|52\18, 2012.903
|20\7, 2000
'''1578.947…'''
|48\17, 1986.207
|28\10, 1976.471
|'''41\18'''
|36\13, 1963.636
'''1587.096…'''
|'''16\7'''
'''1600'''
|'''39\17'''
'''1613.793…'''
|'''23\10'''
'''1623.529…'''
|'''30\13'''
'''1636.{{Overline|36}}'''
|-
|-
! 0, D
|Re#, La#
!45\15, 2076.923
!33\11, 2084.211
|G#
!54\18, 2090.323
!21\7, 2100
|9#, G#
!51\17, 2110.345
|9#
!30\10, 2117.647
|35\15
!39\13, 2127.273
|}
1615.384…
 
{| class="wikitable"
|26\11
|+Cents
!Notation
1642.105…
!Supersoft
!Soft
| 43\18
!Semisoft
! Basic
1664.516…
!Semihard
!Hard
| rowspan="2" | 17\7
!Superhard
1700
|42\17
1737.931…
|25\10
1764.705…
|33\13
1800
|-
|-
!Hextone
|Mib, Sib
!~15edf
!~11edf
|Ab
!~18edf
!~7edf
|Xb, Ac
!~17edf
|Af
!~10edf
|37\15
!~13edf
|-
1707.692…
|0#, G#
|1\15, 46.154
|27\11
|1\11, 63.158
|2\18, 77.419
1705.263…
| rowspan="2" |1\7, 100
|3\17, 124.138
|44\18
|2\10, 141.176
|3\13, 163.636
1703.225…
|-
| 1f
|41\17
|3\15, 138.462
|2\11. 126.316
1696.551…
|3\18, 116.129
|2\17, 82.759
|24\10
|1\10, 70.588
|1\13, 54.545
1694.117…
|-
|'''1'''
|31\13
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
1690.{{Overline|90}}
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|-
|1#
|Mi, Si
|5\15, 230.769
|4\11, 252.632
|A
|7\18, 270.968
| rowspan="2" |3\7, 300
|X, A
|8\17, 331.034
|A
|5\10, 352.941
|38\15
|7\13, 381.818
|-
1753.846…
|2f
|7\15, 323.077
|28\11
|5\11, 315.789
|8\18, 309.677
1768.421…
|7\17, 289.655
|4\10, 282.353
|46\18
|5\13, 272.727
|-
1780.645…
|2
|8\15, 369.231
|18\7
|6\11, 378.947
|10\18, 387.097
1800
| 4\7, 400
|10\17, 413.793
|44\17
|6\10, 423.529
|8\13, 436.364
1820.689…
|-
|2#
|26\10
|9\15, 415.385
| rowspan="2" |7\11, 442.105
1835.294…
|12\18, 464.516
|5\7, 500
|34\13
|13\17, 537.069
|8\10, 564.706
1854.{{Overline|54}}
|11\13, 600
|-
|-
|3f
|Mi#, Si#
| 10\15, 461.538
|11\18, 425.806
| A#
|4\7, 400
|9\17, 372.414
|X#, A#
|5\10, 352.941
|A#
|6\13, 327.273
|39\15
|-
|'''3'''
1800
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
| rowspan="2" |29\11
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
1831.578…
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|48\18
|'''9\13,''' '''490.909'''
|-
1858.064…
|3#
|12\15, 553.846
|19\7
|9\11, 568.421
|15\18, 580.645
1900
|6\7, 600
|15\17, 620.690
|47\17
|9\10, 635.294
|12\13, 654.545
1944.827…
|-
| 3x
|28\10
|13\15, 600
| rowspan="2" | 10\11, 631.579
1976.470…
|17\18, 658.064
|7\7, 700
| 37\13
|18\17, 744.828
|11\10, 776.471
2018.{{Overline|18}}
|15\13, 818.182
|-
|4f
| 14\15, 646.154
|16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
|-
|-
!4
|Fab, Dob
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
|Bbb
!'''18\18,''' '''696.774'''
!7\7, 700
|Ebb, Ccc
!'''17\17,''' '''703.448'''
|Bf
!'''10\10,''' '''705.882'''
|40\15
!'''13\13,''' '''709.091'''
|-
1846.153…
| 4#
|16\15, 738.462
|47\18
|12\11, 757.895
|20\18, 774.194
1819.354…
| rowspan="2" |8\8, 800
|20\17, 827.586
| 18\7
|12\10, 847.059
|16\13, 872.727
1800
|-
|5
|43\17
|18\15, 830.769
|13\11, 821.053
1779.310…
|21\18, 812.903
|19\17, 786.207
|25\10
| 11\10, 776.471
|14\13, 763.63
1764.705…
|-
|'''5'''
| 32\13
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
1745.{{Overline|45}}
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
|-
|5#
|20\15, 923.077
|15\11, 947.368
| 25\18, 967.742
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|15\10, 1058.824
|20\13, 1090.909
|-
|-
|6f
|'''Fa, Do'''
|22\15, 1015.385
|16\11, 1010.526
|'''Bb'''
|26\18, 1006.452
|24\17, 993.103
|'''Eb, Cc'''
|14\10, 988.235
|'''B'''
|18\13, 981.818
|'''41\15'''
|-
|6
'''1892.307…'''
|23\15, 1061.538
|17\11, 1073.684
|'''30\11'''
|28\18, 1083.871
|11\7, 1100
'''1894.736…'''
|27\17, 1117.241
|16\10, 1129.412
|'''49\18'''
|21\9, 1145.455
|-
'''1896.774…'''
|6#
|24\15, 1107.923
|'''19\7'''
| rowspan="2" |18\11, 1136.842
|30\18, 1161.290
'''1900'''
|12\7, 1200
|30\17, 1241.379
|'''46\17'''
|18\10, 1270.588
|24\13, 1309.091
'''1903.448…'''
|-
| 7f
|'''27\10'''
|25\15, 1153.846
|29\18, 1122.581
'''1905.882…'''
|11\7, 1100
|26\17, 1075.862
|'''35\13'''
|15\10, 1058.824
|19\13, 1036.364
'''1909.{{Overline|09}}'''
|-
|'''7'''
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|7#
|27\15, 1246.154
|20\11, 1263.158
|33\18, 1277.419
|13\7, 1300
|32\17, 1324.138
|19\10, 1341.176
|25\13, 1363.636
|-
|-
|7x
|Fa#, Do#
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
| B
|35\18, 1354.834
|14\7, 1400
|E, C
|35\17, 1448.275
|B#
|21\10, 1482.353
|42\15
|28\13, 1527.273
|-
1938.461…
|8f
|29\15, 1338.462
|31\11
| 34\18, 1316.129
|13\7, 1300
1957.894…
|31\17, 1282.759
|18\10, 1270.588
| 51\18
|23\13, 1254.545
|-
1974.193…
! 8
!30\15, 1384.615
|20\7
!22\11, 1389.473
!36\18, 1393.548
2000
!14\7, 1400
!34\17, 1406.897
|49\17
!20\10, 1411.765
!26\13, 1418.182
2027.586…
|-
|8#
|29\10
|31\15, 1430.769
|23\11, 1452.632
1976.470…
| 38\18, 1470.968
| rowspan="2" |15\7, 1500
|38\13
|37\17, 1531.034
|22\10, 1552.941
2072.{{Overline|72}}
|29\13, 1581.818
|-
|9f
|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
|Fax, Dox
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
|B#
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
|Ex, Cx
|'''39\17,''' '''1613.793'''
|Bx
|'''23\10,''' '''1623.529'''
|43\15
|'''30\13,''' '''1636.364'''
|-
1984.615…
|9#
|35\15, 1615.385
| rowspan="2" |32\11
|26\11, 1642.105
|43\18, 1664.516
2021.052…
| rowspan="2" |17\7, 1700
|42\17, 1737.069
|53\18
|25\10, 1764.706
|33\13, 1800
2051.612…
|-
|Af
|21\7
| 37\15, 1707.692
| 27\11, 1705.263
2100
|44\18, 1703.226
|41\17, 1696.552
|52\17
|24\10, 1694.118
|31\13, 1690.909
2151.724…
|-
|A
|31\10
| 38\15, 1753.846
|28\11, 1768.421
2188.235…
|46\18, 1780.645
|18\7, 1800
|41\13
|44\17, 1820.690
|26\10, 1835.294
2236.{{Overline|36}}
|34\13, 1854.545
|-
|A#
| 39\15, 1800
| rowspan="2" |29\11, 1831.579
| 48\18, 1858.064
|19\7, 1900
|47\17, 1944.828
|28\10, 1976.471
|37\13, 2018.182
|-
|-
|Ax
|Dob, Solb
|40\15, 1846.154
|47\18, 1819.355
|Hb
|18\7, 1800
|43\17, 1779.310
|0b, Dc
|25\10, 1764.706
|Cf
|32\13, 1745.545
|44\15
|-
|'''Bf'''
2030.769…
|'''41\15,''' '''1892.308'''
|'''30\11,''' '''1894.737'''
|52\18
|'''49\18,''' '''1896.774'''
|'''19\7, 1900'''
2012.903…
