Xenharmonic Wiki

User:Moremajorthanmajor/3L 1s (perfect fifth-equivalent): Difference between revisions

← Older edit
VisualWikitext
CompactStar (talk | contribs)
5,020 edits
Redirected page to 3L 1s (3/2-equivalent)
Tag: New redirect
 
(25 intermediate revisions by the same user not shown)
Line 1: Line 1:
#redirect [[3L 1s (3/2-equivalent)]]
'''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).
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.
 
'''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==
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"
|+
Cents
! Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
!Diatonic
!~15edf
!~11edf
!~18edf
!~7edf
!~17edf
!~10edf
!~13edf
|-
|Do#, Fa#, Sol#
|1\15, 46.154
|1\11, 63.158
|2\18, 77.419
| rowspan="2" | 1\7, 100
|3\17, 124.138
|2\10, 141.176
|3\13, 163.636
|-
|Reb, Solb, Lab
|3\15, 138.462
|2\11. 126.316
|3\18, 116.129
|2\17, 82.759
|1\10, 70.588
|1\13, 54.545
|-
|'''Re, Sol, La'''
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|Re#, Sol#, La#
|5\15, 230.769
|4\11, 252.632
|7\18, 270.968
| rowspan="2" | 3\7, 300
|8\17, 331.034
|5\10, 352.941
|7\13, 381.818
|-
|Mib, Lab, Sib
|7\15, 323.077
|5\11, 315.789
|8\18, 309.677
|7\17, 289.655
|4\10, 282.353
|5\13, 272.727
|-
|Mi, La, Si
|8\15, 369.231
|6\11, 378.947
|10\18, 387.097
|4\7, 400
|10\17, 413.793
|6\10, 423.529
|8\13, 436.364
|-
|Mi#, La#, Si#
|9\15, 415.385
| rowspan="2" | 7\11, 442.105
|12\18, 464.516
|5\7, 500
|13\17, 537.069
|8\10, 564.706
|11\13, 600
|-
|Fab, Sibb, Dob
|10\15, 461.538
|11\18, 425.806
|4\7, 400
|9\17, 372.414
|5\10, 352.941
|6\13, 327.273
|-
|'''Fa, Sib, Do'''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|Fa#, Si, Do#
|12\15, 553.846
|9\11, 568.421
|15\18, 580.645
|6\7, 600
|15\17, 620.690
|9\10, 635.294
|12\13, 654.545
|-
|Fax, Si#, Dox
|13\15, 600
| rowspan="2" | 10\11, 631.579
|17\18, 658.064
|7\7, 700
|18\17, 744.828
|11\10, 776.471
|15\13, 818.182
|-
|Dob, Fab, Solb
|14\15, 646.154
|16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
|-
!Do, Fa, Sol
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
!7\7, 700
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
|}
{| class="wikitable"
|+
Cents
!Notation
!Supersoft
! Soft
!Semisoft
!Basic
!Semihard
! Hard
! Superhard
|-
!Napoli
! ~15edf
! ~11edf
!~18edf
!~7edf
!~17edf
!~10edf
!~13edf
|-
|F#
|1\15, 46.154
|1\11, 63.158
| 2\18, 77.419
| rowspan="2" |1\7, 100
|3\17, 124.138
| 2\10, 141.176
|3\13, 163.636
|-
| Gb, Ge
|3\15, 138.462
| 2\11. 126.316
|3\18, 116.129
|2\17, 82.759
|1\10, 70.588
|1\13, 54.545
|-
|'''G'''
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
|'''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
|-
|Ab, Æ
|7\15, 323.077
|5\11, 315.789
|8\18, 309.677
|7\17, 289.655
|4\10, 282.353
|5\13, 272.727
|-
|A
| 8\15, 369.231
|6\11, 378.947
|10\18, 387.097
| 4\7, 400
|10\17, 413.793
|6\10, 423.529
|8\13, 436.364
|-
|A#
| 9\15, 415.385
| rowspan="2" |7\11, 442.105
|12\18, 464.516
|5\7, 500
|13\17, 537.069
|8\10, 564.706
|11\13, 600
|-
|Bbb, Bee
|10\15, 461.538
|11\18, 425.806
|4\7, 400
|9\17, 372.414
| 5\10, 352.941
|6\13, 327.273
|-
|'''Bb, Be'''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|B
|12\15, 553.846
|9\11, 568.421
|15\18, 580.645
|6\7, 600
| 15\17, 620.690
|9\10, 635.294
|12\13, 654.545
|-
| B#
| 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
|-
|Hb, He
|14\15, 646.154
| 16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
|-
! H
!'''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'''
|-
|Η#
|16\15, 738.462
|12\11, 757.895
|20\18, 774.194
| rowspan="2" |8\8, 800
|20\17, 827.586
|12\10, 847.059
|16\13, 872.727
|-
|Cb, Ce
|18\15, 830.769
|13\11, 821.053
|21\18, 812.903
