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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"
 
 
|+
|+
 
 
Cents<ref name=":0">Fractions repeating more than 4 digits written as continued fractions</ref>
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; 6.5
 
 
|1\11
| rowspan="2" | 1\7, 100
63: 6.{{Overline|3}}
 
 
|2\18
|3\17, 124.138
77; 2, 2.6
 
 
| rowspan="2" |1\7
|2\10, 141.176
 
 
100
|3\13, 163.636
 
 
|3\17
|-
124; 7.25
 
 
|2\10
|Reb, Solb, Lab
141; 5.{{Overline|6}}
|3\15, 138.462
 
 
|3\13
|2\11. 126.316
 
 
163.{{Overline|63}}
|3\18, 116.129
 
 
|-
|2\17, 82.759
 
 
|Reb, Lab
|1\10, 70.588
 
 
|Gb
|1\13, 54.545
 
 
|1b, 1c
|-
|1f
|3\15
138; 3.25
 
 
|2\11
|'''Re, Sol, La'''
126; 3.1{{Overline|6}}
|'''4\15,''' '''184.615'''
 
 
|3\18
|'''3\11,''' '''189.474'''
116; 7.75
|'''5\18,''' '''193.548'''
 
 
|2\17
|'''2\7,''' '''200'''
82; 1.13{{Overline|63}}
 
 
|1\10
|'''5\17,''' '''206.897'''
70; 1.7
 
 
|1\13
|'''3\10,''' '''211.765'''
 
 
54.{{Overline|54}}
|'''4\13,''' '''218.182'''
 
 
|-
|-
 
 
|'''Re, La'''
|Re#, Sol#, La#
|5\15, 230.769
 
 
|'''G'''
|4\11, 252.632
 
 
|'''1'''
|7\18, 270.968
|'''1'''
 
 
|'''4\15'''
| rowspan="2" | 3\7, 300
'''184; 1.625'''
 
 
|'''3\11'''
|8\17, 331.034
'''189; 2.{{Overline|1}}'''
|'''5\18'''
'''193; 1, 1, 4.{{Overline|6}}'''
 
 
|'''2\7'''
|5\10, 352.941
 
 
'''200'''
|7\13, 381.818
 
 
|'''5\17'''
|-
'''206; 1, 8.{{Overline|6}}'''
 
 
|'''3\10'''
|Mib, Lab, Sib
'''211; 1, 3.25'''
|7\15, 323.077
 
 
|'''4\13'''
|5\11, 315.789
 
 
'''218.{{Overline|18}}'''
|8\18, 309.677
 
 
|-
|7\17, 289.655
 
 
|Re#, La#
|4\10, 282.353
 
 
|G#
|5\13, 272.727
 
 
|1#
|-
|1#
|5\15
230; 1.3
 
 
|4\11
|Mi, La, Si
252; 1.58{{Overline|3}}
|8\15, 369.231
 
 
|7\18
|6\11, 378.947
270; 1.0{{Overline|3}}
 
 
| rowspan="2" |3\7
|10\18, 387.097
 
 
300
|4\7, 400
 
 
|8\17
|10\17, 413.793
331; 29
 
 
|5\10
|6\10, 423.529
352; 1.0625
 
 
|7\13
|8\13, 436.364
381.{{Overline|81}}
 
 
|-
|-
 
 
|Mib, Sib
|Mi#, La#, Si#
|9\15, 415.385
|Ab
|2b, 2c
|2f
|7\15
323; 13
 
 
|5\11
| rowspan="2" | 7\11, 442.105
315; 1.2{{Overline|6}}
 
 
|8\18
|12\18, 464.516
309; 1, 2.1
 
 
|7\17
|5\7, 500
289; 1, 1.9
 
 
|4\10
|13\17, 537.069
282; 2.8{{Overline|3}}
 
 
|5\13
|8\10, 564.706
 
 
272.{{Overline|72}}
|11\13, 600
 
 
|-
|-
 
 
|Mi, Si
|Fab, Sibb, Dob
|10\15, 461.538
 
 
|A
|11\18, 425.806
 
 
|2
|4\7, 400
|2
|8\15
369; 4.{{Overline|3}}
 
 
|6\11
|9\17, 372.414
378; 1.0{{Overline|5}}
 
 
|10\18
|5\10, 352.941
387; 10.{{Overline|3}}
 
 
|4\7
|6\13, 327.273
 
 
400
|-
 
 
|10\17
|'''Fa, Sib, Do'''
413; 1, 3.8{{Overline|3}}
|'''11\15,''' '''507.692'''
 
 
|6\10
|'''8\11,''' '''505.263'''
423; 1.{{Overline|8}}
 
 
|8\13
|'''13\18,''' '''503.226'''
 
 
436.{{Overline|36}}
|'''5\7, 500'''
 
 
|-
|'''12\17,''' '''496.552'''
 
 
|Mi#, Si#
|'''7\10,''' '''494.118'''
 
 
|A#
|'''9\13,''' '''490.909'''
 
 
|2#
|-
|2#
|9\15
415; 2.6
 
 
| rowspan="2" |7\11
|Fa#, Si, Do#
442; 9.5
|12\15, 553.846
 
 
|12\18
|9\11, 568.421
464; 1.0625
 
 
|5\7
|15\18, 580.645
 
 
500
|6\7, 600
 
 
|13\17
|15\17, 620.690
537; 14.5
 
 
|8\10
|9\10, 635.294
564; 1.41{{Overline|6}}
 
 
|11\13
|12\13, 654.545
600
 
 
|-
|-
|Fax, Si#, Dox
|13\15, 600
 
 
|Fab, Dob
| rowspan="2" | 10\11, 631.579
 
 
|Bbb
|17\18, 658.064
 
 
|3b, 3c
|7\7, 700
|3f
|10\15
461; 1, 1.1{{Overline|6}}
 
 
|11\18
|18\17, 744.828
425; 1.24
 
 
|4\7
|11\10, 776.471
 
 
400
|15\13, 818.182
 
 
|9\17
|-
372; 2.41{{Overline|6}}
|5\10
352; 1.0625
|6\13
 
 
327.{{Overline|27}}
|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
 
 
|-
|-
 
 
|'''Fa, Do'''
!Do, Fa, Sol
!'''15\15,''' '''692.308'''
 
 
|'''Bb'''
!'''11\11,''' '''694.737'''
 
 
|'''3'''
!'''18\18,''' '''696.774'''
|'''3'''
 
 
|'''11\15'''
!7\7, 700
'''507; 1.{{Overline|4}}'''
 
 
|'''8\11'''
!'''17\17,''' '''703.448'''
'''505; 3.8'''
 
 
|'''13\18'''
!'''10\10,''' '''705.882'''
'''503; 4, 2.{{Overline|3}}'''
 
 
|'''5\7'''
!'''13\13,''' '''709.091'''
 
 
'''500'''
|}
 
 
|'''12\17'''
{| class="wikitable"
'''496; 1.8125'''
 
 
|'''7\10'''
|+
'''494; 8.5'''
 
 
|'''9\13'''
Cents
!Notation
!Supersoft
 
 
'''490.{{Overline|90}}'''
! Soft
 
 
|-
!Semisoft
 
 
|Fa#, Do#
!Basic
 
 
|B
!Semihard
 
 
|3#
! Hard
|3#
|12\15
553; 1.{{Overline|18}}
 
 
|9\11
! Superhard
568; 2.375
 
 
|15\18
|-
580; 1.55
 
 
|6\7
!Napoli
! ~15edf
 
 
600
! ~11edf
 
 
|15\17
!~18edf
620; 1.45
 
 
|9\10
!~7edf
635; 3.4
 
 
|12\13
!~17edf
 
 
654.{{Overline|54}}
!~10edf
!~13edf
 
 
|-
|-
|Fax, Dox
 
 
|B#
|F#
|1\15, 46.154
|3x
|3x
|13\15
 
 
600
|1\11, 63.158
 
 
| rowspan="2" |10\11
| 2\18, 77.419
 
 
631; 1.{{Overline|72}}
| rowspan="2" |1\7, 100
 
 
|17\18
|3\17, 124.138
 
 
658; 15.5
| 2\10, 141.176
 
 
|7\7
|3\13, 163.636
 
 
700
|-
 
 
|18\17
| Gb, Ge
|3\15, 138.462
 
 
744; 1.208{{Overline|3}}
| 2\11. 126.316
 
 
|11\10
|3\18, 116.129
 
 
776; 2.125
|2\17, 82.759
 
 
|15\13
|1\10, 70.588
 
 
818.{{Overline|18}}
|1\13, 54.545
 
 
|-
|-
 
 
|Dob, Solb
|'''G'''
|Hb
|'''4\15,''' '''184.615'''
| 4b, 4c
|4f
|'''3\11,''' '''189.474'''
|14\15
   
   
646; 6.5
|'''5\18,''' '''193.548'''
|16\18
|'''2\7,''' '''200'''
619; 2.{{Overline|81}}
|6\7
|'''5\17,''' '''206.897'''
600
|'''3\10,''' '''211.765'''
|14\17
579; 3.{{Overline|2}}
|8\10
564; 1.41{{Overline|6}}
|10\13
 
 
545.{{Overline|45}}
|'''4\13,''' '''218.182'''
 
 
|-
|-
 
 
!Do, Sol
|G#
|5\15, 230.769
 
 
!H
|4\11, 252.632
 
 
!4
|7\18, 270.968
!4
!'''15\15'''
 
 
'''692; 3.25'''
| rowspan="2" |3\7, 300
 
 
!'''11\11'''
| 8\17, 331.034
'''694; 1, 2.8'''
 
 
!'''18\18'''
|5\10, 352.941
 
 
'''696; 1.291'''{{Overline|6}}
|7\13, 381.818
 
 
!'''7\7'''
|-
 
 
'''700'''
|Ab, Æ
|7\15, 323.077
 
 
!'''17\17'''
|5\11, 315.789
 
 
'''703; 2, 2.1'''{{Overline|6}}
|8\18, 309.677
 
 
!'''10\10'''
|7\17, 289.655
 
 
'''705; 1.1'''{{Overline|3}}
|4\10, 282.353
 
 
!'''13\13'''
|5\13, 272.727
'''709.'''{{Overline|09}}
 
 
|-
|-
 
 
|Do#, Sol#
|A
| 8\15, 369.231
 
 
|Η#
|6\11, 378.947
 
 
|4#
|10\18, 387.097
|4#
|16\15
 
 
738; 2.1{{Overline|6}}
| 4\7, 400
 
 
|12\11
|10\17, 413.793
 
 
757; 1, 8.5
|6\10, 423.529
 
 
| 20\18
|8\13, 436.364
 
 
774; 5, 6
|-
 
 
| rowspan="2" | 8\8
|A#
| 9\15, 415.385
 
 
800
| rowspan="2" |7\11, 442.105
 
 
|20\17
|12\18, 464.516
 
 
827; 1, 1.41{{Overline|6}}
|5\7, 500
 
 
|12\10
|13\17, 537.069
 
 
847; 17
|8\10, 564.706
 
 
| 16\13
|11\13, 600
872.{{Overline|72}}
 
 
|-
|-
 
 
|Reb, Lab
|Bbb, Bee
|10\15, 461.538
 
 
|Cb
|11\18, 425.806
 
 
|5b, 5c
|4\7, 400
|5
|18\15
 
 
830; 1.3
|9\17, 372.414
 
 
|13\11
| 5\10, 352.941
 
 
821; 19
|6\13, 327.273
 
 
| 21\18
|-
 
 
812; 1, 9.{{Overline|3}}
|'''Bb, Be'''
|'''11\15,''' '''507.692'''
 
 
| 19\17
|'''8\11,''' '''505.263'''
 
 
786; 4.8{{Overline|3}}
|'''13\18,''' '''503.226'''
 
 
| 11\10
|'''5\7, 500'''
 
 
776; 2.125
|'''12\17,''' '''496.552'''
 
 
| 14\13
|'''7\10,''' '''494.118'''
 
 
763.{{Overline|63}}
|'''9\13,''' '''490.909'''
 
 
|-
|-
 
 
|'''Re, La'''
|B
|12\15, 553.846
|9\11, 568.421
 
 
|'''C'''
|15\18, 580.645
 
 
|'''5'''
|6\7, 600
|'''5'''
 
 
|'''19\15'''
| 15\17, 620.690
 
 
'''876; 1.08{{Overline|3}}'''
|9\10, 635.294
 
 
|'''14\11'''
|12\13, 654.545
 
 
'''884; 4.75'''
|-
| B#
| 13\15, 600
 
 
|'''23\18'''
| rowspan="2" |10\11, 631.579
 
 
'''890; 3.1'''
|17\18, 658.064
 
 
|'''9\5'''
|7\7, 700
 
 
'''900'''
|18\17, 744.828
 
 
|'''22\17'''
|11\10, 776.471
 
 
'''910; 2.9'''
|15\13, 818.182
 
 
|'''13\10'''
|-
|Hb, He
'''917; 1.{{Overline|54}}'''
|14\15, 646.154
| 16\18, 619.355
|'''17\13'''
|6\7, 600
|14\17, 579.310
'''927.{{Overline|27}}'''
|8\10, 564.706
|10\13, 545.455
 
 
|-
|-
 
 
| Re#, La#
! H
!'''15\15,''' '''692.308'''
 
 
|C#
!'''11\11,''' '''694.737'''
 
 
| 5#
!'''18\18,''' '''696.774'''
|5#
|20\15
 
 
923: 13
! 7\7, 700
 
 
|15\11
!'''17\17,''' '''703.448'''
 
