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'''3L1s<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.
'''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.


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).  
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).  
Line 9: Line 9:
==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 36: Line 36:
 
 
!Diatonic
!Diatonic
!Napoli
!Bijou
!Hextone
!~15edf
!~15edf
 
 
Line 57: Line 52:
|-
|-
 
 
|Do#, Sol#
|Do#, Fa#, Sol#
|1\15, 46.154
 
 
|F#
|1\11, 63.158
 
 
|0#, D#
|2\18, 77.419
|0#, G#
|1\15
46; 6.5
 
 
|1\11
| rowspan="2" | 1\7, 100
63: 6.{{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; 1.3{{Overline|18}}
 
 
|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'''
'''211; 1, 3.25'''
 
 
|'''4\13'''
|Mib, Lab, Sib
|7\15, 323.077
 
 
'''218.{{Overline|18}}'''
|5\11, 315.789
 
 
|-
|8\18, 309.677
 
 
|Re#, La#
|7\17, 289.655
 
 
|G#
|4\10, 282.353
 
 
|1#
|5\13, 272.727
|1#
|5\15
230; 1.3
 
 
|4\11
|-
252; 1.58{{Overline|3}}
 
 
|7\18
|Mi, La, Si
270; 1.0{{Overline|3}}
|8\15, 369.231
 
 
| rowspan="2" |3\7
|6\11, 378.947
 
 
300
|10\18, 387.097
 
 
|8\17
|4\7, 400
331; 29
 
 
|5\10
|10\17, 413.793
352; 1.0625
 
 
|7\13
|6\10, 423.529
 
 
381.{{Overline|81}}
|8\13, 436.364
 
 
|-
|-
 
 
|Mib, Sib
|Mi#, La#, Si#
|9\15, 415.385
 
 
|Ab
| rowspan="2" | 7\11, 442.105
 
 
|2b, 2c
|12\18, 464.516
|2f
|7\15
323; 13
 
 
|5\11
|5\7, 500
315; 1.2{{Overline|6}}
 
 
|8\18
|13\17, 537.069
309; 1, 2.1
 
 
|7\17
|8\10, 564.706
289; 1, 1.9
 
 
|4\10
|11\13, 600
282; 2.8{{Overline|3}}
 
 
|5\13
|-
|Fab, Sibb, Dob
|10\15, 461.538
 
 
272.{{Overline|72}}
|11\18, 425.806
 
 
|-
|4\7, 400
 
 
|Mi, Si
|9\17, 372.414
 
 
|A
|5\10, 352.941
 
 
|2
|6\13, 327.273
|2
|8\15
369; 4.{{Overline|3}}
 
 
|6\11
|-
378; 1.0{{Overline|5}}
 
 
|10\18
|'''Fa, Sib, Do'''
387; 10.{{Overline|3}}
|'''11\15,''' '''507.692'''
 
 
|4\7
|'''8\11,''' '''505.263'''
 
 
400
|'''13\18,''' '''503.226'''
 
 
|10\17
|'''5\7, 500'''
413; 1, 3.8{{Overline|3}}
 
 
|6\10
|'''12\17,''' '''496.552'''
423; 1.{{Overline|8}}
 
 
|8\13
|'''7\10,''' '''494.118'''
 
 
436.{{Overline|36}}
|'''9\13,''' '''490.909'''
 
 
|-
|-
 
 
|Mi#, Si#
|Fa#, Si, Do#
|12\15, 553.846
 
 
|A#
|9\11, 568.421
 
 
|2#
|15\18, 580.645
|2#
|9\15
415; 2.6
 
 
| rowspan="2" |7\11
|6\7, 600
442; 9.5
 
 
|12\18
|15\17, 620.690
464; 1.0625
 
 
|5\7
|9\10, 635.294
 
 
500
|12\13, 654.545
 
 
|13\17
|-
537; 14.5
|Fax, Si#, Dox
|13\15, 600
 
 
|8\10
| rowspan="2" | 10\11, 631.579
564; 1.41{{Overline|6}}
 
 
|11\13
|17\18, 658.064
 
 
600
|7\7, 700
 
 
|-
|18\17, 744.828
 
 
|Fab, Dob
|11\10, 776.471
 
 
|Bbb
|15\13, 818.182
 
 
|3b, 3c
|-
|3f
|10\15
461; 1, 1.1{{Overline|6}}
 
 
|11\18
|Dob, Fab, Solb
425; 1.24
|14\15, 646.154
|16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
 
 
|4\7
|-
 
 
400
!Do, Fa, Sol
!'''15\15,''' '''692.308'''
 
 
|9\17
!'''11\11,''' '''694.737'''
372; 2.41{{Overline|6}}
 
 
|5\10
!'''18\18,''' '''696.774'''
352; 1.0625
 
 
|6\13
!7\7, 700
 
 
327.{{Overline|27}}
!'''17\17,''' '''703.448'''
 
 
|-
!'''10\10,''' '''705.882'''
 
 
|'''Fa, Do'''
!'''13\13,''' '''709.091'''
 
 
|'''Bb'''
|}
 
 
|'''3'''
{| class="wikitable"
|'''3'''
 
 
|'''11\15'''
|+
'''507; 1.{{Overline|4}}'''
 
 
|'''8\11'''
Cents
'''505; 3.8'''
!Notation
!Supersoft
 
 
|'''13\18'''
! Soft
'''503; 4, 2.{{Overline|3}}'''
 
 
|'''5\7'''
!Semisoft
 
 
'''500'''
!Basic
 
 
|'''12\17'''
!Semihard
'''496; 1.8125'''
 
 
|'''7\10'''
! Hard
'''494; 8.5'''
 
 
|'''9\13'''
! Superhard
'''490.{{Overline|90}}'''
 
 
|-
|-
 
 
|Fa#, Do#
!Napoli
! ~15edf
 
 
|B
! ~11edf
 
 
|3#
!~18edf
|3#
|12\15
553; 1.{{Overline|18}}
 
 
|9\11
!~7edf
568; 2.375
 
 
|15\18
!~17edf
580; 1.55
 
 
|6\7
!~10edf
 
 
600
!~13edf
 
 
|15\17
|-
620; 1.45
 
 
|9\10
|F#
635; 3.4
|1\15, 46.154
 
 
|12\13
|1\11, 63.158
 
 
654.{{Overline|54}}
| 2\18, 77.419
|-
|Fax, Dox
 
 
|B#
| rowspan="2" |1\7, 100
 
 
|3x
|3\17, 124.138
|3x
|13\15
 
 
600
| 2\10, 141.176
 
 
| rowspan="2" |10\11
|3\13, 163.636
 
 
631; 1.{{Overline|72}}
|-
 
 
|17\18
| Gb, Ge
|3\15, 138.462
 
 
658; 15.5
| 2\11. 126.316
 
 
|7\7
|3\18, 116.129
 
 
700
|2\17, 82.759
 
 
|18\17
|1\10, 70.588
 
 
744; 1.208{{Overline|3}}
|1\13, 54.545
 
 
|11\10
|-
 
 
776; 2.125
|'''G'''
|'''4\15,''' '''184.615'''
 
 
|15\13
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
 
 
818.{{Overline|18}}
|'''2\7,''' '''200'''
 
 
|-
|'''5\17,''' '''206.897'''
 
 
|Dob, Solb
|'''3\10,''' '''211.765'''
|Hb
|4b, 4c
|4f
|14\15
646; 6.5
|16\18
619; 2.{{Overline|81}}
|6\7
600
|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
 
 
|'''C'''
|9\11, 568.421
 
 
|'''5'''
|15\18, 580.645
|'''5'''
 
 
|'''19\15'''
|6\7, 600
 
 
'''876; 1.08{{Overline|3}}'''
| 15\17, 620.690
 
 
|'''14\11'''
|9\10, 635.294
 
 
'''884; 4.75'''
|12\13, 654.545
 
 
|'''23\18'''
|-
| B#
| 13\15, 600
 
 
'''890; 3.1'''
| rowspan="2" |10\11, 631.579
 
 
|'''9\5'''
|17\18, 658.064
 
 
'''900'''
|7\7, 700
 
 
|'''22\17'''
|18\17, 744.828
 
 
'''910; 2.9'''
|11\10, 776.471
 
 
|'''13\10'''
|15\13, 818.182
 
 
'''917; 1.{{Overline|54}}'''
|-
|Hb, He
|'''17\13'''
|14\15, 646.154
| 16\18, 619.355
'''927.{{Overline|27}}'''
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
 
 
|-
|-
 
 
|Re#, La#
! H
!'''15\15,''' '''692.308'''
 
 
|C#
!'''11\11,''' '''694.737'''
 
 
|5#
!'''18\18,''' '''696.774'''
|5#
|20\15
 
 
923: 13
! 7\7, 700
 
 
|15\11
!'''17\17,''' '''703.448'''
 
 
947; 2, 1.4
!'''10\10,''' '''705.882'''
 
 
|25\18
!'''13\13,''' '''709.091'''
 
 
967; 1, 2.875
|-
 
 
| rowspan="2" |10\7
|Η#
|16\15, 738.462
1000
 
 
|25\17
|12\11, 757.895
 
 
1034; 2, 14
|20\18, 774.194
 
 
|15\10
| rowspan="2" |8\8, 800
 
 
1058; 1, 4.{{Overline|6}}
|20\17, 827.586
 
 
|20\13
|12\10, 847.059
 
 
1090.{{Overline|90}}
|16\13, 872.727
 
 
|-
|-
 
 
|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
| rowspan="2" |18\11, 1136.842
 
 
|30\17
|30\18, 1161.29
 
 
1241; 2.{{Overline|63}}
|12\7, 1200
 
 
|18\10
|30\17, 1241.379
 
 
1270; 1.7
|18\10, 1270.588
 
 
|24\13
|24\13, 1309.091
1309.{{Overline|09}}
 
 
|-
|-
 
 
|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'''
| rowspan="2" |21\11, 1326.318
 