|19\17, 786.207
|11\10, 776.471
|14\13, 763.63
|-
|'''C'''
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
|-
|C#
|20\15, 923.077
|15\11, 947.368
|25\18, 967.742
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|15\10, 1058.824
|20\13, 1090.909
|-
| Db, De
|22\15, 1015.385
|16\11, 1010.526
|26\18, 1006.452
|24\17, 993.103
|14\10, 988.235
|18\13, 981.818
|-
|D
|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
|-
|D#
|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
|-
|Ebb, Ëe
|25\15, 1153.846
|29\18, 1122.581
|11\7, 1100
|26\17, 1075.862
|15\10, 1058.824
| 19\13, 1036.364
|-
|'''Eb, Ë'''
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|E
|27\15, 1246.154
|20\11, 1263.158
|33\18, 1277.419
|13\7, 1300
|32\17, 1324.138
|19\10, 1341.176
|25\13, 1363.636
|-
|E#
|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
|-
| Fb, Fe
|29\15, 1338.462
|34\18, 1316.129
|13\7, 1300
|31\17, 1282.759
|18\10, 1270.588
|23\13, 1254.545
|-
!F
!30\15, 1384.615
!22\11, 1389.473
!36\18, 1393.548
!14\7, 1400
!34\17, 1406.897
!20\10, 1411.765
!26\13, 1418.182
|}
 
{| class="wikitable"
|+Cents
! Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
! Superhard
|-
!Bijou
!~15edf
!~11edf
!~18edf
!~7edf
!~17edf
!~10edf
!~13edf
|-
|0#, D#
|1\15, 46.154
|1\11, 63.158
|2\18, 77.419
| rowspan="2" |1\7, 100
|3\17, 124.138
|2\10, 141.176
|3\13, 163.636
|-
|1b, 1c
|3\15, 138.462
| 2\11. 126.316
|3\18, 116.129
|2\17, 82.759
|1\10, 70.588
|1\13, 54.545
|-
|'''1'''
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|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
|-
|2b, 2c
|7\15, 323.077
|5\11, 315.789
| 8\18, 309.677
| 7\17, 289.655
|4\10, 282.353
|5\13, 272.727
|-
|2
|8\15, 369.231
|6\11, 378.947
|10\18, 387.097
|4\7, 400
|10\17, 413.793
|6\10, 423.529
|8\13, 436.364
|-
|2#
| 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
| 10\15, 461.538
| 11\18, 425.806
|4\7, 400
|9\17, 372.414
|5\10, 352.941
|6\13, 327.273
|-
|'''3'''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|3#
|12\15, 553.846
|9\11, 568.421
|15\18, 580.645
|6\7, 600
|15\17, 620.690
|9\10, 635.294
|12\13, 654.545
|-
|3x
|13\15, 600
| rowspan="2" |10\11, 631.579
|17\18, 658.064
|7\7, 700
|18\17, 744.828
|11\10, 776.471
|15\13, 818.182
|-
|4b, 4c
|14\15, 646.154
|16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
|-
!4
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
!7\7, 700
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
|-
|4#
| 16\15, 738.462
|12\11, 757.895
|20\18, 774.194
| rowspan="2" |8\8, 800
|20\17, 827.586
|12\10, 847.059
| 16\13, 872.727
|-
|5b, 5c
|18\15, 830.769
|13\11, 821.053
|21\18, 812.903
|19\17, 786.207
|11\10, 776.471
|14\13, 763.63
|-
|'''5'''
|'''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#
|20\15, 923.077
|15\11, 947.368
|25\18, 967.742
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|15\10, 1058.824
|20\13, 1090.909
|-
|6b, 6c
|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
|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#
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
|30\18, 1161.290
|12\7, 1200
|30\17, 1241.379
|18\10, 1270.588
|24\13, 1309.091
|-
| 7b, 7c
|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#
|27\15, 1246.154
|20\11, 1263.158
|33\18, 1277.419
|13\7, 1300
|32\17, 1324.138
|19\10, 1341.176
|25\13, 1363.636
|-
|7x
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
|35\18, 1354.834
|14\7, 1400
|35\17, 1448.275
|21\10, 1482.353
|28\13, 1527.273
|-
|8b, Fc
|29\15, 1338.462
|34\18, 1316.129
|13\7, 1300
|31\17, 1282.759
|18\10, 1270.588
|23\13, 1254.545
|-
!8, F
!30\15, 1384.615
!22\11, 1389.473
!36\18, 1393.548
!14\7, 1400
!34\17, 1406.897
!20\10, 1411.765
!26\13, 1418.182