 
947; 2, 1.4
!'''10\10,''' '''705.882'''
 
 
|25\18
!'''13\13,''' '''709.091'''
 
 
967; 1, 2.875
|-
 
 
| rowspan="2" |10\7
|Η#
|16\15, 738.462
 
 
1000
|12\11, 757.895
 
 
|25\17
|20\18, 774.194
 
 
1034; 2, 14
| rowspan="2" |8\8, 800
 
 
| 15\10
|20\17, 827.586
 
 
1058; 1, 4.{{Overline|6}}
|12\10, 847.059
 
 
|20\13
|16\13, 872.727
1090.{{Overline|90}}
 
 
|-
|-
 
 
|Mib, Sib
|Cb, Ce
|18\15, 830.769
 
 
|Db
|13\11, 821.053
 
 
|6b, 6c
|21\18, 812.903
|6f
|22\15
 
 
1015; 2.6
|19\17, 786.207
 
 
|16\11
|11\10, 776.471
 
 
1010; 1.9
|14\13, 763.63
 
 
| 26\18
|-
 
 
1006; 2, 4.{{Overline|6}}
|'''C'''
|'''19\15,''' '''876.923'''
 
 
|24\17
|'''14\11,''' '''884.211'''
 
 
993; 9.{{Overline|6}}
|'''23\18,''' '''890.323'''
 
 
|14\10
|'''9\5,''' '''900'''
 
 
988; 4.25
|'''22\17,''' '''910.345'''
 
 
|18\13
|'''13\10,''' '''917.647'''
 
 
981.{{Overline|81}}
|'''17\13,''' '''927.273'''
 
 
|-
|-
 
 
|Mi, Si
|C#
|20\15, 923.077
 
 
|D
|15\11, 947.368
 
 
|6
|25\18, 967.742
|6
|23\15
 
 
1061; 1, 1.1{{Overline|6}}
| rowspan="2" |10\7, 1000
 
 
|17\11
|25\17, 1034.483
 
 
1073; 1, 2.1{{Overline|6}}
|15\10, 1058.824
 
 
| 28\18
|20\13, 1090.909
 
 
1083; 1.{{Overline|148}}
|-
 
 
|11\7
| Db, De
|22\15, 1015.385
 
 
1100
|16\11, 1010.526
 
 
| 27\17
|26\18, 1006.452
 
 
1117; 4, 7
|24\17, 993.103
 
 
| 16\10
|14\10, 988.235
 
 
1129; 2, 2.{{Overline|3}}
|18\13, 981.818
| 21\9
1145.{{Overline|45}}
 
 
|-
|-
 
 
|Mi#, Si#
|D
|23\15, 1061.538
 
 
| D#
|17\11, 1073.684
 
 
|6#
|28\18, 1083.871
|6#
| 24\15
 
 
1107; 1.{{Overline|4}}
|11\7, 1100
 
 
| rowspan="2" | 18\11
|27\17, 1117.241
 
 
1136; 1.1875
|16\10, 1129.412
 
 
|30\18
|21\9, 1145.455
 
 
1161; 3.{{Overline|4}}
|-
 
 
| 12\7
|D#
|24\15, 1107.923
1200
 
 
|30\17
| rowspan="2" |18\11, 1136.842
 
 
1241; 2.{{Overline|63}}
|30\18, 1161.29
 
 
|18\10
|12\7, 1200
 
 
1270; 1.7
|30\17, 1241.379
 
 
|24\13
|18\10, 1270.588
 
 
1309.{{Overline|09}}
|24\13, 1309.091
 
 
|-
|-
 
 
|Fab, Dob
|Ebb, Ëe
|25\15, 1153.846
 
 
|Ebb
|29\18, 1122.581
 
 
|7b, 7c
|11\7, 1100
|7f
|25\15
 
 
1153; 1.{{Overline|18}}
|26\17, 1075.862
 
 
|29\18
|15\10, 1058.824
 
 
1121; 1, 1, 2.6
| 19\13, 1036.364
 
 
| 11\7
|-
 
 
1100
|'''Eb, Ë'''
|'''26\15,''' '''1200'''
 
 
|26\17
|'''19\11,''' '''1200'''
 
 
1075; 1.16
|'''31\18,''' '''1200'''
 
 
|15\10
|'''12\7, 1200'''
 
 
1058; 1, 4.{{Overline|6}}
|'''29\17,''' '''1200'''
 
 
|19\13
|'''17\10,''' '''1200'''
 
 
1036.{{Overline|36}}
|'''22\13,''' '''1200'''
 
 
|-
|-
 
 
|'''Fa, Do'''
|E
|27\15, 1246.154
 
 
|'''Eb'''
|20\11, 1263.158
 
 
|'''7'''
|33\18, 1277.419
|'''7'''
 
 
|'''26\15'''
|13\7, 1300
 
 
'''1200'''
|32\17, 1324.138
 
 
|'''19\11'''
|19\10, 1341.176
 
 
'''1200'''
|25\13, 1363.636
 
 
|'''31\18'''
|-
 
 
'''1200'''
|E#
|28\15, 1292.308
|'''12\7'''
'''1200'''
 
 
|'''29\17'''
| rowspan="2" |21\11, 1326.318
 
 
'''1200'''
|35\18, 1354.834
 
 
|'''17\10'''
|14\7, 1400
 
 
'''1200'''
|35\17, 1448.275
 
 
|'''22\13'''
| 21\10, 1482.353
 
 
'''1200'''
|28\13, 1527.273
 
 
|-
|-
 
 
|Fa#, Do#
| Fb, Fe
|29\15, 1338.462
 
 
| E
|34\18, 1316.129
 
 
|7#
|13\7, 1300
|7#
|27\15
 
 
1246; 6.5
|31\17, 1282.759
 
 
|20\11
|18\10, 1270.588
 
 
1263; 6.{{Overline|3}}
|23\13, 1254.545
 
 
| 33\18
|-
 
 
1277; 2, 2.6
!F
!30\15, 1384.615
 
 
|13\7
!22\11, 1389.473
 
 
1300
!36\18, 1393.548
 
 
|32\17
!14\7, 1400
 
 
1324; 7.25
!34\17, 1406.897
 
 
|19\10
!20\10, 1411.765
1341; 5.{{Overline|6}}
|25\13
1363.{{Overline|63}}
 
 
!26\13, 1418.182
|}
{| class="wikitable"
|+Cents
! Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
! Superhard
|-
|-
!Bijou
|Fax, Dox
!~15edf
!~11edf
|E#
!~18edf
!~7edf
|7x
!~17edf
|7x
!~10edf
|28\15
!~13edf
1292; 3.25
| rowspan="2" |21\11
1326; 3.1{{Overline|6}}
|35\18
1354; 1, 5.2
| 14\7
1400
|35\17
1448; 3.625
|21\10
1482; 2.8{{Overline|3}}
|28\13
1527.{{Overline|27}}
|-
|-
|0#, D#
|Dob, Solb
|1\15, 46.154
|1\11, 63.158
|Fb
|2\18, 77.419
| rowspan="2" |1\7, 100
|8b, Fc
|3\17, 124.138
|8f
|2\10, 141.176
|29\15
|3\13, 163.636
|-
1338; 2.1{{Overline|6}}
|1b, 1c
|3\15, 138.462
|34\18
| 2\11. 126.316
|3\18, 116.129
1316; 7.75
|2\17, 82.759
|1\10, 70.588
|13\7
|1\13, 54.545
|-
1300
|'''1'''
|'''4\15,''' '''184.615'''
|31\17
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
1282; 1.13{{Overline|63}}
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|18\10
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
1270; 1.7
| 23\13
1254.{{Overline|54}}
|-
|-
|1#
!Do, Sol
|5\15, 230.769
|4\11, 252.632
!F
|7\18, 270.968
| rowspan="2" |3\7, 300
! 8, F
|8\17, 331.034
!8
|5\10, 352.941
! 30\15
|7\13, 381.818
|-
1384; 1.625
|2b, 2c
|7\15, 323.077
! 22\11
|5\11, 315.789
| 8\18, 309.677
1389; 2.{{Overline|1}}
| 7\17, 289.655
|4\10, 282.353
!36\18
|5\13, 272.727
|-
1393; 1, 1, 4.{{Overline|6}}
|2
|8\15, 369.231
!14\7
|6\11, 378.947
|10\18, 387.097
1400
|4\7, 400
|10\17, 413.793
! 34\17
|6\10, 423.529
|8\13, 436.364
1406; 1, 8.{{Overline|6}}
|-
|2#
! 20\10
| 9\15, 415.385
| rowspan="2" |7\11, 442.105
1411; 1, 3.25
|12\18, 464.516
|5\7, 500
!26\13
|13\17, 537.069
|8\10, 564.706
1418.{{Overline|18}}
|11\13, 600
|-
|-
|3b, 3c
|Do#, Sol#
| 10\15, 461.538
| 11\18, 425.806
|F#
|4\7, 400
|9\17, 372.414
|8#, F#
|5\10, 352.941
|8#
|6\13, 327.273
|31\15
|-
|'''3'''
1430; 1.3
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
| 23\11
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
1452; 1.58{{Overline|3}}
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|38\18
|'''9\13,''' '''490.909'''
|-
1470; 1.0{{Overline|3}}
|3#
|12\15, 553.846
| rowspan="2" |15\7
|9\11, 568.421
|15\18, 580.645
1500
|6\7, 600
|15\17, 620.690
| 37\17
|9\10, 635.294
|12\13, 654.545
1531; 29
|-
|3x
| 22\10
|13\15, 600
| rowspan="2" |10\11, 631.579
1552; 1.0625
|17\18, 658.064
|7\7, 700
|29\13
|18\17, 744.828
|11\10, 776.471
1581.{{Overline|81}}
|15\13, 818.182
|-
|-
|4b, 4c
| Reb, Lab
|14\15, 646.154
|16\18, 619.355
|Gb
|6\7, 600
|14\17, 579.310
|9b, Gc
|8\10, 564.706
|9f
|10\13, 545.455
|33\15
|-
!4
1523; 13
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
|24\11
!'''18\18,''' '''696.774'''
!7\7, 700
1515; 1.2{{Overline|6}}
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
| 39\18
!'''13\13,''' '''709.091'''
|-
1509; 1, 2.1
|4#
| 16\15, 738.462
|36\17
|12\11, 757.895
|20\18, 774.194
1489; 1, 1.9
| rowspan="2" |8\8, 800
|20\17, 827.586
|21\10
|12\10, 847.059
| 16\13, 872.727
1482; 2.8{{Overline|3}}
|-
|5b, 5c
|27\13
|18\15, 830.769
|13\11, 821.053
1472.{{Overline|72}}
|21\18, 812.903
|19\17, 786.207
|11\10, 776.471
|14\13, 763.63
|-
|'''5'''
|'''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'''
|-
|-
|5#
|'''Re, La'''
|20\15, 923.077
|15\11, 947.368
|'''G'''
|25\18, 967.742
| rowspan="2" |10\7, 1000
|'''9, G'''
|25\17, 1034.483
|9
|15\10, 1058.824
|'''34\15'''
|20\13, 1090.909
|-
'''1569; 4.{{Overline|3}}'''
|6b, 6c
|22\15, 1015.385
|'''25\11'''
|16\11, 1010.526
|26\18, 1006.452
'''1578; 1.0{{Overline|5}}'''
|24\17, 993.103
|14\10, 988.235
|'''41\18'''
|18\13, 981.818
|-
'''1587; 10.{{Overline|3}}'''
|6
|23\15, 1061.538
|'''16\7'''
|17\11, 1073.684
| 28\18, 1083.871
'''1600'''
|11\7, 1100
|27\17, 1117.241
|'''39\17'''
|16\10, 1129.412
|21\9, 1145.455
'''1613; 1, 3.8{{Overline|3}}'''
|-
|6#
|'''23\10'''
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
'''1623; 1.{{Overline|8}}'''
|30\18, 1161.290
|12\7, 1200
|'''30\13'''
|30\17, 1241.379
|18\10, 1270.588
'''1636.{{Overline|36}}'''
|24\13, 1309.091
|-
|-
| 7b, 7c
|Re#, La#
|25\15, 1153.846
|29\18, 1122.581
|G#
|11\7, 1100
|26\17, 1075.862
|9#, G#
|15\10, 1058.824
|9#
|19\13, 1036.364
|35\15
|-
|'''7'''
1615; 2.6
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
|26\11
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
1642; 9.5
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
| 43\18
|'''22\13,''' '''1200'''
|-
1664; 1.0625
|7#
|27\15, 1246.154
| rowspan="2" | 17\7
|20\11, 1263.158
|33\18, 1277.419
1700
|13\7, 1300
|32\17, 1324.138
|42\17
|19\10, 1341.176
|25\13, 1363.636
1737; 14.5
|-
|7x
|25\10
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
1764; 1.41{{Overline|6}}
|35\18, 1354.834
|14\7, 1400
|33\13
|35\17, 1448.275
|21\10, 1482.353
1800
|28\13, 1527.273
|-
|-
|8b, Fc
|Mib, Sib
|29\15, 1338.462
|34\18, 1316.129
|Ab
|13\7, 1300
|31\17, 1282.759
|Xb, Ac
|18\10, 1270.588
|Af
|23\13, 1254.545
|37\15
|-
!8, F
1707; 1.{{Overline|4}}
!30\15, 1384.615
!22\11, 1389.473
|27\11
!36\18, 1393.548
!14\7, 1400
1705; 3.8
!34\17, 1406.897
!20\10, 1411.765
|44\18
!26\13, 1418.182
|-
1703; 4, 2.{{Overline|3}}
|8#, F#
|31\15, 1430.769
|41\17
|23\11, 1452.632
|38\18, 1470.968
1696; 1.8125
| rowspan="2" |15\7, 1500
|37\17, 1531.034
|24\10
|22\10, 1552.941
|29\13, 1581.818
1694; 8.5
|-
|9b, Gc
|31\13
|33\15, 1523.077
|24\11, 1515.789
1690.{{Overline|90}}
|39\18, 1509.677
|36\17, 1489.655
|21\10, 1482.759
|27\13, 1472.273
|-
|'''9, G'''
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.364'''
|-
|9#, G#
|35\15, 1615.385
|26\11, 1642.105
|43\18, 1664.516
| rowspan="2" |17\7, 1700
|42\17, 1737.069
|25\10, 1764.706
|33\13, 1800
|-
|Xb, Ac
|37\15, 1707.692
|27\11, 1705.263
|44\18, 1703.226
|41\17, 1696.552
|24\10, 1694.118
|31\13, 1690.909
|-
|-
|Mi, Si
|A
|X, A
|X, A
|A
|38\15, 1753.846
|38\15
|28\11, 1768.421
|46\18, 1780.645
1753; 1.{{Overline|18}}
|18\7, 1800
|44\17, 1820.690
|28\11
|26\10, 1835.294
|34\13, 1854.545
1768; 2.375
|-
|X#, A#
|46\18
|39\15, 1800
| rowspan="2" |29\11, 1831.579
1780; 1.55
|48\18, 1858.064
|19\7, 1900
|18\7
|47\17, 1944.828
|28\10, 1976.471
1800
|37\13, 2018.182
|-
|44\17
|Ebb, Ccc
|40\15, 1846.154
1820; 1.45
|47\18, 1819.355
|18\7, 1800
|26\10
|43\17, 1779.310
|25\10, 1764.706
1835; 3.4
|32\13, 1745.545
|-
|34\13
|'''Eb, Cc'''
|'''41\15,''' '''1892.308'''
1854.{{Overline|54}}
|'''30\11,''' '''1894.737'''
|'''49\18,''' '''1896.774'''
|'''19\7, 1900'''
|'''46\17,''' '''1903.448'''
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
|-
|-
|E, C
|Mi#, Si#
|42\15, 1938.462
|31\11, 1957.895
| A#
|51\18, 1974.194
|20\7, 2000
|X#, A#
|49\17, 2027.586
|A#
|29\10, 2047.059
|39\15
|38\13, 2072.727
|-
1800
|Ex, Cx
|43\15, 1984.615
| rowspan="2" |29\11
| rowspan="2" |32\11, 2021.053
|53\18, 2051.612
1831; 1.{{Overline|72}}
|21\7, 2100
|52\17, 2151.725
|48\18
|31\10, 2188.235
|41\13, 2236.364
1858; 15.5
|-
|0b, Dc
|19\7
|44\15, 2030.769
|52\18, 2012.903
1900
|20\7, 2000
|48\17, 1986.207
|47\17
|28\10, 1976.471
|36\13, 1963.636
1944; 1.208{{Overline|3}}
|28\10
1976; 2.125
| 37\13
2018.{{Overline|18}}
|-
|-
! 0, D
|Fab, Dob
!45\15, 2076.923
!33\11, 2084.211
|Bbb
!54\18, 2090.323
!21\7, 2100
|Ebb, Ccc
!51\17, 2110.345
|Bf
!30\10, 2117.647
|40\15
!39\13, 2127.273
|}
1846; 6.5
 