 
'''1200'''
|35\18, 1354.834
 
 
|'''29\17'''
|14\7, 1400
 
 
'''1200'''
|35\17, 1448.275
 
 
|'''17\10'''
| 21\10, 1482.353
 
 
'''1200'''
|28\13, 1527.273
 
 
|'''22\13'''
|-
 
 
'''1200'''
| Fb, Fe
|29\15, 1338.462
 
 
|-
|34\18, 1316.129
 
 
|Fa#, Do#
|13\7, 1300
 
 
|E
|31\17, 1282.759
 
 
|7#
|18\10, 1270.588
|7#
|27\15
 
 
1246; 6.5
|23\13, 1254.545
 
 
|20\11
|-
 
 
1263; 6.{{Overline|3}}
!F
!30\15, 1384.615
 
 
|33\18
!22\11, 1389.473
 
 
1277; 2, 2.6
!36\18, 1393.548
 
 
|13\7
!14\7, 1400
 
 
1300
!34\17, 1406.897
 
 
|32\17
!20\10, 1411.765
1324; 7.25
|19\10
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
|0#, D#
|1\15, 46.154
| rowspan="2" |21\11
|1\11, 63.158
|2\18, 77.419
1326; 3.1{{Overline|6}}
| rowspan="2" |1\7, 100
|3\17, 124.138
|35\18
|2\10, 141.176
|3\13, 163.636
1354; 1, 5.2
|-
|1b, 1c
|14\7
|3\15, 138.462
| 2\11. 126.316
1400
|3\18, 116.129
|2\17, 82.759
|35\17
|1\10, 70.588
|1\13, 54.545
1448; 3.625
|21\10
1482; 2.8{{Overline|3}}
|28\13
1527.{{Overline|27}}
|-
|-
|'''1'''
|Dob, Solb
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
|Fb
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|8b, Fc
|'''5\17,''' '''206.897'''
|8f
|'''3\10,''' '''211.765'''
|29\15
|'''4\13,''' '''218.182'''
|-
1338; 2.1{{Overline|6}}
|1#
|5\15, 230.769
|34\18
|4\11, 252.632
|7\18, 270.968
1316; 7.75
| rowspan="2" |3\7, 300
|8\17, 331.034
|13\7
|5\10, 352.941
|7\13, 381.818
1300
|-
|2b, 2c
|31\17
|7\15, 323.077
|5\11, 315.789
1282; 1.3{{Overline|18}}
| 8\18, 309.677
| 7\17, 289.655
|18\10
|4\10, 282.353
|5\13, 272.727
1270; 1.7
|-
|2
|23\13
|8\15, 369.231
|6\11, 378.947
1254.{{Overline|54}}
|10\18, 387.097
|4\7, 400
|10\17, 413.793
|6\10, 423.529
|8\13, 436.364
|-
|2#
| 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
|-
|-
|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
!30\15
|-
|'''3'''
1384; 1.625
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
!22\11
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
1389; 2.{{Overline|1}}
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
!36\18
|'''9\13,''' '''490.909'''
|-
1393; 1, 1, 4.{{Overline|6}}
|3#
|12\15, 553.846
!14\7
|9\11, 568.421
|15\18, 580.645
1400
|6\7, 600
|15\17, 620.690
!34\17
|9\10, 635.294
|12\13, 654.545
1406; 1, 8.{{Overline|6}}
|-
|3x
!20\10
|13\15, 600
| rowspan="2" |10\11, 631.579
1411; 1, 3.25
|17\18, 658.064
|7\7, 700
!26\13
|18\17, 744.828
|11\10, 776.471
1418.{{Overline|18}}
|15\13, 818.182
|-
|4b, 4c
|14\15, 646.154
|16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
|-
|-
!4
|Do#, Sol#
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
|F#
!'''18\18,''' '''696.774'''
!7\7, 700
|8#, F#
!'''17\17,''' '''703.448'''
|8#
!'''10\10,''' '''705.882'''
|31\15
!'''13\13,''' '''709.091'''
|-
1430; 1.3
|4#
| 16\15, 738.462
|23\11
|12\11, 757.895
|20\18, 774.194
1452; 1.58{{Overline|3}}
| rowspan="2" |8\8, 800
|20\17, 827.586
|38\18
|12\10, 847.059
| 16\13, 872.727
1470; 1.0{{Overline|3}}
|-
|5b, 5c
| rowspan="2" |15\7
|18\15, 830.769
|13\11, 821.053
1500
|21\18, 812.903
|19\17, 786.207
|37\17
|11\10, 776.471
|14\13, 763.63
1531; 29
|-
|'''5'''
|22\10
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
1552; 1.0625
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
|29\13
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
1581.{{Overline|81}}
|'''17\13,''' '''927.273'''
|-
|-
|5#
|Reb, Lab
|20\15, 923.077
|15\11, 947.368
|Gb
|25\18, 967.742
| rowspan="2" |10\7, 1000
|9b, Gc
|25\17, 1034.483
|9f
|15\10, 1058.824
|33\15
|20\13, 1090.909
|-
1523; 13
|6b, 6c
|22\15, 1015.385
|24\11
|16\11, 1010.526
|26\18, 1006.452
1515; 1.2{{Overline|6}}
|24\17, 993.103
|14\10, 988.235
|39\18
|18\13, 981.818
|-
1509; 1, 2.1
|6
|23\15, 1061.538
|36\17
|17\11, 1073.684
| 28\18, 1083.871
1489; 1, 1.9
|11\7, 1100
|27\17, 1117.241
|21\10
|16\10, 1129.412
|21\9, 1145.455
1482; 2.8{{Overline|3}}
|-
|6#
|27\13
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
1472.{{Overline|72}}
|30\18, 1161.290
|12\7, 1200
|30\17, 1241.379
|18\10, 1270.588
|24\13, 1309.091
|-
| 7b, 7c
|25\15, 1153.846
|29\18, 1122.581
|11\7, 1100
|26\17, 1075.862
|15\10, 1058.824
|19\13, 1036.364
|-
|'''7'''
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|-
|7#
|'''Re, La'''
|27\15, 1246.154
|20\11, 1263.158
|'''G'''
|33\18, 1277.419
|13\7, 1300
|'''9, G'''
|32\17, 1324.138
|9
|19\10, 1341.176
|'''34\15'''
|25\13, 1363.636
|-
'''1569; 4.{{Overline|3}}'''
|7x
|28\15, 1292.308
|'''25\11'''
| rowspan="2" |21\11, 1326.318
|35\18, 1354.834
'''1578; 1.0{{Overline|5}}'''
|14\7, 1400
|35\17, 1448.275
|'''41\18'''
|21\10, 1482.353
|28\13, 1527.273
'''1587; 10.{{Overline|3}}'''
|-
|8b, Fc
|'''16\7'''
|29\15, 1338.462
|34\18, 1316.129
'''1600'''
|13\7, 1300
|31\17, 1282.759
|'''39\17'''
|18\10, 1270.588
|23\13, 1254.545
'''1613; 1, 3.8{{Overline|3}}'''
|-
!8, F
|'''23\10'''
!30\15, 1384.615
!22\11, 1389.473
'''1623; 1.{{Overline|8}}'''
!36\18, 1393.548
!14\7, 1400
|'''30\13'''
!34\17, 1406.897
!20\10, 1411.765
'''1636.{{Overline|36}}'''
!26\13, 1418.182
|-
|8#, F#
|31\15, 1430.769
|23\11, 1452.632
|38\18, 1470.968
| rowspan="2" |15\7, 1500
|37\17, 1531.034
|22\10, 1552.941
|29\13, 1581.818
|-
|9b, Gc
|33\15, 1523.077
|24\11, 1515.789
|39\18, 1509.677
|36\17, 1489.655
|21\10, 1482.759
|27\13, 1472.273
|-
|'''9, G'''
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.364'''
|-
|-
|Re#, La#
|G#
|9#, G#
|9#, G#
|9#
|35\15, 1615.385
|35\15
|26\11, 1642.105
|43\18, 1664.516
1615; 2.6
| rowspan="2" |17\7, 1700
|42\17, 1737.069
|26\11
|25\10, 1764.706
|33\13, 1800
1642; 9.5
|43\18
1664; 1.0625
| rowspan="2" |17\7
1700
|42\17
1737; 14.5
|25\10
1764; 1.41{{Overline|6}}
|33\13
1800
|-
|-
|Mib, Sib
|Ab
|Xb, Ac
|Xb, Ac
|Af
|37\15, 1707.692
|37\15
|27\11, 1705.263
|44\18, 1703.226
1707; 1.{{Overline|4}}
|41\17, 1696.552
|24\10, 1694.118
|27\11
|31\13, 1690.909
|-
1705; 3.8
|X, A
|38\15, 1753.846
|44\18
|28\11, 1768.421
|46\18, 1780.645
1703; 4, 2.{{Overline|3}}
|18\7, 1800
|44\17, 1820.690
|41\17
|26\10, 1835.294
|34\13, 1854.545
1696; 1.8125
|-
|X#, A#
|24\10
|39\15, 1800
| rowspan="2" |29\11, 1831.579
1694; 8.5
|48\18, 1858.064
|19\7, 1900
|31\13
|47\17, 1944.828
|28\10, 1976.471
1690.{{Overline|90}}
|37\13, 2018.182
|-
|Ebb, Ccc
|40\15, 1846.154
|47\18, 1819.355
|18\7, 1800
|43\17, 1779.310
|25\10, 1764.706
|32\13, 1745.545
|-
|'''Eb, Cc'''
|'''41\15,''' '''1892.308'''
|'''30\11,''' '''1894.737'''
|'''49\18,''' '''1896.774'''
|'''19\7, 1900'''
|'''46\17,''' '''1903.448'''
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
|-
|E, C
|42\15, 1938.462
|31\11, 1957.895
|51\18, 1974.194
|20\7, 2000
|49\17, 2027.586
|29\10, 2047.059
|38\13, 2072.727
|-
|Ex, Cx
|43\15, 1984.615
| rowspan="2" |32\11, 2021.053
|53\18, 2051.612
|21\7, 2100
|52\17, 2151.725
|31\10, 2188.235
|41\13, 2236.364
|-
|0b, Dc
|44\15, 2030.769
|52\18, 2012.903
|20\7, 2000
|48\17, 1986.207
|28\10, 1976.471
|36\13, 1963.636
|-
|-
! 0, D
|Mi, Si
!45\15, 2076.923
!33\11, 2084.211
|A
!54\18, 2090.323
!21\7, 2100
|X, A
!51\17, 2110.345
|A
!30\10, 2117.647
|38\15
!39\13, 2127.273
|}
1753; 1.{{Overline|18}}
 
