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Pyotr Ilyich Tchaikovsky drew from the Obikhod style for his ''1812 Overture'', as did Nikolai Rimsky-Korsakov in his ''Russian Easter Festival Overture.'' Anatoly Lyadov also drew from them in his ''Ten Arrangements from Obikhod'' Op.61, as did Alexander Raskatov in his  ''Obikhod'' (2002).
Pyotr Ilyich Tchaikovsky drew from the Obikhod style for his ''1812 Overture'', as did Nikolai Rimsky-Korsakov in his ''Russian Easter Festival Overture.'' Anatoly Lyadov also drew from them in his ''Ten Arrangements from Obikhod'' Op.61, as did Alexander Raskatov in his  ''Obikhod'' (2002).


The pitch set used in these chants traditionally consists of four three-note groups. Each note within a group is separated by a whole tone, and each group is separated by a semitone. If starting from G, the result is: G, A, B / C, D, E / F, G, A / B♭, C, D. Theoretically, more groups can be added either above or below, which has been done by some 20th-century Russian composers. This pitch set also influenced Russian folk music: for example, the Livenka accordion contains the pitch set on its melody side. On a common Livenka accordion, the pitch set will not span a pure tritave.<ref>[https://en.wikipedia.org/wiki/Obikhod Obikhod - Wikipedia]. ''en.wikipedia.org''. Retrieved July 28, 2021.</ref>
The pitch set used in these chants traditionally consists of four three-note groups. Each note within a group is separated by a whole tone, and each group is separated by a semitone. If starting from G, the result is: G, A, B / C, D, E / F, G, A / B♭, C, D. Theoretically, more groups can be added either above or below, which has been done by some 20th-century Russian composers. This pitch set also influenced Russian folk music: for example, the Livenka accordion contains the pitch set on its melody side. On a common Livenka accordion, the pitch set will not span a pure tritave.<ref>[https://en.wikipedia.org/wiki/Obikhod Obikhod - Wikipedia]. ''en.wikipedia.org''. Retrieved July 28, 2021.</ref> A pathological trait the pitch set exhibits is that normalization to [[edo]] collapses the range for the [[dark]] [[generator]] to the octave.
==Standing assumptions==
==Standing assumptions==
The tempered generalized Livenka accordion is used in this article to refer to tunings of the pitch set.
The tempered generalized Livenka accordion is used in this article to refer to tunings of the pitch set.
Line 15: Line 15:
The [[TAMNAMS]] system is used in this article to refer to 8L 3s (perfect twelfth equivalent) step size ratios and step ratio ranges.
The [[TAMNAMS]] system is used in this article to refer to 8L 3s (perfect twelfth equivalent) step size ratios and step ratio ranges.


The notation used in this article is GHJKLABCDEFG = LLsLLLsLLLs (Ionian #11), #/f = up/down by chroma (mnemonic f = F molle in Latin).
The notation used in this article is GHJKLABCDEFG = LLsLLLsLLLs (Ionian #11) or LLLsLLsLLLs (Lydian), #/f = up/down by chroma (mnemonic f = F molle in Latin).


Thus the [[19edt]] gamut is as follows:
Thus the [[19edt]] gamut is as follows:


'''G/F#''' G#/Hf '''H''' H#/Jf '''J K''' K#/Lf '''L''' L#/Af '''A''' ''A#/Bf'' '''B C''' C#/Df '''D''' D#/Ef '''E''' ''E#/Ff''  '''F/Gf'''
'''G/F#''' G#/Hf '''H''' H#/Jf '''J K''' K#/Lf '''L''' L#/Af '''A''' ''A#/Bf'' '''B C''' C#/Df '''D''' D#/Ef '''E''' ''E#/Ff''  '''F/Gf'''
'''G/F#''' G#/Hf '''H''' H#/Jf '''J''' J#/Kf '''K''' '''L''' L#/Af '''A''' ''A#/Bf'' '''B C''' C#/Df '''D''' D#/Ef '''E''' ''E#/Ff''  '''F/Gf'''


The [[27edt]] gamut is notated as follows:
The [[27edt]] gamut is notated as follows:


'''G''' F#/Hf G# '''H''' Jf H#/Kf '''J K''' J#/Lf K# '''L''' Af L# '''A''' ''Bf'' A#/Cf '''B''' '''C''' B#/Df C# '''D''' Ef D# '''E''' ''Ff'' E#/Gf '''F'''
'''G''' F#/Hf G# '''H''' Jf H#/Kf '''J K''' J#/Lf K# '''L''' Af L# '''A''' ''Bf'' A#/Cf '''B''' '''C''' B#/Df C# '''D''' Ef D# '''E''' ''Ff'' E#/Gf '''F'''
'''G''' F#/Hf G# '''H''' Jf H#/Kf '''J''' Kf J#/Lf '''K''' '''L''' Af L# '''A''' ''Bf'' A#/Cf '''B''' '''C''' B#/Df C# '''D''' Ef D# '''E''' ''Ff'' E#/Gf '''F'''


The [[30edt]] gamut:
The [[30edt]] gamut:


'''G''' Hf G# '''H''' Jf H# '''J''' J#/Kf '''K''' K# Lf '''L''' L# Af '''A''' A# ''Bf'' '''B''' B#/Cf '''C''' C# Df '''D''' D# Ef '''E''' E# ''Ff'' '''F''' F#/Gf
'''G''' G# Hf '''H''' H# Jf '''J''' J#/Kf '''K''' K# Lf '''L''' L# Af '''A''' A# ''Bf'' '''B''' B#/Cf '''C''' C# Df '''D''' D# Ef '''E''' E# ''Ff'' '''F''' F#/Gf
 
'''G''' G# Hf '''H''' H# Jf '''J''' J# Kf '''K''' K#/Lf '''L''' L# Af '''A''' A# ''Bf'' '''B''' B#/Cf '''C''' C# Df '''D''' D# Ef '''E''' E# ''Ff'' '''F''' F#/Gf