{| class="wikitable"
|47\18
|+Cents
!Notation
1819; 2.{{Overline|81}}
!Supersoft
!Soft
| 18\7
!Semisoft
! Basic
1800
!Semihard
!Hard
|43\17
!Superhard
1779; 3.{{Overline|2}}
|25\10
1764; 1.41{{Overline|6}}
| 32\13
1745.{{Overline|45}}
|-
|-
!Hextone
|'''Fa, Do'''
!~15edf
!~11edf
|'''Bb'''
!~18edf
!~7edf
|'''Eb, Cc'''
!~17edf
|'''B'''
!~10edf
|'''41\15'''
!~13edf
|-
'''1892; 3.25'''
|0#, G#
|1\15, 46.154
|'''30\11'''
|1\11, 63.158
|2\18, 77.419
'''1894; 1, 2.8'''
| rowspan="2" |1\7, 100
|3\17, 124.138
|'''49\18'''
|2\10, 141.176
|3\13, 163.636
'''1896; 1.291{{Overline|6}}'''
|-
| 1f
|'''19\7'''
|3\15, 138.462
|2\11. 126.316
'''1900'''
|3\18, 116.129
|2\17, 82.759
|'''46\17'''
|1\10, 70.588
|1\13, 54.545
'''1903; 2.1{{Overline|6}}'''
|-
|'''1'''
|'''27\10'''
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
'''1905; 1.1{{Overline|3}}'''
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|'''35\13'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
'''1909.{{Overline|09}}'''
|'''4\13,''' '''218.182'''
|-
|1#
|5\15, 230.769
|4\11, 252.632
|7\18, 270.968
| rowspan="2" |3\7, 300
|8\17, 331.034
|5\10, 352.941
|7\13, 381.818
|-
|-
|2f
|Fa#, Do#
|7\15, 323.077
|5\11, 315.789
| B
|8\18, 309.677
|7\17, 289.655
|E, C
|4\10, 282.353
|B#
|5\13, 272.727
|42\15
|-
|2
1938; 2.1{{Overline|6}}
|8\15, 369.231
|6\11, 378.947
|31\11
|10\18, 387.097
| 4\7, 400
1957; 1, 8.5
|10\17, 413.793
|6\10, 423.529
| 51\18
|8\13, 436.364
|-
1974; 5.1{{Overline|6}}
|2#
|9\15, 415.385
|20\7
| rowspan="2" |7\11, 442.105
|12\18, 464.516
2000
|5\7, 500
|13\17, 537.069
|49\17
|8\10, 564.706
|11\13, 600
2027; 1, 1.41{{Overline|6}}
|-
|3f
|29\10
| 10\15, 461.538
|11\18, 425.806
2047; 17
|4\7, 400
|9\17, 372.414
|38\13
|5\10, 352.941
|6\13, 327.273
2072.{{Overline|72}}
|-
|-
|'''3'''
|Fax, Dox
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|B#
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|Ex, Cx
|'''12\17,''' '''496.552'''
|Bx
|'''7\10,''' '''494.118'''
|43\15
|'''9\13,''' '''490.909'''
|-
1984; 1.625
|3#
|12\15, 553.846
| rowspan="2" |32\11
|9\11, 568.421
|15\18, 580.645
2021; 19
|6\7, 600
|15\17, 620.690
|53\18
|9\10, 635.294
|12\13, 654.545
2051; 1, 1, 1, 1.4
|-
| 3x
|21\7
|13\15, 600
| rowspan="2" | 10\11, 631.579
2100
|17\18, 658.064
|7\7, 700
|52\17
|18\17, 744.828
|11\10, 776.471
2151; 2.625
|15\13, 818.182
|-
|31\10
|4f
| 14\15, 646.154
2188; 4.25
|16\18, 619.355
|6\7, 600
|41\13
|14\17, 579.310
|8\10, 564.706
2236.{{Overline|36}}
|10\13, 545.455
|-
!4
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
!7\7, 700
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
|-
|-
| 4#
|Dob, Solb
|16\15, 738.462
|12\11, 757.895
|Hb
|20\18, 774.194
| rowspan="2" |8\8, 800
|0b, Dc
|20\17, 827.586
|Cf
|12\10, 847.059
|44\15
|16\13, 872.727
|-
2030; 1.3
|5
|18\15, 830.769
|52\18
|13\11, 821.053
|21\18, 812.903
2012; 1, 9,{{Overline|3}}
|19\17, 786.207
| 11\10, 776.471
|20\7
|14\13, 763.63
|-
2000
|'''5'''
|'''19\15,''' '''876.923'''
|48\17
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
1986; 4.8{{Overline|3}}
|'''9\5,''' '''900'''
|'''22\17,''' '''910.345'''
|28\10
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
1976; 2.125
|-
|5#
|36\13
|20\15, 923.077
|15\11, 947.368
1963.{{Overline|63}}
| 25\18, 967.742
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|15\10, 1058.824
|20\13, 1090.909
|-
|6f
|22\15, 1015.385
|16\11, 1010.526
|26\18, 1006.452
|24\17, 993.103
|14\10, 988.235
|18\13, 981.818
|-
|-
|6
!Do, Sol
|23\15, 1061.538
|17\11, 1073.684
!H
|28\18, 1083.871
|11\7, 1100
!0, D
|27\17, 1117.241
!C
|16\10, 1129.412
!45\15
|21\9, 1145.455
2076; 1.08'''{{Overline|3}}'''
!33\11
2084; 4.75
!54\18
2090; 3.1
!21\7
2100
!51\17
2110; 2.9
!30\10
2117; 1.{{Overline|54}}
!39\13
2127.{{Overline|27}}
|-
|-
|Do#, Sol#
|6#
|Η#
|24\15, 1107.923
|0#, D#
| rowspan="2" |18\11, 1136.842
|C#
|30\18, 1161.290
|46\15
|12\7, 1200
2123; 13
|30\17, 1241.379
|34\11
|18\10, 1270.588
2147; 2, 1.4
|24\13, 1309.091
|56\18
2167; 1, 2.875
| rowspan="2" |22\7
2200
|54\17
2234; 2, 14
|32\10
2258; 1, 4.{{Overline|6}}
|42\13
2090.{{Overline|90}}
|-
|-
|Reb, Lab
| 7f
|Cb
|25\15, 1153.846
|1b, 1c
|29\18, 1122.581
|Df
|11\7, 1100
|48\15
|26\17, 1075.862
2215; 2.6
|15\10, 1058.824
|35\11
|19\13, 1036.364
2210; 1.9
|57\18
2206; 2, 4.{{Overline|6}}
|53\17
2193; 9.{{Overline|6}}
|31\10
2188; 4.25
|40\13
2181.{{Overline|81}}
|-
|-
|'''Re, La'''
|'''7'''
|'''C'''
|'''26\15,''' '''1200'''
|'''1'''
|'''19\11,''' '''1200'''
|'''D'''
|'''31\18,''' '''1200'''
|'''49\15'''
|'''12\7, 1200'''
'''2261; 1, 1.1{{Overline|6}}'''
|'''29\17,''' '''1200'''
|'''36\11'''
|'''17\10,''' '''1200'''
'''2273; 1, 2.1{{Overline|6}}'''
|'''22\13,''' '''1200'''
|'''59\18'''
'''2283; 1.{{Overline|148}}'''
|'''23\7'''
'''2300'''
|'''56\17'''
'''2317; 4, 7'''
|'''33\10'''
'''2329; 2, 2.{{Overline|3}}'''
|'''43\13'''
'''2245.{{Overline|45}}'''
|-
|-
|Re#, La#
|7#
|C#
|27\15, 1246.154
|1#
|20\11, 1263.158
|D#
|33\18, 1277.419
|50\15
|13\7, 1300
2307; 1.{{Overline|4}}
|32\17, 1324.138
|37\11
|19\10, 1341.176
2336; 1.1875
|25\13, 1363.636
|61\18
2361; 3.{{Overline|4}}
| rowspan="2" |24\7
2400
|59\17
2441; 2.{{Overline|63}}
|35\10
2470; 1.7
|46\13
2509.{{Overline|09}}
|-
|-
|Mib, Sib
|7x
|Db
|28\15, 1292.308
|2b, 2c
| rowspan="2" |21\11, 1326.318
|Ef
|35\18, 1354.834
|52\15
|14\7, 1400
2400
|35\17, 1448.275
|38\11
|21\10, 1482.353
2400
|28\13, 1527.273
|62\18
2400
|58\17
2400
|34\10
2400
|44\13
2400
|-
|-
|Mi, Si
|8f
|D
|29\15, 1338.462
|2
| 34\18, 1316.129
|E
|13\7, 1300
|53\15
|31\17, 1282.759
2446; 6.5
|18\10, 1270.588
|39\11
|23\13, 1254.545
2463; 6.{{Overline|3}}
|-
|64\18
! 8
2477; 2, 2.6
!30\15, 1384.615
|25\7
!22\11, 1389.473
2500
!36\18, 1393.548
|61\17
!14\7, 1400
2524; 7.25
!34\17, 1406.897
|36\10
!20\10, 1411.765
2541; 5.{{Overline|6}}
!26\13, 1418.182
|47\13
2563.{{Overline|63}}
|-
|-
|Mi#, Si#
|8#
|D#
|31\15, 1430.769
|2#
|23\11, 1452.632
|E#
| 38\18, 1470.968
|54\15
| rowspan="2" |15\7, 1500
2492; 3.25
|37\17, 1531.034
| rowspan="2" |40\11
|22\10, 1552.941
2526; 3.1
|29\13, 1581.818
|66\18
2554; 1, 5.2
|26\7
2600
|64\17
2648; 2.625
|38\10
2682; 2.8{{Overline|3}}
|50\13
2727.{{Overline|27}}
|-
|-
|Fab, Dob
|9f
|Ebb
|33\15, 1523.077
|3b, 3c
|24\11, 1515.789
|Fff
|39\18, 1509.677
|55\15
| 36\17, 1489.655
2538; 2.1{{Overline|6}}
|21\10, 1482.759
|65\18
|27\13, 1472.273
2516; 7.75
|25\7
2500
|60\17
2482; 1.13{{Overline|63}}
|35\10
2470; 1.7
|45\13
2454.{{Overline|54}}
|-
|-
|'''Fa, Do'''
|9
|'''Eb'''
|'''34\15,''' '''1569.231'''
|'''3'''
|'''25\11,''' '''1578.947'''
|'''Ff'''
|'''41\18,''' '''1587.097'''
|'''56\15'''
|'''16\7,''' '''1600'''
'''2584; 1.625'''
|'''39\17,''' '''1613.793'''
|'''41\11'''
|'''23\10,''' '''1623.529'''
'''2589; 2.{{Overline|1}}'''
|'''30\13,''' '''1636.364'''
|'''67\18'''
'''2593; 1, 1, 4.{{Overline|6}}'''
|'''26\7'''
'''2600'''
|'''63\17'''
'''2606; 1, 8.'''{{Overline|6}}
|'''37\10'''
'''2611; 1, 3.25'''
|'''48\13'''
'''2618.{{Overline|18}}'''
|-
|-
|Fa#, Do#
|9#
|E
|35\15, 1615.385
|3#
|26\11, 1642.105
|F
|43\18, 1664.516
|57\15
| rowspan="2" |17\7, 1700
2630; 1.3
|42\17, 1737.069
|42\11
|25\10, 1764.706
2652; 1.58{{Overline|3}}
|33\13, 1800
|69\18
2670; 1.0{{Overline|3}}
|27\7
2700
|66\17
2731; 29
|39\10
2752; 1.0625
|51\13
2781.{{Overline|81}}
|-
|-
|Fax, Dox
|Af
|E#
| 37\15, 1707.692
|3x
| 27\11, 1705.263
|F#
|44\18, 1703.226
|58\15
|41\17, 1696.552
2676; 1.08{{Overline|3}}
|24\10, 1694.118
| rowspan="2" |43\11
|31\13, 1690.909
2715; 1.2{{Overline|6}}
|71\18
2748; 2.58{{Overline|3}}
|28\7
2800
|69\17
2855; 4.8
|41\10
2894; 8.5
|54\13
2945.{{Overline|45}}
|-
|-
|Dob, Solb
|A
|Fb
| 38\15, 1753.846
|4b, 4c
|28\11, 1768.421
|0f, Gf
|46\18, 1780.645
|59\15
|18\7, 1800
2723; 13
|44\17, 1820.690
|70\18
|26\10, 1835.294
2709; 1, 2.1
|34\13, 1854.545
|27\7
2700
|65\17
2689; 1, 1.9
|38\10
2682; 2.8{{Overline|3}}
|49\13
2672.{{Overline|72}}
|-
|-
!Do, Sol
|A#
!F
| 39\15, 1800
!4
| rowspan="2" |29\11, 1831.579
!0, G
| 48\18, 1858.064
!60\15
|19\7, 1900
2769; 4.'''{{Overline|3}}'''
|47\17, 1944.828
!44\11
|28\10, 1976.471
2778; 1.0{{Overline|5}}
|37\13, 2018.182
!72\18
|-
2787; 3.1
|Ax
!28\7
|40\15, 1846.154
2800
|47\18, 1819.355
!68\17
|18\7, 1800
2813; 1, 3.8{{Overline|3}}
|43\17, 1779.310
!40\10
|25\10, 1764.706
2823; 1.{{Overline|8}}
|32\13, 1745.545
!52\13
|-
2836.{{Overline|36}}
|'''Bf'''
|}
|'''41\15,''' '''1892.308'''
|'''30\11,''' '''1894.737'''
{| class="wikitable"
|'''49\18,''' '''1896.774'''
|+Relative cents<ref name=":02">Fractions repeating more than 4 digits written as continued fractions</ref>
|'''19\7, 1900'''
! colspan="4" | Notation
|'''46\17,''' '''1903.448'''
!Supersoft
|'''27\10,''' '''1905.882'''
!Soft
|'''35\13,''' '''1909.091'''
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
|-
! Diatonic
|B
!Napoli
|42\15, 1938.462
! Bijou
|31\11, 1957.895
!Hextone
|51\18, 1974.194
!~15edf
|20\7, 2000
!~11edf
|49\17, 2027.586
!~18edf
| 29\10, 2047.059
!~7edf
|38\13, 2072.727
!~17edf
!~10edf
!~13edf
|-
|-
|Do#, Sol#
|B#
|F#
|43\15, 1984.615
|0#, D#
| rowspan="2" |32\11, 2021.053
|0#, G#
|53\18, 2051.612
|1\15
|21\7, 2100
|52\17, 2151.725
''46.{{Overline|6}}''
|31\10, 2188.235
|1\11
|41\13, 2236.364
''63.{{Overline|63}}''
|2\18
''77.7̄''
| rowspan="2" |1\7
''100''
| 3\17
''123.529…''
| 2\10
''140''
|3\13
''161.538…''
|-
|-
|Reb, Lab
|Cf
| Gb
|44\15, 2030.769
|1b, 1c
|52\18, 2012.903
|1f
|20\7, 2000
|3\15
|48\17, 1986.207
|28\10, 1976.471
''140''
|36\13, 1963.636
|2\11
''127.{{Overline|27}}''
|3\18
''116.{{Overline|6}}''
| 2\17
''82.352…''
|1\10
''70''
|1\13
''53.846…''
|-
|-
|'''Re, La'''
!C
|'''G'''
!45\15, 2076.923
|'''1'''
!33\11, 2084.211
|'''1'''
!54\18, 2090.323
|'''4\15'''
!21\7, 2100
!51\17, 2110.345
'''''186.{{Overline|6}}'''''
!30\10, 2117.647
|'''3\11'''
!39\13, 2127.273
'''''190.{{Overline|90}}'''''
|'''5\18'''
'''''194.{{Overline|4}}'''''
|'''2\7'''
'''''200'''''
|'''5\17'''
'''''205.882…'''''
|'''3\10'''
'''''210'''''
|'''4\13'''
'''''215.384…'''''
|-
|-
|Re#, La#
|C#
| G#
|46\15, 2123.077
| 1#
|34\11, 2147.368
|1#
|56\15, 2167.742
|5\15
| rowspan="2" |22\7, 2200
|54\17, 2234.483
''233.{{Overline|3}}''
|32\10, 2258.824
|4\11
|42\13, 2090.909
|-
''254.{{Overline|54}}''
|Df
|7\18
|48\15, 2215.385
|35\11, 2210.526
''272.2̄''
|57\15, 2206.452
| rowspan="2" |3\7
|53\17, 2193.103
|31\10, 2188.235
''300''
|40\13, 2181.818
|8\17
|-
|'''D'''
''329.411…''
|'''49\15, 2261.538'''
|5\10
|'''36\11, 1073.684'''
|'''59\18, 2283.871'''
''350''
|'''23\7, 2300'''
|7\13
|'''56\17, 2317.241'''
|'''33\10, 2329.412'''
''376.923…''
|'''43\13,''' '''2345.455'''
|-
|-
|Mib, Sib
|D#
|Ab
|50\15, 2307.692
|2b, 2c
|37\11, 2336.842
|2f
|61\18, 2361.290
|7\15
| rowspan="2" |24\7, 2400
|59\17, 2441.379
''326.{{Overline|6}}''
|35\10, 2470.588
|5\11
|46\13, 2509.091
''318.{{Overline|18}}''
| 8\18
''311.{{Overline|1}}''
|7\17
''288.235…''
| 4\10
''280''
|5\13
''269.230…''
|-
|-
|Mi, Si
|Ef
|A
|52\15, 2400
| 2
|38\11, 2400
|2
|62\18, 2400
|8\15
|58\17, 2400
|34\10, 2400
''373.{{Overline|3}}''
| 44\13, 2400
|6\11
''381.{{Overline|81}}''
|10\18
''388.{{Overline|8}}''
|4\7
''400''
|10\17
''411.764…''
|6\10
''420''
|8\13
''430.769…''
|-
|-
|Mi#, Si#
|E
|A#
|53\15, 2446.154
|2#
| 39\11, 2463.158
|2#
|64\18, 2477,419
|9\15
|25\7, 2500
|61\17, 2524.138
''420''
|36\10, 2541.176
| rowspan="2" |7\11
|47\13, 2563.636
''445.{{Overline|45}}''
|12\18
''466.{{Overline|6}}''
|5\7
''500''
|13\17
''535.294…''
|8\10
''560''
|11\13
''592.307…''
|-
|-
|Fab, Dob
|E#
|Bbb
|54\15, 2492.308
|3b, 3c
| rowspan="2" |40\11, 2526.316
|3f
|66\18, 2554.838
|10\15
|26\7, 2600
|64\17, 2648.275
''466.{{Overline|6}}''
|38\10, 2682.353
|11\18
|50\13, 2727.273
''427.{{Overline|7}}''
|4\7
''400''
|9\17
''370.588…''
|5\10
''350''
|6\13
''323.076.…''
|-
|-
|'''Fa, Do'''
|Fff
|'''Bb'''
| 55\15, 2538.462
|'''3'''
| 65\18, 2516.129
|'''3'''
|25\7, 2500
|'''11\15'''
|60\17, 2482.759
|35\10, 2470.588
'''''513.{{Overline|3}}'''''
|45\13, 2454.545
|'''8\11'''
|-
|'''Ff'''
'''''509.{{Overline|09}}'''''
|'''56\15, 2584.615'''
|'''13\18'''
|'''41\11, 2589.474'''
|'''67\18, 2593.548'''
'''''505.{{Overline|5}}'''''
|'''26\7, 2600'''
|'''5\7'''
|'''63\17, 2606.897'''
|'''37\10, 2611.765'''
'''''500'''''
|'''48\13,''' '''2618.182'''
|'''12\17'''
|-
|F
'''''494.117…'''''
|57\15, 2630.769
|'''7\10'''
|42\11, 2652.632
|69\18, 2670.968
'''''490'''''
|27\7, 2700
|'''9\13'''
|66\17, 2731.034
|39\10, 2752.941
'''''484.615…'''''
|51\13, 2781.818
|-
| F#
| rowspan="2" |58\15, 2676.923
|43\11, 2715.789
|71\18, 2748.387
| 28\7, 2800
|69\17, 2855.172
|41\10, 2894.118
|54\13, 2945.455
|-
|-
|Fa#, Do#
|0ff, Gff
| B
|42\11, 2652.632
|3#
|68\18, 2632.258
|3#
|26\7, 2600
|12\15
|62\17, 2565.517
|36\10, 2541.176
''560''
|46\13, 2509.091
|9\11
''572.{{Overline|72}}''
| 15\18
''583.{{Overline|3}}''
|6\7
''600''
|15\17
''617.647…''
|9\10
''630''
|12\13
''646.153…''
|-
|-
| Fax, Dox
|0f, Gf
|B#
|59\15, 2723.077
|3x
|43\11, 2715.789
|3x
|70\18, 2709.677
|13\15
|27\7, 2700
|65\17, 2689.552
''606. {{Overline|6}}''
|38\10, 2682.353
| rowspan="2" |10\11
|49\13, 2672.273
''636.{{Overline|36}}''
|17\18
''661.{{Overline|1}}''
|7\7
''700''
|18\17
''741.176…''
|11\10
''770''
|15\13
''807.692…''
|-
|-
|Dob, Solb
!0, G
|Hb
!60\15, 2769.231
|4b, 4c
!44\11, 2778.947
|4f
!72\18, 2787.097
|14\15
!28\7, 2800
!68\17, 2813.793
''653.{{Overline|3}}''
!40\10, 2823.529
|16\18
!52\13, 2836.364
|}
''622.{{Overline|2}}''
 