{| class="wikitable"
|28\11
|+Cents
!Notation
1768; 2.375
!Supersoft
!Soft
|46\18
!Semisoft
! Basic
1780; 1.55
!Semihard
!Hard
|18\7
!Superhard
1800
|44\17
1820; 1.45
|26\10
1835; 3.4
|34\13
1854.{{Overline|54}}
|-
|-
!Hextone
|Mi#, Si#
!~15edf
!~11edf
|A#
!~18edf
!~7edf
|X#, A#
!~17edf
|A#
!~10edf
|39\15
!~13edf
|-
1800
|0#, G#
|1\15, 46.154
| rowspan="2" |29\11
|1\11, 63.158
|2\18, 77.419
1831; 1.{{Overline|72}}
| rowspan="2" |1\7, 100
|3\17, 124.138
|48\18
|2\10, 141.176
|3\13, 163.636
1858; 15.5
|-
| 1f
|19\7
|3\15, 138.462
|2\11. 126.316
1900
|3\18, 116.129
|2\17, 82.759
|47\17
|1\10, 70.588
|1\13, 54.545
1944; 1.208{{Overline|3}}
|-
|'''1'''
|28\10
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
1976; 2.125
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|37\13
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
2018.{{Overline|18}}
|'''4\13,''' '''218.182'''
|-
|-
|1#
|Fab, Dob
|5\15, 230.769
|4\11, 252.632
|Bbb
|7\18, 270.968
| rowspan="2" |3\7, 300
|Ebb, Ccc
|8\17, 331.034
|Bf
|5\10, 352.941
|40\15
|7\13, 381.818
|-
1846; 6.5
|2f
|7\15, 323.077
|47\18
|5\11, 315.789
|8\18, 309.677
1819; 2.{{Overline|81}}
|7\17, 289.655
|4\10, 282.353
|18\7
|5\13, 272.727
|-
1800
|2
|8\15, 369.231
|43\17
|6\11, 378.947
|10\18, 387.097
1779; 3.{{Overline|2}}
| 4\7, 400
|10\17, 413.793
|25\10
|6\10, 423.529
|8\13, 436.364
1764; 1.41{{Overline|6}}
|-
|2#
|32\13
|9\15, 415.385
| rowspan="2" |7\11, 442.105
1745.{{Overline|45}}
|12\18, 464.516
|5\7, 500
|13\17, 537.069
|8\10, 564.706
|11\13, 600
|-
|3f
| 10\15, 461.538
|11\18, 425.806
|4\7, 400
|9\17, 372.414
|5\10, 352.941
|6\13, 327.273
|-
|-
|'''3'''
|'''Fa, Do'''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|'''Bb'''
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|'''Eb, Cc'''
|'''12\17,''' '''496.552'''
|'''B'''
|'''7\10,''' '''494.118'''
|'''41\15'''
|'''9\13,''' '''490.909'''
|-
'''1892; 3.25'''
|3#
|12\15, 553.846
|'''30\11'''
|9\11, 568.421
|15\18, 580.645
'''1894; 1, 2.8'''
|6\7, 600
|15\17, 620.690
|'''49\18'''
|9\10, 635.294
|12\13, 654.545
'''1896; 1.291{{Overline|6}}'''
|-
| 3x
|'''19\7'''
|13\15, 600
| rowspan="2" | 10\11, 631.579
'''1900'''
|17\18, 658.064
|7\7, 700
|'''46\17'''
|18\17, 744.828
|11\10, 776.471
'''1903; 2.1{{Overline|6}}'''
|15\13, 818.182
|-
|'''27\10'''
|4f
| 14\15, 646.154
'''1905; 1.1{{Overline|3}}'''
|16\18, 619.355
|6\7, 600
|'''35\13'''
|14\17, 579.310
|8\10, 564.706
'''1909.{{Overline|09}}'''
|10\13, 545.455
|-
!4
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
!7\7, 700
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
|-
| 4#
|16\15, 738.462
|12\11, 757.895
|20\18, 774.194
| rowspan="2" |8\8, 800
|20\17, 827.586
|12\10, 847.059
|16\13, 872.727
|-
|-
|5
|Fa#, Do#
|18\15, 830.769
|13\11, 821.053
|B
|21\18, 812.903
|19\17, 786.207
|E, C
| 11\10, 776.471
|B#
|14\13, 763.63
|42\15
|-
|'''5'''
1938; 2.1{{Overline|6}}
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
|31\11
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
1957; 1, 8.5
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|51\18
|'''17\13,''' '''927.273'''
|-
1974; 5.1{{Overline|6}}
|5#
|20\15, 923.077
|20\7
|15\11, 947.368
| 25\18, 967.742
2000
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|49\17
|15\10, 1058.824
|20\13, 1090.909
2027; 1, 1.41{{Overline|6}}
|-
|6f
|29\10
|22\15, 1015.385
|16\11, 1010.526
2047; 17
|26\18, 1006.452
|24\17, 993.103
|38\13
|14\10, 988.235
|18\13, 981.818
2072.{{Overline|72}}
|-
|6
|23\15, 1061.538
|17\11, 1073.684
|28\18, 1083.871
|11\7, 1100
|27\17, 1117.241
|16\10, 1129.412
|21\9, 1145.455
|-
|-
|6#
|Fax, Dox
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
|B#
|30\18, 1161.290
|12\7, 1200
|Ex, Cx
|30\17, 1241.379
|Bx
|18\10, 1270.588
|43\15
|24\13, 1309.091
|-
1984; 1.625
| 7f
|25\15, 1153.846
| rowspan="2" |32\11
|29\18, 1122.581
|11\7, 1100
2021; 19
|26\17, 1075.862
|15\10, 1058.824
|53\18
|19\13, 1036.364
|-
2051; 1, 1, 1, 1.4
|'''7'''
|'''26\15,''' '''1200'''
|21\7
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
2100
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|52\17
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
2151; 2.625
|-
|7#
|31\10
|27\15, 1246.154
|20\11, 1263.158
2188; 4.25
|33\18, 1277.419
|13\7, 1300
|41\13
|32\17, 1324.138
|19\10, 1341.176
2236.{{Overline|36}}
|25\13, 1363.636
|-
|7x
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
|35\18, 1354.834
|14\7, 1400
|35\17, 1448.275
|21\10, 1482.353
|28\13, 1527.273
|-
|-
|8f
|Dob, Solb
|29\15, 1338.462
| 34\18, 1316.129
|Hb
|13\7, 1300
|31\17, 1282.759
|0b, Dc
|18\10, 1270.588
|Cf
|23\13, 1254.545
|44\15
2030; 1.3
|52\18
2012; 1, 9,{{Overline|3}}
|20\7
2000
|48\17
1986; 4.8{{Overline|3}}
|28\10
1976; 2.125
|36\13
1963.{{Overline|63}}
|-
|-
! 8
!Do, Sol
!30\15, 1384.615
!22\11, 1389.473
!H
!36\18, 1393.548
!14\7, 1400
!0, D
!34\17, 1406.897
!C
!20\10, 1411.765
!45\15
!26\13, 1418.182
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#
|8#
|Η#
|31\15, 1430.769
|0#, D#
|23\11, 1452.632
|C#
| 38\18, 1470.968
|46\15
| rowspan="2" |15\7, 1500
2123; 13
|37\17, 1531.034
|34\11
|22\10, 1552.941
2147; 2, 1.4
|29\13, 1581.818
|56\18
|-
2167; 1, 2.875
|9f
| rowspan="2" |22\7
|33\15, 1523.077
2200
|24\11, 1515.789
|54\17
|39\18, 1509.677
2234; 2, 14
| 36\17, 1489.655
|32\10
|21\10, 1482.759
2258; 1, 4.{{Overline|6}}
|27\13, 1472.273
|42\13
2090.{{Overline|90}}
|-
|-
|Reb, Lab
|9
|Cb
|'''34\15,''' '''1569.231'''
|1b, 1c
|'''25\11,''' '''1578.947'''
|Df
|'''41\18,''' '''1587.097'''
|48\15
|'''16\7,''' '''1600'''
2215; 2.6
|'''39\17,''' '''1613.793'''
|35\11
|'''23\10,''' '''1623.529'''
2210; 1.9
|'''30\13,''' '''1636.364'''
|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'''
|9#
|'''C'''
|35\15, 1615.385
|'''1'''
|26\11, 1642.105
|'''D'''
|43\18, 1664.516
|'''49\15'''
| rowspan="2" |17\7, 1700
'''2261; 1, 1.1{{Overline|6}}'''
|42\17, 1737.069
|'''36\11'''
|25\10, 1764.706
'''2273; 1, 2.1{{Overline|6}}'''
|33\13, 1800
|'''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#
|Af
|C#
| 37\15, 1707.692
|1#
| 27\11, 1705.263
|D#
|44\18, 1703.226
|50\15
|41\17, 1696.552
2307; 1.{{Overline|4}}
|24\10, 1694.118
|37\11
|31\13, 1690.909
2336; 1.1875
|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
|A
|Db
| 38\15, 1753.846
|2b, 2c
|28\11, 1768.421
|Ef
|46\18, 1780.645
|52\15
|18\7, 1800
2400
|44\17, 1820.690
|38\11
|26\10, 1835.294
2400
|34\13, 1854.545
|62\18
2400
|58\17
2400
|34\10
2400
|44\13
2400
|-
|-
|Mi, Si
|A#
|D
| 39\15, 1800
|2
| rowspan="2" |29\11, 1831.579
|E
| 48\18, 1858.064
|53\15
|19\7, 1900
2446; 6.5
|47\17, 1944.828
|39\11
|28\10, 1976.471
2463; 6.{{Overline|3}}
|37\13, 2018.182
|64\18
2477; 2, 2.6
|25\7
2500
|61\17
2524; 7.25
|36\10
2541; 5.{{Overline|6}}
|47\13
2563.{{Overline|63}}
|-
|-
|Mi#, Si#
|Ax
|D#
|40\15, 1846.154
|2#
|47\18, 1819.355
|E#
|18\7, 1800
|54\15
|43\17, 1779.310
2492; 3.25
|25\10, 1764.706
| rowspan="2" |40\11
|32\13, 1745.545
2526; 3.1
|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
|'''Bf'''
|Ebb
|'''41\15,''' '''1892.308'''
|3b, 3c
|'''30\11,''' '''1894.737'''
|Fff
|'''49\18,''' '''1896.774'''
|55\15
|'''19\7, 1900'''
2538; 2.1{{Overline|6}}
|'''46\17,''' '''1903.448'''
|65\18
|'''27\10,''' '''1905.882'''
2516; 7.75
|'''35\13,''' '''1909.091'''
|25\7
2500
|60\17
2482; 1.3{{Overline|18}}
|35\10
2470; 1.7
|45\13
2454.{{Overline|54}}
|-
|-
|'''Fa, Do'''
|B
|'''Eb'''
|42\15, 1938.462
|'''3'''
|31\11, 1957.895
|'''Ff'''
|51\18, 1974.194
|'''56\15'''
|20\7, 2000
'''2584; 1.625'''
|49\17, 2027.586
|'''41\11'''
| 29\10, 2047.059
'''2589; 2.{{Overline|1}}'''
|38\13, 2072.727
|'''67\18'''
|-
'''2593; 1, 1, 4.{{Overline|6}}'''
|B#
|'''26\7'''
|43\15, 1984.615
'''2600'''
| rowspan="2" |32\11, 2021.053
|'''63\17'''
|53\18, 2051.612
'''2606; 1, 8.{{Overline|6}}'''
|21\7, 2100
|'''37\10'''
|52\17, 2151.725
'''2611; 1, 3.25'''
|31\10, 2188.235
|'''48\13'''
|41\13, 2236.364
'''2618.{{Overline|18}}'''
|-
|Cf
|44\15, 2030.769
|52\18, 2012.903
|20\7, 2000
|48\17, 1986.207
|28\10, 1976.471
|36\13, 1963.636
|-
!C
!45\15, 2076.923
!33\11, 2084.211
!54\18, 2090.323
!21\7, 2100
!51\17, 2110.345
!30\10, 2117.647
!39\13, 2127.273
|-
|C#
|46\15, 2123.077
|34\11, 2147.368
|56\15, 2167.742
| rowspan="2" |22\7, 2200
|54\17, 2234.483
|32\10, 2258.824
|42\13, 2090.909
|-
|Df
|48\15, 2215.385
|35\11, 2210.526
|57\15, 2206.452
|53\17, 2193.103
|31\10, 2188.235
|40\13, 2181.818
|-
|'''D'''
|'''49\15, 2261.538'''
|'''36\11, 1073.684'''
|'''59\18, 2283.871'''
|'''23\7, 2300'''
|'''56\17, 2317.241'''
|'''33\10, 2329.412'''
|'''43\13,''' '''2345.455'''
|-
|D#
|50\15, 2307.692
|37\11, 2336.842
|61\18, 2361.290
| rowspan="2" |24\7, 2400
|59\17, 2441.379
|35\10, 2470.588
|46\13, 2509.091
|-
|Ef
|52\15, 2400
|38\11, 2400
|62\18, 2400
|58\17, 2400
|34\10, 2400
| 44\13, 2400
|-
|-
|Fa#, Do#
|E
|E
|3#
|53\15, 2446.154
|F
| 39\11, 2463.158
|57\15
|64\18, 2477,419
2630; 1.3
|25\7, 2500
|42\11
|61\17, 2524.138
2652; 1.58{{Overline|3}}
|36\10, 2541.176
|69\18
|47\13, 2563.636
2670; 1.0{{Overline|3}}
|27\7
2700
|66\17
2731; 29
|39\10
2752; 1.0625
|51\13
2781.{{Overline|81}}
|-
|-
|Fax, Dox
|E#
|E#
|3x
|54\15, 2492.308
|F#
| rowspan="2" |40\11, 2526.316
|58\15
|66\18, 2554.838
2676; 1.08{{Overline|3}}
|26\7, 2600
| rowspan="2" |43\11
|64\17, 2648.275
2715; 1.2{{Overline|6}}
|38\10, 2682.353
|71\18
|50\13, 2727.273
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
|Fff
|Fb
| 55\15, 2538.462
|4b, 4c
| 65\18, 2516.129
|0f, Gf
|25\7, 2500
|59\15
|60\17, 2482.759
2723; 13
|35\10, 2470.588
|70\18
|45\13, 2454.545
2709; 1, 2.1
|-
|27\7
|'''Ff'''
2700
|'''56\15, 2584.615'''
|65\17
|'''41\11, 2589.474'''
2689; 1, 1.9
|'''67\18, 2593.548'''
|38\10
|'''26\7, 2600'''
2682; 2.8{{Overline|3}}
|'''63\17, 2606.897'''
|49\13
|'''37\10, 2611.765'''
2672.{{Overline|72}}
|'''48\13,''' '''2618.182'''
|-
|F
|57\15, 2630.769
|42\11, 2652.632
|69\18, 2670.968
|27\7, 2700
|66\17, 2731.034
|39\10, 2752.941
|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
|-
|0ff, Gff
|42\11, 2652.632
|68\18, 2632.258
|26\7, 2600
|62\17, 2565.517
|36\10, 2541.176
|46\13, 2509.091
|-
|0f, Gf
|59\15, 2723.077
|43\11, 2715.789
|70\18, 2709.677
|27\7, 2700
|65\17, 2689.552
|38\10, 2682.353
|49\13, 2672.273
|-
|-
!Do, Sol
!F
!4
!0, G
!0, G
!60\15
!60\15, 2769.231
2769; 4.'''{{Overline|3}}'''
!44\11, 2778.947
!44\11
!72\18, 2787.097
2778; 1.0{{Overline|5}}
!28\7, 2800
!72\18
!68\17, 2813.793
2787; 3.1
!40\10, 2823.529
!28\7
!52\13, 2836.364
2800
!68\17
2813; 1, 3.8{{Overline|3}}
!40\10
2823; 1.{{Overline|8}}
!52\13
2836.{{Overline|36}}
|}
|}
 