==Intervals==
==Intervals==
The table of Obikhodic intervals below takes the fifth as the generator. Given the size of the fifth generator ''g'', any Obikhodic interval can easily be found by noting what multiple of ''g'' it is, and multiplying the size by the number ''k'' of generators it takes to reach the interval and reducing mod 1900<ref>For relative cents</ref> if necessary (so you can use "''k''*''g'' % 1900" for search engines, for plugged-in values of ''k'' and ''g''). For example, since the major 3rd is reached by six fifth generators, [[27edt]]'s major 3rd is 6*703.7 mod 1900 = 4222.22 mod 1900 = 422.22r¢.
The table of Obikhodic intervals below takes the fifth as the generator.
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 67: Line 73:
|6L+2s
|6L+2s
| -2
| -2
|K
|K, Kf
|natural 4th
|natural 4th
|2L+1s
|2L+1s
Line 126: Line 132:
|-
|-
|9
|9
|K#
|K, K#
|augmented 4th
|augmented 4th
|3L
|3L
Line 152: Line 158:
|7L+4s
|7L+4s
|-
|-
| colspan="8" style="text-align:center" |The chromatic 19-note MOS (either [[8L 11s (tritave equivalent)|8L 11s]], [[11L 8s (tritave equivalent)|11L 8s]], or [[19edt]]) also has the following intervals (from some root):
| colspan="8" style="text-align:center" |The chromatic 19-note MOS (either [[8L 11s (perfect twelfth equivalent)|8L 11s]], [[11L 8s (perfect twelfth equivalent)|11L 8s]], or [[19edt]]) also has the following intervals (from some root):
|-
|-
|12
|12
Line 238: Line 244:
|minor 2nd
|minor 2nd
|1\19, 100.00
|1\19, 100.00
|1\27, 70.59 (70.37)
|1\27, 70.59
|2\30, 126.32 (126.67)
|2\30, 126.32  
|Hf
|Hf
| -8
| -8
Line 245: Line 251:
|major 2nd
|major 2nd
|2\19, 200.00
|2\19, 200.00
|3\27, 211.765 (211.11)
|3\27, 211.76
|3\30, 189.47 (190.00)
|3\30, 189.47
|H
|H
|3
|3
Line 252: Line 258:
|minor 3rd
|minor 3rd
|3\19, 300.00
|3\19, 300.00
|4\27, 282.35 (281.48)
|4\27, 282.35
|5\30, 315.79 (316.67)
|5\30, 315.79
|Jf
|Jf
| -5
| -5
Line 259: Line 265:
|major 3rd
|major 3rd
|4\19, 400.00
|4\19, 400.00
|6\27, 423.53 (422.22)
|6\27, 423.53
|6\30, 378.95 (380.00)
|6\30, 378.95
|J
|J
|6
|6
Line 266: Line 272:
|natural 4th
|natural 4th
|5\19, 500.00
|5\19, 500.00
|7\27, 494.12 (493.59)
|7\27, 494.12
|8\30, 505,26 (506.67)
|8\30, 505,26
|K
|K, Kf
| -2
| -2
|-
|-
|augmented 4th
|augmented 4th
| rowspan="2" |6\19, 600.00
| rowspan="2" |6\19, 600.00
|9\27, 635.29 (633.33)
|9\27, 635.29
|9\30, 568.42 (570.00)
|9\30, 568.42
|K#
|K, K#
|9
|9
|-
|-
|diminished 5th
|diminished 5th
|8\27, 564.71 (562.96)
|8\27, 564.71
|10\30, 631.58 (633.33)
|10\30, 631.58
|Lf
|Lf
| -10
| -10
Line 286: Line 292:
|perfect 5th
|perfect 5th
|7\19, 700.00
|7\19, 700.00
|10\27, 705.88 (703.70)
|10\27, 705.88
|11\30, 694.74 (696.67)
|11\30, 694.74
|L
|L
|1
|1
Line 293: Line 299:
|minor 6th
|minor 6th
|8\19, 800.00
|8\19, 800.00
|11\27, 776.47 (774.07)
|11\27, 776.47
|13\30, 821.05 (823.33)
|13\30, 821.05
|Af
|Af
| -7
| -7
Line 300: Line 306:
|major 6th
|major 6th
|9\19, 900.00
|9\19, 900.00
|13\27, 917.65 (914.81)
|13\27, 917.65
|14\30, 884.21 (886.67)
|14\30, 884.21
|A
|A
|4
|4
Line 307: Line 313:
|minor 7th
|minor 7th
|10\19, 1000.00
|10\19, 1000.00
|14\27, 988.235 (985.19)
|14\27, 988.235
|16\30, 1010.53 (1013.33)
|16\30, 1010.53
|Bf
|Bf
| -4
| -4
Line 314: Line 320:
|major 7th
|major 7th
|11\19, 1100.00
|11\19, 1100.00
|16\27, 1129.42 (1125.93)
|16\27, 1129.42
|17\30, 1073.68 (1076.67)
|17\30, 1073.68
|B
|B
|7
|7
Line 321: Line 327:
|perfect octave
|perfect octave
|12\19, 1200.00
|12\19, 1200.00
|17\27, 1200.00 (1196.30)
|17\27, 1200.00
|19\30, 1200.00 (1203.33)
|19\30, 1200.00
|C
|C
| -1
| -1
Line 328: Line 334:
|augmented octave
|augmented octave
| rowspan="2" |13\19, 1300.00
| rowspan="2" |13\19, 1300.00
|19\27, 1341.18 (1337.04)
|19\27, 1341.18
|20\30, 1263.16 (1266.67)
|20\30, 1263.16
|C#
|C#
|10
|10
|-
|-
|minor 9th
|minor 9th
|18\27, 1270.59 (1266.67)
|18\27, 1270.59
|21\30, 1326.32 (1330.00)
|21\30, 1326.32
|Df
|Df
| -9
| -9
Line 341: Line 347:
|major 9th
|major 9th
|14\19, 1400.00
|14\19, 1400.00
|20\27, 1411.765 (1406.07)
|20\27, 1411.76
|22\30, 1389.47 (1393.33)
|22\30, 1389.47
|D
|D
|2
|2
Line 348: Line 354:
|minor 10th
|minor 10th
|15\19, 1500.00
|15\19, 1500.00
|21\27, 1482.35 (1477.78)
|21\27, 1482.35
|24\30, 1515.79 (1520.00)
|24\30, 1515.79
|Ef
|Ef
| -6
| -6
Line 355: Line 361:
|major 10th
|major 10th
|16\19, 1600.00
|16\19, 1600.00
|23\27, 1623.53 (1618.52)
|23\27, 1623.53
|25\30, 1578.95 (1583.33)
|25\30, 1578.95
|E
|E
|5
|5
Line 362: Line 368:
|natural 11th
|natural 11th
|17\19, 1700.00
|17\19, 1700.00
|24\27, 1694.12 (1688.89)
|24\27, 1694.12
|27\30, 1705.26 (1710.00)
|27\30, 1705.26
|Ff
|Ff
| -3
| -3
Line 369: Line 375:
|augmented 11th
|augmented 11th
|18\19, 1800.00
|18\19, 1800.00
|26\27, 1835.29 (1829.63)
|26\27, 1835.29  
|28\30, 1768.42 (1773.33)
|28\30, 1768.42
|F
|F
|8
|8
Line 392: Line 398:
|generator (g)
|generator (g)
|7\19, 700.00
|7\19, 700.00
|10\27, 705.88 (703.70)
|10\27, 705.88
|17\46, 703.45 (702.17)
|17\46, 703.45
|-
|-
|L (3g - ~tritave)
|L (3g - ~tritave)
|2\19, 200.00
|2\19, 200.00
|3\27, 211.765 (211.11)
|3\27, 211.765
|5\46, 206.90 (206.52)
|5\46, 206.90
|-
|-
|s (-8g + 3 ~tritaves)
|s (-8g + 3 ~tritaves)
|1\19, 100.00
|1\19, 100.00
|1\27, 70.59 (70.37)
|1\27, 70.59
|2\46, 82.76 (82.61)
|2\46, 82.76
|}
|}
====Intervals====
====Intervals====
Line 425: Line 431:
|minor 2nd
|minor 2nd
|1\19, 100.00
|1\19, 100.00
|1\27, 70.59 (70.37)
|1\27, 70.59
|2\46, 82.76 (82.61)
|2\46, 82.76
|Hf
|Hf
| -8
| -8
Line 432: Line 438:
|major 2nd
|major 2nd
|2\19, 200.00
|2\19, 200.00
|3\27, 211.765 (211.11)
|3\27, 211.76
|5\46, 206.90 (206.52)
|5\46, 206.90
|H
|H
|3
|3
Line 439: Line 445:
|minor 3rd
|minor 3rd
|3\19, 300.00
|3\19, 300.00
|4\27, 282.35 (281.48)
|4\27, 282.35
|7\46, 289.655 (289.13)
|7\46, 289.655
|Jf
|Jf
| -5
| -5
Line 446: Line 452:
|major 3rd
|major 3rd
|4\19, 400.00
|4\19, 400.00
|6\27, 423.53 (422.22)
|6\27, 423.53
|10\46, 413.79 (413.04)
|10\46, 413.79
|J
|J
|6
|6
Line 453: Line 459:
|natural 4th
|natural 4th
|5\19, 500.00
|5\19, 500.00
|7\27, 494.12 (493.59)
|7\27, 494.12
|12\46, 496.55 (495.65)
|12\46, 496.55
|K
|K, Kf
| -2
| -2
|-
|-
|augmented 4th
|augmented 4th
| rowspan="2" |6\19, 600.00
| rowspan="2" |6\19, 600.00
|9\27, 635.29 (633.33)
|9\27, 635.29
|15\46, 620.69 (619.565)
|15\46, 620.69
|K#
|K, K#
|9
|9
|-
|-
|diminished 5th
|diminished 5th
|8\27, 564.71 (562.96)
|8\27, 564.71
|14\46, 579.31 (578.26)
|14\46, 579.31
|Lf
|Lf
| -10
| -10
Line 473: Line 479:
|perfect 5th
|perfect 5th
|7\19, 700.00
|7\19, 700.00
|10\27, 705.88 (703.70)
|10\27, 705.88
|17\46, 703.45 (702.17)
|17\46, 703.45
|L
|L
|1
|1
Line 480: Line 486:
|minor 6th
|minor 6th
|8\19, 800.00
|8\19, 800.00
|11\27, 776.47 (774.07)
|11\27, 776.47
|19\46, 786.21 (784.78)
|19\46, 786.21
|Af
|Af
| -7
| -7
Line 487: Line 493:
|major 6th
|major 6th
|9\19, 900.00
|9\19, 900.00
|13\27, 917.65 (914.81)
|13\27, 917.65
|22\46, 910.345 (908.70)
|22\46, 910.34
|A
|A
|4
|4
Line 494: Line 500:
|minor 7th
|minor 7th
|10\19, 1000.00
|10\19, 1000.00
|14\27, 988.235 (985.19)
|14\27, 988.235
|24\46, 993.10 (991.30)
|24\46, 993.10
|Bf
|Bf
| -4
| -4
Line 501: Line 507:
|major 7th
|major 7th
|11\19, 1100.00
|11\19, 1100.00
|16\27, 1129.42 (1125.93)
|16\27, 1129.42
|27\46, 1117.24 (1115.22)
|27\46, 1117.24
|B
|B
|7
|7
Line 508: Line 514:
|perfect octave
|perfect octave
|12\19, 1200.00
|12\19, 1200.00
|17\27, 1200.00 (1196.30)
|17\27, 1200.00
|29\46, 1200.00 (1197.83)
|29\46, 1200.00
|C
|C
| -1
| -1
Line 515: Line 521:
|augmented octave
|augmented octave
| rowspan="2" |13\19, 1300.00
| rowspan="2" |13\19, 1300.00
|19\27, 1341.18 (1337.04)
|19\27, 1341.18
|32\46, 1324.14 (1321.74)
|32\46, 1324.14
|C#
|C#
|10
|10
|-
|-
|minor 9th
|minor 9th
|18\27, 1270.59 (1266.67)
|18\27, 1270.59
|31\46, 1282.76 (1280.435)
|31\46, 1282.76
|Df
|Df
| -9
| -9
Line 528: Line 534:
|major 9th
|major 9th
|14\19, 1400.00
|14\19, 1400.00
|20\27, 1411.765 (1406.07)
|20\27, 1411.76
|34\46, 1406.90 (1404.35)
|34\46, 1406.90
|D
|D
|2
|2
Line 535: Line 541:
|minor 10th
|minor 10th
|15\19, 1500.00
|15\19, 1500.00
|21\27, 1482.35 (1477.78)
|21\27, 1482.35
|36\46, 1489.655 (1486.96)