|6\7
{| class="wikitable"
|+Cents
''600''
!Notation
| 14\17
!Supersoft
!Soft
''576.470…''
! Semisoft
| 8\10
! Basic
!Semihard
''560''
!Hard
|10\13
!Superhard
''538.461…''
|-
|-
!Do, Sol
!Guidotonic
!H
!~15edf
!4
!~11edf
!4
!~18edf
! colspan="7" |''700''
!~7edf
!~17edf
!~10edf
!~13edf
|-
|F ut#
|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
|-
|G reb
|3\15, 138.462
|2\11. 126.316
|3\18, 116.129
|2\17, 82.759
|1\10, 70.588
|1\13, 54.545
|-
|-
|Do#, Sol#
|'''G re'''
|Η#
|'''4\15,''' '''184.615'''
|4#
|'''3\11,''' '''189.474'''
|4#
|'''5\18,''' '''193.548'''
|16\15
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
''746.{{Overline|6}}''
|'''3\10,''' '''211.765'''
|12\11
|'''4\13,''' '''218.182'''
''763.{{Overline|63}}''
|20\18
''777.{{Overline|7}}''
| rowspan="2" |8\7
''800''
|20\17
''823.529…''
|12\10
''840''
|16\13
''861.538…''
|-
|-
|Reb, Lab
|G re#
|Cb
|5\15, 230.769
|5b, 5c
|4\11, 252.632
|5
|7\18, 270.968
|18\15
| rowspan="2" |3\7, 300
|8\17, 331.034
''840''
|5\10, 352.941
|13\11
|7\13, 381.818
''827.{{Overline|27}}''
|21\18
''816.{{Overline|6}}''
| 19\17
''782.352…''
|11\10
''770''
|14\13
''753.846…''
|-
|-
|'''Re, La'''
|A mib
|'''C'''
|7\15, 323.077
|'''5'''
|5\11, 315.789
|'''5'''
|8\18, 309.677
|'''19\15'''
|7\17, 289.655
|4\10, 282.353
'''''886.{{Overline|6}}'''''
|5\13, 272.727
|'''14\11'''
|-
|A mi
'''''890.{{Overline|90}}'''''
|8\15, 369.231
|'''23\18'''
| 6\11, 378.947
|10\18, 387.097
'''''894.{{Overline|4}}'''''
|4\7, 400
|'''9\7'''
|10\17, 413.793
|6\10, 423.529
'''''900'''''
|8\13, 436.364
|'''22\17'''
'''''905.882…'''''
|'''13\10'''
'''''910'''''
|'''17\13'''
'''''915.384…'''''
|-
|-
| Re#, La#
| A mi#
|C#
|9\15, 415.385
|5#
| rowspan="2" |7\11, 442.105
|5#
|12\18, 464.516
|20\15
|5\7, 500
|13\17, 537.069
''933.{{Overline|3}}''
|8\10, 564.706
|15\11
|11\13, 600
''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
|B fa utb
|Db
|10\15, 461.538
|6b, 6c
|11\18, 425.806
|6f
|4\7, 400
|22\15
|9\17, 372.414
|5\10, 352.941
''1026.{{Overline|6}}''
|6\13, 327.273
|16\11
''1018.{{Overline|18}}''
|26\18
''1011.{{Overline|1}}''
|24\17
''988.235…''
|14\10
''980''
|18\13
''969.230…''
|-
|-
|Mi, Si
|'''B fa ut'''
|D
|'''11\15,''' '''507.692'''
|6
|'''8\11,''' '''505.263'''
|6
|'''13\18,''' '''503.226'''
| 23\15
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
''1073.{{Overline|3}}''
|'''7\10,''' '''494.118'''
|17\11
|'''9\13,''' '''490.909'''
|-
''1081.{{Overline|81}}''
|B fa ut#
|28\18
|12\15, 553.846
|9\11, 568.421
''1088.{{Overline|8}}''
|15\18, 580.645
|11\7
|6\7, 600
|15\17, 620.690
''1100''
|9\10, 635.294
|27\17
|12\13, 654.545
''1111.764…''
|16\10
''1120''
|21\13
''1130.769…''
|-
|-
|Mi#, Si#
|B fa utx
| D#
| 13\15, 600
|6#
| rowspan="2" |10\11, 631.579
|6#
|17\18, 658.064
|24\15
|7\7, 700
|18\17, 744.828
''1120''
|11\10, 776.471
| rowspan="2" | 18\11
|15\13, 818.182
''1145.{{Overline|45}}''
|30\18
''1166.{{Overline|6}}''
|12\7
''1200''
| 30\17
''1235.294…''
|18\10
''1260''
|24\13
''1292.307…''
|-
|-
| Fab, Dob
|C sol re utb
| Ebb
| 14\15, 646.154
| 7b, 7c
|16\18, 619.355
|7f
|6\7, 600
|25\15
|14\17, 579.310
|8\10, 564.706
''1166.{{Overline|6}}''
|10\13, 545.455
|29\18
''1127.{{Overline|7}}''
|11\7
''1100''
|26\17
''1070.588…''
|15\10
''1050''
|19\13
''1023.076…''
|-
|-
|'''Fa, Do'''
!C sol re ut
|'''Eb'''
!'''15\15,''' '''692.308'''
|'''7'''
!'''11\11,''' '''694.737'''
|'''7'''
!'''18\18,''' '''696.774'''
|'''26\15'''
!7\7, 700
!'''17\17,''' '''703.448'''
'''''1213.{{Overline|3}}'''''
!'''10\10,''' '''705.882'''
|'''19\11'''
!'''13\13,''' '''709.091'''
|-
'''''1209.{{Overline|09}}'''''
|C sol re ut#
|'''31\18'''
|16\15, 738.462
|12\11, 757.895
'''''1205.{{Overline|5}}'''''
|20\18, 774.194
|'''12\7'''
| rowspan="2" |8\8, 800
|20\17, 827.586
'''''1200'''''
|12\10, 847.059
|'''29\17'''
|16\13, 872.727
|-
'''''1194.117…'''''
|D la mi reb
|'''17\10'''
|18\15, 830.769
|13\11, 821.053
'''''1190'''''
|21\18, 812.903
|'''22\13'''
|19\17, 786.207
|11\10, 776.471
'''''1184.615…'''''
|14\13, 763.63
|-
|'''D la mi re'''
|'''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'''
|-
|D la mi re#
|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
|-
|-
|Fa#, Do#
|E fa utb
|E
|21\15, 969.231
|7#
|24\18, 929.032
|7#
| 9\5, 900
|27\15
|21\17, 868.966
|12\10, 847.059
''1260''
|15\13, 818.182
|20\11
''1272.{{Overline|72}}''
| 33\18
''1283.{{Overline|3}}''
|13\7
''1300''
|32\17
''1317.647…''
|19\10
''1330''
| 25\13
''1346.153…''
|-
|-
|Fax, Dox
|E fa ut
|E#
| 22\15, 1015.385
|7x
|16\11, 1010.526
|7x
|26\18, 1006.452
|28\15
|10\7, 1000
|24\17, 993.103
''1306.{{Overline|6}}''
|14\10, 988.235
| rowspan="2" |21\11
|18\13, 981.818
|-
''1336.{{Overline|36}}''
|E si mi re
|35\18
|23\15, 1061.538
|17\11, 1073.684
''1361.{{Overline|1}}''
|28\18, 1083.871
|14\7
|11\7, 1100
|27\17, 1117.241
''1400''
|16\10, 1129.412
|35\17
|21\9, 1145.455
''1441.176…''
|21\10
''1470''
|28\13
''1507.692…''
|-
|-
|Dob, Solb
| E si mi re#
|Fb
|24\15, 1107.923
|8b, Fc
| rowspan="2" |18\11, 1136.842
|8f
|30\18, 1161.29
|29\15
|12\7, 1200
|30\17, 1241.379
''1333.{{Overline|3}}''
| 18\10, 1270.588
|34\18
|24\13, 1309.091
''1322.{{Overline|2}}''
|13\7
''1300''
|31\17
''1276.470…''
|18\10
''1260''
|23\13
''1238.461…''
|-
|-
!Do, Sol
|F sol fa ut reb
!F
|25\15, 1153.846
!8, F
|29\18, 1122.581
!8
|11\7, 1100
! colspan="7" |''1400''
|26\17, 1075.862
|15\10, 1058.824
|19\13, 1036.364
|-
|-
|Do#, Sol#
|'''F sol fa ut re'''
|F#
|'''26\15,''' '''1200'''
|8#, F#
|'''19\11,''' '''1200'''
|8#
|'''31\18,''' '''1200'''
|31\15
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
''1446.{{Overline|6}}''
|'''17\10,''' '''1200'''
|23\11
|'''22\13,''' '''1200'''
''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
|F sol fa ut re#
|Gb
|27\15, 1246.154
| 9b, Gc
|20\11, 1263.158
|9f
|33\18, 1277.419
|33\15
|13\7, 1300
|32\17, 1324.138
''1540''
| 19\10, 1341.176
|24\11
| 25\13, 1363.636
''1527.{{Overline|27}}''
|39\18
''1516.{{Overline|6}}''
| 36\17
''1482.352…''
|21\10
''1470''
|27\13
''1453.846…''
|-
|-
|'''Re, La'''
|F sol fa ut rex
|'''G'''
|28\15, 1292.308
|'''9, G'''
| rowspan="2" |21\11, 1326.318
|9
|35\18, 1354.834
|'''34\15'''
| 14\7, 1400
|35\17, 1448.275
'''''1586.{{Overline|6}}'''''
|21\10, 1482.353
|'''25\11'''
|28\13, 1527.273
'''''1590.{{Overline|90}}'''''
|'''41\18'''
'''''1594.{{Overline|4}}'''''
|'''16\7'''
'''''1600'''''
|'''39\17'''
'''''1605.882…'''''
|'''23\10'''
'''''1610'''''
|'''30\13'''
'''''1615.384…'''''
|-
|-
|Re#, La#
|G la sol re mib
|G#
| 29\15, 1338.462
|9#, G#
|34\18, 1316.129
|9#
| 13\7, 1300
|35\15
|31\17, 1282.759
|18\10, 1270.588
''1633.{{Overline|3}}''
|23\13, 1254.545
|26\11
''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
!G la sol re mi
| Ab
!30\15, 1384.615
|Xb, Ac
!22\11, 1389.473
|Af
!36\18, 1393.548
|37\15
!14\7, 1400
!34\17, 1406.897
''1726.{{Overline|6}}''
!20\10, 1411.765
| 27\11
!26\13, 1418.182
|-
''1718.{{Overline|18}}''
|G la sol re mi#
|44\18
|31\15, 1430.769
|23\11, 1452.632
''1711.{{Overline|1}}''
|38\18, 1470.968
|41\17
| rowspan="2" |15\7, 1500
|37\17, 1531.034
''1688.235…''
|22\10, 1552.941
| 24\10
|29\13, 1581.818
|-
''1680''
|A si la mi fab
|31\13
|33\15, 1523.077
| 24\11, 1515.789
''1669.230…''
|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'''
|'''25\11,''' '''1578.947'''
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.364'''
|-
|A si la mi fa#
| 35\15, 1615.385
| rowspan="2" |26\11, 1642.105
|43\18, 1664.516
|17\7, 1700
|42\17, 1737.069
| 25\10, 1764.706
|33\13, 1800
|-
|B sol fa utb
|36\61, 1661.538
|42\18, 1625.806
|16\7, 1600
|38\29, 1572.414
|22\10, 1552.941
|28\13, 1527.273
|-
|-
|Mi, Si
|B sol fa ut
|A
|37\15, 1707.692
|X, A
|27\11, 1705.263
|A
| 44\18, 1703.226
|38\15
| 17\7, 1700
|41\17, 1696.552
''1773.{{Overline|3}}''
|24\10, 1694.118
|28\11
|31\13, 1690.909
''1781.{{Overline|81}}''
|46\18
''1788.{{Overline|8}}''
|18\7
''1800''
| 44\17
''1811.764…''
|26\10
''1820''
|34\13
''1830.769…''
|-
|-
|Mi#, Si#
|B si
|A#
|38\15, 1753.846
|X#, A#
| 28\11, 1768.421
|A#
|46\18, 1780.645
|39\15
|18\7, 1800
|44\17, 1820.690
''1820''
|26\10, 1835.294
| rowspan="2" |29\11
|34\13, 1854.545
|-
''1845.{{Overline|45}}''
|B si
|48\18
|39\15, 1800
| rowspan="2" |29\11, 1831.579
''1866.{{Overline|6}}''
|48\18, 1858.064
|19\7
|19\7, 1900
|47\17, 1944.828
''1900''
|28\10, 1976.471
|47\17
|37\13, 2018.182
|-
''1935.294…''
|C la sol re utb
|28\10
|40\15, 1846.154
|47\18, 1819.355
''1960''
| 18\7, 1800
| 37\13