|'''46\17,''' '''1903.448'''
|'''27\10,''' '''1905.882'''
|20\7
|'''35\13,''' '''1909.091'''
|-
2000
|B
|42\15, 1938.462
|48\17
|31\11, 1957.895
|51\18, 1974.194
1986.206…
|20\7, 2000
|49\17, 2027.586
|28\10
| 29\10, 2047.059
|38\13, 2072.727
1967.470…
|-
|B#
|36\13
|43\15, 1984.615
| rowspan="2" |32\11, 2021.053
1963.{{Overline|63}}
|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
|-
|-
!Do, Sol
!H
!0, D
!C
!C
!45\15
!45\15, 2076.923
!33\11, 2084.211
2076.923…
!54\18, 2090.323
!21\7, 2100
!33\11
!51\17, 2110.345
!30\10, 2117.647
2084.210…
!39\13, 2127.273
|-
!54\18
|C#
|46\15, 2123.077
2090.322…
|34\11, 2147.368
|56\15, 2167.742
!21\7
| rowspan="2" |22\7, 2200
|54\17, 2234.483
2100
|32\10, 2258.824
|42\13, 2090.909
!51\17
|-
2110.344…
!30\10
2117.647…
!39\13
2127.{{Overline|27}}
|-
|Do#, Sol#
|Η#
|0#, D#
|C#
|46\15
2123.076…
|34\11
2147.368…
|56\18
2167.741…
| rowspan="2" |22\7
2200
|54\17
2234.582…
|32\10
2258.823…
|42\13
2090.{{Overline|90}}
|-
|Reb, Lab
|Cb
|1b, 1c
|Df
|Df
|48\15
|48\15, 2215.385
2215.384…
|35\11, 2210.526
|35\11
|57\15, 2206.452
2210.526…
|53\17, 2193.103
|57\18
|31\10, 2188.235
2206.451…
|40\13, 2181.818
|53\17
2193.103…
|31\10
2188.235…
|40\13
2181.{{Overline|81}}
|-
|-
|'''Re, La'''
|'''C'''
|'''1'''
|'''D'''
|'''D'''
|'''49\15'''
|'''49\15, 2261.538'''
'''2261.538…'''
|'''36\11, 1073.684'''
|'''36\11'''
|'''59\18, 2283.871'''
'''2273.684…'''
|'''23\7, 2300'''
|'''59\18'''
|'''56\17, 2317.241'''
'''2283.870…'''
|'''33\10, 2329.412'''
|'''23\7'''
|'''43\13,''' '''2345.455'''
'''2300'''
|'''56\17'''
'''2317.241…'''
|'''33\10'''
'''2329.411…'''
|'''43\13'''
'''2245.{{Overline|45}}'''
|-
|-
|Re#, La#
|C#
|1#
|D#
|D#
|50\15
|50\15, 2307.692
2307.692…
|37\11, 2336.842
|37\11
|61\18, 2361.290
2336.842…
| rowspan="2" |24\7, 2400
|61\18
|59\17, 2441.379
2361.290…
|35\10, 2470.588
| rowspan="2" |24\7
|46\13, 2509.091
2400
|59\17
2441.379…
|35\10
2470.588…
|46\13
2509.{{Overline|09}}
|-
|-
|Mib, Sib
|Db
|2b, 2c
|Ef
|Ef
|52\15
|52\15, 2400
2400
|38\11, 2400
|38\11
|62\18, 2400
2400
|58\17, 2400
|62\18
|34\10, 2400
2400
| 44\13, 2400
|58\17
2400
|34\10
2400
|44\13
2400
|-
|-
|Mi, Si
|D
|2
|E
|E
|53\15
|53\15, 2446.154
2446.153…
| 39\11, 2463.158
|39\11
|64\18, 2477,419
2463.158…
|25\7, 2500
|64\18
|61\17, 2524.138
2477.419…
|36\10, 2541.176
|25\7
|47\13, 2563.636
2500
|61\17
2524.137…
|36\10
2541.176…
|47\13
2563.{{Overline|63}}
|-
|-
|Mi#, Si#
|D#
|2#
|E#
|E#
|54\15
|54\15, 2492.308
2492.307…
| rowspan="2" |40\11, 2526.316
| rowspan="2" |40\11
|66\18, 2554.838
2526.315…
|26\7, 2600
|66\18
|64\17, 2648.275
2554.838…
|38\10, 2682.353
|26\7
|50\13, 2727.273
2600
|64\17
2648.275…
|38\10
2682.352…
|50\13
2727.{{Overline|27}}
|-
|-
|Fab, Dob
|Ebb
|3b, 3c
|Fff
|Fff
|55\15
| 55\15, 2538.462
2538.461…
| 65\18, 2516.129
|65\18
|25\7, 2500
2516.129…
|60\17, 2482.759
|25\7
|35\10, 2470.588
2500
|45\13, 2454.545
|60\17
2482.758…
|35\10
2470.588…
|45\13
2454.{{Overline|54}}
|-
|-
|'''Fa, Do'''
|'''Eb'''
|'''3'''
|'''Ff'''
|'''Ff'''
|'''56\15'''
|'''56\15, 2584.615'''
'''2584.615…'''
|'''41\11, 2589.474'''
|'''41\11'''
|'''67\18, 2593.548'''
'''2589.473…'''
|'''26\7, 2600'''
|'''67\18'''
|'''63\17, 2606.897'''
'''2593.548…'''
|'''37\10, 2611.765'''
|'''26\7'''
|'''48\13,''' '''2618.182'''
'''2600'''
|'''63\17'''
'''2606.896…'''
|'''37\10'''
'''2611.764…'''
|'''48\13'''
'''2618.{{Overline|18}}'''
|-
|-
|Fa#, Do#
|E
|3#
|F
|F
|57\15
|57\15, 2630.769
2630.769…
|42\11, 2652.632
|42\11
|69\18, 2670.968
2652.632…
|27\7, 2700
|69\18
|66\17, 2731.034
2670.967…
|39\10, 2752.941
|27\7
|51\13, 2781.818
2700
|-
|66\17
| F#
2731.034…
| rowspan="2" |58\15, 2676.923
|39\10
|43\11, 2715.789
2752.941…
|71\18, 2748.387
|51\13
| 28\7, 2800
2781.{{Overline|81}}
|69\17, 2855.172
|41\10, 2894.118
|54\13, 2945.455
|-
|-
|Fax, Dox
|0ff, Gff
|E#
|42\11, 2652.632
|3x
|68\18, 2632.258
|F#
|26\7, 2600
|58\15
|62\17, 2565.517
2676.923…
|36\10, 2541.176
| rowspan="2" |43\11
|46\13, 2509.091
2715.789…
|71\18
2748.387…
|28\7
2800
|69\17
2855.168…
|41\10
2894.117…
|54\13
2945.{{Overline|45}}
|-
|-
|Dob, Solb
|Fb
|4b, 4c
|0f, Gf
|0f, Gf
|59\15
|59\15, 2723.077
2723.076…
|43\11, 2715.789
|70\18
|70\18, 2709.677
2709.677…
|27\7, 2700
|27\7
|65\17, 2689.552
2700
|38\10, 2682.353
|65\17
|49\13, 2672.273
2689.655…
|38\10
2682.352…
|49\13
2672.{{Overline|72}}
|-
|-
!Do, Sol
!F
!4
!0, G
!0, G
!60\15
!60\15, 2769.231
2769.230…
!44\11, 2778.947
!44\11
!72\18, 2787.097
2778.947…
!28\7, 2800
!72\18
!68\17, 2813.793
2787.097…
!40\10, 2823.529
!28\7
!52\13, 2836.364
2800
!68\17
2813.793…
!40\10
2823.529…
!52\113
2836.{{Overline|36}}
|}
|}
 
{| class="wikitable"
{| class="wikitable"
|+Relative cents
|+Cents
! colspan="4" | Notation
!Notation
!Supersoft
!Supersoft
!Soft
!Soft
!Semisoft
! Semisoft
!Basic
! Basic
!Semihard
!Semihard
!Hard
!Hard
!Superhard
!Superhard
|-
|-
! Diatonic
!Guidotonic
!Napoli
! Bijou
!Hextone
!~15edf
!~15edf
!~11edf
!~11edf
Line 1,686: Line 1,579:
!~13edf
!~13edf
|-
|-
|Do#, Sol#
|F ut#
|F#
|1\15, 46.154
|0#, D#
|1\11, 63.158
|0#, G#
|2\18, 77.419
|1\15
| rowspan="2" |1\7, 100
|3\17, 124.138
''46.{{Overline|6}}''
|2\10, 141.176
|1\11
|3\13, 163.636
|-
''63.{{Overline|63}}''
|G reb
|2\18
|3\15, 138.462
|2\11. 126.316
''77.7̄''
|3\18, 116.129
| rowspan="2" |1\7
|2\17, 82.759
|1\10, 70.588
''100''
|1\13, 54.545
| 3\17
''123.529…''
| 2\10
''140''
|3\13
''161.538…''
|-
|-
|Reb, Lab
|'''G re'''
| Gb
|'''4\15,''' '''184.615'''
|1b, 1c
|'''3\11,''' '''189.474'''
|1f
|'''5\18,''' '''193.548'''
|3\15
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
''140''
|'''3\10,''' '''211.765'''
|2\11
|'''4\13,''' '''218.182'''
|-
''127.{{Overline|27}}''
|G re#
|3\18
|5\15, 230.769
|4\11, 252.632
''116.{{Overline|6}}''
|7\18, 270.968
| 2\17
| rowspan="2" |3\7, 300
|8\17, 331.034
''82.352…''
|5\10, 352.941
|1\10
|7\13, 381.818
''70''
|1\13
''53.846…''
|-
|-
|'''Re, La'''
|A mib
|'''G'''
|7\15, 323.077
|'''1'''
|5\11, 315.789
|'''1'''
|8\18, 309.677
|'''4\15'''
|7\17, 289.655
|4\10, 282.353
'''''186.{{Overline|6}}'''''
|5\13, 272.727
|'''3\11'''
'''''190.{{Overline|90}}'''''
|'''5\18'''
'''''194.{{Overline|4}}'''''
|'''2\7'''
'''''200'''''
|'''5\17'''
'''''205.882…'''''