|-
|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'''
|-
|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
|-
|X, A
|38\15, 1753.846
|28\11, 1768.421
|46\18, 1780.645
|18\7, 1800
|44\17, 1820.690
|26\10, 1835.294
|34\13, 1854.545
|-
|X#, A#
|39\15, 1800
| rowspan="2" |29\11, 1831.579
|48\18, 1858.064
|19\7, 1900
|47\17, 1944.828
|28\10, 1976.471
|37\13, 2018.182
|-
|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
!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
|}
 
{| class="wikitable"
|+Cents
!Notation
!Supersoft
!Soft
!Semisoft
! Basic
!Semihard
!Hard
!Superhard
|-
!Hextone
!~15edf
!~11edf
!~18edf
!~7edf
!~17edf
!~10edf
!~13edf
|-
|0#, G#
|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
|-
| 1f
|3\15, 138.462
|2\11. 126.316
|3\18, 116.129
|2\17, 82.759
|1\10, 70.588
|1\13, 54.545
|-
|'''1'''
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|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
|7\15, 323.077
|5\11, 315.789
|8\18, 309.677
|7\17, 289.655
|4\10, 282.353
|5\13, 272.727
|-
|2
|8\15, 369.231
|6\11, 378.947
|10\18, 387.097
| 4\7, 400
|10\17, 413.793
|6\10, 423.529
|8\13, 436.364
|-
|2#
|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
|-
|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'''
|'''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'''
|-
|3#
|12\15, 553.846
|9\11, 568.421
|15\18, 580.645
|6\7, 600
|15\17, 620.690
|9\10, 635.294
|12\13, 654.545
|-
| 3x
|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
|-
|4f
| 14\15, 646.154
|16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
|-
!4
!'''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
|18\15, 830.769
|13\11, 821.053
|21\18, 812.903
|19\17, 786.207
| 11\10, 776.471
|14\13, 763.63
|-
|'''5'''
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
|-
|5#
|20\15, 923.077
|15\11, 947.368
| 25\18, 967.742
| rowspan="2" |10\7, 1000
|25\17, 1034.483
|15\10, 1058.824
|20\13, 1090.909
|-
|6f
|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
|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#
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
|30\18, 1161.290
|12\7, 1200
|30\17, 1241.379
|18\10, 1270.588
|24\13, 1309.091
|-
| 7f
|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#
|27\15, 1246.154
|20\11, 1263.158
|33\18, 1277.419
|13\7, 1300
|32\17, 1324.138
|19\10, 1341.176
|25\13, 1363.636
|-
|7x
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
|35\18, 1354.834
|14\7, 1400
|35\17, 1448.275
|21\10, 1482.353
|28\13, 1527.273
|-
|8f
|29\15, 1338.462
| 34\18, 1316.129
|13\7, 1300
|31\17, 1282.759
|18\10, 1270.588
|23\13, 1254.545
|-
! 8
!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
|-
|8#
|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
|-
|9f
|33\15, 1523.077
|24\11, 1515.789
|39\18, 1509.677
| 36\17, 1489.655
|21\10, 1482.759
|27\13, 1472.273
|-
|9
|'''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#
|35\15, 1615.385
|26\11, 1642.105
|43\18, 1664.516
| rowspan="2" |17\7, 1700
|42\17, 1737.069
|25\10, 1764.706
|33\13, 1800
|-
|Af
| 37\15, 1707.692
| 27\11, 1705.263
|44\18, 1703.226
|41\17, 1696.552
|24\10, 1694.118
|31\13, 1690.909
|-
|A
| 38\15, 1753.846
|28\11, 1768.421
|46\18, 1780.645
|18\7, 1800
|44\17, 1820.690
|26\10, 1835.294
|34\13, 1854.545
|-
|A#
| 39\15, 1800
| rowspan="2" |29\11, 1831.579
| 48\18, 1858.064
|19\7, 1900
|47\17, 1944.828
|28\10, 1976.471
|37\13, 2018.182
|-
|Ax
|40\15, 1846.154
|47\18, 1819.355
|18\7, 1800
|43\17, 1779.310
|25\10, 1764.706
|32\13, 1745.545
|-
|'''Bf'''
|'''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'''
|-
|B
|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
|-
|B#
|43\15, 1984.615
| rowspan="2" |32\11, 2021.053