| 43\17, 1779.310
|25\10, 1764.706
''1992.307…''
|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
|-
|-
|Fab, Dob
|C la sol re utx
|Bbb
| rowspan="2" |43\15, 1984.615
|Ebb, Ccc
|32\11, 2021.053
|Bf
|53\18, 2051.612
|40\15
|21\7, 2100
|52\17, 2151.725
''1866.{{Overline|6}}''
|31\10, 2188.235
|47\18
|41\13, 2236.364
''1827.{{Overline|7}}''
|18\7
''1800''
|43\17
''1770.588…''
|25\10
''1750''
|32\13
''1723.076…''
|-
|-
|'''Fa, Do'''
|D fa la mi reb
|'''Bb'''
|31\11, 1957.895
|Eb, Cc
|50\18, 1935.484
|'''B'''
|19\7, 1900
|'''41\15'''
|45\17, 1862.069
|26\10, 1835.294
'''''1913.{{Overline|3}}'''''
|33\13, 1800
|'''30\11'''
'''''1909.{{Overline|09}}'''''
|'''49\18'''
'''''1905.{{Overline|5}}'''''
|'''19\7'''
'''''1900'''''
|'''46\17'''
'''''1894.117…'''''
|'''27\10'''
'''''1890'''''
|'''35\13'''
'''''1884.615…'''''
|-
|-
|Fa#, Do#
|D fa la mi re
|B
|44\15, 2030.769
|E, C
|32\11, 2021.053
|B#
|52\18, 2012.903
| 42\15
|20\7, 2000
|48\17, 1986.207
''1960''
|28\10, 1976.471
|31\11
|36\13, 1963.636
|-
''1972.{{Overline|72}}''
!D si la mi re
|51\18
!45\15, 2076.923
!33\11, 2084.211
''1983.{{Overline|3}}''
!54\18, 2090.323
|20\7
!21\7, 2100
! 51\17, 2110.345
''2000''
!30\10, 2117.647
|49\17
!39\13, 2127.273
''2017.647…''
|29\10
''2030''
|38\13
''2046.153…''
|-
|-
|Fax, Dox
|D si la mi re#
|B#
|46\15, 2123.077
|Ex, Cx
| rowspan="2" |34\11, 2147.368
|Bx
|56\18, 2167.742
|43\15
|22\7, 2200
|54\17, 2234.483
''2006.{{Overline|6}}''
| 32\10, 2258.824
| rowspan="2" |32\11
|42\13, 2090.909
''2036.{{Overline|36}}''
|53\18
''2061.{{Overline|1}}''
|21\7
''2100''
|52\17
''2141.176…''
|31\10
''2170''
|41\13
''2207.692…''
|-
|-
| Dob, Solb
|E fab
|Hb
|47\26, 2169.231
|0b, Dc
|55\16, 2129.032
|Cf
|21\7, 2100
|44\15
|50\17, 2068.966
|29\10, 2047.059
''2053.{{Overline|3}}''
|37\13, 2018.182
|52\18
''2022.{{Overline|2}}''
|20\7
''2000''
|48\17
''1976.470…''
|28\10
''1960''
| 36\13
''1938.615…''
|-
|-
!Do, Sol
|E fa
!H
|48\15, 2215.385
!0, D
|35\11, 2210.526
!C
|57\18, 2206.452
! colspan="7" |''2100''
|23\7, 2300
|53\17, 2193.103
|31\10, 2188.235
|40\13, 2181.818
|-
|-
|Do#, Sol#
|E si mi
|Η#
|49\15, 2261.538
|0#, D#
|36\11, 1073.684
|C#
|59\18, 2283.871
|46\15
|24\7, 2400
''2146.{{Overline|6}}''
|56\17, 2317.241
|34\11
|33\10, 2329.412
''2163.{{Overline|63}}''
|43\13, 2345.455
|56\18
|-
''2177.{{Overline|7}}''
|E si mi#
| rowspan="2" |22\7
|50\15, 2307.692
''2200''
| rowspan="2" |37\11, 2336.842
|54\17
|61\18, 2361.290
''2223.529…''
| rowspan="2" |23\7, 2300
|32\10
| 59\17, 2441.379
''2240''
|35\10, 2470.588
|42\13
|46\13, 2509.091
''2261.538…''
|-
|F sol fa utb
|51\15, 2353.846
|60\18, 2322.581
|55\17, 2275.862
|32\10, 2258.824
|41\13, 2236.364
|-
|-
|Reb, Lab
|F sol fa ut
|Cb
|52\15, 2400
|1b, 1c
|38\11, 2400
|Df
|62\18, 2400
|48\15
|24\7, 2400
''2240''
|58\17, 2400
|35\11
|34\10, 2400
''2227.{{Overline|27}}''
|44\13, 2400
|57\18
''2216.{{Overline|6}}''
|53\17
''2182.352…''
|31\10
''2170''
|40\13
''2153.846…''
|-
|-
|'''Re, La'''
|F sol fa ut#
|'''C'''
|53\15, 2446.154
|'''1'''
|39\11, 2463.158
|'''D'''
|64\18, 2477,419
|'''49\15'''
| rowspan="2" |25\7, 2500
'''''2286.{{Overline|6}}'''''
|61\17, 2524.138
|'''36\11'''
|36\10, 2541.176
'''''2290.{{Overline|90}}'''''
|47\13, 2563.636
|'''59\18'''
'''''2294.{{Overline|4}}'''''
|'''23\7'''
'''''2300'''''
|'''56\17'''
'''''2305.882…'''''
|'''33\10'''
'''2310'''
|'''43\13'''
'''''2315.384…'''''
|-
|-
|Re#, La#
|G la sol reb
|C#
|55\15, 2538.462
|1#
|40\11, 2526.316
|D#
|65\18, 2516.129
|50\15
|60\17, 2482.759
''2223.{{Overline|3}}''
|35\10, 2470.588
|37\11
|45\13, 2454.545
''2354.{{Overline|54}}''
|61\18
''2372.''{{Overline|2}}
| rowspan="2" |24\7
''2400''
|59\17
''2429.411…''
|35\10
''2450''
|46\13
''2476.923…''
|-
|-
|Mib, Sib
|'''G la sol re'''
|Db
|'''56\15, 2584.615'''
|2b, 2c
|'''41\11, 2589.474'''
|Ef
|'''67\18, 2593.548'''
|52\15
|'''26\7, 2600'''
''2426.{{Overline|6}}''
|'''63\17, 2606.897'''
|38\11
|'''37\10, 2611.765'''
''2418.{{Overline|18}}''
|'''48\13,''' '''2618.182'''
|62\18
''2411.{{Overline|1}}''
|58\17
''2388.235…''
|34\10
''2380''
|44\13
''2369.230…''
|-
|-
|Mi, Si
|G la sol re#
|D
|57\15, 2630.769
|2
|42\11, 2652.632
|E
|69\18, 2670.968
|53\15
| rowspan="2" |27\7, 2700
''2473,{{Overline|3}}''
|66\17, 2731.034
|39\11
|39\10, 2752.941
''2481.{{Overline|81}}''
|51\13, 2781.818
|64\11
''2488.{{Overline|8}}''
|25\7
''2500''
|61\17
''2511.764…''
|36\10
''2520''
|47\13
''2530.769…''
|-
|-
|Mi#, Si#
|A si la mib
|D#
|59\15, 2723.077
|2#
|43\11, 2715.789
|E#
|70\18, 2709.677
|54\15
|65\17, 2689.552
''2520''
|38\10, 2682.353
| rowspan="2" |40\11
|49\13, 2672.273
''2545.{{Overline|45}}''
|66\18
''2566.{{Overline|6}}''
|26\7
''2600''
|64\17
''2635.294…''
|38\10
''2660''
|50\13
''2692.307…''
|-
|-
|Fab, Dob
!A si la mi
|Ebb
!60\15, 2769.231
|3b, 3c
!44\11, 2778.947
|Fff
!72\18, 2787.097
|55\15
!28\7, 2800
''2566.{{Overline|6}}''
!68\17, 2813.793
|65\18
!40\10, 2823.529
''2527.{{Overline|7}}''
!52\13, 2836.364
|25\7
''2500''
|60\17
''2470.588…''
|35\10
''2450''
|45\13
''2423.076…''
|-
|-
|'''Fa, Do'''
|A si la mi#
|'''Eb'''
|61\15, 2815.385
|'''3'''
| rowspan="2" |45\11, 2842.105
|'''Ff'''
| 74\18, 2864.516
|'''56\15'''
|29\7, 2900
'''''2613.{{Overline|3}}'''''
|71\17, 2937.069
|'''41\11'''
|42\10, 2964.706
'''''2609.{{Overline|09}}'''''
|55\13, 3000
|'''67\18'''
'''''2605.{{Overline|5}}'''''
|'''26\7'''
'''''2600'''''
|'''63\17'''
'''''2594.117…'''''
|'''37\10'''
'''''2590'''''
|'''48\13'''
'''''2584.615…'''''
|-
|-
|Fa#, Do#
|B fab
|E
|62\15, 2861.538
|3#
|73\18, 2825.806
|F
| 28\7, 2800
|57\15
|67\17, 2772.414
''2660''
|39\10, 2752.941
|42\11
|50\13, 2727.273
''2672.{{Overline|72}}''
|69\18
''2683.{{Overline|3}}''
|27\7
''2700''
|66\17
''2717.647…''
|39\10
''2730''
|51\13
''2746.153…''
|-
|-
|Fax, Dox
|B fa
|E#
|63\15, 2907.692
|3x
|46\11, 2905.263
|F#
|75\18, 2903.226
|58\15
|29\7, 2900
|70\17, 2896.552
''2706.{{Overline|6}}''
|41\10, 2894.118
| rowspan="2" |43\11
|53\13, 2890.909
''2736.{{Overline|36}}''
|71\18
''2761.{{Overline|1}}''
|28\7
''2800''
|69\17
''2841.176…''
|41\10
''2870''
|54\13
''2907.692…''
|-
|-
|Dob, Solb
|'''B si'''
|Fb
|'''64\15, 2953.846'''
|4b, 4c
|'''47\11, 2968.421'''
|0f, Gf
|'''77\18, 2980.645'''
|59\15
|'''30\7, 3000'''
|'''73\17, 3020.690'''
''2753.{{Overline|3}}''
|'''43\10, 3035.294'''
|70\18
|'''56\13, 3054.545'''
''2722.{{Overline|2}}''
|27\7
''2700''
|65\17
''2676.470…''
|38\10
''2660''
|49\13
''2638.615…''
|-
|-
!Do, Sol
|B si#
!F
|65\15, 3000
!4
|48\11, 3031.579
!0, G
|79\18, 3058.064
! colspan="7" |''2800''
| rowspan="2" |31\7, 3100
|}
|76\17, 3144.828
|45\10, 3176.471
==Intervals==
|59\13, 3218.182
{| 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):
|C solb
|67\15, 3092.308
|49\11, 3094.737
|80\18, 3096.774
|75\17, 3103.448
|44\10, 3105.882
|57\13, 3109.091
|-
|-
|0
|C sol
|Do, Sol
|68\15, 3138.462
|perfect unison
|50\11, 3157.895
|0
| 82\18, 3174.194
|Do, Sol
|32\7, 3200
|sesquitave (just fifth)
|78\17, 3227.586
| 46\10, 3247.059
|60\13, 3272.273
|-
|-
|1
|C sol#
|Fa, Do
| 69\15, 3184.615
|perfect fourth
| rowspan="2" |51\11, 3221.053
| -1
|84\18, 3251.612
|Re, La
|33\7, 3300
|perfect second
|81\17, 3351.725
|48\10, 3388.235
|63\13, 3436.364
|-
|-
|2
|D labb
|Mib, Sib
|70\15, 3230.769
|minor third
|83\18, 3212.903
| -2
|32\7, 3200
|Mi, Si
|77\17, 3186.207
|major third
|45\10, 3176.471
|58\13, 3163.636
|-
|-
|3
|'''D lab'''
|Reb, Lab
|'''71\15,''' '''3276.923'''
|diminished second
|'''52\11,''' '''3284.211'''
| -3
|'''85\18,''' '''3290.323'''
|Fa#, Do#
|'''33\7, 3300'''
|augmented fourth
|'''80\17,''' '''3310.345'''
|'''47\10,''' '''3317.647'''
|'''61\13,''' '''3327.{{Overline|27}}'''
|-
|-
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|D la
|72\15, 3323.077
|53\11, 3347.368
|87\18, 3367.742
|34\7, 3400
|83\17, 3434.583
|49\10, 3458.824
|64\13, 3490.909
|-
|-
|4
|D la#
|Dob, Solb
|73\15, 3369.231
|diminished sesquitave
| rowspan="2" |54\11, 3410.625
| -4
|89\18, 3445.162
| Do#, Sol#
|35\7, 3500
|augmented unison (chroma)
|86\17, 3558.621
|51\10, 3600
|67\13, 3654.545
|-
|-
|5
|F utb
|Fab, Dob
|74\15, 3415.385
|diminished fourth
|88\18, 3406.452
| -5
|34\7, 3400
|Re#, La#
|82\17, 3393.103
|augmented second
|48\10, 3388.235
|62\13, 3381.818
|-
|-
|6
!F ut
| Mibb, Sibb
!75\15, 3461.538
|diminished third
!55\11, 3473.684
| -6
!90\18, 3483.871
|Mi#, Si#
!35\7, 3500
|augmented third
!85\17, 3517.241
|}  
!50\10, 3529.412
!65\13, 3545.455
==Genchain==
|}
 