|'''3\10'''
'''''210'''''
|'''4\13'''
'''''215.384…'''''
|-
|-
|Re#, La#
|A mi
| G#
|8\15, 369.231
| 1#
| 6\11, 378.947
|1#
|10\18, 387.097
|5\15
|4\7, 400
|10\17, 413.793
''233.{{Overline|3}}''
|6\10, 423.529
|4\11
|8\13, 436.364
''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
| A mi#
|Ab
|9\15, 415.385
|2b, 2c
| rowspan="2" |7\11, 442.105
|2f
|12\18, 464.516
|7\15
|5\7, 500
|13\17, 537.069
''326.{{Overline|6}}''
|8\10, 564.706
|5\11
|11\13, 600
|-
''318.{{Overline|18}}''
|B fa utb
| 8\18
|10\15, 461.538
|11\18, 425.806
''311.{{Overline|1}}''
|4\7, 400
|7\17
|9\17, 372.414
|5\10, 352.941
''288.235…''
|6\13, 327.273
| 4\10
''280''
|5\13
''269.230…''
|-
|-
|Mi, Si
|'''B fa ut'''
|A
|'''11\15,''' '''507.692'''
| 2
|'''8\11,''' '''505.263'''
|2
|'''13\18,''' '''503.226'''
|8\15
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
''373.{{Overline|3}}''
|'''7\10,''' '''494.118'''
|6\11
|'''9\13,''' '''490.909'''
''381.{{Overline|81}}''
|10\18
''388.{{Overline|8}}''
|4\7
''400''
|10\17
''411.764…''
|6\10
''420''
|8\13
''430.769…''
|-
|-
|Mi#, Si#
|B fa ut#
|A#
|12\15, 553.846
|2#
|9\11, 568.421
|2#
|15\18, 580.645
|9\15
|6\7, 600
|15\17, 620.690
''420''
|9\10, 635.294
| rowspan="2" |7\11
|12\13, 654.545
''445.{{Overline|45}}''
|12\18
''466.{{Overline|6}}''
|5\7
''500''
|13\17
''535.294…''
|8\10
''560''
|11\13
''592.307…''
|-
|-
|Fab, Dob
|B fa utx
|Bbb
| 13\15, 600
|3b, 3c
| rowspan="2" |10\11, 631.579
|3f
|17\18, 658.064
|10\15
|7\7, 700
|18\17, 744.828
''466.{{Overline|6}}''
|11\10, 776.471
|11\18
|15\13, 818.182
|-
''427.{{Overline|7}}''
|C sol re utb
|4\7
| 14\15, 646.154
|16\18, 619.355
''400''
|6\7, 600
|9\17
|14\17, 579.310
|8\10, 564.706
''370.588…''
|10\13, 545.455
|5\10
''350''
|6\13
''323.076.…''
|-
|-
|'''Fa, Do'''
!C sol re ut
|'''Bb'''
!'''15\15,''' '''692.308'''
|'''3'''
!'''11\11,''' '''694.737'''
|'''3'''
!'''18\18,''' '''696.774'''
|'''11\15'''
!7\7, 700
!'''17\17,''' '''703.448'''
'''''513.{{Overline|3}}'''''
!'''10\10,''' '''705.882'''
|'''8\11'''
!'''13\13,''' '''709.091'''
'''''509.{{Overline|09}}'''''
|'''13\18'''
'''''505.{{Overline|5}}'''''
|'''5\7'''
'''''500'''''
|'''12\17'''
'''''494.117…'''''
|'''7\10'''
'''''490'''''
|'''9\13'''
'''''484.615…'''''
|-
|-
|Fa#, Do#
|C sol re ut#
| B
|16\15, 738.462
|3#
|12\11, 757.895
|3#
|20\18, 774.194
|12\15
| rowspan="2" |8\8, 800
|20\17, 827.586
''560''
|12\10, 847.059
|9\11
|16\13, 872.727
''572.{{Overline|72}}''
| 15\18
''583.{{Overline|3}}''
|6\7
''600''
|15\17
''617.647…''
|9\10
''630''
|12\13
''646.153…''
|-
|-
| Fax, Dox
|D la mi reb
|B#
|18\15, 830.769
|3x
|13\11, 821.053
|3x
|21\18, 812.903
|13\15
|19\17, 786.207
|11\10, 776.471
''606. {{Overline|6}}''
|14\13, 763.63
| rowspan="2" |10\11
|-
|'''D la mi re'''
''636.{{Overline|36}}''
|'''19\15,''' '''876.923'''
|17\18
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
''661.{{Overline|1}}''
|'''9\5,''' '''900'''
|7\7
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
''700''
|'''17\13,''' '''927.273'''
|18\17
|-
|D la mi re#
''741.176…''
|20\15, 923.077
|11\10
| rowspan="2" |15\11, 947.368
|25\18, 967.742
''770''
|10\7, 1000
|15\13
|25\17, 1034.483
|15\10, 1058.824
''807.692…''
|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
|-
|-
|Dob, Solb
|E si mi re
|Hb
|23\15, 1061.538
|4b, 4c
|17\11, 1073.684
|4f
|28\18, 1083.871
|14\15
|11\7, 1100
|27\17, 1117.241
''653.{{Overline|3}}''
|16\10, 1129.412
|16\18
|21\9, 1145.455
''622.{{Overline|2}}''
|6\7
''600''
| 14\17
''576.470…''
| 8\10
''560''
|10\13
''538.461…''
|-
|-
!Do, Sol
| E si mi re#
!H
|24\15, 1107.923
!4
| rowspan="2" |18\11, 1136.842
!4
|30\18, 1161.29
! colspan="7" |''700''
|12\7, 1200
|30\17, 1241.379
| 18\10, 1270.588
|24\13, 1309.091
|-
|-
|Do#, Sol#
|F sol fa ut reb
|Η#
|25\15, 1153.846
|4#
|29\18, 1122.581
|4#
|11\7, 1100
|16\15
|26\17, 1075.862
|15\10, 1058.824
''746.{{Overline|6}}''
|19\13, 1036.364
|12\11
|-
|'''F sol fa ut re'''
''763.{{Overline|63}}''
|'''26\15,''' '''1200'''
|20\18
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
''777.{{Overline|7}}''
|'''12\7, 1200'''
| rowspan="2" |8\7
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
''800''
|'''22\13,''' '''1200'''
|20\17
''823.529…''
|12\10
''840''
|16\13
''861.538…''
|-
|-
|Reb, Lab
|F sol fa ut re#
|Cb
|27\15, 1246.154
|5b, 5c
|20\11, 1263.158
|5
|33\18, 1277.419
|18\15
|13\7, 1300
|32\17, 1324.138
''840''
| 19\10, 1341.176
|13\11
| 25\13, 1363.636
''827.{{Overline|27}}''
|21\18
''816.{{Overline|6}}''
| 19\17
''782.352…''
|11\10
''770''
|14\13
''753.846…''
|-
|-
|'''Re, La'''
|F sol fa ut rex
|'''C'''
|28\15, 1292.308
|'''5'''
| rowspan="2" |21\11, 1326.318
|'''5'''
|35\18, 1354.834
|'''19\15'''
| 14\7, 1400
|35\17, 1448.275
'''''886.{{Overline|6}}'''''
|21\10, 1482.353
|'''14\11'''
|28\13, 1527.273
'''''890.{{Overline|90}}'''''
|'''23\18'''
'''''894.{{Overline|4}}'''''
|'''9\7'''
'''''900'''''
|'''22\17'''
'''''905.882…'''''
|'''13\10'''
'''''910'''''
|'''17\13'''
'''''915.384…'''''
|-
|-
| Re#, La#
|G la sol re mib
|C#
| 29\15, 1338.462
|5#
|34\18, 1316.129
|5#
| 13\7, 1300
|20\15
|31\17, 1282.759
|18\10, 1270.588
''933.{{Overline|3}}''
|23\13, 1254.545
|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…''
|-
|-
|Mib, Sib
!G la sol re mi
|Db
!30\15, 1384.615
|6b, 6c
!22\11, 1389.473
|6f
!36\18, 1393.548
|22\15
!14\7, 1400
!34\17, 1406.897
''1026.{{Overline|6}}''
!20\10, 1411.765
|16\11
!26\13, 1418.182
''1018.{{Overline|18}}''
|26\18
''1011.{{Overline|1}}''
|24\17
''988.235…''
|14\10
''980''
|18\13
''969.230…''
|-
|-
|Mi, Si
|G la sol re mi#
|D
|31\15, 1430.769
|6
|23\11, 1452.632
|6
|38\18, 1470.968
| 23\15
| rowspan="2" |15\7, 1500
|37\17, 1531.034
''1073.{{Overline|3}}''
|22\10, 1552.941
|17\11
|29\13, 1581.818
''1081.{{Overline|81}}''
|28\18
''1088.{{Overline|8}}''
|11\7
''1100''
|27\17
''1111.764…''
|16\10
''1120''
|21\13
''1130.769…''
|-
|-
|Mi#, Si#
|A si la mi fab
| D#
|33\15, 1523.077
|6#
| 24\11, 1515.789
|6#
|39\18, 1509.677
|24\15
|36\17, 1489.655
|21\10, 1482.759
''1120''
| 27\13, 1472.273
| rowspan="2" | 18\11
|-
|'''A si la mi fa'''
''1145.{{Overline|45}}''
|'''34\15,''' '''1569.231'''
|30\18
|'''25\11,''' '''1578.947'''