{| class="wikitable"
{| class="wikitable"
|+Relative cents<ref name=":02">Fractions repeating more than 4 digits written as continued fractions</ref>
|+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 1,622: 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; 1.{{Overline|8}}''
|2\10
''140''
|3\13
''161; 1, 1.1{{Overline|6}}''
|-
|-
|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; 2.8{{Overline|3}}''
|5\10, 352.941
|1\10
|7\13, 381.818
''70''
|1\13
''53; 1.{{Overline|18}}''
|-
|-
|'''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; 1.1{{Overline|3}}'''''
|'''3\10'''
'''''210'''''
|'''4\13'''
'''''215; 2.6'''''
|-
|-
|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; 2, 2.{{Overline|3}}''
|5\10
''350''
|7\13
''376; 1.08{{Overline|3}}''
|-
|-
|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}}''
|8\18
''311.{{Overline|1}}''
|7\17
''288; 4.25''
|4\10
''280''
|5\13
''269; 4.{{Overline|3}}''
|-
|-
|Mi, Si
|B fa utb
|A
|10\15, 461.538
|2
|11\18, 425.806
|2
|4\7, 400
|8\15
|9\17, 372.414
|5\10, 352.941
''373.{{Overline|3}}''
|6\13, 327.273
|6\11
''381.{{Overline|81}}''
|10\18
''388.{{Overline|8}}''
|4\7
''400''
|10\17
''411; 1, 3.25''
|6\10
''420''
|8\13
''430; 1.3''
|-
|-
|Mi#, Si#
|'''B fa ut'''
|A#
|'''11\15,''' '''507.692'''
|2#
|'''8\11,''' '''505.263'''
|2#
|'''13\18,''' '''503.226'''
|9\15
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
''420''
|'''7\10,''' '''494.118'''
| rowspan="2" |7\11
|'''9\13,''' '''490.909'''
''445.{{Overline|45}}''
|12\18
''466.{{Overline|6}}''
|5\7
''500''
|13\17
''535; 3.4''
|8\10
''560''
|11\13
''592; 3.25''
|-
|-
|Fab, Dob
|B fa ut#
|Bbb
|12\15, 553.846
|3b, 3c
|9\11, 568.421
|3f
|15\18, 580.645
|10\15
|6\7, 600
|15\17, 620.690
''466.{{Overline|6}}''
|9\10, 635.294
|11\18
|12\13, 654.545
|-
''427.{{Overline|7}}''
|B fa utx
|4\7
| 13\15, 600
| rowspan="2" |10\11, 631.579
''400''
|17\18, 658.064
|9\17
|7\7, 700
|18\17, 744.828
''370; 1.7''
|11\10, 776.471
|5\10
|15\13, 818.182
''350''
|6\13
''323; 13''
|-
|-
|'''Fa, Do'''
|C sol re utb
|'''Bb'''
| 14\15, 646.154
|'''3'''
|16\18, 619.355
|'''3'''
|6\7, 600
|'''11\15'''
|14\17, 579.310
|8\10, 564.706
'''''513.{{Overline|3}}'''''
|10\13, 545.455
|'''8\11'''
'''''509.{{Overline|09}}'''''
|'''13\18'''
'''''505.{{Overline|5}}'''''
|'''5\7'''
'''''500'''''
|'''12\17'''
'''''494; 8.5'''''
|'''7\10'''
'''''490'''''
|'''9\13'''
'''''484; 1.625'''''
|-
|-
|Fa#, Do#
!C sol re ut
|B
!'''15\15,''' '''692.308'''
|3#
!'''11\11,''' '''694.737'''
|3#
!'''18\18,''' '''696.774'''
|12\15
!7\7, 700
!'''17\17,''' '''703.448'''
''560''
!'''10\10,''' '''705.882'''
|9\11
!'''13\13,''' '''709.091'''
''572.{{Overline|72}}''
|15\18
''583.{{Overline|3}}''
|6\7
''600''
|15\17
''617; 1.41{{Overline|6}}''
|9\10
''630''
|12\13
''646; 6.5''
|-
|-
|Fax, Dox
|C sol re ut#
|B#
|16\15, 738.462
|3x
|12\11, 757.895
|3x
|20\18, 774.194
|13\15
| rowspan="2" |8\8, 800
|20\17, 827.586
''606.{{Overline|6}}''
|12\10, 847.059
| rowspan="2" |10\11
|16\13, 872.727
|-
''636.{{Overline|36}}''
|D la mi reb
|17\18
|18\15, 830.769
|13\11, 821.053
''661.{{Overline|1}}''
|21\18, 812.903
|7\7
|19\17, 786.207
|11\10, 776.471
''700''
|14\13, 763.63
|18\17
|-
|'''D la mi re'''
''741; 5.{{Overline|6}}''
|'''19\15,''' '''876.923'''
|11\10
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
''770''
|'''9\5,''' '''900'''
|15\13
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
''807; 1.{{Overline|4}}''
|'''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
|-
|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
|-
|-
|Dob, Solb
|E fa ut
|Hb
| 22\15, 1015.385
|4b, 4c
|16\11, 1010.526
|4f
|26\18, 1006.452
|14\15
|10\7, 1000
|24\17, 993.103
''653.{{Overline|3}}''
|14\10, 988.235
|16\18
|18\13, 981.818
''622.{{Overline|2}}''
|6\7
''600''
|14\17
''576; 2.125''
|8\10
''560''
|10\13
''538; 2.1{{Overline|6}}''
|-
|-
!Do, Sol
|E si mi re
!H
|23\15, 1061.538
!4
|17\11, 1073.684
!4
|28\18, 1083.871
! colspan="7" |''700''
|11\7, 1100
|27\17, 1117.241
|16\10, 1129.412
|21\9, 1145.455
|-
|-
|Do#, Sol#
| E si mi re#
|Η#
|24\15, 1107.923
|4#
| rowspan="2" |18\11, 1136.842
|4#
|30\18, 1161.29
|16\15
|12\7, 1200
|30\17, 1241.379
''746.{{Overline|6}}''
| 18\10, 1270.588
|12\11
|24\13, 1309.091
|-
''763.{{Overline|63}}''
|F sol fa ut reb
|20\18
|25\15, 1153.846
|29\18, 1122.581
''777.{{Overline|7}}''
|11\7, 1100
| rowspan="2" |8\7
|26\17, 1075.862
|15\10, 1058.824
''800''
|19\13, 1036.364
|20\17
|-
|'''F sol fa ut re'''
''823; 1.{{Overline|8}}''
|'''26\15,''' '''1200'''
|12\10
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
''840''
|'''12\7, 1200'''
|16\13
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
''861; 1, 1.1{{Overline|6}}''
|'''22\13,''' '''1200'''
|-
|-
|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; 2.8{{Overline|3}}''
|11\10
''770''
|14\13
''753; 1.{{Overline|18}}''
|-
|-
|'''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; 1.1{{Overline|3}}'''''
|'''13\10'''
'''''910'''''
|'''17\13'''
'''''915; 2.6'''''
|-
|-
|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
|-
!G la sol re mi
''954.{{Overline|54}}''
!30\15, 1384.615
|25\18
!22\11, 1389.473
!36\18, 1393.548
''972.{{Overline|2}}''
!14\7, 1400
| rowspan="2" |10\7
!34\17, 1406.897
!20\10, 1411.765
''1000''
!26\13, 1418.182
|25\17
''1029; 2, 2.{{Overline|3}}''
|15\10
''1050''
|20\13
''1076; 1.08{{Overline|3}}''
|-
|-
|Mib, Sib
|G la sol re mi#
|Db
|31\15, 1430.769
|6b, 6c
|23\11, 1452.632
|6f
|38\18, 1470.968
|22\15
| rowspan="2" |15\7, 1500
|37\17, 1531.034
''1026.{{Overline|6}}''
|22\10, 1552.941
|16\11
|29\13, 1581.818
''1018.{{Overline|18}}''
|26\18
''1011.{{Overline|1}}''
|24\17
''988; 4.25''
|14\10
''980''
|18\13
''969; 4.{{Overline|3}}''
|-
|-
|Mi, Si
|A si la mi fab
|D
|33\15, 1523.077
|6
| 24\11, 1515.789
|6
|39\18, 1509.677
|23\15
|36\17, 1489.655
|21\10, 1482.759
''1073.{{Overline|3}}''
| 27\13, 1472.273
|17\11
''1081.{{Overline|81}}''
|28\18
''1088.{{Overline|8}}''
|11\7
''1100''
|27\17
''1111; 1, 3.25''
|16\10
''1120''
|21\13
''1130; 1.3''
|-
|-
|Mi#, Si#
|'''A si la mi fa'''
|D#
|'''34\15,''' '''1569.231'''
|6#
|'''25\11,''' '''1578.947'''
|6#
|'''41\18,''' '''1587.097'''
|24\15
|'''16\7,''' '''1600'''
|'''39\17,''' '''1613.793'''
''1120''
|'''23\10,''' '''1623.529'''
| rowspan="2" |18\11
|'''30\13,''' '''1636.364'''
|-
''1145.{{Overline|45}}''
|A si la mi fa#
|30\18
| 35\15, 1615.385
| rowspan="2" |26\11, 1642.105
''1166.{{Overline|6}}''
|43\18, 1664.516
|12\7
|17\7, 1700
|42\17, 1737.069
''1200''
| 25\10, 1764.706
|30\17
|33\13, 1800
|-
''1235; 3.4''
|B sol fa utb
|18\10
|36\61, 1661.538
|42\18, 1625.806
''1260''
|16\7, 1600
|24\13
|38\29, 1572.414
|22\10, 1552.941
''1292; 3.25''
|28\13, 1527.273
|-
|-
|Fab, Dob
|B sol fa ut
|Ebb
|37\15, 1707.692
|7b, 7c
|27\11, 1705.263
|7f
| 44\18, 1703.226
|25\15
| 17\7, 1700
|41\17, 1696.552
''1166.{{Overline|6}}''
|24\10, 1694.118
|29\18
|31\13, 1690.909
''1127.{{Overline|7}}''
|11\7
''1100''
|26\17
''1070; 1.7''
|15\10
''1050''
|19\13
''1023; 13''
|-
|-
|'''Fa, Do'''
|B si
|'''Eb'''
|38\15, 1753.846
|'''7'''
| 28\11, 1768.421
|'''7'''
|46\18, 1780.645
|'''26\15'''
|18\7, 1800
|44\17, 1820.690
'''''1213.{{Overline|3}}'''''
|26\10, 1835.294
|'''19\11'''
|34\13, 1854.545
'''''1209.{{Overline|09}}'''''
|'''31\18'''
'''''1205.{{Overline|5}}'''''
|'''12\7'''
'''''1200'''''
|'''29\17'''
'''''1194; 8.5'''''
|'''17\10'''
'''''1190'''''
|'''22\13'''
'''''1184; 1.625'''''
|-
|-
|Fa#, Do#
|B si
|E
|39\15, 1800
|7#
| rowspan="2" |29\11, 1831.579
|7#
|48\18, 1858.064
|27\15
|19\7, 1900
|47\17, 1944.828
''1260''
|28\10, 1976.471
|20\11
|37\13, 2018.182
''1272.{{Overline|72}}''
|33\18
''1283.{{Overline|3}}''
|13\7
''1300''
|32\17
''1317; 1.41{{Overline|6}}''
|19\10
''1330''
|25\13
''1346; 6.5''
|-
|-
|Fax, Dox
|C la sol re utb
|E#
|40\15, 1846.154
|7x
|47\18, 1819.355
|7x
| 18\7, 1800
|28\15
| 43\17, 1779.310
|25\10, 1764.706
''1306.{{Overline|6}}''
|32\13, 1745.545
| rowspan="2" |21\11
''1336.{{Overline|36}}''
|35\18
''1361.{{Overline|1}}''
|14\7
''1400''
|35\17
''1441; 5.{{Overline|6}}''
|21\10
''1470''
|28\13
''1507; 1.{{Overline|4}}''
|-
|-
|Dob, Solb
|'''C la sol re ut'''
|Fb
|'''41\15,''' '''1892.308'''
|8b, Fc
|'''30\11,''' '''1894.737'''
|8f
|'''49\18,''' '''1896.774'''
|29\15
|'''19\7, 1900'''
|'''46\17,''' '''1903.448'''
''1333.{{Overline|3}}''
|'''27\10,''' '''1905.882'''
|34\18
|'''35\13,''' '''1909.091'''
''1322.{{Overline|2}}''
|13\7
''1300''
|31\17
''1276; 2.125''
|18\10
''1260''
|23\13
''1238; 2.1{{Overline|6}}''
|-
|-
!Do, Sol
|C la sol re ut#
!F
|42\15, 1938.462
!8, F
|31\11, 1957.895
!8
|51\18, 1974.194
! colspan="7" |''1400''
|20\7, 2000
|49\17, 2027.586
| 29\10, 2047.059
|38\13, 2072.727
|-
|-
|Do#, Sol#
|C la sol re utx
|F#
| rowspan="2" |43\15, 1984.615
|8#, F#
|32\11, 2021.053
|8#
|53\18, 2051.612
|31\15
|21\7, 2100
|52\17, 2151.725
''1446.{{Overline|6}}''
|31\10, 2188.235
|23\11
|41\13, 2236.364
''1463.{{Overline|63}}''
|38\18
''1477.7̄''
| rowspan="2" |15\7
''1500''
|37\17
''1523; 1.{{Overline|8}}''
|22\10
''1540''
|29\13
''1561; 1, 1.1{{Overline|6}}''
|-
|-
|Reb, Lab
|D fa la mi reb