|36\46, 1489.66
|Ef
|Ef
| -6
| -6
Line 542: Line 548:
|major 10th
|major 10th
|16\19, 1600.00
|16\19, 1600.00
|23\27, 1623.53 (1618.52)
|23\27, 1623.53
|39\46, 1613.79 (1610.87)
|39\46, 1613.79
|E
|E
|5
|5
Line 549: Line 555:
|natural 11th
|natural 11th
|17\19, 1700.00
|17\19, 1700.00
|24\27, 1694.12 (1688.89)
|24\27, 1694.12
|41\46, 1696.55 (1693.48)
|41\46, 1696.55
|Ff
|Ff
| -3
| -3
Line 556: Line 562:
|augmented 11th
|augmented 11th
|18\19, 1800.00
|18\19, 1800.00
|26\27, 1835.29 (1829.63)
|26\27, 1835.29  
|44\46, 1820.69 (1817.39)
|44\46, 1820.69
|F
|F
|8
|8
Line 565: Line 571:
*The large step is between near the meantone and near the Pythagorean 9/8 whole tone, somewhere between as in [[19edo]] and as in [[17edo|12edo]].
*The large step is between near the meantone and near the Pythagorean 9/8 whole tone, somewhere between as in [[19edo]] and as in [[17edo|12edo]].
*The major 3rd (made of two large steps) is a near-[[Just intonation|just]] to near-[[Pythagorean]] major third.
*The major 3rd (made of two large steps) is a near-[[Just intonation|just]] to near-[[Pythagorean]] major third.
The sizes of the generator, large step and small step of oneirotonic are as follows in various hyposoft Obikhod tunings (~19edt not shown).
The sizes of the generator, large step and small step of Obikhodic are as follows in various hyposoft Obikhod tunings (~19edt not shown).
{| class="wikitable right-2 right-3 right-4 right-5"
{| class="wikitable right-2 right-3 right-4 right-5"
|-
|-
Line 573: Line 579:
|-
|-
|generator (g)
|generator (g)
|11\30, 694.74 (696.67)
|11\30, 694.74
|18\49, 696.77 (697.96)
|18\49, 696.77
|-
|-
|L (3g - ~tritave)
|L (3g - ~tritave)
|3\30, 189.47 (190.00)
|3\30, 189.47
|5\49, 193.55 (193.87)
|5\49, 193.55  
|-
|-
|s (-8g + 3 ~tritaves)
|s (-8g + 3 ~tritaves)
|2\30, 126.32 (126.67)
|2\30, 126.32  
|3\49, 116.13 (116.33)
|3\49, 116.13
|}
|}
====Intervals====
====Intervals====
Line 603: Line 609:
|-
|-
|minor 2nd
|minor 2nd
|2\30, 126.32 (126.67)
|2\30, 126.32  
|3\49, 116.13 (116.33)
|3\49, 116.13
|Hf
|Hf
|16/15
|16/15
Line 610: Line 616:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 2nd
|major 2nd
|3\30, 189.47 (190.00)
|3\30, 189.47
|5\49, 193.55 (193.87)
|5\49, 193.55  
|H
|H
|10/9, 9/8
|10/9, 9/8
Line 617: Line 623:
|-
|-
|minor 3rd
|minor 3rd
|5\30, 315.79 (316.67)
|5\30, 315.79
|8\49, 309.68 (310.20)
|8\49, 309.68
|Jf
|Jf
|6/5
|6/5
Line 624: Line 630:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 3rd
|major 3rd
|6\30, 378.95 (380.00)
|6\30, 378.95
|10\49, 387.10 (387.755)
|10\49, 387.10
|J
|J
|5/4
|5/4
Line 631: Line 637:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 4th
|natural 4th
|8\30, 505,26 (506.67)
|8\30, 505,26
|13\49, 503.23 (504.08)
|13\49, 503.23
|K
|K, Kf
|4/3
|4/3
| -2
| -2
|-
|-
|augmented 4th
|augmented 4th
|9\30, 568.42 (570.00)
|9\30, 568.42
|15\49, 580.645 (581.63)
|15\49, 580.65
|K#
|K, K#
|7/5
|7/5
|9
|9
|-
|-
|diminished 5th
|diminished 5th
|10\30, 631.58 (633.33)
|10\30, 631.58
|16\49, 619.355 (620.41)
|16\49, 619.35
|Lf
|Lf
|10/7
|10/7
Line 652: Line 658:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect 5th
|perfect 5th
|11\30, 694.74 (696.67)
|11\30, 694.74
|18\49, 696.77 (697.96)
|18\49, 696.77
|L
|L
|3/2
|3/2
Line 659: Line 665:
|-
|-
|minor 6th
|minor 6th
|13\30, 821.05 (823.33)
|13\30, 821.05
|21\49, 812.90 (814.29)
|21\49, 812.90
|Af
|Af
|8/5
|8/5
Line 666: Line 672:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 6th
|major 6th
|14\30, 884.21 (886.67)
|14\30, 884.21
|23\49, 890.32 (891.84)
|23\49, 890.32
|A
|A
|5/3
|5/3
Line 673: Line 679:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 7th
|minor 7th
|16\30, 1010.53 (1013.33)
|16\30, 1010.53
|26\49, 1006.45 (1008.16)
|26\49, 1006.45
|Bf
|Bf
|16/9, 9/5
|16/9, 9/5
Line 680: Line 686:
|-
|-
|major 7th
|major 7th
|17\30, 1073.68 (1076.67)
|17\30, 1073.68
|28\49, 1083.87 (1085.71)
|28\49, 1083.87
|B
|B
|15/8
|15/8
Line 687: Line 693:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect octave
|perfect octave
|19\30, 1200.00 (1203.33)
|19\30, 1200.00
|31\49, 1200.00 (1202.04)
|31\49, 1200.00
|C
|C
|2/1
|2/1
Line 694: Line 700:
|-
|-
|augmented octave
|augmented octave
|20\30, 1263.16 (1266.67)
|20\30, 1263.16
|33\49, 1277.42 (1279.59)
|33\49, 1277.42
|C#
|C#
|25/24
|25/24
Line 701: Line 707:
|-
|-
|minor 9th
|minor 9th
|21\30, 1326.32 (1330.00)
|21\30, 1326.32
|34\49, 1316.13 (1318.37)
|34\49, 1316.13
|Df
|Df
|15/7
|15/7
Line 708: Line 714:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 9th
|major 9th
|22\30, 1389.47 (1393.33)
|22\30, 1389.47
|36\49, 1393.55 (1395.92)
|36\49, 1393.55
|D
|D
|20/9, 9/4
|20/9, 9/4
Line 715: Line 721:
|-
|-
|minor 10th
|minor 10th
|24\30, 1515.79 (1520.00)
|24\30, 1515.79
|39\49, 1508.68 (1512.245)
|39\49, 1508.68
|Ef
|Ef
|12/5
|12/5
Line 722: Line 728:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 10th
|major 10th
|25\30, 1578.95 (1583.33)
|25\30, 1578.95
|41\49, 1587.10 (1590.80)
|41\49, 1587.10
|E
|E
|5/2
|5/2
Line 729: Line 735:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 11th
|natural 11th
|27\30, 1705.26 (1710.00)
|27\30, 1705.26
|44\49, 1703.23 (1706.13j
|44\49, 1703.23
|Ff
|Ff
|8/3
|8/3
Line 736: Line 742:
|-
|-
|augmented 11th
|augmented 11th
|28\30, 1768.42 (1773.33)
|28\30, 1768.42
|46\49, 1780.645 (1783.67)
|46\49, 1780.65
|F
|F
|14/5
|14/5
Line 753: Line 759:
|-
|-
|generator (g)
|generator (g)
|15\41, 692.31 (695.12)
|15\41, 692.31
|19\52, 690.91 (694.23)
|19\52, 690.91
|-
|-
|L (3g - ~tritave)
|L (3g - ~tritave)
|4\41, 184.615 (185.37)
|4\41, 184.62
|5\52, 181.81 (182.69)
|5\52, 181.81
|-
|-
|s (-8g + 3 ~tritaves)
|s (-8g + 3 ~tritaves)
|3\41, 138.46 (139.02)
|3\41, 138.46  
|4\52, 145.455 (146.15)
|4\52, 145.455
|}
|}
====Intervals====
====Intervals====
Line 781: Line 787:
|-
|-
|chroma
|chroma
|1\41, 46.15 (46.34)
|1\41, 46.15
|G#
|G#
|[[33/32]], [[49/48]], [[36/35]], [[25/24]]
|[[33/32]], [[49/48]], [[36/35]], [[25/24]]
Line 787: Line 793:
|-
|-
|diminished 2nd
|diminished 2nd
|2\41, 92.31 (92.68)
|2\41, 92.31
|Hff
|Hff
|[[21/20]], [[22/21]], [[26/25]]
|[[21/20]], [[22/21]], [[26/25]]
Line 793: Line 799:
|-
|-
|minor 2nd
|minor 2nd
|3\41, 138.46 (139.02)
|3\41, 138.46
|Hf
|Hf
|[[12/11]], [[13/12]], [[14/13]], [[16/15]]
|[[12/11]], [[13/12]], [[14/13]], [[16/15]]
Line 799: Line 805:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 2nd
|major 2nd
|4\41, 184.615 (185.37)
|4\41, 184.62
|H
|H
|[[9/8]], [[10/9]], [[11/10]]
|[[9/8]], [[10/9]], [[11/10]]
Line 805: Line 811:
|-
|-
|augmented 2nd
|augmented 2nd
|5\41, 230.77 (231.71)
|5\41, 230.77
|H#
|H#
|[[8/7]], [[15/13]]
|[[8/7]], [[15/13]]
Line 811: Line 817:
|-
|-
|diminished 3rd
|diminished 3rd
|6\41, 276.92 (278.05)
|6\41, 276.92
|Jff
|Jff
|[[7/6]], [[13/11]], [[33/28]]
|[[7/6]], [[13/11]], [[33/28]]
Line 817: Line 823:
|-
|-
|minor 3rd
|minor 3rd
|7\41, 323.08 (324.39)
|7\41, 323.08
|Jf
|Jf
|[[135/112]], [[6/5]]
|[[135/112]], [[6/5]]
Line 823: Line 829:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 3rd
|major 3rd
|8\41, 369.23 (370.73)
|8\41, 369.23
|J
|J
|[[5/4]], [[11/9]], [[16/13]]
|[[5/4]], [[11/9]], [[16/13]]
Line 829: Line 835:
|-
|-
|augmented 3rd
|augmented 3rd
|9\41, 415.385 (417.07)
|9\41, 415.38
|J#
|J#
|[[9/7]], [[14/11]], [[33/26]]
|[[9/7]], [[14/11]], [[33/26]]
Line 835: Line 841:
|-
|-
|diminished 4th
|diminished 4th
|10\41, 461.54 (463.415)
|10\41, 461.54
|Kff
|Kf, Kff
|[[21/16]], [[13/10]]
|[[21/16]], [[13/10]]
| -13
| -13
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 4th
|natural 4th
|11\41, 507.69 (509.76)
|11\41, 507.69
|Kf
|K, Kf
|[[75/56]], [[4/3]]
|[[75/56]], [[4/3]]
| -2
| -2
|-
|-
|augmented 4th
|augmented 4th
|12\41, 553.85 (556.10)
|12\41, 553.85
|K
|K, K#
|[[11/8]], [[18/13]]
|[[11/8]], [[18/13]]
|9
|9
|-
|-
|doubly augmented 4th, doubly diminished 5th
|doubly augmented 4th, doubly diminished 5th
|13\41, 600.00 (602.44)
|13\41, 600.00
|K#, Lff
|K#, Kx, Lff
|[[7/5]], [[10/7]]
|[[7/5]], [[10/7]]
|20,-21
|20,-21
|-
|-
|diminished 5th
|diminished 5th
|14\41, 646.15 (648.78)
|14\41, 646.15
|Lf
|Lf
|[[16/11]], [[13/9]]
|[[16/11]], [[13/9]]