|'''41\18,''' '''1587.097'''
''1166.{{Overline|6}}''
|'''16\7,''' '''1600'''
|12\7
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
''1200''
|'''30\13,''' '''1636.364'''
| 30\17
''1235.294…''
|18\10
''1260''
|24\13
''1292.307…''
|-
|-
| Fab, Dob
|A si la mi fa#
| Ebb
| 35\15, 1615.385
| 7b, 7c
| rowspan="2" |26\11, 1642.105
|7f
|43\18, 1664.516
|25\15
|17\7, 1700
|42\17, 1737.069
''1166.{{Overline|6}}''
| 25\10, 1764.706
|29\18
|33\13, 1800
''1127.{{Overline|7}}''
|11\7
''1100''
|26\17
''1070.588…''
|15\10
''1050''
|19\13
''1023.076…''
|-
|-
|'''Fa, Do'''
|B sol fa utb
|'''Eb'''
|36\61, 1661.538
|'''7'''
|42\18, 1625.806
|'''7'''
|16\7, 1600
|'''26\15'''
|38\29, 1572.414
|22\10, 1552.941
'''''1213.{{Overline|3}}'''''
|28\13, 1527.273
|'''19\11'''
'''''1209.{{Overline|09}}'''''
|'''31\18'''
'''''1205.{{Overline|5}}'''''
|'''12\7'''
'''''1200'''''
|'''29\17'''
'''''1194.117…'''''
|'''17\10'''
'''''1190'''''
|'''22\13'''
'''''1184.615…'''''
|-
|-
|Fa#, Do#
|B sol fa ut
|E
|37\15, 1707.692
|7#
|27\11, 1705.263
|7#
| 44\18, 1703.226
|27\15
| 17\7, 1700
|41\17, 1696.552
''1260''
|24\10, 1694.118
|20\11
|31\13, 1690.909
''1272.{{Overline|72}}''
| 33\18
''1283.{{Overline|3}}''
|13\7
''1300''
|32\17
''1317.647…''
|19\10
''1330''
| 25\13
''1346.153…''
|-
|-
|Fax, Dox
|B si
|E#
|38\15, 1753.846
|7x
| 28\11, 1768.421
|7x
|46\18, 1780.645
|28\15
|18\7, 1800
|44\17, 1820.690
''1306.{{Overline|6}}''
|26\10, 1835.294
| rowspan="2" |21\11
|34\13, 1854.545
''1336.{{Overline|36}}''
|35\18
''1361.{{Overline|1}}''
|14\7
''1400''
|35\17
''1441.176…''
|21\10
''1470''
|28\13
''1507.692…''
|-
|-
|Dob, Solb
|B si
|Fb
|39\15, 1800
|8b, Fc
| rowspan="2" |29\11, 1831.579
|8f
|48\18, 1858.064
|29\15
|19\7, 1900
|47\17, 1944.828
''1333.{{Overline|3}}''
|28\10, 1976.471
|34\18
|37\13, 2018.182
''1322.{{Overline|2}}''
|13\7
''1300''
|31\17
''1276.470…''
|18\10
''1260''
|23\13
''1238.461…''
|-
|-
!Do, Sol
|C la sol re utb
!F
|40\15, 1846.154
!8, F
|47\18, 1819.355
!8
| 18\7, 1800
! colspan="7" |''1400''
| 43\17, 1779.310
|25\10, 1764.706
|32\13, 1745.545
|-
|'''C la sol re ut'''
|'''41\15,''' '''1892.308'''
|'''30\11,''' '''1894.737'''
|'''49\18,''' '''1896.774'''
|'''19\7, 1900'''
|'''46\17,''' '''1903.448'''
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
|-
|C la sol re ut#
|42\15, 1938.462
|31\11, 1957.895
|51\18, 1974.194
|20\7, 2000
|49\17, 2027.586
| 29\10, 2047.059
|38\13, 2072.727
|-
|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
|50\18, 1935.484
|19\7, 1900
|45\17, 1862.069
|26\10, 1835.294
|33\13, 1800
|-
|-
|Do#, Sol#
|D fa la mi re
|F#
|44\15, 2030.769
|8#, F#
|32\11, 2021.053
|8#
|52\18, 2012.903
|31\15
|20\7, 2000
|48\17, 1986.207
''1446.{{Overline|6}}''
|28\10, 1976.471
|23\11
|36\13, 1963.636
''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
!D si la mi re
|Gb
!45\15, 2076.923
| 9b, Gc
!33\11, 2084.211
|9f
!54\18, 2090.323
|33\15
!21\7, 2100
! 51\17, 2110.345
''1540''
!30\10, 2117.647
|24\11
!39\13, 2127.273
''1527.{{Overline|27}}''
|39\18
''1516.{{Overline|6}}''
| 36\17
''1482.352…''
|21\10
''1470''
|27\13
''1453.846…''
|-
|-
|'''Re, La'''
|D si la mi re#
|'''G'''
|46\15, 2123.077
|'''9, G'''
| rowspan="2" |34\11, 2147.368
|9
|56\18, 2167.742
|'''34\15'''
|22\7, 2200
|54\17, 2234.483
'''''1586.{{Overline|6}}'''''
| 32\10, 2258.824
|'''25\11'''
|42\13, 2090.909
|-
'''''1590.{{Overline|90}}'''''
|E fab
|'''41\18'''
|47\26, 2169.231
|55\16, 2129.032
'''''1594.{{Overline|4}}'''''
|21\7, 2100
|'''16\7'''
|50\17, 2068.966
|29\10, 2047.059
'''''1600'''''
|37\13, 2018.182
|'''39\17'''
|-
|E fa
'''''1605.882…'''''
|48\15, 2215.385
|'''23\10'''
|35\11, 2210.526
|57\18, 2206.452
'''''1610'''''
|23\7, 2300
|'''30\13'''
|53\17, 2193.103
|31\10, 2188.235
'''''1615.384…'''''
|40\13, 2181.818
|-
|-
|Re#, La#
|E si mi
|G#
|49\15, 2261.538
|9#, G#
|36\11, 1073.684
|9#
|59\18, 2283.871
|35\15
|24\7, 2400
|56\17, 2317.241
''1633.{{Overline|3}}''
|33\10, 2329.412
|26\11
|43\13, 2345.455
''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
|E si mi#
| Ab
|50\15, 2307.692
|Xb, Ac
| rowspan="2" |37\11, 2336.842
|Af
|61\18, 2361.290
|37\15
| rowspan="2" |23\7, 2300
| 59\17, 2441.379
''1726.{{Overline|6}}''
|35\10, 2470.588
| 27\11
|46\13, 2509.091
''1718.{{Overline|18}}''
|44\18
''1711.{{Overline|1}}''
|41\17
''1688.235…''
| 24\10
''1680''
|31\13
''1669.230…''
|-
|-
|Mi, Si
|F sol fa utb
|A
|51\15, 2353.846
|X, A
|60\18, 2322.581
|A
|55\17, 2275.862
|38\15
|32\10, 2258.824
|41\13, 2236.364
''1773.{{Overline|3}}''
|-
|28\11
|F sol fa ut
|52\15, 2400
''1781.{{Overline|81}}''
|38\11, 2400
|46\18
|62\18, 2400
|24\7, 2400
''1788.{{Overline|8}}''
|58\17, 2400
|18\7
|34\10, 2400
|44\13, 2400
''1800''
| 44\17
''1811.764…''
|26\10
''1820''
|34\13
''1830.769…''
|-
|-
|Mi#, Si#
|F sol fa ut#
|A#
|53\15, 2446.154
|X#, A#
|39\11, 2463.158
|A#
|64\18, 2477,419
|39\15
| rowspan="2" |25\7, 2500
|61\17, 2524.138
''1820''
|36\10, 2541.176
| rowspan="2" |29\11
|47\13, 2563.636
''1845.{{Overline|45}}''
|48\18
''1866.{{Overline|6}}''
|19\7
''1900''
|47\17
''1935.294…''
|28\10
''1960''
| 37\13
''1992.307…''
|-
|-
|Fab, Dob
|G la sol reb
|Bbb
|55\15, 2538.462
|Ebb, Ccc
|40\11, 2526.316
|Bf
|65\18, 2516.129
|40\15
|60\17, 2482.759
|35\10, 2470.588
''1866.{{Overline|6}}''
|45\13, 2454.545
|47\18
''1827.{{Overline|7}}''
|18\7
''1800''
|43\17
''1770.588…''
|25\10
''1750''
|32\13
''1723.076…''
|-
|-
|'''Fa, Do'''
|'''G la sol re'''
|'''Bb'''
|'''56\15, 2584.615'''
|Eb, Cc
|'''41\11, 2589.474'''
|'''B'''
|'''67\18, 2593.548'''
|'''41\15'''
|'''26\7, 2600'''
|'''63\17, 2606.897'''
'''''1913.{{Overline|3}}'''''
|'''37\10, 2611.765'''
|'''30\11'''
|'''48\13,''' '''2618.182'''
|-
'''''1909.{{Overline|09}}'''''
|G la sol re#
|'''49\18'''
|57\15, 2630.769
|42\11, 2652.632
'''''1905.{{Overline|5}}'''''
|69\18, 2670.968
|'''19\7'''
| rowspan="2" |27\7, 2700
|66\17, 2731.034
'''''1900'''''
|39\10, 2752.941
|'''46\17'''
|51\13, 2781.818
'''''1894.117…'''''
|'''27\10'''
'''''1890'''''
|'''35\13'''
'''''1884.615…'''''
|-
|-
|Fa#, Do#
|A si la mib
|B
|59\15, 2723.077
|E, C
|43\11, 2715.789
|B#
|70\18, 2709.677
| 42\15
|65\17, 2689.552
|38\10, 2682.353
''1960''
|49\13, 2672.273