The generator chain for this scale is as follows:
{| class="wikitable"
{| class="wikitable"
|Mibb
|+Cents
!Notation
Sibb
!Supersoft
|Fab
!Soft
! Semisoft
Dob
!Basic
|Dob
!Semihard
!Hard
Solb
!Superhard
|Reb
|-
!Subdozenal
Lab
!~15edf
|Mib
!~11edf
!~18edf
Sib
!~7edf
|Fa
!~17edf
!~10edf
Do
!~13edf
|Do
|-
|F#
Sol
|1\15, 46.154
|Re
|1\11, 63.158
|2\18, 77.419
La
| rowspan="2" |1\7, 100
|Mi
|3\17, 124.138
|2\10, 141.176
Si
|3\13, 163.636
|Fa#
|-
|Gb, Ge
Do#
|3\15, 138.462
|Do#
|2\11. 126.316
|3\18, 116.129
Sol#
|2\17, 82.759
|Re#
|1\10, 70.588
|1\13, 54.545
La#
|-
|Mi#
|'''G'''
|'''4\15,''' '''184.615'''
Si#
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|G#
|5\15, 230.769
|4\11, 252.632
|7\18, 270.968
| rowspan="2" |3\7, 300
|8\17, 331.034
|5\10, 352.941
|7\13, 381.818
|-
|Hb, He
|7\15, 323.077
|5\11, 315.789
|8\18, 309.677
|7\17, 289.655
|4\10, 282.353
|5\13, 272.727
|-
|H
|8\15, 369.231
|6\11, 378.947
|10\18, 387.097
|4\7, 400
|10\17, 413.793
|6\10, 423.529
|8\13, 436.364
|-
|H#
|9\15, 415.385
| rowspan="2" |7\11, 442.105
|12\18, 464.516
|5\7, 500
|13\17, 537.069
|8\10, 564.706
|11\13, 600
|-
|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
|-
|'''Jb, Je'''
|'''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'''
|-
|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
| 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
|-
|-
|d3
|Kb, Ke
|d4
|14\15, 646.154
|d5
|16\18, 619.355
|d2
|6\7, 600
| m3
|14\17, 579.310
|P4
|8\10, 564.706
|P1
|10\13, 545.455
|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
!K
!pattern
!'''15\15,''' '''692.308'''
!notation
!'''11\11,''' '''694.737'''
!2nd
!'''18\18,''' '''696.774'''
!3rd
!7\7, 700
!4th
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
|-
|-
|Lydian
|K#
|LLLs
|16\15, 738.462
|<nowiki>3|0</nowiki>
|12\11, 757.895
|P
|20\18, 774.194
|M
| rowspan="2" |8\8, 800
| A
|20\17, 827.586
|12\10, 847.059
|16\13, 872.727
|-
|Lb, Le
|18\15, 830.769
|13\11, 821.053
|21\18, 812.903
|19\17, 786.207
|11\10, 776.471
|14\13, 763.63
|-
|'''L'''
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
|-
|L#
|20\15, 923.077
| rowspan="2" |15\11, 947.368
|25\18, 967.742
|10\7, 1000
|25\17, 1034.483
|15\10, 1058.824
|20\13, 1090.909
|-
|Mbb, Mee
|21\15, 969.231
|24\18, 929.032
|9\5, 900
|21\17, 868.966
|12\10, 847.059
|15\13, 818.182
|-
|Mb, Me
|22\15, 1015.385
|16\11, 1010.526
|26\18, 1006.452
|10\7, 1000
|24\17, 993.103
|14\10, 988.235
|18\13, 981.818
|-
|-
|Major
|LLsL
|<nowiki>2|1</nowiki>
|P
|M
|M
|P
|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
|-
|-
| Minor
|P#
|LLsL
|31\15, 1430.769
|<nowiki>1|2</nowiki>
|23\11, 1452.632
| P
|38\18, 1470.968
|m
| rowspan="2" |15\7, 1500
|P
|37\17, 1531.034
|22\10, 1552.941
|29\13, 1581.818
|-
|-
|Phrygian
|Qb, Qe
|sLLL
|33\15, 1523.077
|<nowiki>0|3</nowiki>
|24\11, 1515.789
|d
|39\18, 1509.677
|m
|36\17, 1489.655
| P
|21\10, 1482.759
|}
|27\13, 1472.273
==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<ref name=":03">Fractions repeating more than 4 digits written as continued fractions</ref></u>
|'''Q'''
!''ed7\12<ref name=":04">Fractions repeating more than 4 digits written as continued fractions</ref>''
|'''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'''
|-
|-
| 1\4
|Q#
|
|35\15, 1615.385
|
| rowspan="2" |26\11, 1642.105
|<u>171.428…</u>
|43\18, 1664.516
|''175''
|17\7, 1700
|1
|42\17, 1737.069
|1
|25\10, 1764.706
|1.000
|33\13, 1800
|Equalised
|-
|-
|6\23
|Rb, Re
|
|36\61, 1661.538
|
|42\18, 1625.806
|<u>180</u>
|16\7, 1600
|''182.608…''
|38\29, 1572.414
|6
|22\10, 1552.941
|5
|28\13, 1527.273
|1.200
|-
|
|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#
| 11\42
|39\15, 1800
|
| rowspan="2" |29\11, 1831.579
|<u>180.821…</u>
|48\18, 1858.064
|''183.{{Overline|3}}''
|19\7, 1900
|11
|47\17, 1944.828
|9
|28\10, 1976.471
|1.222
|37\13, 2018.182
|
|-
|-
|5\19
|Sb, Se
|
|40\15, 1846.154
|
|47\18, 1819.355
|<u>181.{{Overline|81}}</u>
|18\7, 1800
|''184.210…''
|43\17, 1779.310
|5
|25\10, 1764.706
|4
|32\13, 1745.545
|1.250
|
|-
|-
|
|'''S'''
|14\53
|'''41\15,''' '''1892.308'''
|
|'''30\11,''' '''1894.737'''
|<u>182.608…</u>
|'''49\18,''' '''1896.774'''
|''184.905…''
|'''19\7, 1900'''
|14
|'''46\17,''' '''1903.448'''
|11
|'''27\10,''' '''1905.882'''
|1.273
|'''35\13,''' '''1909.091'''
|
|-
|-
|
|S#
|9\34
|42\15, 1938.462
|
|31\11, 1957.895
|<u>183.050…</u>
|51\18, 1974.194
|''185.294…''
|20\7, 2000
| 9
|49\17, 2027.586
|7
|29\10, 2047.059
|1.286
|38\13, 2072.727
|
|-
|-
|4\15
|Sx
|
|43\15, 1984.615
|
| rowspan="2" |32\11, 2021.053
|<u>184.615…</u>
|53\18, 2051.612
|''186.{{Overline|6}}''
|21\7, 2100
|4
|52\17, 2151.725
|3
|31\10, 2188.235
|1.333
|41\13, 2236.364
|
|-
|-
|
|Tb, Te
|11\41
|44\15, 2030.769
|
|52\18, 2012.903
|<u>185.915…</u>
|20\7, 2000
|''187.804…''
|48\17, 1986.207
|11
|28\10, 1976.471
| 8
|36\13, 1963.636
|1.375
|
|-
|-
|
!T
|7\26
!45\15, 2076.923
|
!33\11, 2084.211
|<u>186.{{Overline|6}}</u>
!54\18, 2090.323
|''188.461…''
!21\7, 2100
|7
!51\17, 2110.345
|5
!30\10, 2117.647
|1.400
!39\13, 2127.273
|
|-
|-
|
|T#
|10\37
|46\15, 2123.077
|
| rowspan="2" |34\11, 2147.368
|<u>187.5</u>
|56\18, 2167.742
|''189.{{Overline|189}}''
|22\7, 2200
|10
|54\17, 2234.483
| 7
|32\10, 2258.824
| 1.429
|42\13, 2090.909
|
|-
|-
|
|Ub, Üe
|13\48
|47\26, 2169.231
|
|55\16, 2129.032
|<u>187.951…</u>
|21\7, 2100
|''189.58{{Overline|3}}''
|50\17, 2068.966
|13
|29\10, 2047.059
|9
|37\13, 2018.182
|1.444
|
|-
|-
|
|Ub, Ü
|16\59
|48\15, 2215.385
|
|35\11, 2210.526
|<u>188.235…</u>
|57\18, 2206.452
|''189.830…''
|23\7, 2300
|53\17, 2193.103
|16
|31\10, 2188.235
|11
|40\13, 2181.818
|1.4545
|
|-
|-
| 3\11
|U
|  
|49\15, 2261.538
|
|36\11, 1073.684
|<u>189.473…</u>
|59\18, 2283.871
|''190.{{Overline|90}}''
|24\7, 2400
| 3
|56\17, 2317.241
|2
|33\10, 2329.412
|1.500
|43\13, 2345.455
|Napoli-Meantone starts here
|-
|-
|
|U#
|14\51
|50\15, 2307.692
|
| rowspan="2" |37\11, 2336.842
|<u>190.{{Overline|90}}</u>
|61\18, 2361.290
|''192.156…''
| rowspan="2" |23\7, 2300
|14
|59\17, 2441.379
| 9
|35\10, 2470.588
| 1.556
|46\13, 2509.091
|
|-
|-
|
|Vb, Ve
|11\40
|51\15, 2353.846
|
|60\18, 2322.581
|<u>191.304…</u>
|55\17, 2275.862
|''192.5''
|32\10, 2258.824
|11
|41\13, 2236.364
| 7
| 1.571
|
|-
|-
|
|V
|8\29
|52\15, 2400
|
|38\11, 2400
|<u>192</u>
|62\18, 2400
|''193.103…''
|24\7, 2400
| 8
|58\17, 2400
| 5
|34\10, 2400
|1.600
|44\13, 2400
|
|-
|V#
|53\15, 2446.154
|39\11, 2463.158
|64\18, 2477,419
| rowspan="2" |25\7, 2500
|61\17, 2524.138
|36\10, 2541.176
|47\13, 2563.636
|-
|Wb, We
|55\15, 2538.462
|40\11, 2526.316
|65\18, 2516.129
|60\17, 2482.759
|35\10, 2470.588
|45\13, 2454.545
|-
|'''Wb'''
|'''56\15, 2584.615'''
|'''41\11, 2589.474'''
|'''67\18, 2593.548'''
|'''26\7, 2600'''
|'''63\17, 2606.897'''
|'''37\10, 2611.765'''
|'''48\13,''' '''2618.182'''
|-
|-
|
|W#
|5\18
|57\15, 2630.769
|  
|42\11, 2652.632
|<u>193.548…</u>
|69\18, 2670.968
|''194.{{Overline|4}}''
| rowspan="2" |27\7, 2700
|5
|66\17, 2731.034
|3
|39\10, 2752.941
|1.667
|51\13, 2781.818
|
|-
|-
|
|Xb, Xe
|
|59\15, 2723.077
|12\43
|43\11, 2715.789
|<u>194.{{Overline|594}}</u>
|70\18, 2709.677
|''195.348…''
|65\17, 2689.552
| 12
|38\10, 2682.353
| 7
|49\13, 2672.273
|1.714
|
|-
|-
|
!X
|7\25
!60\15, 2769.231
|
!44\11, 2778.947
|<u>195.348…</u>
!72\18, 2787.097
|''196''
!28\7, 2800
|7
!68\17, 2813.793
|4
!40\10, 2823.529
|1.750
!52\13, 2836.364
|
|-
|-
|  
|X#
|9\32
|61\15, 2815.385
|
| rowspan="2" |45\11, 2842.105
|<u>196.{{Overline|36}}</u>
|74\18, 2864.516
|''196.875''
|29\7, 2900
|9
|71\17, 2937.069
|5
|42\10, 2964.706
|1.800
|55\13, 3000
|
|-
|-
|
|Ybb, Yee
|11\39
|62\15, 2861.538
|
|73\18, 2825.806
|<u>197.014…</u>
|28\7, 2800
|''197.435…''
|67\17, 2772.414
|11
|39\10, 2752.941
| 6
|50\13, 2727.273
|1.833
|-
|
|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'''