Line 865: Line 871:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect 5th
|perfect 5th
|15\41, 692.31 (695.12)
|15\41, 692.31
|L
|L
|[[112/75]], [[3/2]]
|[[112/75]], [[3/2]]
Line 871: Line 877:
|-
|-
|augmented 5th
|augmented 5th
|16\41, 738.46 (741.46)
|16\41, 738.46
|L#
|L#
|[[32/21]], [[20/13]]
|[[32/21]], [[20/13]]
Line 877: Line 883:
|-
|-
|diminished 6th
|diminished 6th
|17\41, 784.615 (787.805)
|17\41, 784.62
|Aff
|Aff
|[[11/7]], [[14/9]]
|[[11/7]], [[14/9]]
Line 883: Line 889:
|-
|-
|minor 6th
|minor 6th
|18\41, 830.77 (834.15)
|18\41, 830.77
|Af
|Af
|[[13/8]], [[8/5]]
|[[13/8]], [[8/5]]
Line 889: Line 895:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 6th
|major 6th
|19\41, 876.92 (880.49)
|19\41, 876.92
|A
|A
|[[5/3]], [[224/135]]
|[[5/3]], [[224/135]]
Line 895: Line 901:
|-
|-
|augmented 6th
|augmented 6th
|20\41, 923.08 (926.83)
|20\41, 923.08
|A#
|A#
|[[12/7]], [[22/13]]
|[[12/7]], [[22/13]]
Line 901: Line 907:
|-
|-
|diminished 7th
|diminished 7th
|21\41, 969.23 (973.17)
|21\41, 969.23
|Bff
|Bff
|[[7/4]], [[26/15]]
|[[7/4]], [[26/15]]
Line 907: Line 913:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 7th
|minor 7th
|22\41, 1015.385 (1019.51)
|22\41, 1015.38
|Bf
|Bf
|[[9/5]], [[16/9]], [[20/11]]
|[[9/5]], [[16/9]], [[20/11]]
Line 913: Line 919:
|-
|-
|major 7th
|major 7th
|23\41, 1061.54 (1065.85)
|23\41, 1061.54
|B
|B
|[[11/6]], [[13/7]], [[15/8]], [[24/13]]
|[[11/6]], [[13/7]], [[15/8]], [[24/13]]
Line 919: Line 925:
|-
|-
|augmented 7th
|augmented 7th
|24\41, 1107.69 (1112.195)
|24\41, 1107.69
|B#
|B#
|[[21/11]], [[25/13]], [[40/21]]
|[[21/11]], [[25/13]], [[40/21]]
Line 925: Line 931:
|-
|-
|diminished octave
|diminished octave
|25\41, 1153.85 (1158.54)
|25\41, 1153.85
|Cf
|Cf
|[[64/33]], [[96/49]], [[35/18]], [[48/25]]
|[[64/33]], [[96/49]], [[35/18]], [[48/25]]
Line 931: Line 937:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect octave
|perfect octave
|26\41, 1200.00 (1204.88)
|26\41, 1200.00
|C
|C
|2/1
|2/1
Line 937: Line 943:
|-
|-
|augmented octave
|augmented octave
|27\41, 1246.15 (1251.22)
|27\41, 1246.15
|C#
|C#
|33/16, 49/24, 72/35, 25/12
|33/16, 49/24, 72/35, 25/12
Line 943: Line 949:
|-
|-
|doubly augmented octave, diminished 9th
|doubly augmented octave, diminished 9th
|28\41, 1292.31 (1297.56)
|28\41, 1292.31
|Cx, Dff
|Cx, Dff
|21/10, 44/21, 52/25
|21/10, 44/21, 52/25
Line 949: Line 955:
|-
|-
|minor 9th
|minor 9th
|29\41, 1338.46 (1343.90)
|29\41, 1338.46
|Df
|Df
|24/11, 13/6, 28/13, 32/15
|24/11, 13/6, 28/13, 32/15
Line 955: Line 961:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 9th
|major 9th
|30\41, 1384.615 (1390.24)
|30\41, 1384.62
|D
|D
|9/4, 20/9, 11/5
|9/4, 20/9, 11/5
Line 961: Line 967:
|-
|-
|augmented 9th
|augmented 9th
|31\41, 1430.77 (1436.595)
|31\41, 1430.77
|D#
|D#
|16/7, 30/13
|16/7, 30/13
Line 967: Line 973:
|-
|-
|diminished 10th
|diminished 10th
|32\41, 1476.92 (1492.93)
|32\41, 1476.92
|Eff
|Eff
|7/3, 26/11, 33/14
|7/3, 26/11, 33/14
Line 973: Line 979:
|-
|-
|minor 10th
|minor 10th
|33\41, 1523.08 (1529.27)
|33\41, 1523.08
|Ef
|Ef
|135/56, 12/5
|135/56, 12/5
Line 979: Line 985:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 10th
|major 10th
|34\41, 1569.23 (1575.61)
|34\41, 1569.23
|E
|E
|5/2, 22/9, 32/13
|5/2, 22/9, 32/13
Line 985: Line 991:
|-
|-
|augmented 10th
|augmented 10th
|35\41, 1615.385 (1621.95)
|35\41, 1615.38
|E#
|E#
|18/7, 28/11, 33/13
|18/7, 28/11, 33/13
Line 991: Line 997:
|-
|-
|diminished 11th
|diminished 11th
|36\41, 1661.54 (1668.29)
|36\41, 1661.54
|Ff
|Ff
|21/8, 13/5
|21/8, 13/5
Line 997: Line 1,003:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 11th
|natural 11th
|37\41, 1709.69 (1714.63)
|37\41, 1709.69
|F
|F
|75/28, 8/3
|75/28, 8/3
Line 1,003: Line 1,009:
|-
|-
|augmented 11th
|augmented 11th
|38\41, 1753.85 (1760.98)
|38\41, 1753.85
|F#
|F#
|11/4, 36/13
|11/4, 36/13
Line 1,009: Line 1,015:
|-
|-
|doubly augmented 11th, doubly diminished 12th
|doubly augmented 11th, doubly diminished 12th
|39\41, 1800.00 (1807.32)
|39\41, 1800.00
|Fx, Gff
|Fx, Gff
|14/5, 20/7
|14/5, 20/7
Line 1,015: Line 1,021:
|-
|-
|diminished 12th
|diminished 12th
|40\41, 1846.15 (1853.66)
|40\41, 1846.15
|Gf
|Gf
|32/11, 26/9
|32/11, 26/9
Line 1,039: Line 1,045:
|-
|-
|chroma
|chroma
|3\35, 163.64 (162.86)
|3\35, 163.64
|G#
|G#
|[[12/11]], [[11/10]], [[10/9]]
|[[12/11]], [[11/10]], [[10/9]]
Line 1,045: Line 1,051:
|-
|-
|minor 2nd
|minor 2nd
|1\35, 54.545 (54.29)
|1\35, 54.55
|Hf
|Hf
|[[36/35]], [[34/33]], [[33/32]], [[32/31]]
|[[36/35]], [[34/33]], [[33/32]], [[32/31]]
Line 1,051: Line 1,057:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 2nd
|major 2nd
|4\35, 218.18 (217.14)
|4\35, 218.18
|H
|H
|[[9/8]], [[17/15]], [[8/7]]
|[[9/8]], [[17/15]], [[8/7]]
Line 1,057: Line 1,063:
|-
|-
|augmented 2nd
|augmented 2nd
|7\35, 381.818 (380.00)
|7\35, 381.82
|H#
|H#
|[[5/4]], [[96/77]]
|[[5/4]], [[96/77]]
Line 1,063: Line 1,069:
|-
|-
|diminished 3rd
|diminished 3rd
|2\35, 109.09 (108.57)
|2\35, 109.09
|Jff
|Jff
|[[18/17]], [[17/16]], [[16/15]], [[15/14]]
|[[18/17]], [[17/16]], [[16/15]], [[15/14]]
Line 1,069: Line 1,075:
|-
|-
|minor 3rd
|minor 3rd
|5\35, 272.73 (271.43)
|5\35, 272.73
|Jf
|Jf
|[[20/17]], [[7/6]]
|[[20/17]], [[7/6]]
Line 1,075: Line 1,081:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 3rd
|major 3rd
|8\35, 436.36 (434.29)
|8\35, 436.36
|J
|J
|[[14/11]], [[9/7]], [[22/17]]
|[[14/11]], [[9/7]], [[22/17]]
Line 1,081: Line 1,087:
|-
|-
|augmented 3rd
|augmented 3rd
|11\35, 600.00 (542.86)
|11\35, 600.00
|J#
|J#
|[[7/5]], [[24/17]], [[17/12]], [[10/7]]
|[[7/5]], [[24/17]], [[17/12]], [[10/7]]
Line 1,087: Line 1,093:
|-
|-
|diminished 4th
|diminished 4th
|6\35, 327.27 (325.71)
|6\35, 327.27
|Kff
|Kf, Kff
|[[6/5]], [[17/14]], [[11/9]]
|[[6/5]], [[17/14]], [[11/9]]
| -13
| -13
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 4th
|natural 4th
|9\35, 490.91 (488.57)
|9\35, 490.91
|Kf
|K, Kf
|[[4/3]]
|[[4/3]]
| -2
| -2
|-
|-
|augmented 4th
|augmented 4th
|12\35, 654.545 (651.43)
|12\35, 654.55
|K
|K, K#
|[[16/11]], [[22/15]]
|[[16/11]], [[22/15]]
|9
|9
|-
|-
|diminished 5th
|diminished 5th
|10\35, 545.455 (542.86)
|10\35, 545.45
|Lf
|Lf
|[[15/11]], [[11/8]]
|[[15/11]], [[11/8]]
Line 1,111: Line 1,117:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect 5th
|perfect 5th
|13\35, 709.09 (705.71)
|13\35, 709.09
|L
|L
|[[3/2]]
|[[3/2]]
Line 1,117: Line 1,123:
|-
|-
|augmented 5th
|augmented 5th
|16\35, 872.73 (868.57)
|16\35, 872.73
|L#
|L#
|[[18/11]], [[28/17]], [[5/3]]
|[[18/11]], [[28/17]], [[5/3]]
Line 1,123: Line 1,129:
|-
|-
|diminished 6th
|diminished 6th
|11\35, 600.00 (597.14)
|11\35, 600.00
|Aff
|Aff
|[[7/5]], [[24/17]], [[17/12]], [[10/7]]
|[[7/5]], [[24/17]], [[17/12]], [[10/7]]
Line 1,129: Line 1,135:
|-
|-
|minor 6th
|minor 6th
|14\35, 763.64 (760.00)
|14\35, 763.64
|Af
|Af
|[[17/11]], [[14/9]], [[11/7]]
|[[17/11]], [[14/9]], [[11/7]]
Line 1,135: Line 1,141:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 6th
|major 6th
|17\35, 927.27 (822.86)
|17\35, 927.27
|A
|A
|[[17/10]], [[12/7]]
|[[17/10]], [[12/7]]
Line 1,141: Line 1,147:
|-
|-
|augmented 6th
|augmented 6th
|20\35, 1090.909 (1085.71)
|20\35, 1090.91
|A#
|A#
|[[28/15]], [[15/8]], [[32/17]], [[17/9]]
|[[28/15]], [[15/8]], [[32/17]], [[17/9]]
Line 1,147: Line 1,153:
|-
|-
|diminished 7th
|diminished 7th
|15\35, 818.182 (814.29)
|15\35, 818.18
|Bff
|Bff
|[[8/5]], [[77/48]]
|[[8/5]], [[77/48]]
Line 1,153: Line 1,159:
|-
|-
|minor 7th
|minor 7th
|18/35, 981.82 (977.14)
|18/35, 981.82
|Bf
|Bf
|[[7/4]], [[30/17]], [[16/9]]
|[[7/4]], [[30/17]], [[16/9]]
Line 1,159: Line 1,165:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 7th
|major 7th
|21\35, 1145.455 (1140.00)
|21\35, 1145.45
|B
|B
|[[31/16]], [[64/33]], [[33/17]], [[35/18]]
|[[31/16]], [[64/33]], [[33/17]], [[35/18]]
Line 1,165: Line 1,171:
|-
|-
|augmented 7th
|augmented 7th
|24\35, 1309.09 (1302.86)
|24\35, 1309.09
|B#
|B#
|36/17, 17/8, 32/15, 15/7
|36/17, 17/8, 32/15, 15/7
Line 1,171: Line 1,177:
|-
|-
|diminished octave
|diminished octave
|19\22, 1036.36 (1031.43)
|19\22, 1036.36
|Cf
|Cf
|[[9/5]], [[11/6]], [[20/11]]