|31\11
''1972.{{Overline|72}}''
|51\18
''1983.{{Overline|3}}''
|20\7
''2000''
|49\17
''2017.647…''
|29\10
''2030''
|38\13
''2046.153…''
|-
|-
|Fax, Dox
!A si la mi
|B#
!60\15, 2769.231
|Ex, Cx
!44\11, 2778.947
|Bx
!72\18, 2787.097
|43\15
!28\7, 2800
!68\17, 2813.793
''2006.{{Overline|6}}''
!40\10, 2823.529
| rowspan="2" |32\11
!52\13, 2836.364
''2036.{{Overline|36}}''
|53\18
''2061.{{Overline|1}}''
|21\7
''2100''
|52\17
''2141.176…''
|31\10
''2170''
|41\13
''2207.692…''
|-
|-
| Dob, Solb
|A si la mi#
|Hb
|61\15, 2815.385
|0b, Dc
| rowspan="2" |45\11, 2842.105
|Cf
| 74\18, 2864.516
|44\15
|29\7, 2900
|71\17, 2937.069
''2053.{{Overline|3}}''
|42\10, 2964.706
|52\18
|55\13, 3000
|-
''2022.{{Overline|2}}''
|B fab
|20\7
|62\15, 2861.538
|73\18, 2825.806
''2000''
| 28\7, 2800
|48\17
|67\17, 2772.414
|39\10, 2752.941
''1976.470…''
|50\13, 2727.273
|28\10
''1960''
| 36\13
''1938.615…''
|-
|-
!Do, Sol
|B fa
!H
|63\15, 2907.692
!0, D
|46\11, 2905.263
!C
|75\18, 2903.226
! colspan="7" |''2100''
|29\7, 2900
|70\17, 2896.552
|41\10, 2894.118
|53\13, 2890.909
|-
|-
|Do#, Sol#
|'''B si'''
|Η#
|'''64\15, 2953.846'''
|0#, D#
|'''47\11, 2968.421'''
|C#
|'''77\18, 2980.645'''
|46\15
|'''30\7, 3000'''
''2146.{{Overline|6}}''
|'''73\17, 3020.690'''
|34\11
|'''43\10, 3035.294'''
''2163.{{Overline|63}}''
|'''56\13, 3054.545'''
|56\18
''2177.{{Overline|7}}''
| rowspan="2" |22\7
''2200''
|54\17
''2223.529…''
|32\10
''2240''
|42\13
''2261.538…''
|-
|-
|Reb, Lab
|B si#
|Cb
|65\15, 3000
|1b, 1c
|48\11, 3031.579
|Df
|79\18, 3058.064
|48\15
| rowspan="2" |31\7, 3100
''2240''
|76\17, 3144.828
|35\11
|45\10, 3176.471
''2227.{{Overline|27}}''
|59\13, 3218.182
|57\18
''2216.{{Overline|6}}''
|53\17
''2182.352…''
|31\10
''2170''
|40\13
''2153.846…''
|-
|-
|'''Re, La'''
|C solb
|'''C'''
|67\15, 3092.308
|'''1'''
|49\11, 3094.737
|'''D'''
|80\18, 3096.774
|'''49\15'''
|75\17, 3103.448
'''''2286.{{Overline|6}}'''''
|44\10, 3105.882
|'''36\11'''
|57\13, 3109.091
'''''2290.{{Overline|90}}'''''
|'''59\18'''
'''''2294.{{Overline|4}}'''''
|'''23\7'''
'''''2300'''''
|'''56\17'''
'''''2305.882…'''''
|'''33\10'''
'''2310'''
|'''43\13'''
'''''2315.384…'''''
|-
|-
|Re#, La#
|C sol
|C#
|68\15, 3138.462
|1#
|50\11, 3157.895
|D#
| 82\18, 3174.194
|50\15
|32\7, 3200
''2223.{{Overline|3}}''
|78\17, 3227.586
|37\11
| 46\10, 3247.059
''2354.{{Overline|54}}''
|60\13, 3272.273
|61\18
''2372.''{{Overline|2}}
| rowspan="2" |24\7
''2400''
|59\17
''2429.411…''
|35\10
''2450''
|46\13
''2476.923…''
|-
|-
|Mib, Sib
|C sol#
|Db
| 69\15, 3184.615
|2b, 2c
| rowspan="2" |51\11, 3221.053
|Ef
|84\18, 3251.612
|52\15
|33\7, 3300
''2426.{{Overline|6}}''
|81\17, 3351.725
|38\11
|48\10, 3388.235
''2418.{{Overline|18}}''
|63\13, 3436.364
|62\18
''2411.{{Overline|1}}''
|58\17
''2388.235…''
|34\10
''2380''
|44\13
''2369.230…''
|-
|-
|Mi, Si
|D labb
|D
|70\15, 3230.769
|2
|83\18, 3212.903
|E
|32\7, 3200
|53\15
|77\17, 3186.207
''2473,{{Overline|3}}''
|45\10, 3176.471
|39\11
|58\13, 3163.636
''2481.{{Overline|81}}''
|64\11
''2488.{{Overline|8}}''
|25\7
''2500''
|61\17
''2511.764…''
|36\10
''2520''
|47\13
''2530.769…''
|-
|-
|Mi#, Si#
|'''D lab'''
|D#
|'''71\15,''' '''3276.923'''
|2#
|'''52\11,''' '''3284.211'''
|E#
|'''85\18,''' '''3290.323'''
|54\15
|'''33\7, 3300'''
''2520''
|'''80\17,''' '''3310.345'''
| rowspan="2" |40\11
|'''47\10,''' '''3317.647'''
''2545.{{Overline|45}}''
|'''61\13,''' '''3327.{{Overline|27}}'''
|66\18
''2566.{{Overline|6}}''
|26\7
''2600''
|64\17
''2635.294…''
|38\10
''2660''
|50\13
''2692.307…''
|-
|-
|Fab, Dob
|D la
|Ebb
|72\15, 3323.077
|3b, 3c
|53\11, 3347.368
|Fff
|87\18, 3367.742
|55\15
|34\7, 3400
''2566.{{Overline|6}}''
|83\17, 3434.583
|65\18
|49\10, 3458.824
''2527.{{Overline|7}}''
|64\13, 3490.909
|25\7
''2500''
|60\17
''2470.588…''
|35\10
''2450''
|45\13
''2423.076…''
|-
|-
|'''Fa, Do'''
|D la#
|'''Eb'''
|73\15, 3369.231
|'''3'''
| rowspan="2" |54\11, 3410.625
|'''Ff'''
|89\18, 3445.162
|'''56\15'''
|35\7, 3500
'''''2613.{{Overline|3}}'''''
|86\17, 3558.621
|'''41\11'''
|51\10, 3600
'''''2609.{{Overline|09}}'''''
|67\13, 3654.545
|'''67\18'''
'''''2605.{{Overline|5}}'''''
|'''26\7'''
'''''2600'''''
|'''63\17'''
'''''2594.117…'''''
|'''37\10'''
'''''2590'''''
|'''48\13'''
'''''2584.615…'''''
|-
|-
|Fa#, Do#
|F utb
|E
|74\15, 3415.385
|3#
|88\18, 3406.452
|F
|34\7, 3400
|57\15
|82\17, 3393.103
''2660''
|48\10, 3388.235
|42\11
|62\13, 3381.818
''2672.{{Overline|72}}''
|69\18
''2683.{{Overline|3}}''
|27\7
''2700''
|66\17
''2717.647…''
|39\10
''2730''
|51\13
''2746.153…''
|-
|-
|Fax, Dox
!F ut
|E#
!75\15, 3461.538
|3x
!55\11, 3473.684
|F#
!90\18, 3483.871
|58\15
!35\7, 3500
!85\17, 3517.241
''2706.{{Overline|6}}''
!50\10, 3529.412
| rowspan="2" |43\11
!65\13, 3545.455
''2736.{{Overline|36}}''
|}
|71\18
 
{| class="wikitable"
''2761.{{Overline|1}}''
|+Cents
|28\7
!Notation
''2800''
!Supersoft
|69\17
!Soft
! Semisoft
''2841.176…''
!Basic
|41\10
!Semihard
''2870''
!Hard
|54\13
!Superhard
''2907.692…''
|-
|-
|Dob, Solb
!Subdozenal
|Fb
!~15edf
|4b, 4c
!~11edf
|0f, Gf
!~18edf
|59\15
!~7edf
!~17edf
''2753.{{Overline|3}}''
!~10edf
|70\18
!~13edf
''2722.{{Overline|2}}''
|27\7
''2700''
|65\17
''2676.470…''
|38\10
''2660''
|49\13
''2638.615…''
|-
|-
!Do, Sol
|F#
!F
|1\15, 46.154
!4
|1\11, 63.158
!0, G
|2\18, 77.419
! colspan="7" |''2800''
| rowspan="2" |1\7, 100
|}
|3\17, 124.138
|2\10, 141.176
==Intervals==
|3\13, 163.636
{| 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):
|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
|-
|-
|0
|'''G'''
|Do, Sol
|'''4\15,''' '''184.615'''
|perfect unison
|'''3\11,''' '''189.474'''
|0
|'''5\18,''' '''193.548'''
|Do, Sol
|'''2\7,''' '''200'''
|sesquitave (just fifth)
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|G#
|5\15, 230.769
|4\11, 252.632
|7\18, 270.968
| rowspan="2" |3\7, 300
|8\17, 331.034
|5\10, 352.941
|7\13, 381.818
|-
|-
|1
|Hb, He
|Fa, Do
|7\15, 323.077
|perfect fourth
|5\11, 315.789
| -1
|8\18, 309.677
|Re, La
|7\17, 289.655
|perfect second
|4\10, 282.353
|5\13, 272.727
|-
|-
|2
|H
|Mib, Sib
|8\15, 369.231
|minor third
|6\11, 378.947
| -2
|10\18, 387.097
|Mi, Si
|4\7, 400
|major third
|10\17, 413.793