|13\46
|'''64\15, 2953.846'''
|
|'''47\11, 2968.421'''
|<u>197.468…</u>
|'''77\18, 2980.645'''
|''197.826…''
|'''30\7, 3000'''
| 13
|'''73\17, 3020.690'''
| 7
|'''43\10, 3035.294'''
| 1.857
|'''56\13, 3054.545'''
|
|-
|-
|
|Y#
|15\53
|65\15, 3000
|
|48\11, 3031.579
|<u>197.802…</u>
|79\18, 3058.064
|''198.113…''
| rowspan="2" |31\7, 3100
|15
|76\17, 3144.828
|8
|45\10, 3176.471
|1.875
|59\13, 3218.182
|
|-
|-
|
|Zb. Ze
| 17\60
|67\15, 3092.308
|  
|49\11, 3094.737
|<u>198.058…</u>
|80\18, 3096.774
|''198.{{Overline|3}}''
|75\17, 3103.448
|17
|44\10, 3105.882
| 9
|57\13, 3109.091
| 1.889
|
|-
|-
|
|Z
|19\67
|68\15, 3138.462
|  
|50\11, 3157.895
|<u>198.260…</u>
|82\18, 3174.194
|''198.507…''
|32\7, 3200
|19
|78\17, 3227.586
| 10
|46\10, 3247.059
|1.900
|60\13, 3272.273
|
|-
|-
|
|Z#
|21\74
|69\15, 3184.615
|
| rowspan="2" |51\11, 3221.053
|<u>198.425…</u>
|84\18, 3251.612
| ''198.{{Overline |''198.{{Overline|648}}''
|33\7, 3300
|21
|81\17, 3351.725
| 11
|48\10, 3388.235
|1.909
|63\13, 3436.364
|  
|-
|-
|
|Ab, Æ
|23\81
|70\15, 3230.769
|
|83\18, 3212.903
|<u>198.561…</u>
|32\7, 3200
|''198.765…''
|77\17, 3186.207
|23
|45\10, 3176.471
|12
|58\13, 3163.636
| 1.917
|
|-
|-
|
|'''A'''
| 25\88
|'''71\15,''' '''3276.923'''
|  
|'''52\11,''' '''3284.211'''
|<u>198.675…</u>
|'''85\18,''' '''3290.323'''
|''198.8{{Overline|63}}''
|'''33\7, 3300'''
|25
|'''80\17,''' '''3310.345'''
| 13
|'''47\10,''' '''3317.647'''
|1.923
|'''61\13,''' '''3327.{{Overline|27}}'''
|
|-
|-
|
|A#
|27\95
|72\15, 3323.077
|  
|53\11, 3347.368
|<u>198.773…</u>
|87\18, 3367.742
|''198.947…''
|34\7, 3400
|27
|83\17, 3434.583
|14
|49\10, 3458.824
|1.929
|64\13, 3490.909
|
|-
|-
|
|Ax
|29\102
|73\15, 3369.231
|
| rowspan="2" |54\11, 3410.625
|<u>198.857…</u>
|89\18, 3445.162
|''199.019…''
|35\7, 3500
|29
|86\17, 3558.621
|15
|51\10, 3600
|1.933
|67\13, 3654.545
|
|-
|-
|  
|Bb, Be
| 31\109
|74\15, 3415.385
|
|88\18, 3406.452
|<u>198.930…</u>
|34\7, 3400
|''199.082…''
|82\17, 3393.103
|31
|48\10, 3388.235
|16
|62\13, 3381.818
|1.9375
|
|-
|-
|
!B
|33\116
!75\15, 3461.538
|
!55\11, 3473.684
|<u>198.994…</u>
!90\18, 3483.871
|''199.137…''
!35\7, 3500
|33
!85\17, 3517.241
|17
!50\10, 3529.412
|1.941
!65\13, 3545.455
|
|-
|-
|
|B#
|35\123
|76\15, 3507.692
|
|56\11, 3536.842
|<u>199.052…</u>
|92\18, 3561.290
|''199.186…''
| rowspan="2" |36\7, 3600
|35
|88\17, 3641.379
|18
|52\10, 3670.588
|1.944
|68\13, 3709.091
|
|-
|-
|2\7
|Cb, Ce
|
|78\15, 3600
|
|57\11, 3600
|<u>200</u>
|93\18, 3600
|''200''
|87\17, 3600
|2
|51\10, 3600
|1
|66\13, 3600
|2.000
| Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|-
|
|'''C'''
|17\59
|'''79\15,''' '''3646.154'''
|
|'''58\11,''' '''3663.158'''
|<u>201.980…</u>
|'''95\18,''' '''3677.419'''
|''201.694…''
|'''37\7,''' '''3700'''
|17
|'''90\17,''' '''3724.138'''
|8
|'''53\10,''' '''3741.176'''
|2.125
|'''69\13,''' '''3763.636'''
|
|-
|-
|
|C#
| 15\52
|80\15, 3692.308
|  
|59\11, 3726.316
|<u>202.247…</u>
|97\18, 3755.838
|''201.923…''
| rowspan="2" |38\7, 3800
|15
|93\17, 3848.275
|7
|55\10, 3882.353
|2.143
|72\13, 3927.273
|
|-
|-
|
|Db, De
|13\45
|82\15, 3784.615
|
|60\11, 3789.474
|<u>202.597…</u>
|98\18, 3793.548
|''202.{{Overline|2}}''
|92\17, 3806.897
|13
|54\10, 3811.765
|6
|70\13, 3818.182
|2.167
|
|-
|-
|
|D
|11\38
|83\15, 3830.769
|
|61\11, 3852.632
|<u>203.076…</u>
|100\18, 3870.968
|''202.631…''
|39\7, 3900
|11
|95\17, 3931.03$
|5
|56\10, 3952.941
|2.200
|73\13, 3981.818
|
|-
|-
|
|D#
|9\31
|84\15, 3876.923
|
| rowspan="2" |62\11, 3915.789
|<u>203.773…</u>
|102\18, 3948.387
|''203.225…''
|40\7, 4000
|9
|98\17, 4055.172
|4
|58\10, 4094.118
| 2.250
|76\13, 4145.455
|
|-
|-
|
|Ebb, Ëe
|7\24
|85\15, 3923.077
|
|101\18, 3909.677
|<u>204.878…</u>
|39\7, 3900
|''204.1{{Overline|6}}''
|94\17, 3889.552
| 7
|55\10, 3882.353
|3
|71\13, 3872.727
|2.333
|-
|
|'''Eb, Ë'''
|'''86\15,''' '''3969.231'''
|'''63\11,''' '''3978.947'''
|'''103\18,''' '''3987.097'''
|'''40\7, 4000'''
|'''97\17,''' '''4013.793'''
|'''57\10,''' '''4023.529'''
|'''74\13,''' '''4036.364'''
|-
|-
|
|E
|
|87\15, 4015.385
|12\41
|64\11, 4042.105
|<u>205.714…</u>
|105\18, 4064.516
|''204.878…''
|41\7, 4100
|12
|100\17, 4137.931
|5
|59\10, 4164.706
|2.400
|77\13, 4200
|
|-
|-
|
|E#
|5\17
|88\15, 4061.583
|
| rowspan="2" |65\11, 4105.263
|<u>206.896…</u>
|107\18, 4141.956
|''205.882…''
|42\7, 4200
|5
|103\17, 4262.069
|2
|61\10, 4305.882
|2.500
|80\13, 4363.636
|Napoli-Neogothic heartland is from here…
|-
|-
|
|Fb, Fe
|
|89\15, 4107.692
|18\61
|106\18, 4103.226
|<u>207.692…</u>
|41\7, 4100
|''206.557…''
|99\17, 4096.552
|18
|58\10, 4094.118
|7
|75\13, 4090.909
| 2.571
|
|-
|-
|
!F
|
!90\15, 4153.846
|13\44
!66\11, 4168.421
|<u>208</u>
!108\18, 4180.645
|''206.{{Overline|81}}''
!42\7, 4200
|13
!102\17, 4220.690
| 5
!60\10, 4235.294
| 2.600
!78\13, 4254.545
|
|}
==Intervals==
{| class="wikitable"
!Generators
!Sesquitave notation
!Interval category name
!Generators
!Notation of 3/2 inverse
!Interval category name
|-
|-
|
| colspan="6" |The 4-note MOS has the following intervals (from some root):
|8\27
|
|<u>208.695…</u>
|''207.{{Overline|407}}''
| 8
|3
|2.667
|…to here
|-
|-
|
|0
|11\37
|Do, Fa, Sol
|
|perfect unison
|<u>209.523…</u>
|0
|''208.{{Overline|108}}''
|Do, Fa, Sol
|11
|sesquitave (just fifth)
|4
| 2.750
|
|-
|-
|
|1
|14\47
|Fa, Sib, Do
|
|perfect fourth
|<u>210</u>
| -1
|''208.510…''
|Re, Sol, La
| 14
|perfect second
| 5
|-
|2.800
|2
|
|Mib, Lab, Sib
|minor third
| -2
|Mi, La, Si
|major third
|-
|-
|
|3
|17\57
|Reb, Solb, Lab
|
|diminished second
|<u>210.309…</u>
| -3
|''208.771…''
|Fa#, Si, Do#
|17
|augmented fourth
|6
|2.833
|  
|-
|-
|
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
| 20\67
|
|<u>210.526…</u>
|''208.955…''
| 20
|7
|2.857
|
|-
|-
|
|4
| 23\77
|Dob, Fab, Solb
|
|diminished sesquitave
|<u>210.687…</u>
| -4
|''209.{{Overline|09}}''
|Do#, Fa#, Sol#
|23
|augmented unison (chroma)
|8
|2.875
|
|-
|-
|3\10
|5
|
|Fab, Sibb, Dob
|
|diminished fourth
|<u>211.764…</u>
| -5
|''210''
|Re#, Sol#, La#
|3
|augmented second
| 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
|6
|3.167
|Mibb, Labb, Sibb
|
|diminished third
|-
| -6
|
|Mi#, La#, Si#
|16\53
|augmented third
|
|}
|<u>213.{{Overline|3}}</u>
|''211.320…''
==Genchain==
|16
|5
The generator chain for this scale is as follows:
|3.200
{| class="wikitable"
|
|Mibb
|-
Labb
|
|13\43
Sibb
|
|Fab
|<u>213.698…</u>
Sibb
|''211.627…''
|13
Dob
|4
|Dob
|3.250
Fab
|
|-
Solb
|
|Reb
| 10\33
Solb
|
|<u>214.285…</u>
Lab
|''212.{{Overline|12}}''
|Mib
|10
Lab
|3
|3.333
Sib
|
|Fa
|-
Sib
|
|7\23
Do
|
|Do
|<u>215.384…</u>
Fa
|''213.043…''
|7
Sol
|2
|Re
|3.500
Sol
|
|-
La
|
|Mi
|11\36
La
|
|<u>216.393…</u>
Si
|''213.{{Overline|3}}''
|Fa#
| 11
Si
|3
|3.667
Do#
|
|Do#
|-
Fa#
|
|15\49
Sol#
|
|Re#
|<u>216.867…</u>
Sol#
|''214.285…''
|15
La#
|4
|Mi#
|3.750
La#
|
Si#
|-
|-
|4\13
|d3
|
|d4
|
|d5
|<u>218.{{Overline|18}}</u>
|d2
|''215.385…''
|m3
|4
|P4
|1
|P1
|4.000
|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
|13\42
!pattern
|
!notation
|<u>219.718…</u>
!2nd
|''216.{{Overline|6}}''
!3rd
|13
!4th
|3
|4.333
|
|-
|-
|
|Lydian
|9\29
|LLLs
|
|<nowiki>3|0</nowiki>
|<u>220.408…</u>
|P
|''217.241…''
|M
|9
|A
|2
|4.500
|  
|-
|-
|
|Major
|14\45
|LLsL
|
|<nowiki>2|1</nowiki>
|<u>221.052…</u>
|P
|''217.{{Overline|7}}''
|M
|14
|P
| 3
| 4.667
|
|-
|-
|5\16
|Minor
|
|LsLL
|
|<nowiki>1|2</nowiki>
|<u>222.{{Overline|2}}</u>
|P
|''218.75''
|m
|5
|P
| 1
|5.000
|Napoli-Superpyth ends
|-
|-
|
|Phrygian
|16\51
|sLLL
|
|<nowiki>0|3</nowiki>
|<u>223.255…</u>
|d
|''219.607…''
|m
|16
|P
|3
|}
|5.333
|
==Temperaments==
|-
|
The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
|11\35
==='''Napoli-Meantone (Hex meantone)'''===
|
|<u>223.728…</u>
[[Subgroup]]: 3/2.6/5.8/5 (5.2.3)
|''220''
|11
[[Comma]] list: [[81/80]]
|2
 