|Gb
|31\11, 1957.895
|9b, Gc
|50\18, 1935.484
|9f
|19\7, 1900
|33\15
|45\17, 1862.069
|26\10, 1835.294
''1540''
|33\13, 1800
|24\11
''1527.{{Overline|27}}''
|39\18
''1516.{{Overline|6}}''
|36\17
''1482; 2.8{{Overline|3}}''
|21\10
''1470''
|27\13
''1453; 1.{{Overline|18}}''
|-
|-
|'''Re, La'''
|D fa la mi re
|'''G'''
|44\15, 2030.769
|'''9, G'''
|32\11, 2021.053
|9
|52\18, 2012.903
|'''34\15'''
|20\7, 2000
|48\17, 1986.207
'''''1586.{{Overline|6}}'''''
|28\10, 1976.471
|'''25\11'''
|36\13, 1963.636
'''''1590.{{Overline|90}}'''''
|'''41\18'''
'''''1594.{{Overline|4}}'''''
|'''16\7'''
'''''1600'''''
|'''39\17'''
'''''1605; 1.1{{Overline|3}}'''''
|'''23\10'''
'''''1610'''''
|'''30\13'''
'''''1615; 2.6'''''
|-
|-
|Re#, La#
!D si la mi re
|G#
!45\15, 2076.923
|9#, G#
!33\11, 2084.211
|9#
!54\18, 2090.323
|35\15
!21\7, 2100
! 51\17, 2110.345
''1633.{{Overline|3}}''
!30\10, 2117.647
|26\11
!39\13, 2127.273
''1654.{{Overline|54}}''
|43\18
''1672.{{Overline|2}}''
| rowspan="2" |17\7
''1700''
|42\17
''1729; 2, 2.{{Overline|3}}''
|25\10
''1750''
|33\13
''1776; 1.08{{Overline|3}}''
|-
|-
|Mib, Sib
|D si la mi re#
|Ab
|46\15, 2123.077
|Xb, Ac
| rowspan="2" |34\11, 2147.368
|Af
|56\18, 2167.742
|37\15
|22\7, 2200
|54\17, 2234.483
''1726.{{Overline|6}}''
| 32\10, 2258.824
|27\11
|42\13, 2090.909
''1718.{{Overline|18}}''
|44\18
''1711.{{Overline|1}}''
|41\17
''1688; 4.25''
|24\10
''1680''
|31\13
''1669; 4.{{Overline|3}}''
|-
|-
|Mi, Si
|E fab
|A
|47\26, 2169.231
|X, A
|55\16, 2129.032
|A
|21\7, 2100
|38\15
|50\17, 2068.966
|29\10, 2047.059
''1773.{{Overline|3}}''
|37\13, 2018.182
|28\11
''1781.{{Overline|81}}''
|46\18
''1788.{{Overline|8}}''
|18\7
''1800''
|44\17
''1811; 1, 3.25''
|26\10
''1820''
|34\13
''1830; 1.3''
|-
|-
|Mi#, Si#
|E fa
|A#
|48\15, 2215.385
|X#, A#
|35\11, 2210.526
|A#
|57\18, 2206.452
|39\15
|23\7, 2300
|53\17, 2193.103
''1820''
|31\10, 2188.235
| rowspan="2" |29\11
|40\13, 2181.818
|-
''1845.{{Overline|45}}''
|E si mi
|48\18
|49\15, 2261.538
|36\11, 1073.684
''1866.{{Overline|6}}''
|59\18, 2283.871
|19\7
|24\7, 2400
|56\17, 2317.241
''1900''
|33\10, 2329.412
|47\17
|43\13, 2345.455
|-
''1935; 3.4''
|E si mi#
|28\10
|50\15, 2307.692
| rowspan="2" |37\11, 2336.842
''1960''
|61\18, 2361.290
|37\13
| rowspan="2" |23\7, 2300
| 59\17, 2441.379
''1992; 3.25''
|35\10, 2470.588
|46\13, 2509.091
|-
|-
|Fab, Dob
|F sol fa utb
|Bbb
|51\15, 2353.846
|Ebb, Ccc
|60\18, 2322.581
|Bf
|55\17, 2275.862
|40\15
|32\10, 2258.824
|41\13, 2236.364
''1866.{{Overline|6}}''
|47\18
''1827.{{Overline|7}}''
|18\7
''1800''
|43\17
''1770; 1.7''
|25\10
''1750''
|32\13
''1723; 13''
|-
|-
|'''Fa, Do'''
|F sol fa ut
|'''Bb'''
|52\15, 2400
|Eb, Cc
|38\11, 2400
|'''B'''
|62\18, 2400
|'''41\15'''
|24\7, 2400
|58\17, 2400
'''''1913.{{Overline|3}}'''''
|34\10, 2400
|'''30\11'''
|44\13, 2400
'''''1909.{{Overline|09}}'''''
|'''49\18'''
'''''1905.{{Overline|5}}'''''
|'''19\7'''
'''''1900'''''
|'''46\17'''
'''''1894; 8.5'''''
|'''27\10'''
'''''1890'''''
|'''35\13'''
'''''1884; 1.625'''''
|-
|-
|Fa#, Do#
|F sol fa ut#
|B
|53\15, 2446.154
|E, C
|39\11, 2463.158
|B#
|64\18, 2477,419
|42\15
| rowspan="2" |25\7, 2500
|61\17, 2524.138
''1960''
|36\10, 2541.176
|31\11
|47\13, 2563.636
|-
''1972.{{Overline|72}}''
|G la sol reb
|51\18
|55\15, 2538.462
|40\11, 2526.316
''1983.{{Overline|3}}''
|65\18, 2516.129
|20\7
|60\17, 2482.759
|35\10, 2470.588
''2000''
|45\13, 2454.545
|49\17
''2017; 1.41{{Overline|6}}''
|29\10
''2030''
|38\13
''2046; 6.5''
|-
|-
|Fax, Dox
|'''G la sol re'''
|B#
|'''56\15, 2584.615'''
|Ex, Cx
|'''41\11, 2589.474'''
|Bx
|'''67\18, 2593.548'''
|43\15
|'''26\7, 2600'''
|'''63\17, 2606.897'''
''2006.{{Overline|6}}''
|'''37\10, 2611.765'''
| rowspan="2" |32\11
|'''48\13,''' '''2618.182'''
''2036.{{Overline|36}}''
|53\18
''2061.{{Overline|1}}''
|21\7
''2100''
|52\17
''2141; 5.{{Overline|6}}''
|31\10
''2170''
|41\13
''2207; 1.{{Overline|4}}''
|-
|-
|Dob, Solb
|G la sol re#
|Hb
|57\15, 2630.769
|0b, Dc
|42\11, 2652.632
|Cf
|69\18, 2670.968
|44\15
| rowspan="2" |27\7, 2700
|66\17, 2731.034
''2053.{{Overline|3}}''
|39\10, 2752.941
|52\18
|51\13, 2781.818
''2022.{{Overline|2}}''
|20\7
''2000''
|48\17
''1976; 2.125''
|28\10
''1960''
|36\13
''1938; 2.1{{Overline|6}}''
|-
|-
!Do, Sol
|A si la mib
!H
|59\15, 2723.077
!0, D
|43\11, 2715.789
!C
|70\18, 2709.677
! colspan="7" |''2100''
|65\17, 2689.552
|38\10, 2682.353
|49\13, 2672.273
|-
|-
|Do#, Sol#
!A si la mi
|Η#
!60\15, 2769.231
|0#, D#
!44\11, 2778.947
|C#
!72\18, 2787.097
|46\15
!28\7, 2800
''2146.{{Overline|6}}''
!68\17, 2813.793
|34\11
!40\10, 2823.529
''2163.{{Overline|63}}''
!52\13, 2836.364
|56\18
''2177.{{Overline|7}}''
| rowspan="2" |22\7
''2200''
|54\17
''2223; 1.{{Overline|8}}''
|32\10
''2240''
|42\13
''2261; 1, 1.1{{Overline|6}}''
|-
|-
|Reb, Lab
|A si la mi#
|Cb
|61\15, 2815.385
|1b, 1c
| rowspan="2" |45\11, 2842.105
|Df
| 74\18, 2864.516
|48\15
|29\7, 2900
''2240''
|71\17, 2937.069
|35\11
|42\10, 2964.706
''2227.{{Overline|27}}''
|55\13, 3000
|57\18
''2216.{{Overline|6}}''
|53\17
''2182; 2.8{{Overline|3}}''
|31\10
''2170''
|40\13
''2153; 1.{{Overline|18}}''
|-
|-
|'''Re, La'''
|B fab
|'''C'''
|62\15, 2861.538
|'''1'''
|73\18, 2825.806
|'''D'''
| 28\7, 2800
|'''49\15'''
|67\17, 2772.414
'''''2286.{{Overline|6}}'''''
|39\10, 2752.941
|'''36\11'''
|50\13, 2727.273
'''''2290.{{Overline|90}}'''''
|'''59\18'''
'''''2294.{{Overline|4}}'''''
|'''23\7'''
'''''2300'''''
|'''56\17'''
'''''2305; 1.1{{Overline|3}}'''''
|'''33\10'''
'''2310'''
|'''43\13'''
'''''2315; 2.6'''''
|-
|-
|Re#, La#
|B fa
|C#
|63\15, 2907.692
|1#
|46\11, 2905.263
|D#
|75\18, 2903.226
|50\15
|29\7, 2900
''2223.{{Overline|3}}''
|70\17, 2896.552
|37\11
|41\10, 2894.118
''2354.{{Overline|54}}''
|53\13, 2890.909
|61\18
''2372.''{{Overline|2}}
| rowspan="2" |24\7
''2400''
|59\17
''2429; 2, 2.{{Overline|3}}''
|35\10
''2450''
|46\13
''2476; 1.08{{Overline|3}}''
|-
|-
|Mib, Sib
|'''B si'''
|Db
|'''64\15, 2953.846'''
|2b, 2c
|'''47\11, 2968.421'''
|Ef
|'''77\18, 2980.645'''
|52\15
|'''30\7, 3000'''
''2426.{{Overline|6}}''
|'''73\17, 3020.690'''
|38\11
|'''43\10, 3035.294'''
''2418.{{Overline|18}}''
|'''56\13, 3054.545'''
|62\18
''2411.{{Overline|1}}''
|58\17
''2388; 4.25''
|34\10
''2380''
|44\13
''2369; 4.{{Overline|3}}''
|-
|-
|Mi, Si
|B si#
|D
|65\15, 3000
|2
|48\11, 3031.579
|E
|79\18, 3058.064
|53\15
| rowspan="2" |31\7, 3100
''2473,{{Overline|3}}''
|76\17, 3144.828
|39\11
|45\10, 3176.471
''2481.{{Overline|81}}''
|59\13, 3218.182
|64\11
''2488.{{Overline|8}}''
|25\7
''2500''
|61\17
''2511; 1, 3.25''
|36\10
''2520''
|47\13
''2530; 1.3''
|-
|-
|Mi#, Si#
|C solb
|D#
|67\15, 3092.308
|2#
|49\11, 3094.737
|E#
|80\18, 3096.774
|54\15
|75\17, 3103.448
''2520''
|44\10, 3105.882
| rowspan="2" |40\11
|57\13, 3109.091
''2545.{{Overline|45}}''
|66\18
''2566.{{Overline|6}}''
|26\7
''2600''
|64\17
''2635; 3.4''
|38\10
''2660''
|50\13
''2692; 3.25''
|-
|-
|Fab, Dob
|C sol
|Ebb
|68\15, 3138.462
|3b, 3c
|50\11, 3157.895
|Fff
| 82\18, 3174.194
|55\15
|32\7, 3200
''2566.{{Overline|6}}''
|78\17, 3227.586
|65\18
| 46\10, 3247.059
''2527.{{Overline|7}}''
|60\13, 3272.273
|25\7
''2500''
|60\17
''2470; 1.7''
|35\10
''2450''
|45\13
''2423; 13''
|-
|-
|'''Fa, Do'''
|C sol#
|'''Eb'''
| 69\15, 3184.615
|'''3'''
| rowspan="2" |51\11, 3221.053
|'''Ff'''
|84\18, 3251.612
|'''56\15'''
|33\7, 3300
'''''2613.{{Overline|3}}'''''
|81\17, 3351.725
|'''41\11'''
|48\10, 3388.235
'''''2609.{{Overline|09}}'''''
|63\13, 3436.364
|'''67\18'''
'''''2605.{{Overline|5}}'''''
|'''26\7'''
'''''2600'''''
|'''63\17'''
'''''2594; 8.5'''''
|'''37\10'''
'''''2590'''''
|'''48\13'''
'''''2584; 1.625'''''
|-
|-
|Fa#, Do#
|D labb
|E
|70\15, 3230.769
|3#
|83\18, 3212.903
|F
|32\7, 3200
|57\15
|77\17, 3186.207
''2660''
|45\10, 3176.471
|42\11
|58\13, 3163.636
''2672.{{Overline|72}}''
|69\18
''2683.{{Overline|3}}''
|27\7
''2700''
|66\17
''2717; 1.41{{Overline|6}}''
|39\10
''2730''
|51\13
''2746; 6.5''
|-
|-
|Fax, Dox
|'''D lab'''
|E#
|'''71\15,''' '''3276.923'''
|3x
|'''52\11,''' '''3284.211'''
|F#
|'''85\18,''' '''3290.323'''
|58\15
|'''33\7, 3300'''
|'''80\17,''' '''3310.345'''
''2706.{{Overline|6}}''
|'''47\10,''' '''3317.647'''
| rowspan="2" |43\11
|'''61\13,''' '''3327.{{Overline|27}}'''
''2736.{{Overline|36}}''
|-
|71\18
|D la
|72\15, 3323.077
''2761.{{Overline|1}}''
|53\11, 3347.368
|28\7
|87\18, 3367.742
''2800''
|34\7, 3400
|69\17
|83\17, 3434.583
|49\10, 3458.824
''2841; 5.{{Overline|6}}''
|64\13, 3490.909
|41\10
|-
''2870''
|D la#
|54\13
|73\15, 3369.231
| rowspan="2" |54\11, 3410.625
''2907; 1.{{Overline|4}}''
|89\18, 3445.162
|35\7, 3500
|86\17, 3558.621
|51\10, 3600
|67\13, 3654.545
|-
|-
|Dob, Solb
|F utb
|Fb
|74\15, 3415.385
|4b, 4c
|88\18, 3406.452
|0f, Gf
|34\7, 3400
|59\15
|82\17, 3393.103
|48\10, 3388.235
''2753.{{Overline|3}}''
|62\13, 3381.818
|70\18
''2722.{{Overline|2}}''
|27\7
''2700''
|65\17
''2676; 2.125''
|38\10
''2660''
|49\13
''2638; 2.1{{Overline|6}}''
|-
|-
!Do, Sol
!F ut
!F
!75\15, 3461.538
!4
!55\11, 3473.684
!0, G
!90\18, 3483.871
! colspan="7" |''2800''
!35\7, 3500
!85\17, 3517.241
!50\10, 3529.412
!65\13, 3545.455
|}
|}
 