|6\10, 423.529
|8\13, 436.364
|-
|-
|3
|H#
|Reb, Lab
|9\15, 415.385
|diminished second
| rowspan="2" |7\11, 442.105
| -3
|12\18, 464.516
|Fa#, Do#
|5\7, 500
|augmented fourth
|13\17, 537.069
|8\10, 564.706
|11\13, 600
|-
|-
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|Jbb, Jee
|10\15, 461.538
|11\18, 425.806
|4\7, 400
|9\17, 372.414
|5\10, 352.941
|6\13, 327.273
|-
|-
|4
|'''Jb, Je'''
|Dob, Solb
|'''11\15,''' '''507.692'''
|diminished sesquitave
|'''8\11,''' '''505.263'''
| -4
|'''13\18,''' '''503.226'''
| Do#, Sol#
|'''5\7, 500'''
|augmented unison (chroma)
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|-
|5
|J
|Fab, Dob
|12\15, 553.846
|diminished fourth
|9\11, 568.421
| -5
|15\18, 580.645
|Re#, La#
|6\7, 600
|augmented second
|15\17, 620.690
|9\10, 635.294
|12\13, 654.545
|-
|-
|6
|J#
| Mibb, Sibb
|13\15, 600
|diminished third
| rowspan="2" |10\11, 631.579
| -6
|17\18, 658.064
|Mi#, Si#
|7\7, 700
|augmented third
|18\17, 744.828
|}
|11\10, 776.471
|15\13, 818.182
==Genchain==
|-
|Kb, Ke
The generator chain for this scale is as follows:
|14\15, 646.154
{| class="wikitable"
|16\18, 619.355
|Mibb
|6\7, 600
|14\17, 579.310
Sibb
|8\10, 564.706
|Fab
|10\13, 545.455
|-
Dob
!K
|Dob
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
Solb
!'''18\18,''' '''696.774'''
|Reb
!7\7, 700
!'''17\17,''' '''703.448'''
Lab
!'''10\10,''' '''705.882'''
|Mib
!'''13\13,''' '''709.091'''
|-
Sib
|K#
|Fa
|16\15, 738.462
|12\11, 757.895
Do
|20\18, 774.194
|Do
| rowspan="2" |8\8, 800
|20\17, 827.586
Sol
|12\10, 847.059
|Re
|16\13, 872.727
|-
La
|Lb, Le
|Mi
|18\15, 830.769
|13\11, 821.053
Si
|21\18, 812.903
|Fa#
|19\17, 786.207
|11\10, 776.471
Do#
|14\13, 763.63
|Do#
|-
|'''L'''
Sol#
|'''19\15,''' '''876.923'''
|Re#
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
La#
|'''9\5,''' '''900'''
|Mi#
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
Si#
|'''17\13,''' '''927.273'''
|-
|L#
|20\15, 923.077
| rowspan="2" |15\11, 947.368
|25\18, 967.742
|10\7, 1000
|25\17, 1034.483
|15\10, 1058.824
|20\13, 1090.909
|-
|Mbb, Mee
|21\15, 969.231
|24\18, 929.032
|9\5, 900
|21\17, 868.966
|12\10, 847.059
|15\13, 818.182
|-
|Mb, Me
|22\15, 1015.385
|16\11, 1010.526
|26\18, 1006.452
|10\7, 1000
|24\17, 993.103
|14\10, 988.235
|18\13, 981.818
|-
|M
|23\15, 1061.538
|17\11, 1073.684
|28\18, 1083.871
|11\7, 1100
|27\17, 1117.241
|16\10, 1129.412
|21\9, 1145.455
|-
|M#
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
|30\18, 1161.29
|12\7, 1200
|30\17, 1241.379
|18\10, 1270.588
|24\13, 1309.091
|-
|Nbb, Nee
|25\15, 1153.846
|29\18, 1122.581
|11\7, 1100
|26\17, 1075.862
|15\10, 1058.824
|19\13, 1036.364
|-
|'''Nb, Ne'''
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|N
|27\15, 1246.154
|20\11, 1263.158
|33\18, 1277.419
|13\7, 1300
|32\17, 1324.138
|19\10, 1341.176
|25\13, 1363.636
|-
|N#
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
|35\18, 1354.834
|14\7, 1400
|35\17, 1448.275
|21\10, 1482.353
|28\13, 1527.273
|-
|Pb, Pe
|29\15, 1338.462
|34\18, 1316.129
|13\7, 1300
|31\17, 1282.759
|18\10, 1270.588
|23\13, 1254.545
|-
!P
!30\15, 1384.615
!22\11, 1389.473
!36\18, 1393.548
!14\7, 1400
!34\17, 1406.897
!20\10, 1411.765
!26\13, 1418.182
|-
|P#
|31\15, 1430.769
|23\11, 1452.632
|38\18, 1470.968
| rowspan="2" |15\7, 1500
|37\17, 1531.034
|22\10, 1552.941
|29\13, 1581.818
|-
|Qb, Qe
|33\15, 1523.077
|24\11, 1515.789
|39\18, 1509.677
|36\17, 1489.655
|21\10, 1482.759
|27\13, 1472.273
|-
|'''Q'''
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.364'''
|-
|Q#
|35\15, 1615.385
| rowspan="2" |26\11, 1642.105
|43\18, 1664.516
|17\7, 1700
|42\17, 1737.069
|25\10, 1764.706
|33\13, 1800
|-
|Rb, Re
|36\61, 1661.538
|42\18, 1625.806
|16\7, 1600
|38\29, 1572.414
|22\10, 1552.941
|28\13, 1527.273
|-
|R
|37\15, 1707.692
|27\11, 1705.263
|44\18, 1703.226
|17\7, 1700
|41\17, 1696.552
|24\10, 1694.118
|31\13, 1690.909
|-
|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
|-
|Sx
|43\15, 1984.615
| rowspan="2" |32\11, 2021.053
|53\18, 2051.612
|21\7, 2100
|52\17, 2151.725
|31\10, 2188.235
|41\13, 2236.364
|-
|Tb, Te
|44\15, 2030.769
|52\18, 2012.903
|20\7, 2000
|48\17, 1986.207
|28\10, 1976.471
|36\13, 1963.636
|-
|-
|d3
!T
|d4
!45\15, 2076.923
|d5
!33\11, 2084.211
|d2
!54\18, 2090.323
| m3
!21\7, 2100
|P4
!51\17, 2110.345
|P1
!30\10, 2117.647
|P2
!39\13, 2127.273
|M3
|-
|A4
|T#
| A1
|46\15, 2123.077
|A2
| rowspan="2" |34\11, 2147.368
|A3
|56\18, 2167.742
|}
|22\7, 2200
|54\17, 2234.483
==Modes==
|32\10, 2258.824
|42\13, 2090.909
The mode names are based on the species of fifth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
|-
|-
!name
|Ub, Üe
!pattern
|47\26, 2169.231
!notation
|55\16, 2129.032
!2nd
|21\7, 2100
!3rd
|50\17, 2068.966
!4th
|29\10, 2047.059
|37\13, 2018.182
|-
|-
|Lydian
|Ub, Ü
|LLLs
|48\15, 2215.385
|<nowiki>3|0</nowiki>
|35\11, 2210.526
|P
|57\18, 2206.452
|M
|23\7, 2300
| A
|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
|-
|V
|52\15, 2400
|38\11, 2400
|62\18, 2400
|24\7, 2400
|58\17, 2400
|34\10, 2400
|44\13, 2400
|-
|V#
|53\15, 2446.154
|39\11, 2463.158
|64\18, 2477,419
| rowspan="2" |25\7, 2500
|61\17, 2524.138
|36\10, 2541.176
|47\13, 2563.636
|-
|Wb, We
|55\15, 2538.462
|40\11, 2526.316
|65\18, 2516.129
|60\17, 2482.759
|35\10, 2470.588
|45\13, 2454.545
|-
|'''Wb'''
|'''56\15, 2584.615'''
|'''41\11, 2589.474'''
|'''67\18, 2593.548'''
|'''26\7, 2600'''
|'''63\17, 2606.897'''
|'''37\10, 2611.765'''
|'''48\13,''' '''2618.182'''
|-
|-
|Major
|W#
|LLsL
|57\15, 2630.769
|<nowiki>2|1</nowiki>
|42\11, 2652.632
|P
|69\18, 2670.968
|M
| rowspan="2" |27\7, 2700
|P
|66\17, 2731.034
|39\10, 2752.941
|51\13, 2781.818
|-
|-
| Minor
|Xb, Xe
|LLsL
|59\15, 2723.077
|<nowiki>1|2</nowiki>
|43\11, 2715.789
| P
|70\18, 2709.677
|m
|65\17, 2689.552
|P
|38\10, 2682.353
|49\13, 2672.273
|-
|-
|Phrygian
!X
|sLLL
!60\15, 2769.231
|<nowiki>0|3</nowiki>
!44\11, 2778.947
|d
!72\18, 2787.097
|m
!28\7, 2800
| P
!68\17, 2813.793
|}
!40\10, 2823.529
!52\13, 2836.364
==Temperaments==
The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
==='''Napoli-Meantone'''===
[[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>
|X#
!''ed7\12''