|5.500
[[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
|
|
|17\54
|-
|5\19
|181.818
|5
|4
|1.250
|
|
|<u>224.175…</u>
|-
|''220.{{Overline|370}}''
|14\53
| 17
|182.609
| 3
|14
|5.667
|11
|1.273
|
|
|-
|-
|6\19
|9\34
|
|183.051
|  
|9
|<u>225</u>
|7
|''221.052…''
|1.286
|6
|
|1
|-
|6.000
|4\15
|
|184.615
|-
|4
|1\3
|3
|
|1.333
|
|
|<u>240</u>
|-
|''233.{{Overline|3}}''
|11\41
|1
|185.915
|0
|11
|→ inf
|8
|Paucitonic
|1.375
|
|-
|7\26
|186.667
|7
|5
|1.400
|
|-
|10\37
|187.5
|10
|7
|1.429
|
|-
|13\48
|187.952
|13
|9
|1.444
|
|-
|16\59
|188.253
|16
|11
|1.455
|
|-
|3\11
|189.474
|3
|2
|1.500
|Napoli-Meantone starts here
|-
|14\51
|190.909
|14
|9
|1.556
|
|-
|11\40
|191.304
|11
|7
|1.571
|
|-
|8\29
|192.000
|8
|5
|1.600
|
|-
|5\18
|193.548
|5
|3
|1.667
|
|-
|12\43
|194.595
|12
|7
|1.714
|
|-
|7\25
|195.348
|7
|4
|1.750
|
|-
|9\32
|196.364
|9
|5
|1.800
|
|-
|11\39
|197.015
|11
|6
|1.833
|
|-
|13\46
|197.468
|13
|7
|1.857
|
|-
|15\53
|197.802
|15
|8
|1.875
|
|-
|17\60
|198.058
|17
|9
|1.889
|
|-
|19\67
|198.261
|19
|10
|1.900
|
|-
|21\74
|198.425
|21
|11
|1.909
|
|-
|23\81
|198.561
|23
|12
|1.917
|
|-
|25\88
|198.675
|25
|13
|1.923
|
|-
|27\95
|198.773
|27
|14
|1.929
|
|-
|29\102
|198.857
|29
|15
|1.933
|
|-
|31\109
|198.930
|31
|16
|1.9375
|
|-
|33\116
|198.995
|33
|17
|1.941
|
|-
|35\123
|199.009
|35
|18
|1.944
|
|-
|2\7
|200
|2
|1
|2.000
|Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|17\59
|201.980
|17
|8
|2.125
|
|-
|15\52
|202.247
|15
|7
|2.143
|
|-
|13\45
|202.597
|13
|6
|2.167
|
|-
|11\38
|203.077
|11
|5
|2.200
|
|-
|9\31
|203.774
|9
|4
|2.250
|
|-
|7\24
|204.878
|7
|3
|2.333
|
|-
|12\41
|205.714
|12
|5
|2.400
|
|-
|5\17
|206.897
|5
|2
|2.500
|Napoli-Neogothic heartland is from here…
|-
|18\61
|207.693
|18
|7
|2.571
|
|-
|13\44
|208.000
|13
|5
|2.600
|
|-
|8\27
|208.696
|8
|3
|2.667
|…to here
|-
|11\37
|209.524
|11
|4
|2.750
|
|-
|14\47
|210.000
|14
|5
|2.800
|
|-
|3\10
|211.765
|3
|1
|3.000
|Napoli-Pythagorean ends, Napoli-Archy begins
|-
|22\73
|212.903
|22
|7
|3.143
|
|-
|19\63
|213.084
|19
|6
|3.167
|
|-
|16\53
|213.333
|16
|5
|3.200
|
|-
|13\43
|213.699
|13
|4
|3.250
|
|-
|10\33
|214.286
|10
|3
|3.333
|
|-
|7\23
|215.385
|7
|2
|3.500
|
|-
|11\36
|216.393
|11
|3
|3.667
|
|-
|15\49
|216.867
|15
|4
|3.750
|
|-
|19\62
|217.143
|19
|5
|3.800
|
|-
|4\13
|218.182
|4
|1
|4.000
|
|-
|13\42
|219.718
|13
|3
|4.333
|
|-
|9\29
|220.408
|9
|2
|4.500
|
|-
|14\45
|221.053
|14
|3
|4.667
|
|-
|5\16
|222.222
|5
|1
|5.000
|Napoli-Archy ends
|-
|11\35
|223.728
|11
|2
|5.500
|
|-
|17\54
|224.176
|17
|3
|5.667
|
|-
|6\19
|225.000
|6
|1
|6.000
|
|-
|1\3
|240.000
|1
|0
|→ inf
|Paucitonic
|}
|}
==See also==
[[3L 1s (3/2-equivalent)]] - idealized tuning
[[6L 2s (20/9-equivalent)]] - Neapolitan 1/2-comma meantone
[[6L 2s (88/39-equivalent)]] - Neapolitan gentle temperament
[[6L 2s (16/7-equivalent)]] - Neapolitan 1/2-comma archy
[[9L 3s (10/3-equivalent)]] - Bijou 1/3-comma meantone
[[9L 3s (44/13-equivalent)]] - Bijou gentle temperament
[[9L 3s (24/7-equivalent)]] - Bijou 1/3-comma archy
[[12L 4s (5/1-equivalent)]] - Hex meantone
[[12L 4s (56/11-equivalent)]] - Hextone gentle temperament
[[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
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