==Intervals==
{| class="wikitable"
{| class="wikitable"
!Generators
|+Cents
!Sesquitave notation
!Notation
!Interval category name
!Supersoft
!Generators
!Soft
!Notation of 3/2 inverse
! Semisoft
!Interval category name
!Basic
!Semihard
!Hard
!Superhard
|-
!Subdozenal
!~15edf
!~11edf
!~18edf
!~7edf
!~17edf
!~10edf
!~13edf
|-
|-
| colspan="6" |The 4-note MOS has the following intervals (from some root):
|F#
|1\15, 46.154
|1\11, 63.158
|2\18, 77.419
| rowspan="2" |1\7, 100
|3\17, 124.138
|2\10, 141.176
|3\13, 163.636
|-
|-
|0
|Gb, Ge
|Do, Sol
|3\15, 138.462
|perfect unison
|2\11. 126.316
|0
|3\18, 116.129
|Do, Sol
|2\17, 82.759
|sesquitave (just fifth)
|1\10, 70.588
|1\13, 54.545
|-
|-
|1
|'''G'''
|Fa, Do
|'''4\15,''' '''184.615'''
|perfect fourth
|'''3\11,''' '''189.474'''
| -1
|'''5\18,''' '''193.548'''
|Re, La
|'''2\7,''' '''200'''
|perfect second
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|-
|2
|G#
|Mib, Sib
|5\15, 230.769
|minor third
|4\11, 252.632
| -2
|7\18, 270.968
|Mi, Si
| rowspan="2" |3\7, 300
|major third
|8\17, 331.034
|5\10, 352.941
|7\13, 381.818
|-
|-
|3
|Hb, He
|Reb, Lab
|7\15, 323.077
|diminished second
|5\11, 315.789
| -3
|8\18, 309.677
|Fa#, Do#
|7\17, 289.655
|augmented fourth
|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
|-
|Kb, Ke
|14\15, 646.154
|16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
|-
!K
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
!7\7, 700
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
|-
|-
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|K#
|16\15, 738.462
|12\11, 757.895
|20\18, 774.194
| rowspan="2" |8\8, 800
|20\17, 827.586
|12\10, 847.059
|16\13, 872.727
|-
|-
|4
|Lb, Le
|Dob, Solb
|18\15, 830.769
|diminished sesquitave
|13\11, 821.053
| -4
|21\18, 812.903
|Do#, Sol#
|19\17, 786.207
|augmented unison (chroma)
|11\10, 776.471
|14\13, 763.63
|-
|-
|5
|'''L'''
|Fab, Dob
|'''19\15,''' '''876.923'''
|diminished fourth
|'''14\11,''' '''884.211'''
| -5
|'''23\18,''' '''890.323'''
|Re#, La#
|'''9\5,''' '''900'''
|augmented second
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
|-
|-
|6
|L#
|Mibb, Sibb
|20\15, 923.077
|diminished third
| rowspan="2" |15\11, 947.368
| -6
|25\18, 967.742
|Mi#, Si#
|10\7, 1000
|augmented third
|25\17, 1034.483
|}
|15\10, 1058.824
|20\13, 1090.909
==Genchain==
|-
|Mbb, Mee
The generator chain for this scale is as follows:
|21\15, 969.231
{| class="wikitable"
|24\18, 929.032
|Mibb
|9\5, 900
|21\17, 868.966
Sibb
|12\10, 847.059
|Fab
|15\13, 818.182
|-
Dob
|Mb, Me
|Dob
|22\15, 1015.385
|16\11, 1010.526
Solb
|26\18, 1006.452
|Reb
|10\7, 1000
|24\17, 993.103
Lab
|14\10, 988.235
|Mib
|18\13, 981.818
|-
Sib
|M
|Fa
|23\15, 1061.538
|17\11, 1073.684
Do
|28\18, 1083.871
|Do
|11\7, 1100
|27\17, 1117.241
Sol
|16\10, 1129.412
|Re
|21\9, 1145.455
|-
La
|M#
|Mi
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
Si
|30\18, 1161.29
|Fa#
|12\7, 1200
|30\17, 1241.379
Do#
|18\10, 1270.588
|Do#
|24\13, 1309.091
|-
Sol#
|Nbb, Nee
|Re#
|25\15, 1153.846
|29\18, 1122.581
La#
|11\7, 1100
|Mi#
|26\17, 1075.862
|15\10, 1058.824
Si#
|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
|-
|-
|d3
|Rb, Re
|d4
|36\61, 1661.538
|d5
|42\18, 1625.806
|d2
|16\7, 1600
|m3
|38\29, 1572.414
|P4
|22\10, 1552.941
|P1
|28\13, 1527.273
|P2
|-
|M3
|R
|A4
|37\15, 1707.692
|A1
|27\11, 1705.263
|A2
|44\18, 1703.226
|A3
|17\7, 1700
|}
|41\17, 1696.552
|24\10, 1694.118
==Modes==
|31\13, 1690.909
|-
The mode names are based on the species of fifth:
|R#
{| class="wikitable"
|38\15, 1753.846
!Mode
|28\11, 1768.421
!Scale
|46\18, 1780.645
![[Modal UDP Notation|UDP]]
|18\7, 1800
! colspan="3" |Interval type
|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
|-
|-
!name
|Sb, Se
!pattern
|40\15, 1846.154
!notation
|47\18, 1819.355
!2nd
|18\7, 1800
!3rd
|43\17, 1779.310
!4th
|25\10, 1764.706
|32\13, 1745.545
|-
|'''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
|-
|-
|Lydian
|Tb, Te
|LLLs
|44\15, 2030.769
|<nowiki>3|0</nowiki>
|52\18, 2012.903
|P
|20\7, 2000
|M
|48\17, 1986.207
|A
|28\10, 1976.471
|36\13, 1963.636
|-
|-
|Major
!T
|LLsL
!45\15, 2076.923
|<nowiki>2|1</nowiki>
!33\11, 2084.211
|P
!54\18, 2090.323
|M
!21\7, 2100
|P
!51\17, 2110.345
!30\10, 2117.647
!39\13, 2127.273
|-
|-
|Minor
|T#
|LLsL
|46\15, 2123.077
|<nowiki>1|2</nowiki>
| rowspan="2" |34\11, 2147.368
|P
|56\18, 2167.742
|m
|22\7, 2200
|P
|54\17, 2234.483
|32\10, 2258.824
|42\13, 2090.909
|-
|-
|Phrygian
|Ub, Üe
|sLLL
|47\26, 2169.231
|<nowiki>0|3</nowiki>
|55\16, 2129.032
|d
|21\7, 2100
|m
|50\17, 2068.966
|P
|29\10, 2047.059
|}
|37\13, 2018.182
|-
==Temperaments==
|Ub, Ü
|48\15, 2215.385
The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
|35\11, 2210.526
==='''Napoli-Meantone'''===
|57\18, 2206.452
|23\7, 2300
[[Subgroup]]: 3/2.6/5.8/5
|53\17, 2193.103
|31\10, 2188.235
[[Comma]] list: [[81/80]]
|40\13, 2181.818
 