|[[9/5]], [[11/6]], [[20/11]]
Line 1,177: Line 1,183:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect octave
|perfect octave
|22\35, 1200.00 (1194.29)
|22\35, 1200.00
|C
|C
|[[2/1]]
|[[2/1]]
Line 1,183: Line 1,189:
|-
|-
|augmented octave
|augmented octave
|25\35, 1363.64 (1357.14)
|25\35, 1363.64
|C#
|C#
|24/11, 11/5, 20/9
|24/11, 11/5, 20/9
Line 1,189: Line 1,195:
|-
|-
|minor 9th
|minor 9th
|23\35, 1254.55 (1248.57)
|23\35, 1254.55
|Df
|Df
|72/35, 68/33, 33/16, 64/31
|72/35, 68/33, 33/16, 64/31
Line 1,195: Line 1,201:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 9th
|major 9th
|26\35, 1418.18 (1411.43)
|26\35, 1418.18
|D
|D
|9/4, 34/15, 16/7
|9/4, 34/15, 16/7
Line 1,201: Line 1,207:
|-
|-
|augmented 9th
|augmented 9th
|29\35, 1581.81 (1574.29)
|29\35, 1581.81
|D#
|D#
|5/2, 192/77
|5/2, 192/77
Line 1,207: Line 1,213:
|-
|-
|diminished 10th
|diminished 10th
|24\35, 1309.09 (1302.86)
|24\35, 1309.09
|Eff
|Eff
|36/17, 17/8, 32/15, 15/7
|36/17, 17/8, 32/15, 15/7
Line 1,213: Line 1,219:
|-
|-
|minor 10th
|minor 10th
|27\35, 1472.72 (1465.71)
|27\35, 1472.72
|Ef
|Ef
|40/17, 7/3
|40/17, 7/3
Line 1,219: Line 1,225:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 10th
|major 10th
|30\35, 1636.36 (1628.57)
|30\35, 1636.36
|E
|E
|28/11, 18/7, 44/17
|28/11, 18/7, 44/17
Line 1,225: Line 1,231:
|-
|-
|augmented 10th
|augmented 10th
|33\35, 1800.00 (1791.43)
|33\35, 1800.00
|E#
|E#
|14/5, 48/17, 17/6, 20/7
|14/5, 48/17, 17/6, 20/7
Line 1,231: Line 1,237:
|-
|-
|diminished 11th
|diminished 11th
|28\35, 1527.27 (1520.00)
|28\35, 1527.27
|Ff
|Ff
|12/5, 17/7, 22/9
|12/5, 17/7, 22/9
Line 1,237: Line 1,243:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 11th
|natural 11th
|31\35, 1690.91 (1682.86)
|31\35, 1690.91
|F
|F
|8/3
|8/3
Line 1,243: Line 1,249:
|-
|-
|augmented 11th
|augmented 11th
|34\35, 1854.545 (1845.71)
|34\35, 1854.55
|F#
|F#
|32/11, 44/15
|32/11, 44/15
Line 1,249: Line 1,255:
|-
|-
|diminished 12th
|diminished 12th
|32\35, 1745.455 (1737.14)
|32\35, 1745.45
|Gf
|Gf
|30/11, 11/4
|30/11, 11/4
Line 1,274: Line 1,280:
|generator (g)
|generator (g)
|22\59, 713.51
|22\59, 713.51
|31\83, 715.385
|31\83, 715.38
|34\91, 715.79
|34\91, 715.79
|37\99, 716.13
|37\99, 716.13
Line 1,307: Line 1,313:
!Size in PHTE tuning
!Size in PHTE tuning
!Note name on D
!Note name on D
!Note name on H
! class="unsortable" |Approximate ratios
! class="unsortable" |Approximate ratios
!#Gens up
!#Gens up
Line 1,317: Line 1,324:
|0.00
|0.00
|D
|D
|H
|1/1
|1/1
|0
|0
Line 1,327: Line 1,335:
|230.55
|230.55
|E
|E
|J
|8/7
|8/7
| +3
| +3
Line 1,337: Line 1,346:
|461.10
|461.10
|F
|F
|K
|13/10, 9/7
|13/10, 9/7
| +6
| +6
Line 1,342: Line 1,352:
|4
|4
|15\59, 486.49
|15\59, 486.49
|21\83, 484.615
|21\83, 484.62
|23\91, 484.21
|23\91, 484.21
|25\99, 483.87
|25\99, 483.87
|482.06
|482.06
|G
|G
|L
|4/3
|4/3
| -2
| -2
Line 1,352: Line 1,363:
|5
|5
|22\59, 713.51
|22\59, 713.51
|31\83, 715.385
|31\83, 715.38
|34\91, 715.79
|34\91, 715.79
|37\99, 716.13
|37\99, 716.13
|712.61
|712.61
|H
|H
|A
|3/2
|3/2
| +1
| +1
Line 1,367: Line 1,379:
|943.16
|943.16
|J
|J
|B
|12/7, 26/15
|12/7, 26/15
| +4
| +4
Line 1,377: Line 1,390:
|964.12
|964.12
|K
|K
|C
|7/4
|7/4
| -4
| -4
Line 1,387: Line 1,401:
|1194.67
|1194.67
|L
|L
|D
|2/1
|2/1
| -1
| -1
Line 1,393: Line 1,408:
|44\59, 1427.03
|44\59, 1427.03
|62\83, 1430.77
|62\83, 1430.77
|68\91, 1430.58
|68\91, 1431.58
|74\99, 1432.26
|74\99, 1432.26
|1425.22
|1425.22
|A
|A
|E
|16/7
|16/7
| +2
| +2
Line 1,407: Line 1,423:
|1655.77
|1655.77
|B
|B
|F
|13/5, 18/7
|13/5, 18/7
| +5
| +5
Line 1,413: Line 1,430:
|52\59, 1686.49
|52\59, 1686.49
|73\83,
|73\83,
1684.615
1684.62
|80\91,
|80\91,
1684.21
1684.21
Line 1,419: Line 1,436:
|1676.32
|1676.32
|C
|C
|G
|4/3
|4/3
| -3
| -3
Line 1,426: Line 1,444:
{| class="wikitable"
{| class="wikitable"
|-
|-
| style="text-align:center;" |[[Modal UDP Notation|'''UDP''']]
| style="text-align:center;" |'''Mode'''
| style="text-align:center;" |'''Mode'''
| style="text-align:center;" |[[Modal UDP Notation|'''UDP''']]
| style="text-align:center;" |'''Name'''
| style="text-align:center;" |'''Name'''
|-
|-
| style="text-align:center;" |<nowiki>10|0</nowiki>
|LLLsLLLsLLs
|LLLsLLLsLLs
| style="text-align:center;" |<nowiki>10|0</nowiki>
|(Great) Lydian #8 (Tanagran)
|(Great) Lydian #8 (Tanagran)
|-
|-
| style="text-align:center;" |<nowiki>9|1</nowiki>
|LLLsLLsLLLs
|LLLsLLsLLLs
| style="text-align:center;" |<nowiki>9|1</nowiki>
|(Great) Lydian
|(Great) Lydian
|-
|-
| style="text-align:center;" |<nowiki>8|2</nowiki>
|LLsLLLsLLLs
|LLsLLLsLLLs
| style="text-align:center;" |<nowiki>8|2</nowiki>
|(Great) Lydian f4, Ionian #11 (Distomian)
|(Great) Lydian b4, Ionian #11 (Distomian)
|-
|-
| style="text-align:center;" |<nowiki>7|3</nowiki>
| |LLsLLLsLLsL
| |LLsLLLsLLsL
| style="text-align:center;" |<nowiki>7|3</nowiki>
| |(Great) Ionian
| |(Great) Ionian
|-
|-
| style="text-align:center;" |<nowiki>6|4</nowiki>
| |LLsLLsLLLsL
| |LLsLLsLLLsL
| style="text-align:center;" |<nowiki>6|4</nowiki>
| |(Great) Mixolydian
| |(Great) Mixolydian
|-
|-
| style="text-align:center;" |<nowiki>5|5</nowiki>
| |LsLLLsLLLsL
| |LsLLLsLLLsL
| style="text-align:center;" |<nowiki>5|5</nowiki>
| |(Great) Mixolydian f3, Dorian #10 (Livadeian)
| |(Great) Mixolydian b3, Dorian #10 (Livadeian)
|-
|-
| style="text-align:center;" |<nowiki>4|6</nowiki>
| |LsLLLsLLsLL
| |LsLLLsLLsLL
| style="text-align:center;" |<nowiki>4|6</nowiki>
| |(Great) Dorian
| |(Great) Dorian
|-
|-
| style="text-align:center;" |<nowiki>3|7</nowiki>
| |LsLLsLLLsLL
| |LsLLsLLLsLL
| style="text-align:center;" |<nowiki>3|7</nowiki>
| |(Great) Aeolian
| |(Great) Aeolian
|-
|-
| style="text-align:center;" |<nowiki>2|8</nowiki>
| |sLLLsLLLsLL
| |sLLLsLLLsLL
| style="text-align:center;" |<nowiki>2|8</nowiki>
| |(Great) Aeolian f2, Phrygian #9 (Theban)
| |(Great) Aeolian b2, Phrygian #9 (Theban)
|-
|-
| style="text-align:center;" |<nowiki>1|9</nowiki>
| |sLLLsLLsLLL
| |sLLLsLLsLLL
| style="text-align:center;" |<nowiki>1|9</nowiki>
| |(Great) Phrygian
| |(Great) Phrygian
|-
|-
| style="text-align:center;" |<nowiki>0|10</nowiki>
| |sLLsLLLsLLL
| |sLLsLLLsLLL
| style="text-align:center;" |<nowiki>0|10</nowiki>
| |(Great) Locrian
| |(Great) Locrian
|}
|}
===Cyclic Permutation order===
This temperament is named Obikhodic because the Obikhod pitch set is the Mixolydian mode with the tenth flattened or the Dorian mode with the third sharpened.
{| class="wikitable"
{| class="wikitable"
|+
|+
!Spelling
|'''Mode'''
!'''Mode'''
|[[Modal UDP Notation|'''UDP''']] 1
![[Modal UDP Notation|'''UDP''']]
|[[Modal UDP Notation|'''UDP''']] 2
!'''Name'''
|'''Name 1'''
|'''Name 2'''
|-
|LLsLLsLLsLL
|<nowiki>6|4 b10</nowiki>
|<nowiki>4|6 #3</nowiki>
|(Great) Mixolydian f10
|(Great) Dorian #3
|-
|-
|GHJKLABCDEFG
|LLsLLsLLLLs
|<nowiki>8|2 b7</nowiki>
|<nowiki>6|4 #11</nowiki>
|(Great) Lydian f4 f7, Ionian f7 #11 (Distomian Dominant)
|(Great) Mixolydian #11
|-
|LLsLLLLsLLs
|<nowiki>10|0 b4</nowiki>
|<nowiki>8|2 #8</nowiki>
|(Great) Lydian f4 #8 (Tanagran f4)
|(Great) Lydian f4 #8, Ionian #8 #11 (Distomian #8)
|-
|LLLLsLLsLLs
|<nowiki>1|9 *b1</nowiki>
|<nowiki>10|0 #5</nowiki>
|(Great) Phrygian *f1
|(Great) Lydian #5 #8 (Tanagran #5)
|-
|LsLLsLLsLLL
|<nowiki>3|7 b9</nowiki>
|<nowiki>1|9 #2</nowiki>
|(Great) Aeolian f9
|(Great) Phrygian #2
|-
|LsLLsLLLLsL
|<nowiki>5|5 b6</nowiki>
|<nowiki>3|7 #10</nowiki>
|(Great) Mixolydian f3 f6, Dorian f6 #10 (Livadeian f6)
|(Great) Aeolian #10
|-
|sLLLLsLLsLL
|<nowiki>7|3 b3</nowiki>
|<nowiki>5|5 #7</nowiki>
|(Great) Ionian f3
|(Great) Mixolydian f3 #7, Dorian #7 #10 (Livadeian #7)
|-
|LLLsLLsLLsL
|<nowiki>9|1 b11</nowiki>
|<nowiki>7|3 #4</nowiki>
|(Great) Lydian f11
|(Great) Ionian #4
|-
|sLLsLLsLLLL
|<nowiki>0|10 b8</nowiki>
|<nowiki>9|1 *#1</nowiki>
|(Great) Locrian f8
|(Great) Lydian *#1
|-
|sLLsLLLLsLL
|<nowiki>2|8 b5</nowiki>
|<nowiki>0|10 #9</nowiki>
|(Great) Aeolian f2 f5, Phrygian f5 #9 (Theban f5)
|(Great) Locrian #9
|-
|LsLLLLsLLsL
|<nowiki>4|6 b2</nowiki>
|<nowiki>2|8 #6</nowiki>
|(Great) Dorian f2
|(Great) Aeolian f2 #6, Phrygian #6 #9 (Theban #6)
|}
 