|53\18, 2051.612
|21\7, 2100
|52\17, 2151.725
|31\10, 2188.235
|41\13, 2236.364
|-
|Cf
|44\15, 2030.769
|52\18, 2012.903
|20\7, 2000
|48\17, 1986.207
|28\10, 1976.471
|36\13, 1963.636
|-
!C
!45\15, 2076.923
!33\11, 2084.211
!54\18, 2090.323
!21\7, 2100
!51\17, 2110.345
!30\10, 2117.647
!39\13, 2127.273
|-
|C#
|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
|-
|E
|53\15, 2446.154
| 39\11, 2463.158
|64\18, 2477,419
|25\7, 2500
|61\17, 2524.138
|36\10, 2541.176
|47\13, 2563.636
|-
|E#
|54\15, 2492.308
| rowspan="2" |40\11, 2526.316
|66\18, 2554.838
|26\7, 2600
|64\17, 2648.275
|38\10, 2682.353
|50\13, 2727.273
|-
|Fff
| 55\15, 2538.462
| 65\18, 2516.129
|25\7, 2500
|60\17, 2482.759
|35\10, 2470.588
|45\13, 2454.545
|-
|'''Ff'''
|'''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'''
|-
|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
|-
!0, G
!60\15, 2769.231
!44\11, 2778.947
!72\18, 2787.097
!28\7, 2800
!68\17, 2813.793
!40\10, 2823.529
!52\13, 2836.364
|}
 
{| class="wikitable"
|+Cents
!Notation
!Supersoft
!Soft
! Semisoft
! Basic
!Semihard
!Hard
!Superhard
|-
!Guidotonic
!~15edf
!~11edf
!~18edf
!~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
|-
|'''G re'''
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
|'''2\7,''' '''200'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.182'''
|-
|G re#
|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
|-
|A mib
|7\15, 323.077
|5\11, 315.789
|8\18, 309.677
|7\17, 289.655
|4\10, 282.353
|5\13, 272.727
|-
|A mi
|8\15, 369.231
| 6\11, 378.947
|10\18, 387.097
|4\7, 400
|10\17, 413.793
|6\10, 423.529
|8\13, 436.364
|-
| A mi#
|9\15, 415.385
| rowspan="2" |7\11, 442.105
|12\18, 464.516
|5\7, 500
|13\17, 537.069
|8\10, 564.706
|11\13, 600
|-
|B fa utb
|10\15, 461.538
|11\18, 425.806
|4\7, 400
|9\17, 372.414
|5\10, 352.941
|6\13, 327.273
|-
|'''B fa ut'''
|'''11\15,''' '''507.692'''
|'''8\11,''' '''505.263'''
|'''13\18,''' '''503.226'''
|'''5\7, 500'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.909'''
|-
|B fa ut#
|12\15, 553.846
|9\11, 568.421
|15\18, 580.645
|6\7, 600
|15\17, 620.690
|9\10, 635.294
|12\13, 654.545
|-
|B fa utx
| 13\15, 600
| 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
|-
|C sol re utb
| 14\15, 646.154
|16\18, 619.355
|6\7, 600
|14\17, 579.310
|8\10, 564.706
|10\13, 545.455
|-
!C sol re ut
!'''15\15,''' '''692.308'''
!'''11\11,''' '''694.737'''
!'''18\18,''' '''696.774'''
!7\7, 700
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.091'''
|-
|C sol re ut#
|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
|-
|D la mi reb
|18\15, 830.769
|13\11, 821.053
|21\18, 812.903
|19\17, 786.207
|11\10, 776.471
|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
|-
|E fa utb
|21\15, 969.231
|24\18, 929.032
| 9\5, 900
|21\17, 868.966
|12\10, 847.059
|15\13, 818.182
|-
|E fa ut
| 22\15, 1015.385
|16\11, 1010.526
|26\18, 1006.452
|10\7, 1000
|24\17, 993.103
|14\10, 988.235
|18\13, 981.818
|-
|E si mi re
|23\15, 1061.538
|17\11, 1073.684
|28\18, 1083.871
|11\7, 1100
|27\17, 1117.241
|16\10, 1129.412
|21\9, 1145.455
|-
| E si mi re#
|24\15, 1107.923
| 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
|-
|F sol fa ut reb
|25\15, 1153.846
|29\18, 1122.581
|11\7, 1100
|26\17, 1075.862
|15\10, 1058.824
|19\13, 1036.364
|-
|'''F sol fa ut re'''
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|F sol fa ut re#
|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
|-
|F sol fa ut rex
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
|35\18, 1354.834
| 14\7, 1400
|35\17, 1448.275
|21\10, 1482.353
|28\13, 1527.273
|-
|G la sol re mib
| 29\15, 1338.462
|34\18, 1316.129
| 13\7, 1300
|31\17, 1282.759
|18\10, 1270.588