[[POL2]] generator: ~9/8 = [[Tel:192.6406|192.6406]]
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Optimal ET sequence]]: ~(7edf, 11edf, 18edf)
==='''Napoli-Archy'''===
[[Subgroup]]: 3/2.7/6.14/9
[[Comma]] list: [[64/63]]
 
[[POL2]] generator: ~8/7 = [[Tel:218.6371|218.6371]]
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Optimal ET sequence]]: ~(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>
|U
!''ed7\12<ref name=":04">Fractions repeating more than 4 digits written as continued fractions</ref>''
|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
|-
|-
|1\4
|U#
|
|50\15, 2307.692
|
| rowspan="2" |37\11, 2336.842
|<u>171; 2.{{Overline|3}}</u>
|61\18, 2361.290
|''175''
| rowspan="2" |23\7, 2300
|1
|59\17, 2441.379
|1
|35\10, 2470.588
|1.000
|46\13, 2509.091
|Equalised
|-
|Vb, Ve
|51\15, 2353.846
|60\18, 2322.581
|55\17, 2275.862
|32\10, 2258.824
|41\13, 2236.364
|-
|-
|6\23
|V
|
|52\15, 2400
|
|38\11, 2400
|<u>180</u>
|62\18, 2400
|''182; 1, 1.{{Overline|5}}''
|24\7, 2400
|6
|58\17, 2400
|5
|34\10, 2400
|1.200
|44\13, 2400
|
|-
|-
|
|V#
|11\42
|53\15, 2446.154
|
|39\11, 2463.158
|<u>180; 1.21{{Overline|6}}</u>
|64\18, 2477,419
|''183.{{Overline|3}}''
| rowspan="2" |25\7, 2500
|11
|61\17, 2524.138
|9
|36\10, 2541.176
|1.222
|47\13, 2563.636
|
|-
|-
|5\19
|Wb, We
|
|55\15, 2538.462
|
|40\11, 2526.316
|<u>181.{{Overline|81}}</u>
|65\18, 2516.129
|''184; 4.75''
|60\17, 2482.759
|5
|35\10, 2470.588
|4
|45\13, 2454.545
|1.250
|
|-
|-
|
|'''Wb'''
|14\53
|'''56\15, 2584.615'''
|
|'''41\11, 2589.474'''
|<u>182; 1, 1.5</u>
|'''67\18, 2593.548'''
|''184; 1, 9.6''
|'''26\7, 2600'''
|14
|'''63\17, 2606.897'''
|11
|'''37\10, 2611.765'''
|1.273
|'''48\13,''' '''2618.182'''
|
|-
|W#
|57\15, 2630.769
|42\11, 2652.632
|69\18, 2670.968
| rowspan="2" |27\7, 2700
|66\17, 2731.034
|39\10, 2752.941
|51\13, 2781.818
|-
|-
|
|Xb, Xe
|9\34
|59\15, 2723.077
|
|43\11, 2715.789
|<u>183; 19.{{Overline|6}}</u>
|70\18, 2709.677
|''185; 3.4''
|65\17, 2689.552
|9
|38\10, 2682.353
|7
|49\13, 2672.273
|1.286
|
|-
|-
|4\15
!X
|
!60\15, 2769.231
|
!44\11, 2778.947
|<u>184; 1.625</u>
!72\18, 2787.097
|''186.{{Overline|6}}''
!28\7, 2800
|4
!68\17, 2813.793
|3
!40\10, 2823.529
|1.333
!52\13, 2836.364
|
|-
|-
|
|X#
|11\41
|61\15, 2815.385
|
| rowspan="2" |45\11, 2842.105
|<u>185, 1, 10.8{{Overline|3}}</u>
|74\18, 2864.516
|''187; 1.{{Overline|24}}''
|29\7, 2900
|11
|71\17, 2937.069
|8
|42\10, 2964.706
|1.375
|55\13, 3000
|
|-
|-
|
|Ybb, Yee
|7\26
|62\15, 2861.538
|
|73\18, 2825.806
|<u>186.{{Overline|6}}</u>
|28\7, 2800
|''188; 2.1{{Overline|6}}''
|67\17, 2772.414
|7
|39\10, 2752.941
|5
|50\13, 2727.273
|1.400
|-
|
|Yb, Ye
|63\15, 2907.692
|46\11, 2905.263
|75\18, 2903.226
|29\7, 2900
|70\17, 2896.552
|41\10, 2894.118
|53\13, 2890.909
|-
|'''Y'''
|'''64\15, 2953.846'''
|'''47\11, 2968.421'''
|'''77\18, 2980.645'''
|'''30\7, 3000'''
|'''73\17, 3020.690'''
|'''43\10, 3035.294'''
|'''56\13, 3054.545'''
|-
|Y#
|65\15, 3000
|48\11, 3031.579
|79\18, 3058.064
| rowspan="2" |31\7, 3100
|76\17, 3144.828
|45\10, 3176.471
|59\13, 3218.182
|-
|Zb. Ze
|67\15, 3092.308
|49\11, 3094.737
|80\18, 3096.774
|75\17, 3103.448
|44\10, 3105.882
|57\13, 3109.091
|-
|-
|
|Z
|10\37
|68\15, 3138.462
|
|50\11, 3157.895
|<u>187.5</u>
|82\18, 3174.194
|''189.{{Overline|189}}''
|32\7, 3200
|10
|78\17, 3227.586
|7
|46\10, 3247.059
|1.429
|60\13, 3272.273
|
|-
|-
|
|Z#
|13\48
|69\15, 3184.615
|
| rowspan="2" |51\11, 3221.053
|<u>187; 1, 19.75</u>
|84\18, 3251.612
|''189.58{{Overline|3}}''
|33\7, 3300
|13
|81\17, 3351.725
|9
|48\10, 3388.235
|1.444
|63\13, 3436.364
|
|-
|-
|
|Ab, Æ
|16\59
|70\15, 3230.769
|
|83\18, 3212.903
|<u>188; 4.25</u>
|32\7, 3200
|''189; 1, 4.9''
|77\17, 3186.207
|45\10, 3176.471
|16
|58\13, 3163.636
|11
|-
|1.455
|'''A'''
|
|'''71\15,''' '''3276.923'''
|'''52\11,''' '''3284.211'''
|'''85\18,''' '''3290.323'''
|'''33\7, 3300'''
|'''80\17,''' '''3310.345'''
|'''47\10,''' '''3317.647'''
|'''61\13,''' '''3327.{{Overline|27}}'''
|-
|A#
|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
|-
|-
|3\11
|Ax
|
|73\15, 3369.231
|
| rowspan="2" |54\11, 3410.625
|<u>189; 2.{{Overline|1}}</u>
|89\18, 3445.162
|''190.{{Overline|90}}''
|35\7, 3500
|3
|86\17, 3558.621
|2
|51\10, 3600
|1.500
|67\13, 3654.545
|Napoli-Meantone starts here
|-
|-
|
|Bb, Be
|17\62
|74\15, 3415.385
|
|88\18, 3406.452
|<u>190; 1, 1.{{Overline|12}}</u>
|34\7, 3400
|''191; 1, 14.5''
|82\17, 3393.103
|17
|48\10, 3388.235
|11
|62\13, 3381.818
|1.545
|
|-
|-
|
!B
|14\51
!75\15, 3461.538
|
!55\11, 3473.684
|<u>190.{{Overline|90}}</u>
!90\18, 3483.871
|''192; 8.375''
!35\7, 3500
|14
!85\17, 3517.241
|9
!50\10, 3529.412
|1.556
!65\13, 3545.455
|
|-
|-
|
|B#
|11\40
|76\15, 3507.692
|
|56\11, 3536.842
|<u>191; 3, 2.{{Overline|3}}</u>
|92\18, 3561.290
|''192.5''
| rowspan="2" |36\7, 3600
|11
|88\17, 3641.379
|7
|52\10, 3670.588
|1.571
|68\13, 3709.091
|
|-
|Cb, Ce
|78\15, 3600
|57\11, 3600
|93\18, 3600
|87\17, 3600
|51\10, 3600
|66\13, 3600
|-
|'''C'''
|'''79\15,''' '''3646.154'''
|'''58\11,''' '''3663.158'''
|'''95\18,''' '''3677.419'''
|'''37\7,''' '''3700'''
|'''90\17,''' '''3724.138'''
|'''53\10,''' '''3741.176'''
|'''69\13,''' '''3763.636'''
|-
|-
|
|C#
|8\29
|80\15, 3692.308
|
|59\11, 3726.316
|<u>192</u>
|97\18, 3755.838
|''193; 9.{{Overline|6}}''
| rowspan="2" |38\7, 3800
|8
|93\17, 3848.275
|5
|55\10, 3882.353
|1.600
|72\13, 3927.273
|
|-
|-
|
|Db, De
|5\18
|82\15, 3784.615
|
|60\11, 3789.474
|<u>193; 1, 1, 4.{{Overline|6}}</u>
|98\18, 3793.548
|''194.{{Overline|4}}''
|92\17, 3806.897
|5
|54\10, 3811.765
|3
|70\13, 3818.182
|1.667
|
|-
|-
|
|D
|
|83\15, 3830.769
|12\43
|61\11, 3852.632
|<u>194.{{Overline|594}}</u>
|100\18, 3870.968
|''195; 2.8{{Overline|6}}''
|39\7, 3900
|12
|95\17, 3931.03$
|7
|56\10, 3952.941
|1.714
|73\13, 3981.818
|
|-
|-
|
|D#
|7\25
|84\15, 3876.923
|
| rowspan="2" |62\11, 3915.789
|<u>195; 2.8{{Overline|6}}</u>
|102\18, 3948.387
|''196''
|40\7, 4000
|7
|98\17, 4055.172
|4
|58\10, 4094.118
|1.750
|76\13, 4145.455
|
|-
|-
|
|Ebb, Ëe
|9\32
|85\15, 3923.077
|
|101\18, 3909.677
|<u>196.{{Overline|36}}</u>
|39\7, 3900
|''196.875''
|94\17, 3889.552
|9
|55\10, 3882.353
|5
|71\13, 3872.727
|1.800
|
|-
|-
|
|'''Eb, Ë'''
|11\39
|'''86\15,''' '''3969.231'''
|
|'''63\11,''' '''3978.947'''
|<u>197; 67</u>
|'''103\18,''' '''3987.097'''
|''197; 2, 3.4''
|'''40\7, 4000'''
|11
|'''97\17,''' '''4013.793'''
|6
|'''57\10,''' '''4023.529'''
|1.833
|'''74\13,''' '''4036.364'''
|
|-
|-
|
|E
|13\46
|87\15, 4015.385
|
|64\11, 4042.105
|<u>197; 2.{{Overline|135}}</u>
|105\18, 4064.516
|''197; 1, 4.75''
|41\7, 4100
|13
|100\17, 4137.931
|7
|59\10, 4164.706
|1.857
|77\13, 4200
|
|-
|-
|
|E#
|15\53
|88\15, 4061.583
|
| rowspan="2" |65\11, 4105.263
|<u>197; 1, 2, 1, 1.{{Overline|54}}</u>