===Cyclic Permutation order===
{| class="wikitable"
|+
!Spelling 1
!Spelling 2
!'''Mode'''
![[Modal UDP Notation|'''UDP''']]
!'''Name'''
|-
|GHJKLABCDEFG
|LABCDEFGHJKL
|LLsLLLsLLLs
|LLsLLLsLLLs
| style="text-align:center;" |<nowiki>8|2</nowiki>
|<nowiki>8|2</nowiki>
|(Great) Distomian
|(Great) Distomian
|-
|-
|HJKLABCDEFGH
|HJKLABCDEFGH
|ABCDEFGHJKLA
|LsLLLsLLLsL
|LsLLLsLLLsL
| style="text-align:center;" |<nowiki>5|5</nowiki>
|<nowiki>5|5</nowiki>
|(Great) Livadeian
|(Great) Livadeian
|-
|-
|JKLABCDEFGHJ
|JKLABCDEFGHJ
|BCDEFGHJKLAB
|sLLLsLLLsLL
|sLLLsLLLsLL
| style="text-align:center;" |<nowiki>2|8</nowiki>
|<nowiki>2|8</nowiki>
|(Great) Theban
|(Great) Theban
|-
|-
|KLABCDEFGHJK
|KLABCDEFGHJK
|CDEFGHJKLABC
|LLLsLLLsLLs
|LLLsLLLsLLs
| style="text-align:center;" |<nowiki>10|0</nowiki>
|<nowiki>10|0</nowiki>
|(Great) Tanagran
|(Great) Tanagran
|-
|-
|LABCDEFGHJKL
|LABCDEFGHJKL
|DEFGHJKLABCD
|LLsLLLsLLsL
|LLsLLLsLLsL
| style="text-align:center;" |<nowiki>7|3</nowiki>
|<nowiki>7|3</nowiki>
|(Great) Ionian
|(Great) Ionian
|-
|-
|ABCDEFGHJKLA
|ABCDEFGHJKLA
|EFGHJKLABCDE
|LsLLLsLLsLL
|LsLLLsLLsLL
| style="text-align:center;" |<nowiki>4|6</nowiki>
|<nowiki>4|6</nowiki>
|(Great) Dorian
|(Great) Dorian
|-
|-
|BCDEFGHJKLAB
|BCDEFGHJKLAB
|FGHJKLABCDEF
|sLLLsLLsLLL
|sLLLsLLsLLL
| style="text-align:center;" |<nowiki>1|9</nowiki>
|<nowiki>1|9</nowiki>
|(Great) Phrygian
|(Great) Phrygian
|-
|-
|CDEFGHJKLABC
|CDEFGHJKLABC
|GHJKLABCDEFG
|LLLsLLsLLLs
|LLLsLLsLLLs
| style="text-align:center;" |<nowiki>9|1</nowiki>
|<nowiki>9|1</nowiki>
|(Great) Lydian
|(Great) Lydian
|-
|-
|DEFGHJKLABCD
|DEFGHJKLABCD
|HJKLABCDEFGH
|LLsLLsLLLsL
|LLsLLsLLLsL
| style="text-align:center;" |<nowiki>6|4</nowiki>
|<nowiki>6|4</nowiki>
|(Great) Mixolydian
|(Great) Mixolydian
|-
|-
|EFGHJKLABCDE
|EFGHJKLABCDE
|JKLABCDEFGHJ
|LsLLsLLLsLL
|LsLLsLLLsLL
| style="text-align:center;" |<nowiki>3|7</nowiki>
|<nowiki>3|7</nowiki>
|(Great) Aeolian
|(Great) Aeolian
|-
|-
|FGHJKLABCDEF
|FGHJKLABCDEF
|KLABCDEFGHJK
|sLLsLLLsLLL
|sLLsLLLsLLL
| style="text-align:center;" |<nowiki>0|10</nowiki>
|<nowiki>0|10</nowiki>
|(Great) Locrian
|(Great) Locrian
|}
|}
===Notes on Naming===
The modes of the Obikhodic scale are named after the existing modes, but contain the "Great" prefix (e.g. Great Ionian, Great Aeolian, etc.). The "Great" prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.
Each Obikhodic mode contains its corresponding mode in the diatonic scale. This leads to a pattern: LLsLLLsLLLs and LLsLLLsLLsL both contain the meantone LLsLLLs Ionian mode. Additionally, sLLsLLLsLLL contains the diatonic sLLsLLL Locrian mode.
Since there are only seven diatonic modes, four of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These four modes present themselves as "altered" modes, which have an accidental the mode below them lacks, or vice versa. These are the only four modes to exhibit this behavior. They're interspersed on the ranking above and below Lydian, between Dorian and Mixolydian and between Aeolian and Phrygian and on the rotational continuum between Locrian and Ionian.
As were the original modes named after regions of ancient Greece, so are these new Obikhodic extensions. They are called after regions of Boeotia, set up so that the Locrian -> Distomian -> Livadeian -&gt; Theban -&gt; Tanagran -&gt; Ionian cyclic sequence will resemble the geography of ancient Greece.
==Scale tree==
{| class="wikitable"
{| class="wikitable"
|+
|+
! colspan="2" |Generator
!Spelling 1
!Normalized
!Spelling 2
!''ed19\12''
!'''Mode'''
![[Modal UDP Notation|'''UDP''']]
!'''Name'''
|-
|-
|3\8
|GHJKLABfCDEFG
|
|LABCDEFfGHJKL
|<u>720</u>
|LLsLLsLLLLs
|''712.5''
| style="text-align:center;" |<nowiki>8|2 b7</nowiki>
|(Great) Distomian Dominant
|-
|-
|19\51
|HJKLABfCDEFGH
|
|ABCDEFfGHJKLA
|<u>712.5</u>
|LsLLLLsLLsL
|''707.843''
| style="text-align:center;" |<nowiki>5|5 b6</nowiki>
|(Great) Livadeian f6
|-
|-
|
|JKLABfCDEFGHJ
|35\94
|BCDEFfGHJKLAB
|<u>711.864</u>
|sLLsLLLLsLL
|''707.447''
| style="text-align:center;" |<nowiki>2|8 b5</nowiki>
|(Great) Theban f5
|-
|-
|16\43
|KLABfCDEFGHJK
|
|CDEFfGHJKLABC
|<u>711.111</u>
|LLsLLLLsLLs
|''706.977''
| style="text-align:center;" |<nowiki>10|0 b4</nowiki>
|-
|(Great) Tanagran f4
|
|29\78
|<u>710.204</u>
|''706.41''
|-
|-
|13\35
|LABfCDEFGHJKL
|
|DEFfGHJKLABCD
|<u>709.091</u>
|LsLLLLsLLsL
|''705.714''
| style="text-align:center;" |<nowiki>7|3 b3</nowiki>
|(Great) Ionian f3
|-
|-
|
|ABfCDEFGHJKLA
|36\97
|EFfGHJKLABCDE
|<u>708.197</u>
|sLLLLsLLsLL
|705.155
| style="text-align:center;" |<nowiki>4|6 b2</nowiki>
|(Great) Dorian f2
|-
|-
|
|BfCDEFGHJKLABf
|23\62
|FfGHJKLABCDEFf
|<u>707.692</u>
|LsLLsLLsLLL
|''704.839''
| style="text-align:center;" |<nowiki>1|9 *b1</nowiki>
|(Great) Phrygian *f1
|-
|-
|
|CDEFGHJKLABfC
|33\89
|GHJKLABCDEFfG
|<u>707.143</u>
|LLLsLLsLLsL
|''704.494''
| style="text-align:center;" |<nowiki>9|1 b11</nowiki>
|(Great) Lydian f11
|-
|-
|
|DEFGHJKLABfCD
|43\116
|HJKLABCDEFfGH
|<u>706.849</u>
|LLsLLsLLsLL
|''704.31''
| style="text-align:center;" |<nowiki>6|4 b10</nowiki>
|(Great) Mixolydian f10
|-
|-
|10\27
|EFGHJKLABfCDE
|
|JKLABCDEFfGHJ
|<u>705.882</u>
|LsLLsLLsLLL
|''703.704''
| style="text-align:center;" |<nowiki>3|7 b9</nowiki>
|(Great) Aeolian f9
|-
|-
|
|FGHJKLABfCDEF
|27\73
|KLABCDEFfGHJK
|<u>704.348</u>
|sLLsLLsLLLL
|''702.738''
| style="text-align:center;" |<nowiki>0|10 b8</nowiki>
|(Great) Locrian f8
|}
{| class="wikitable"
!Spelling 1
!Spelling 2
!'''Mode'''
![[Modal UDP Notation|'''UDP''']]
!'''Name'''
|-
|-
|
|GHJKLABC#DEFG
|17\46
|LABCDEFG#HJKL
|<u>703.448</u>
|LLsLLsLLLLs
|''702.174''
|<nowiki>8|2 #8</nowiki>
|(Great) Distomian #8
|-
|-
|
|HJKLABC#DEFGH
|24\65
|ABCDEFG#HJKLA
|<u>702.439</u>
|LsLLLLsLLsL
|''701.5385''
|<nowiki>5|5 #7</nowiki>
|-
|(Great) Livadeian #7
|
|31\84
|<u>701.887</u>
|701.1905
|-
|7\19
|
|<u>700</u>
|''700''
|-
|-
|
|JKLABC#DEFGHJ
|60\163
|BCDEFG#HJKLAB
|<u>699.029</u>
|sLLLLsLLsLL
|''699.3865''
|<nowiki>2|8 #6</nowiki>
|(Great) Theban #6
|-
|-
|
|KLABC#DEFGHJK
|53\144
|CDEFG#HJKLABC
|<u>698.901</u>
|LLLLsLLsLLs
|''699.306''
|<nowiki>10|0 #5</nowiki>
|(Great) Tanagran #5
|-
|-
|
|LABC#DEFGHJKL
|46\125
|DEFG#HJKLABCD
|<u>698.734</u>
|LLLsLLsLLsL
|''699.2''
|<nowiki>7|3 #4</nowiki>
|(Great) Ionian #4
|-
|-
|
|ABC#DEFGHJKLA
|39\106
|EFG#HJKLABCDE
|<u>698.5075</u>
|LLsLLsLLsLL
|''699.057''
|<nowiki>4|6 #3</nowiki>
|(Great) Dorian #3
|-
|-
|
|BC#DEFGHJKLAB
|32\87
|FG#HJKLABCDEF
|<u>698.182</u>
|LsLLsLLsLLL
|698.852
|<nowiki>1|9 #2</nowiki>
|(Great) Phrygian #2
|-
|-
|
|C#DEFGHJKLABC#
|25\68
|G#HJKLABCDEFG#
|<u>697.674</u>
|sLLsLLsLLLL
|''698.529''
|<nowiki>9|1 *#1</nowiki>
|(Great) Lydian *#1
|-
|-
|
|DEFGHJKLABC#D
|18\49
|HJKLABCDEFG#H
|<u>696.77</u>
|LLsLLsLLLLs
|''697.959''
|<nowiki>6|4 #11</nowiki>
|(Great) Mixolydian #11
|-
|-
|
|EFGHJKLABC#DE
|29\79
|JKLABCDEFG#HJ
|<u>696</u>
|LsLLsLLLLsL
|''697.468''
|<nowiki>3|7 #10</nowiki>
|(Great) Aeolian #10
|-
|-
|
|FGHJKLABC#DEF
|40\109
|KLABCDEFG#HJK
|<u>695.652</u>
|sLLsLLLLsLL
|''697.248''
|<nowiki>0|10 #9</nowiki>
|(Great) Locrian #9
|}
===Notes on Naming===
The modes of the Obikhodic scale are named after the existing modes, but contain the "Great" prefix (e.g. Great Ionian, Great Aeolian, etc.). The "Great" prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.
 