|23\13, 1254.545
|-
!G la sol re mi
!30\15, 1384.615
!22\11, 1389.473
!36\18, 1393.548
!14\7, 1400
!34\17, 1406.897
!20\10, 1411.765
!26\13, 1418.182
|-
|G la sol re mi#
|31\15, 1430.769
|23\11, 1452.632
|38\18, 1470.968
| rowspan="2" |15\7, 1500
|37\17, 1531.034
|22\10, 1552.941
|29\13, 1581.818
|-
|A si la mi fab
|33\15, 1523.077
| 24\11, 1515.789
|39\18, 1509.677
|36\17, 1489.655
|21\10, 1482.759
| 27\13, 1472.273
|-
|'''A si la mi fa'''
|'''34\15,''' '''1569.231'''
|'''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
|-
|B sol fa ut
|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
|-
|B si
|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
|-
|B si
|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
|-
|C la sol re utb
|40\15, 1846.154
|47\18, 1819.355
| 18\7, 1800
| 43\17, 1779.310
|25\10, 1764.706
|32\13, 1745.545
|-
|'''C la sol re ut'''
|'''41\15,''' '''1892.308'''
|'''30\11,''' '''1894.737'''
|'''49\18,''' '''1896.774'''
|'''19\7, 1900'''
|'''46\17,''' '''1903.448'''
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
|-
|C la sol re ut#
|42\15, 1938.462
|31\11, 1957.895
|51\18, 1974.194
|20\7, 2000
|49\17, 2027.586
| 29\10, 2047.059
|38\13, 2072.727
|-
|C la sol re utx
| rowspan="2" |43\15, 1984.615
|32\11, 2021.053
|53\18, 2051.612
|21\7, 2100
|52\17, 2151.725
|31\10, 2188.235
|41\13, 2236.364
|-
|D fa la mi reb
|31\11, 1957.895
|50\18, 1935.484
|19\7, 1900
|45\17, 1862.069
|26\10, 1835.294
|33\13, 1800
|-
|D fa la mi re
|44\15, 2030.769
|32\11, 2021.053
|52\18, 2012.903
|20\7, 2000
|48\17, 1986.207
|28\10, 1976.471
|36\13, 1963.636
|-
!D si la mi re
!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
|-
|D si la mi re#
|46\15, 2123.077
| rowspan="2" |34\11, 2147.368
|56\18, 2167.742
|22\7, 2200
|54\17, 2234.483
| 32\10, 2258.824
|42\13, 2090.909
|-
|E fab
|47\26, 2169.231
|55\16, 2129.032
|21\7, 2100
|50\17, 2068.966
|29\10, 2047.059
|37\13, 2018.182
|-
|E fa
|48\15, 2215.385
|35\11, 2210.526
|57\18, 2206.452
|23\7, 2300
|53\17, 2193.103
|31\10, 2188.235
|40\13, 2181.818
|-
|E si mi
|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
|-
|E si mi#
|50\15, 2307.692
| rowspan="2" |37\11, 2336.842
|61\18, 2361.290
| rowspan="2" |23\7, 2300
| 59\17, 2441.379
|35\10, 2470.588
|46\13, 2509.091
|-
|F sol fa utb
|51\15, 2353.846
|60\18, 2322.581
|55\17, 2275.862
|32\10, 2258.824
|41\13, 2236.364
|-
|F sol fa ut
|52\15, 2400
|38\11, 2400
|62\18, 2400
|24\7, 2400
|58\17, 2400
|34\10, 2400
|44\13, 2400
|-
|F sol fa ut#
|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
|-
|G la sol reb
|55\15, 2538.462
|40\11, 2526.316
|65\18, 2516.129
|60\17, 2482.759
|35\10, 2470.588
|45\13, 2454.545
|-
|'''G la sol re'''
|'''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'''
|-
|G la sol re#
|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
|-
|A si la mib
|59\15, 2723.077
|43\11, 2715.789
|70\18, 2709.677
|65\17, 2689.552
|38\10, 2682.353
|49\13, 2672.273
|-
!A si la mi
!60\15, 2769.231
!44\11, 2778.947
!72\18, 2787.097
!28\7, 2800
!68\17, 2813.793
!40\10, 2823.529
!52\13, 2836.364
|-
|A si la mi#
|61\15, 2815.385
| rowspan="2" |45\11, 2842.105
| 74\18, 2864.516
|29\7, 2900
|71\17, 2937.069
|42\10, 2964.706
|55\13, 3000
|-
|B fab
|62\15, 2861.538
|73\18, 2825.806
| 28\7, 2800
|67\17, 2772.414
|39\10, 2752.941
|50\13, 2727.273
|-
|B fa
|63\15, 2907.692
|46\11, 2905.263
|75\18, 2903.226
|29\7, 2900
|70\17, 2896.552
|41\10, 2894.118
|53\13, 2890.909
|-
|'''B si'''
|'''64\15, 2953.846'''
|'''47\11, 2968.421'''
|'''77\18, 2980.645'''
|'''30\7, 3000'''
|'''73\17, 3020.690'''
|'''43\10, 3035.294'''
|'''56\13, 3054.545'''
|-
|B si#
|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
|-