|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
|-
|-
| 1\4
|Ybb, Yee
|
|62\15, 2861.538
|
|73\18, 2825.806
|<u>171.428…</u>
|28\7, 2800
|''175''
|67\17, 2772.414
|1
|39\10, 2752.941
|1
|50\13, 2727.273
|1.000
|Equalised
|-
|-
|6\23
|Yb, Ye
|
|63\15, 2907.692
|
|46\11, 2905.263
|<u>180</u>
|75\18, 2903.226
|''182.608…''
|29\7, 2900
|6
|70\17, 2896.552
|5
|41\10, 2894.118
|1.200
|53\13, 2890.909
|
|-
|'''Y'''
|'''64\15, 2953.846'''
|'''47\11, 2968.421'''
|'''77\18, 2980.645'''
|'''30\7, 3000'''
|'''73\17, 3020.690'''
|'''43\10, 3035.294'''
|'''56\13, 3054.545'''
|-
|-
|
|Y#
| 11\42
|65\15, 3000
|
|48\11, 3031.579
|<u>180.821…</u>
|79\18, 3058.064
|''183.{{Overline|3}}''
| rowspan="2" |31\7, 3100
|11
|76\17, 3144.828
|9
|45\10, 3176.471
|1.222
|59\13, 3218.182
|
|-
|-
|5\19
|Zb. Ze
|
|67\15, 3092.308
|
|49\11, 3094.737
|<u>181.{{Overline|81}}</u>
|80\18, 3096.774
|''184.210…''
|75\17, 3103.448
|5
|44\10, 3105.882
|4
|57\13, 3109.091
|1.250
|
|-
|-
|
|Z
|14\53
|68\15, 3138.462
|
|50\11, 3157.895
|<u>182.608…</u>
|82\18, 3174.194
|''184.905…''
|32\7, 3200
|14
|78\17, 3227.586
|11
|46\10, 3247.059
|1.273
|60\13, 3272.273
|
|-
|-
|
|Z#
|9\34
|69\15, 3184.615
|
| rowspan="2" |51\11, 3221.053
|<u>183.050…</u>
|84\18, 3251.612
|''185.294…''
|33\7, 3300
| 9
|81\17, 3351.725
|7
|48\10, 3388.235
|1.286
|63\13, 3436.364
|
|-
|-
|4\15
|Ab, Æ
|
|70\15, 3230.769
|
|83\18, 3212.903
|<u>184.615…</u>
|32\7, 3200
|''186.{{Overline|6}}''
|77\17, 3186.207
|4
|45\10, 3176.471
|3
|58\13, 3163.636
|1.333
|
|-
|-
|
|'''A'''
|11\41
|'''71\15,''' '''3276.923'''
|
|'''52\11,''' '''3284.211'''
|<u>185.915…</u>
|'''85\18,''' '''3290.323'''
|''187.804…''
|'''33\7, 3300'''
|11
|'''80\17,''' '''3310.345'''
| 8
|'''47\10,''' '''3317.647'''
|1.375
|'''61\13,''' '''3327.{{Overline|27}}'''
|
|-
|-
|
|A#
|7\26
|72\15, 3323.077
|
|53\11, 3347.368
|<u>186.{{Overline|6}}</u>
|87\18, 3367.742
|''188.461…''
|34\7, 3400
|7
|83\17, 3434.583
|5
|49\10, 3458.824
|1.400
|64\13, 3490.909
|
|-
|Ax
|73\15, 3369.231
| rowspan="2" |54\11, 3410.625
|89\18, 3445.162
|35\7, 3500
|86\17, 3558.621
|51\10, 3600
|67\13, 3654.545
|-
|-
|
|Bb, Be
|10\37
|74\15, 3415.385
|
|88\18, 3406.452
|<u>187.5</u>
|34\7, 3400
|''189.{{Overline|189}}''
|82\17, 3393.103
|10
|48\10, 3388.235
| 7
|62\13, 3381.818
| 1.429
|
|-
|-
|
!B
|13\48
!75\15, 3461.538
|
!55\11, 3473.684
|<u>187.951…</u>
!90\18, 3483.871
|''189.58{{Overline|3}}''
!35\7, 3500
|13
!85\17, 3517.241
|9
!50\10, 3529.412
|1.444
!65\13, 3545.455
|
|-
|-
|
|B#
|16\59
|76\15, 3507.692
|
|56\11, 3536.842
|<u>188.235…</u>
|92\18, 3561.290
|''189.830…''
| rowspan="2" |36\7, 3600
|88\17, 3641.379
|16
|52\10, 3670.588
|11
|68\13, 3709.091
|1.4545
|
|-
|-
| 3\11
|Cb, Ce
|  
|78\15, 3600
|
|57\11, 3600
|<u>189.473…</u>
|93\18, 3600
|''190.{{Overline|90}}''
|87\17, 3600
| 3
|51\10, 3600
|2
|66\13, 3600
|1.500
|Napoli-Meantone starts here
|-
|-
|
|'''C'''
|14\51
|'''79\15,''' '''3646.154'''
|
|'''58\11,''' '''3663.158'''
|<u>190.{{Overline|90}}</u>
|'''95\18,''' '''3677.419'''
|''192.156…''
|'''37\7,''' '''3700'''
|14
|'''90\17,''' '''3724.138'''
| 9
|'''53\10,''' '''3741.176'''
| 1.556
|'''69\13,''' '''3763.636'''
|
|-
|-
|
|C#
|11\40
|80\15, 3692.308
|
|59\11, 3726.316
|<u>191.304…</u>
|97\18, 3755.838
|''192.5''
| rowspan="2" |38\7, 3800
|11
|93\17, 3848.275
| 7
|55\10, 3882.353
| 1.571
|72\13, 3927.273
|
|-
|Db, De
|82\15, 3784.615
|60\11, 3789.474
|98\18, 3793.548
|92\17, 3806.897
|54\10, 3811.765
|70\13, 3818.182
|-
|-
|
|D
|8\29
|83\15, 3830.769
|
|61\11, 3852.632
|<u>192</u>
|100\18, 3870.968
|''193.103…''
|39\7, 3900
| 8
|95\17, 3931.03$
| 5
|56\10, 3952.941
|1.600
|73\13, 3981.818
|
|-
|-
|
|D#
|5\18
|84\15, 3876.923
|  
| rowspan="2" |62\11, 3915.789
|<u>193.548…</u>
|102\18, 3948.387
|''194.{{Overline|4}}''
|40\7, 4000
|5
|98\17, 4055.172
|3
|58\10, 4094.118
|1.667
|76\13, 4145.455
|
|-
|-
|
|Ebb, Ëe
|
|85\15, 3923.077
|12\43
|101\18, 3909.677
|<u>194.{{Overline|594}}</u>
|39\7, 3900
|''195.348…''
|94\17, 3889.552
| 12
|55\10, 3882.353
| 7
|71\13, 3872.727
|1.714
|
|-
|-
|
|'''Eb, Ë'''
|7\25
|'''86\15,''' '''3969.231'''
|
|'''63\11,''' '''3978.947'''
|<u>195.348…</u>
|'''103\18,''' '''3987.097'''
|''196''
|'''40\7, 4000'''
|7
|'''97\17,''' '''4013.793'''
|4
|'''57\10,''' '''4023.529'''
|1.750
|'''74\13,''' '''4036.364'''
|  
|-
|-
|  
|E
|9\32
|87\15, 4015.385
|
|64\11, 4042.105
|<u>196.{{Overline|36}}</u>
|105\18, 4064.516
|''196.875''
|41\7, 4100
|9
|100\17, 4137.931
|5
|59\10, 4164.706
|1.800
|77\13, 4200
|
|-
|-
|
|E#
|11\39
|88\15, 4061.583
|
| rowspan="2" |65\11, 4105.263
|<u>197.014…</u>
|107\18, 4141.956
|''197.435…''
|42\7, 4200
|11
|103\17, 4262.069
| 6
|61\10, 4305.882
|1.833
|80\13, 4363.636
|
|-
|-
|  
|Fb, Fe
|13\46
|89\15, 4107.692
|
|106\18, 4103.226
|<u>197.468…</u>
|41\7, 4100
|''197.826…''
|99\17, 4096.552
| 13
|58\10, 4094.118
| 7
|75\13, 4090.909
| 1.857
|
|-
|-
|
!F
|15\53
!90\15, 4153.846
|
!66\11, 4168.421
|<u>197.802…</u>
!108\18, 4180.645
|''198.113…''
!42\7, 4200
|15
!102\17, 4220.690
|8
!60\10, 4235.294
|1.875
!78\13, 4254.545
|
|}
|-
==Intervals==
|
{| class="wikitable"
| 17\60
!Generators
|
!Sesquitave notation
|<u>198.058…</u>
!Interval category name
|''198.{{Overline|3}}''
!Generators
|17
!Notation of 3/2 inverse
| 9
!Interval category name
| 1.889
|
|-
|-
|
| colspan="6" |The 4-note MOS has the following intervals (from some root):
|19\67
|
|<u>198.260…</u>
|''198.507…''
|19
| 10
|1.900
|
|-
|-
|
|0
|21\74
|Do, Fa, Sol
|
|perfect unison
|<u>198.425…</u>
|0
| ''198.{{Overline |''198.''{{Overline|648}}
|Do, Fa, Sol
|21
|sesquitave (just fifth)
| 11
|1.909
|  
|-
|-
|
|1
|23\81
|Fa, Sib, Do
|
|perfect fourth
|<u>198.561…</u>
| -1
|''198.765…''
|Re, Sol, La
|23
|perfect second
|12
|-
| 1.917
|2
|
|Mib, Lab, Sib
|minor third
| -2
|Mi, La, Si
|major third
|-
|-
|
|3
| 25\88
|Reb, Solb, Lab
|  
|diminished second
|<u>198.675…</u>
| -3
|''198.8{{Overline|63}}''
|Fa#, Si, Do#
|25
|augmented fourth
| 13
|1.923
|
|-
|-
|
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|27\95
|
|<u>198.773…</u>
|''198.947…''
|27
|14
|1.929
|
|-
|-
|
|4
|29\102
|Dob, Fab, Solb
|
|diminished sesquitave