Each Obikhodic mode contains its corresponding mode in the diatonic scale. This leads to a pattern: LLsLLLsLLLs and LLsLLLsLLsL both contain the meantone LLsLLLs Ionian mode. Additionally, sLLsLLLsLLL contains the diatonic sLLsLLL Locrian mode.
 
Since there are only seven diatonic modes, four of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These four modes present themselves as "altered" modes, which have an accidental the mode below them lacks, or vice versa. These are the only four modes to exhibit this behavior. They're interspersed on the ranking above and below Lydian, between Dorian and Mixolydian and between Aeolian and Phrygian and on the rotational continuum between Locrian and Ionian.
 
As were the original modes named after regions of ancient Greece, so are these new Obikhodic extensions. They are called after regions of Boeotia, set up so that the Locrian -> Distomian -> Livadeian -&gt; Theban -&gt; Tanagran -&gt; Ionian cyclic sequence will resemble the geography of ancient Greece.
==Scale tree==
{| class="wikitable"
|+
!Generator
!Normalized
!Large step
!Small step
|-
|-
|11\30
|3\8
|
|<u>720.000</u>
|<u>694.737</u>
|1\5, <u>240.000</u>
|''696.667''
|0
|-
|-
|
|19\51
|26\71
|<u>712.500</u>
|<u>693.333</u>
|6\51, <u>225.000</u>
|''695.775''
|1\51, <u>37.500</u>
|-
|-
|15\41
|54\145
|
|<u>712.088</u>
|<u>692.308</u>
|17\145, <u>224.175</u>
|''695.122''
|3\145, <u>39.560</u>
|-
|-
|
|35\94
|34\93
|<u>711.864</u>
|<u>691.525</u>
|11\94, <u>223.729</u>
|''694.623''
|2\94, <u>40.678</u>
|-
|-
|19\52
|16\43
|
|<u>711.111</u>
|<u>690.909</u>
|5\43, <u>222.222</u>
|''694.231''
|1\43, <u>44.444</u>
|-
|-
|
|45\121
|42\115
|<u>710.526</u>
|<u>690.411</u>
|14\121, <u>221.053</u>
|''693.913''
|3\121, <u>47.368</u>
|-
|-
|23\63
|29\78
|
|<u>710.204</u>
|<u>690</u>
|9\78, <u>220.408</u>
|''693.651''
|2\78, <u>48.980</u>
|-
|42\113
|<u>709.859</u>
|13\113, <u>219.718</u>
|3\113, <u>50.704</u>
|-
|13\35
|<u>709.091</u>
|4\35, <u>218.182</u>
|1\35, <u>54.545</u>
|-
|49\132
|<u>708.434</u>
|15\132, <u>216.867</u>
|4\132, <u>57.831</u>
|-
|36\97
|<u>708.197</u>
|11\97, <u>216.393</u>
|3\97, <u>59.016</u>
|-
|23\62
|<u>707.692</u>
|7\62, <u>215.385</u>
|2\62, <u>61.538</u>
|-
|33\89
|<u>707.143</u>
|10\89, <u>214.286</u>
|3\89, <u>64.286</u>
|-
|43\116
|<u>706.849</u>
|13\116, <u>213.699</u>
|4\116, <u>65.753</u>
|-
|53\143
|<u>706.667</u>
|16\143, <u>213.333</u>
|5\143, <u>66.667</u>
|-
|63\170
|<u>706.542</u>
|19\170, <u>213.084</u>
|6\170, <u>67.290</u>
|-
|73\197
|<u>706.452</u>
|22\197, <u>212.903</u>
|7\197, <u>67.742</u>
|-
|-
|4\11
|10\27
|
|<u>705.882</u>
|<u>685.714</u>
|3\27, <u>211.765</u>
|''690.909''
|1\27, <u>70.588</u>
|}
|-
 