|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
|-
|C sol
|68\15, 3138.462
|50\11, 3157.895
| 82\18, 3174.194
|32\7, 3200
|78\17, 3227.586
| 46\10, 3247.059
|60\13, 3272.273
|-
|C sol#
| 69\15, 3184.615
| rowspan="2" |51\11, 3221.053
|84\18, 3251.612
|33\7, 3300
|81\17, 3351.725
|48\10, 3388.235
|63\13, 3436.364
|-
|D labb
|70\15, 3230.769
|83\18, 3212.903
|32\7, 3200
|77\17, 3186.207
|45\10, 3176.471
|58\13, 3163.636
|-
|'''D lab'''
|'''71\15,''' '''3276.923'''
|'''52\11,''' '''3284.211'''
|'''85\18,''' '''3290.323'''
|'''33\7, 3300'''
|'''80\17,''' '''3310.345'''
|'''47\10,''' '''3317.647'''
|'''61\13,''' '''3327.{{Overline|27}}'''
|-
|D la
|72\15, 3323.077
|53\11, 3347.368
|87\18, 3367.742
|34\7, 3400
|83\17, 3434.583
|49\10, 3458.824
|64\13, 3490.909
|-
|D la#
|73\15, 3369.231
| rowspan="2" |54\11, 3410.625
|89\18, 3445.162
|35\7, 3500
|86\17, 3558.621
|51\10, 3600
|67\13, 3654.545
|-
|F utb
|74\15, 3415.385
|88\18, 3406.452
|34\7, 3400
|82\17, 3393.103
|48\10, 3388.235
|62\13, 3381.818
|-
!F ut
!75\15, 3461.538
!55\11, 3473.684
!90\18, 3483.871
!35\7, 3500
!85\17, 3517.241
!50\10, 3529.412
!65\13, 3545.455
|}
 
{| class="wikitable"
|+Cents
!Notation
!Supersoft
!Soft
! Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
!Subdozenal
!~15edf
!~11edf
!~18edf
!~7edf
!~17edf
!~10edf
!~13edf
|-
|F#
|1\15, 46.154
|1\11, 63.158
|2\18, 77.419
| rowspan="2" |1\7, 100
|3\17, 124.138
|2\10, 141.176
|3\13, 163.636
|-
|Gb, Ge
|3\15, 138.462
|2\11. 126.316
|3\18, 116.129
|2\17, 82.759
|1\10, 70.588
|1\13, 54.545
|-
|'''G'''
|'''4\15,''' '''184.615'''
|'''3\11,''' '''189.474'''
|'''5\18,''' '''193.548'''
|'''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
|-
|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'''
|-
|K#
|16\15, 738.462
|12\11, 757.895
|20\18, 774.194
| rowspan="2" |8\8, 800
|20\17, 827.586
|12\10, 847.059
|16\13, 872.727
|-
|Lb, Le
|18\15, 830.769
|13\11, 821.053
|21\18, 812.903
|19\17, 786.207
|11\10, 776.471
|14\13, 763.63
|-
|'''L'''
|'''19\15,''' '''876.923'''
|'''14\11,''' '''884.211'''
|'''23\18,''' '''890.323'''
|'''9\5,''' '''900'''
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.273'''
|-
|L#
|20\15, 923.077
| rowspan="2" |15\11, 947.368
|25\18, 967.742
|10\7, 1000
|25\17, 1034.483
|15\10, 1058.824
|20\13, 1090.909
|-
|Mbb, Mee
|21\15, 969.231
|24\18, 929.032
|9\5, 900
|21\17, 868.966
|12\10, 847.059
|15\13, 818.182
|-
|Mb, Me
|22\15, 1015.385
|16\11, 1010.526
|26\18, 1006.452
|10\7, 1000
|24\17, 993.103
|14\10, 988.235
|18\13, 981.818
|-
|M
|23\15, 1061.538
|17\11, 1073.684
|28\18, 1083.871
|11\7, 1100
|27\17, 1117.241
|16\10, 1129.412
|21\9, 1145.455
|-
|M#
|24\15, 1107.923
| rowspan="2" |18\11, 1136.842
|30\18, 1161.29
|12\7, 1200
|30\17, 1241.379
|18\10, 1270.588
|24\13, 1309.091
|-
|Nbb, Nee
|25\15, 1153.846
|29\18, 1122.581
|11\7, 1100
|26\17, 1075.862
|15\10, 1058.824
|19\13, 1036.364
|-
|'''Nb, Ne'''
|'''26\15,''' '''1200'''
|'''19\11,''' '''1200'''
|'''31\18,''' '''1200'''
|'''12\7, 1200'''
|'''29\17,''' '''1200'''
|'''17\10,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|N
|27\15, 1246.154
|20\11, 1263.158
|33\18, 1277.419
|13\7, 1300
|32\17, 1324.138
|19\10, 1341.176
|25\13, 1363.636
|-
|N#
|28\15, 1292.308
| rowspan="2" |21\11, 1326.318
|35\18, 1354.834
|14\7, 1400
|35\17, 1448.275
|21\10, 1482.353
|28\13, 1527.273
|-
|Pb, Pe
|29\15, 1338.462
|34\18, 1316.129
|13\7, 1300
|31\17, 1282.759
|18\10, 1270.588
|23\13, 1254.545
|-
!P
!30\15, 1384.615
!22\11, 1389.473
!36\18, 1393.548
!14\7, 1400
!34\17, 1406.897
!20\10, 1411.765
!26\13, 1418.182
|-
|P#
|31\15, 1430.769
|23\11, 1452.632
|38\18, 1470.968
| rowspan="2" |15\7, 1500
|37\17, 1531.034
|22\10, 1552.941
|29\13, 1581.818
|-
|Qb, Qe
|33\15, 1523.077