|<u>198.857…</u>
| -4
|''199.019…''
|Do#, Fa#, Sol#
|29
|augmented unison (chroma)
|15
|1.933
|
|-
|-
|  
|5
| 31\109
|Fab, Sibb, Dob
|
|diminished fourth
|<u>198.930…</u>
| -5
|''199.082…''
|Re#, Sol#, La#
|31
|augmented second
|16
|1.9375
|
|-
|-
|
|6
|33\116
|Mibb, Labb, Sibb
|
|diminished third
|<u>198.994…</u>
| -6
|''199.137…''
|Mi#, La#, Si#
|33
|augmented third
|17
|}
|1.941
|
==Genchain==
|-
|
The generator chain for this scale is as follows:
|35\123
{| class="wikitable"
|
|Mibb
|<u>199.052…</u>
Labb
|''199.186…''
|35
Sibb
|18
|Fab
|1.944
Sibb
|
|-
Dob
|2\7
|Dob
|
Fab
|
|<u>200</u>
Solb
|''200''
|Reb
|2
Solb
|1
|2.000
Lab
| Napoli-Meantone ends, Napoli-Pythagorean begins
|Mib
|-
Lab
|
|17\59
Sib
|
|Fa
|<u>201.980…</u>
Sib
|''201.694…''
|17
Do
|8
|Do
|2.125
Fa
|
|-
Sol
|
|Re
| 15\52
Sol
|
|<u>202.247…</u>
La
|''201.923…''
|Mi
|15
La
|7
|2.143
Si
|
|Fa#
Si
Do#
|Do#
Fa#
Sol#
|Re#
Sol#
La#
|Mi#
La#
Si#
|-
|-
|
|d3
|13\45
|d4
|
|d5
|<u>202.597…</u>
|d2
|''202.{{Overline|2}}''
|m3
|13
|P4
|6
|P1
|2.167
|P2
|
|M3
|A4
|A1
|A2
|A3
|}  
==Modes==
The mode names are based on the species of fifth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
|-
|-
|
!name
|11\38
!pattern
|
!notation
|<u>203.076…</u>
!2nd
|''202.631…''
!3rd
|11
!4th
|5
|2.200
|
|-
|-
|
|Lydian
|9\31
|LLLs
|
|<nowiki>3|0</nowiki>
|<u>203.773…</u>
|P
|''203.225…''
|M
|9
|A
|4
| 2.250
|
|-
|-
|
|Major
|7\24
|LLsL
|
|<nowiki>2|1</nowiki>
|<u>204.878…</u>
|P
|''204.1{{Overline|6}}''
|M
| 7
|P
|3
|2.333
|
|-
|-
|
|Minor
|
|LsLL
|12\41
|<nowiki>1|2</nowiki>
|<u>205.714…</u>
|P
|''204.878…''
|m
|12
|P
|5
|2.400
|
|-
|-
|
|Phrygian
|5\17
|sLLL
|
|<nowiki>0|3</nowiki>
|<u>206.896…</u>
|d
|''205.882…''
|m
|5
|P
|2
|}
|2.500
|Napoli-Neogothic heartland is from here…
==Temperaments==
The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
==='''Napoli-Meantone (Hex meantone)'''===
[[Subgroup]]: 3/2.6/5.8/5 (5.2.3)
[[Comma]] list: [[81/80]]
 
[[POL2]] generator: ~9/8 = 192.6406¢
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Optimal ET sequence]]: *[[28ed5]], [[44ed5]], [[72ed5]] ≈ [[7edf]], [[11edf]], [[18edf]]
==='''Napoli-Archy (Hex Archytas)'''===
[[Subgroup]]: 3/2.7/6.14/9 (36/7.2.3)
[[Comma]] list: [[64/63]]
 
[[POL2]] generator: ~8/7 = 218.6371¢
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Optimal ET sequence]]: *[[28ed36/7]], [[40ed36/7]], [[52ed36/7]] ≈ [[7edf]], [[10edf]], [[13edf]]
===Scale tree===
The spectrum looks like this:
{| class="wikitable"
!Generator
(bright)
!Cents
!L
!s
!L/s
!Comments
|-
|-
|1\4
|171.429
|1
|1
|1.000
|Equalised
|-
|6\23
|180.000
|6
|5
|1.200
|
|
|
|18\61
|<u>207.692…</u>
|''206.557…''
|18
|7
| 2.571
|
|-
|-
|5\19
|181.818
|5
|4
|1.250
|
|
|
|-
|13\44
|14\53
|<u>208</u>
|182.609
|''206.{{Overline|81}}''
|14
|13
|11
| 5
|1.273
| 2.600
|
|
|-
|-
|9\34
|183.051
|9
|7
|1.286
|
|
|8\27
|-
|4\15
|184.615
|4
|3
|1.333
|
|
|<u>208.695…</u>
|''207.{{Overline|407}}''
| 8
|3
|2.667
|…to here
|-
|-
|
|11\41
|11\37
|185.915
|
|<u>209.523…</u>
|''208.{{Overline|108}}''
|11
|11
|4
|8
| 2.750
|1.375
|
|
|-
|-
|
|7\26
|14\47
|186.667
|
|7
|<u>210</u>
|5
|''208.510…''
|1.400
| 14
| 5
|2.800
|
|
|-
|-
|
|10\37
|17\57
|187.5
|10
|7
|1.429
|
|
|<u>210.309…</u>
|''208.771…''
|17
|6
|2.833
|
|-
|-
|13\48
|187.952
|13
|9
|1.444
|
|
| 20\67
|-
|
|16\59
|<u>210.526…</u>
|188.253
|''208.955…''
|16
| 20
|11
|7
|1.455
|2.857
|
|
|-
|-
|
|3\11
| 23\77
|189.474
|
|3
|<u>210.687…</u>
|2
|''209.{{Overline|09}}''
|1.500
|23
|Napoli-Meantone starts here
|8
|-
|2.875
|14\51
|190.909
|14
|9
|1.556
|
|
|-
|-
|3\10
|11\40
|
|191.304
|11
|7
|1.571
|
|
|<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
|
|-
|-
|
|8\29
|19\63
|192.000
|
|8
|<u>213.084…</u>
|5
|''211.{{Overline|1}}''
|1.600
|19
|6
|3.167
|
|
|-
|-
|
|5\18
|16\53
|193.548
|
|<u>213.{{Overline|3}}</u>
|''211.320…''
|16
|5
|5
|3.200
|3
|1.667
|
|
|-
|-
|
|12\43
|13\43
|194.595
|12
|7
|1.714
|
|
|<u>213.698…</u>
|-
|''211.627…''
|7\25
|13
|195.348
|7
|4
|4
|3.250
|1.750
|
|
|-
|-
|9\32
|196.364
|9
|5
|1.800
|
|
| 10\33
|-
|11\39
|197.015
|11
|6
|1.833
|
|
|<u>214.285…</u>
|-
|''212.{{Overline|12}}''
|13\46
|10
|197.468
|3
|13
|3.333
|7
|1.857
|
|
|-
|-
|
|15\53
|7\23
|197.802
|
|15
|<u>215.384…</u>
|8
|''213.043…''
|1.875
|7
|2
|3.500
|
|
|-
|-
|17\60
|198.058
|17
|9
|1.889
|
|
|11\36
|-
|19\67
|198.261
|19
|10
|1.900
|
|
|<u>216.393…</u>
|''213.{{Overline|3}}''
| 11
|3
|3.667
|
|-
|-
|21\74
|198.425
|21
|11
|1.909
|
|
|15\49
|-
|23\81
|198.561
|23
|12
|1.917
|
|
|<u>216.867…</u>
|-
|''214.285…''
|25\88
|15
|198.675
|4
|25
|3.750
|13
|1.923
|
|
|-
|-
|4\13
|27\95
|198.773
|27
|14
|1.929
|
|
|-
|29\102
|198.857
|29
|15
|1.933
|
|
|<u>218.{{Overline|18}}</u>
|-
|''215.385…''
|31\109
|4
|198.930
|1
|31
|4.000
|16
|1.9375
|
|
|-
|-
|33\116
|198.995
|33
|17
|1.941
|
|
|13\42
|-
|
|35\123
|<u>219.718…</u>
|199.009
|''216.{{Overline|6}}''
|35
|13
|18
|3
|1.944
|4.333
|
|
|-
|-
|
|2\7
|9\29
|200
|
|<u>220.408…</u>
|''217.241…''
|9
|2
|2
|4.500
|1
|  
|2.000
|Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|-
|
|17\59
|14\45
|201.980
|
|17
|<u>221.052…</u>
|8
|''217.{{Overline|7}}''
|2.125
|14
| 3
| 4.667
|
|
|-
|-
|5\16
|15\52
|202.247
|15
|7
|2.143
|
|
|-
|13\45
|202.597
|13
|6
|2.167
|
|
|<u>222.{{Overline|2}}</u>
|-
|''218.75''
|11\38
|203.077
|11
|5
|5
| 1
|2.200
|5.000
|
|Napoli-Superpyth ends
|-
|-
|9\31
|203.774
|9
|4
|2.250
|
|
|16\51
|-
|
|7\24
|<u>223.255…</u>
|204.878
|''219.607…''
|7
|16
|3
|3
|5.333
|2.333
|
|
|-
|-
|12\41
|205.714
|12
|5
|2.400
|
|
|11\35
|-
|
|5\17
|<u>223.728…</u>
|206.897
|''220''
|5
|11
|2
|2
|5.500
|2.500
|Napoli-Neogothic heartland is from here…
|-
|18\61
|207.693
|18
|7
|2.571
|
|
|-
|-
|
|13\44
|17\54
|208.000
|
|13
|<u>224.175…</u>
|5
|''220.{{Overline|370}}''
|2.600
| 17
| 3
|5.667
|
|
|-
|-
|6\19
|8\27
|
|208.696
|  
|8
|<u>225</u>
|3
|''221.052…''
|2.667
|6
|…to here
|1
|-
|6.000
|11\37
|
|209.524
|11
|4
|2.750
|
|-
|-
|1\3
|14\47
|
|210.000
|14
|5
|2.800
|
|
|<u>240</u>
|-
|''233.{{Overline|3}}''
|3\10
|211.765
|3
|1
|1
|0
|3.000
|→ inf
|Napoli-Pythagorean ends, Napoli-Archy begins
|Paucitonic
|-
|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)"