|47\127
|<u>705.000</u>
|14\127, <u>210.000</u>
|5\127, <u>75.000</u>
|-
|37\100
|<u>704.762</u>
|11\100, <u>209.524</u>
|4\100, <u>76.190</u>
|-
|27\73
|<u>704.348</u>
|8\73, <u>208.696</u>
|3\27, <u>78.261</u>
|-
|17\46
|<u>703.448</u>
|5\46, <u>206.897</u>
|2\46, <u>82.759</u>
|-
|41\111
|<u>702.857</u>
|12\111, <u>205.714</u>
|5\111, <u>85.714</u>
|-
|24\65
|<u>702.439</u>
|7\65, <u>204.878</u>
|3\65, <u>87.805</u>
|-
|31\84
|<u>701.887</u>
|9\84, <u>203.774</u>
|4\84, <u>90.566</u>
|-
|…
|…
|…
|…
|-
|59\160
|<u>700.990</u>
|17\160, <u>201.980</u>
|8\160, <u>95.050</u>
|-
|…
|…
|…
|…
|-
|122\331
|<u>700.478</u>
|35\331, <u>200.960</u>
|18\334, <u>97.608</u>
|-
|7\19
|<u>700.000</u>
|2\19, <u>200.000</u>
|1\19, <u>100.000</u>
|-
|123\334
|<u>699.526</u>
|35\334, <u>199.052</u>
|18\334, <u>102.370</u>
|-
|…
|…
|…
|…
|-
|63\163
|<u>699.029</u>
|17\163, <u>198.058</u>
|9\163, <u>104.854</u>
|-
|…
|…
|…
|…
|-
|32\87
|<u>698.182</u>
|9\87, <u>196.364</u>
|5\87, <u>109.091</u>
|-
|25\68
|<u>697.674</u>
|7\68, <u>195.349</u>
|4\68, <u>111.628</u>
|-
|43\117
|<u>697.297</u>
|12\117, <u>194.594</u>
|7\117, <u>113.514</u>
|-
|18\49
|<u>696.774</u>
|5\49, <u>193.548</u>
|3\49, <u>116.129</u>
|-
|29\79
|<u>696.000</u>
|8\79, <u>192.000</u>
|5\79, <u>120.000</u>
|-
|40\109
|<u>695.652</u>
|11\109, <u>191.304</u>
|7\109, <u>121.739</u>
|-
|51\139
|<u>695.455</u>
|14\139, <u>190.909</u>
|9\139, <u>122.727</u>
|-
|11\30
|<u>694.737</u>
|3\30, <u>189.474</u>
|2\30, <u>126.316</u>
|-
|59\161
|<u>694.118</u>
|16\161, <u>188.235</u>
|11\161, <u>129.412</u>
|-
|48\131
|<u>693.976</u>
|13\131, <u>187.952</u>
|9\131, <u>130.120</u>
|-
|37\101
|<u>693.750</u>
|10\101, <u>187.500</u>
|7\101, <u>131.250</u>
|-
|26\71
|<u>693.333</u>
|7\71, <u>186.667</u>
|5\71, <u>133.333</u>
|-
|41\112
|<u>692.958</u>
|11\112, <u>185.915</u>
|8\112, <u>135.211</u>
|-
|15\41
|<u>692.308</u>
|4\41, <u>184.615</u>
|3\41, <u>138.462</u>
|-
|34\93
|<u>691.525</u>
|9\93, <u>183.051</u>
|7\93, <u>142.373</u>
|-
|53\145
|<u>691.304</u>
|14\145, <u>182.609</u>
|11\145, <u>143.478</u>
|-
|19\52
|<u>690.909</u>
|5\52, <u>181.818</u>
|4\52, <u>145.455</u>
|-
|23\63
|<u>690.000</u>
|6\63, <u>180.000</u>
|5\63, <u>150.000</u>
|-
|4\11
|<u>685.714</u>
|1\11, <u>171.429</u>
|1\11, <u>171.429</u>
|}
 
== See also ==
== See also ==
[[8L 3s (3/1-equivalent)]]
[[8L 3s (3/1-equivalent)]]
[[16L 6s (80/9-equivalent)]]
[[16L 6s (352/39-equivalent)]]
[[16L 6s (64/7-equivalent)]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/8L_3s_(perfect_twelfth-equivalent)"