|24\11, 1515.789
|39\18, 1509.677
|36\17, 1489.655
|21\10, 1482.759
|27\13, 1472.273
|-
|'''Q'''
|'''34\15,''' '''1569.231'''
|'''25\11,''' '''1578.947'''
|'''41\18,''' '''1587.097'''
|'''16\7,''' '''1600'''
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.364'''
|-
|Q#
|35\15, 1615.385
| rowspan="2" |26\11, 1642.105
|43\18, 1664.516
|17\7, 1700
|42\17, 1737.069
|25\10, 1764.706
|33\13, 1800
|-
|Rb, Re
|36\61, 1661.538
|42\18, 1625.806
|16\7, 1600
|38\29, 1572.414
|22\10, 1552.941
|28\13, 1527.273
|-
|R
|37\15, 1707.692
|27\11, 1705.263
|44\18, 1703.226
|17\7, 1700
|41\17, 1696.552
|24\10, 1694.118
|31\13, 1690.909
|-
|R#
|38\15, 1753.846
|28\11, 1768.421
|46\18, 1780.645
|18\7, 1800
|44\17, 1820.690
|26\10, 1835.294
|34\13, 1854.545
|-
|R#
|39\15, 1800
| rowspan="2" |29\11, 1831.579
|48\18, 1858.064
|19\7, 1900
|47\17, 1944.828
|28\10, 1976.471
|37\13, 2018.182
|-
|Sb, Se
|40\15, 1846.154
|47\18, 1819.355
|18\7, 1800
|43\17, 1779.310
|25\10, 1764.706
|32\13, 1745.545
|-
|'''S'''
|'''41\15,''' '''1892.308'''
|'''30\11,''' '''1894.737'''
|'''49\18,''' '''1896.774'''
|'''19\7, 1900'''
|'''46\17,''' '''1903.448'''
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.091'''
|-
|S#
|42\15, 1938.462
|31\11, 1957.895
|51\18, 1974.194
|20\7, 2000
|49\17, 2027.586
|29\10, 2047.059
|38\13, 2072.727
|-
|Sx
|43\15, 1984.615
| rowspan="2" |32\11, 2021.053
|53\18, 2051.612
|21\7, 2100
|52\17, 2151.725
|31\10, 2188.235
|41\13, 2236.364
|-
|Tb, Te
|44\15, 2030.769
|52\18, 2012.903
|20\7, 2000
|48\17, 1986.207
|28\10, 1976.471
|36\13, 1963.636
|-
!T
!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
|-
|T#
|46\15, 2123.077
| rowspan="2" |34\11, 2147.368
|56\18, 2167.742
|22\7, 2200
|54\17, 2234.483
|32\10, 2258.824
|42\13, 2090.909
|-
|Ub, Üe
|47\26, 2169.231
|55\16, 2129.032
|21\7, 2100
|50\17, 2068.966
|29\10, 2047.059
|37\13, 2018.182
|-
|Ub, Ü
|48\15, 2215.385
|35\11, 2210.526
|57\18, 2206.452
|23\7, 2300
|53\17, 2193.103
|31\10, 2188.235
|40\13, 2181.818
|-
|U
|49\15, 2261.538
|36\11, 1073.684
|59\18, 2283.871
|24\7, 2400
|56\17, 2317.241
|33\10, 2329.412
|43\13, 2345.455
|-
|U#
|50\15, 2307.692
| rowspan="2" |37\11, 2336.842
|61\18, 2361.290
| rowspan="2" |23\7, 2300
|59\17, 2441.379
|35\10, 2470.588
|46\13, 2509.091
|-
|Vb, Ve
|51\15, 2353.846
|60\18, 2322.581
|55\17, 2275.862
|32\10, 2258.824
|41\13, 2236.364
|-
|V
|52\15, 2400
|38\11, 2400
|62\18, 2400
|24\7, 2400
|58\17, 2400
|34\10, 2400
|44\13, 2400
|-
|V#
|53\15, 2446.154
|39\11, 2463.158
|64\18, 2477,419
| rowspan="2" |25\7, 2500
|61\17, 2524.138
|36\10, 2541.176
|47\13, 2563.636
|-
|Wb, We
|55\15, 2538.462
|40\11, 2526.316
|65\18, 2516.129
|60\17, 2482.759
|35\10, 2470.588
|45\13, 2454.545
|-
|'''Wb'''
|'''56\15, 2584.615'''
|'''41\11, 2589.474'''
|'''67\18, 2593.548'''
|'''26\7, 2600'''
|'''63\17, 2606.897'''
|'''37\10, 2611.765'''
|'''48\13,''' '''2618.182'''
|-
|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
|59\15, 2723.077
|43\11, 2715.789
|70\18, 2709.677
|65\17, 2689.552
|38\10, 2682.353
|49\13, 2672.273
|-
!X
!60\15, 2769.231
!44\11, 2778.947
!72\18, 2787.097
!28\7, 2800
!68\17, 2813.793
!40\10, 2823.529
!52\13, 2836.364
|-
|X#
|61\15, 2815.385
| rowspan="2" |45\11, 2842.105
|74\18, 2864.516
|29\7, 2900
|71\17, 2937.069
|42\10, 2964.706
|55\13, 3000
|-
|Ybb, Yee
|62\15, 2861.538
|73\18, 2825.806
|28\7, 2800
|67\17, 2772.414
|39\10, 2752.941
|50\13, 2727.273
|-
|Yb, Ye
|63\15, 2907.692
|46\11, 2905.263
|75\18, 2903.226
|29\7, 2900
|70\17, 2896.552
|41\10, 2894.118
|53\13, 2890.909
|-
|'''Y'''
|'''64\15, 2953.846'''
|'''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
|68\15, 3138.462
|50\11, 3157.895
|82\18, 3174.194
|32\7, 3200
|78\17, 3227.586