|107\18, 4141.956
|''198; 8.8{{Overline|3}}''
|42\7, 4200
|15
|103\17, 4262.069
|8
|61\10, 4305.882
|1.875
|80\13, 4363.636
|
|-
|-
|
|Fb, Fe
|17\60
|89\15, 4107.692
|
|106\18, 4103.226
|<u>198; 17.1{{Overline|6}}</u>
|41\7, 4100
|''198.{{Overline|3}}''
|99\17, 4096.552
|17
|58\10, 4094.118
|9
|75\13, 4090.909
|1.889
|
|-
|-
|
!F
|19\67
!90\15, 4153.846
|
!66\11, 4168.421
|<u>198: 3, 1, 28</u>
!108\18, 4180.645
|''198, 1, 1.{{Overline|03}}''
!42\7, 4200
|19
!102\17, 4220.690
|10
!60\10, 4235.294
|1.900
!78\13, 4254.545
|
|}
==Intervals==
{| class="wikitable"
!Generators
!Sesquitave notation
!Interval category name
!Generators
!Notation of 3/2 inverse
!Interval category name
|-
| colspan="6" |The 4-note MOS has the following intervals (from some root):
|-
|-
|
|0
|21\74
|Do, Fa, Sol
|
|perfect unison
|<u>198; 2.3{{Overline|518}}</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; 1, 3, 1.7</u>
| -1
|''198; 1, 3, 3.8''
|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; 1, 2, 12.25</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; 1, 3.{{Overline|405}}</u>
|''198; 1.0{{Overline|5}}''
|27
|14
|1.929
|
|-
|-
|
|4
|29\102
|Dob, Fab, Solb
|
|diminished sesquitave
|<u>198; 1, 1.1{{Overline|6}}</u>
| -4
|''199; 51''
|Do#, Fa#, Sol#
|29
|augmented unison (chroma)
|15
|1.933
|
|-
|-
|2\7
|5
|
|Fab, Sibb, Dob
|
|diminished fourth
|<u>200</u>
| -5
|''200''
|Re#, Sol#, La#
|2
|augmented second
|1
|2.000
|Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|-
|
|6
|17\59
|Mibb, Labb, Sibb
|
|diminished third
|<u>201.{{Overline|9801}}</u>
| -6
|''201; 1, 2.2{{Overline|7}}''
|Mi#, La#, Si#
|17
|augmented third
|8
|}  
|2.125
|
==Genchain==
|-
|
The generator chain for this scale is as follows:
|15\52
{| class="wikitable"
|
|Mibb
|<u>202; 4.0{{Overline|45}}</u>
Labb
|''201; 1.08{{Overline|3}}''
|15
Sibb
|7
|Fab
|2.143
Sibb
|
|-
Dob
|
|Dob
|13\45
Fab
|
|<u>202; 1, 1, 2.0{{Overline|6}}</u>
Solb
|''202.{{Overline|2}}''
|Reb
|13
Solb
|6
|2.167
Lab
|
|Mib
|-
Lab
|
|11\38
Sib
|
|Fa
|<u>203; 13</u>
Sib
|''202; 1.58{{Overline|3}}''
|11
Do
|5
|Do
|2.200
Fa
|
|-
Sol
|
|Re
|9\31
Sol
|
|<u>203; 1, 3.41{{Overline|6}}</u>
La
|''203; 4, 2.{{Overline|3}}''
|Mi
|9
La
|4
|2.250
Si
|
|Fa#
|-
Si
|
|7\24
Do#
|
|Do#
|<u>204; 1. 7.2</u>
Fa#
|''204.1{{Overline|6}}''
|7
Sol#
|3
|Re#
|2.333
Sol#
|
La#
|Mi#
La#
Si#
|-
|-
|
|d3
|
|d4
|12\41
|d5
|<u>205; 1.4</u>
|d2
|''204; 1. 7.2''
|m3
|12
|P4
|5
|P1
|2.400
|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
|5\17
!pattern
|
!notation
|<u>206; 1, 8.{{Overline|6}}</u>
!2nd
|''205; 1.1{{Overline|3}}''
!3rd
|5
!4th
|2
|2.500
|Napoli-Neogothic heartland is from here…
|-
|-
|
|Lydian
|
|LLLs
|18\61
|<nowiki>3|0</nowiki>
|<u>207; 1.{{Overline|4}}</u>
|P
|''206; 1.{{Overline|259}}''
|M
|18
|A
|7
|2.571
|
|-
|-
|
|Major
|
|LLsL
|13\44
|<nowiki>2|1</nowiki>
|<u>208</u>
|P
|''206.{{Overline|81}}''
|M
|13
|P
|5
|2.600
|
|-
|-
|
|Minor
|8\27
|LsLL
|
|<nowiki>1|2</nowiki>
|<u>208; 1.4375</u>
|P
|''207.{{Overline|407}}''
|m
|8
|P
|3
|2.667
|…to here
|-
|-
|
|Phrygian
|11\37
|sLLL
|
|<nowiki>0|3</nowiki>
|<u>209; 1.{{Overline|90}}</u>
|d
|''208.{{Overline|108}}''
|m
|11
|P
|4
|}  
|2.750
|
==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
|
|
|14\47
|-
|
|5\19
|<u>210</u>
|181.818
|''208; 1.958{{Overline|3}}''
|14
|5
|5
|2.800
|4
|1.250
|
|
|-
|-
|
|14\53
|17\57
|182.609
|
|14
|<u>210; 3.2{{Overline|3}}</u>
|11
|''208; 1.29{{Overline|54}}''
|1.273
|17
|6
|2.833
|
|
|-
|-
|
|9\34
|20\67
|183.051
|
|9
|<u>210; 1.9</u>
|''208; 1, 21.{{Overline|3}}''
|20
|7
|7
|2.857
|1.286
|
|
|-
|-
|4\15
|184.615
|4
|3
|1.333
|
|
|23\77
|-
|
|11\41
|<u>210; 1.4{{Overline|5}}</u>
|185.915
|''209.{{Overline|09}}''
|11
|23
|8
|8
|2.875
|1.375
|
|
|-
|-
|3\10
|7\26
|
|186.667
|7
|5
|1.400
|
|
|<u>211; 1, 3.25</u>
|''210''
|3
|1
|3.000
|Napoli-Pythagorean ends, Napoli-Archy begins
|-
|-
|
|10\37
|22\73
|187.5
|
|10
|<u>212; 1, 9.{{Overline|3}}</u>
|''210; 1, 23.{{Overline|3}}''
|22
|7
|7
|3.143
|1.429
|
|
|-
|-
|
|13\48
|19\63
|187.952
|
|13
|<u>213; 11.{{Overline|8}}</u>
|9
|''211.{{Overline|1}}''
|1.444
|19
|6
|3.167
|
|
|-
|-
|
|16\59
|16\53
|188.253
|
|<u>213.{{Overline|3}}</u>
|''211; 3, 8.5''
|16
|16
|5
|11
|3.200
|1.455
|
|
|-
|-
|3\11
|189.474
|3
|2
|1.500
|Napoli-Meantone starts here
|-
|14\51
|190.909
|14
|9
|1.556
|
|
|13\43
|-
|11\40
|191.304
|11
|7
|1.571
|
|
|<u>213; 1, 2.3{{Overline|18}}</u>
|-
|''211; 1.{{Overline|592}}''
|8\29
|13
|192.000
|4
|8
|3.250
|5
|1.600
|
|
|-
|-
|
|5\18
|10\33
|193.548
|
|5
|<u>214; 3.5</u>
|''212.{{Overline|12}}''
|10
|3
|3
|3.333
|1.667
|
|
|-
|-
|12\43
|194.595
|12
|7
|1.714
|
|
|7\23
|-
|
|7\25
|<u>215; 2.6</u>
|195.348
|''213; 23''
|7
|7
|2
|4
|3.500
|1.750
|
|
|-
|-
|9\32
|196.364
|9
|5
|1.800
|
|
|11\36
|-
|
|11\39
|<u>216; 2.541{{Overline|6}}</u>
|197.015
|''213.{{Overline|3}}''
|11
|11
|3
|6
|3.667
|1.833
|
|
|-
|-
|13\46
|197.468
|13
|7
|1.857
|
|
|15\49
|-
|
|15\53
|<u>216; 1.152{{Overline|7}}</u>
|197.802
|''214; 3.5''
|15
|15
|4
|8
|3.750
|1.875
|
|
|-
|-
|17\60
|198.058
|17
|9
|1.889
|
|
|19\62
|-
|
|19\67
|<u>217; 7</u>
|198.261
|''214; 1.9375''
|19
|19
|5
|10
|3.800
|1.900
|
|
|-
|-
|4\13
|21\74
|198.425
|21
|11
|1.909
|
|
|
|-
|<u>218.{{Overline|18}}</u>
|23\81
|''215; 2.6''
|198.561
|4
|23
|1
|12
|4.000
|1.917
|
|
|-
|-
|
|25\88
|13\42
|198.675
|
|25
|<u>219; 1, 2.55</u>
|''216.{{Overline|6}}''
|13
|13
|3
|1.923
|4.333
|
|
|-
|-
|27\95
|198.773
|27
|14
|1.929
|
|
|9\29
|-
|29\102
|198.857
|29
|15
|1.933
|
|
|<u>220; 2.45</u>
|-
|''217; 4, 7''
|31\109
|9
|198.930
|2
|31
|4.500
|16
|1.9375
|
|
|-
|-
|33\116
|198.995
|33
|17
|1.941
|
|
|14\45
|-
|35\123
|199.009
|35
|18
|1.944
|
|
|<u>221; 19</u>
|-
|''217.{{Overline|7}}''
|2\7
|14
|200
|3
|2
|4.667
|1
|2.000
|Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|17\59
|201.980
|17
|8
|2.125
|
|
|-
|-
|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''
|5
|1
|5.000
|Napoli-Archy ends
|-
|-
|
|11\38
|16\51
|203.077
|
|11
|<u>223; 3.{{Overline|90}}</u>
|5
|''219; 1, 1.55''
|2.200
|16
|3
|5.333
|
|
|-
|-
|
|9\31
|11\35
|203.774
|
|9
|<u>223; 1, 2.6875</u>
|4
|''220''
|2.250
|11
|2
|5.500
|
|
|-
|-
|
|7\24
|17\54
|204.878
|
|7
|<u>224; 5.7{{Overline|2}}</u>
|''220.{{Overline|370}}''
|17
|3
|3
|5.667
|2.333
|
|
|-
|-
|6\19
|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
|
|
|<u>225</u>
|-
|''221; 19''
|13\44
|6
|208.000
|1
|13
|6.000
|5
|2.600
|
|
|-
|-
|1\3
|8\27
|
|208.696
|
|8
|<u>240</u>
|3
|''233.{{Overline|3}}''
|2.667
|1
|…to here
|0
|-
|→ inf
|11\37
|Paucitonic
|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 ==
==See also==
[[3L 1s (3/2-equivalent)]] - idealized tuning<references />
[[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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