|46\10, 3247.059
|60\13, 3272.273
|-
|Z#
|69\15, 3184.615
| rowspan="2" |51\11, 3221.053
|84\18, 3251.612
|33\7, 3300
|81\17, 3351.725
|48\10, 3388.235
|63\13, 3436.364
|-
|Ab, Æ
|70\15, 3230.769
|83\18, 3212.903
|32\7, 3200
|77\17, 3186.207
|45\10, 3176.471
|58\13, 3163.636
|-
|'''A'''
|'''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
|-
|Ax
|73\15, 3369.231
| rowspan="2" |54\11, 3410.625
|89\18, 3445.162
|35\7, 3500
|86\17, 3558.621
|51\10, 3600
|67\13, 3654.545
|-
|Bb, Be
|74\15, 3415.385
|88\18, 3406.452
|34\7, 3400
|82\17, 3393.103
|48\10, 3388.235
|62\13, 3381.818
|-
!B
!75\15, 3461.538
!55\11, 3473.684
!90\18, 3483.871
!35\7, 3500
!85\17, 3517.241
!50\10, 3529.412
!65\13, 3545.455
|-
|B#
|76\15, 3507.692
|56\11, 3536.842
|92\18, 3561.290
| rowspan="2" |36\7, 3600
|88\17, 3641.379
|52\10, 3670.588
|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#
|80\15, 3692.308
|59\11, 3726.316
|97\18, 3755.838
| rowspan="2" |38\7, 3800
|93\17, 3848.275
|55\10, 3882.353
|72\13, 3927.273
|-
|Db, De
|82\15, 3784.615
|60\11, 3789.474
|98\18, 3793.548
|92\17, 3806.897
|54\10, 3811.765
|70\13, 3818.182
|-
|D
|83\15, 3830.769
|61\11, 3852.632
|100\18, 3870.968
|39\7, 3900
|95\17, 3931.03$
|56\10, 3952.941
|73\13, 3981.818
|-
|D#
|84\15, 3876.923
| rowspan="2" |62\11, 3915.789
|102\18, 3948.387
|40\7, 4000
|98\17, 4055.172
|58\10, 4094.118
|76\13, 4145.455
|-
|Ebb, Ëe
|85\15, 3923.077
|101\18, 3909.677
|39\7, 3900
|94\17, 3889.552
|55\10, 3882.353
|71\13, 3872.727
|-
|'''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
|64\11, 4042.105
|105\18, 4064.516
|41\7, 4100
|100\17, 4137.931
|59\10, 4164.706
|77\13, 4200
|-
|E#
|88\15, 4061.583
| rowspan="2" |65\11, 4105.263
|107\18, 4141.956
|42\7, 4200
|103\17, 4262.069
|61\10, 4305.882
|80\13, 4363.636
|-
|Fb, Fe
|89\15, 4107.692
|106\18, 4103.226
|41\7, 4100
|99\17, 4096.552
|58\10, 4094.118
|75\13, 4090.909
|-
!F
!90\15, 4153.846
!66\11, 4168.421
!108\18, 4180.645
!42\7, 4200
!102\17, 4220.690
!60\10, 4235.294
!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
|Do, Fa, Sol
|perfect unison
|0
|Do, Fa, Sol
|sesquitave (just fifth)
|-
|1
|Fa, Sib, Do
|perfect fourth
| -1
|Re, Sol, La
|perfect second
|-
|2
|Mib, Lab, Sib
|minor third
| -2
|Mi, La, Si
|major third
|-
|3
|Reb, Solb, Lab
|diminished second
| -3
|Fa#, Si, Do#
|augmented fourth
|-
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|-
|4
|Dob, Fab, Solb
|diminished sesquitave
| -4
|Do#, Fa#, Sol#
|augmented unison (chroma)
|-
|5
|Fab, Sibb, Dob
|diminished fourth
| -5
|Re#, Sol#, La#
|augmented second
|-
|6
|Mibb, Labb, Sibb
|diminished third
| -6
|Mi#, La#, Si#
|augmented third
|}
==Genchain==
The generator chain for this scale is as follows:
{| class="wikitable"
|Mibb
Labb
Sibb
|Fab
Sibb
Dob
|Dob
Fab
Solb
|Reb
Solb
Lab
|Mib
Lab
Sib
|Fa
Sib
Do
|Do
Fa
Sol
|Re
Sol
La
|Mi
La
Si
|Fa#
Si
Do#
|Do#
Fa#
Sol#
|Re#
Sol#
La#
|Mi#
La#
Si#
|-
|d3
|d4
|d5
|d2
|m3
|P4
|P1
|P2
|M3
|A4
|A1
|A2
|A3
|}
==Modes==
The mode names are based on the species of fifth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
|-
|Lydian
|LLLs
|<nowiki>3|0</nowiki>
|P
|M
|A
|-
|Major
|LLsL
|<nowiki>2|1</nowiki>
|P
|M
|P
|-
|Minor
|LsLL
|<nowiki>1|2</nowiki>
|P
|m
|P
|-
|Phrygian
|sLLL
|<nowiki>0|3</nowiki>
|d
|m
|P
|}
==Temperaments==
The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
==='''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
|
|-
|5\19
|181.818
|5
|4
|1.250
|
|-
|14\53
|182.609
|14
|11
|1.273
|
|-
|9\34
|183.051
|9
|7
|1.286
|
|-
|4\15
|184.615
|4
|3
|1.333
|
|-
|11\41
|185.915
|11
|8
|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
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/3L_1s_(perfect_fifth-equivalent)"