Xenharmonic Wiki

User:Moremajorthanmajor/5L 3s (11/5-equivalent): Difference between revisions

← Older edit
VisualWikitext
Fredg999 (talk | contribs)
autopatrolled, Interface administrators, Sysops
6,129 edits
m Fredg999 moved page 5L 3s (11/5-equivalent) to User:Moremajorthanmajor/5L 3s (11/5-equivalent): Page not ready for the main namespace
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
 
(4 intermediate revisions by one other user not shown)
Line 1: Line 1:
{{Infobox MOS
{{Infobox MOS
| Name = Neapolitan-oneirotonic
|Tuning=5L 3s<11/5>}}{{MOS intro|Scale Signature=5L 3s<11/5>}}
| Equave = 11/5
| Periods = 1
| nLargeSteps = 5
| nSmallSteps = 3
| Equalized = 3
| Collapsed = 2
| Pattern = LLsLLsLs
| Neutral = 2L 6s
}}The minor ninth of a diatonic scale has a '''5L 3s''' [[MOS]] structure with generators ranging from 2\5 (two degrees of 5ed8\7 = 548.6¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 5ed8\7, s becomes so small it disappears (and all that remains are the five equal L's).


Any edIX of an interval up to 8\7 with an interval between 450¢ and 548.6¢ has a 5L 3s scale. [[13edIX]] is the smallest edIX with a (non-degenerate) 5L 3s scale and thus is the most commonly used 5L 3s tuning.
[[13ed11/5]] is the smallest ed11/5 with a (non-degenerate) 5L 3s scale and thus is the most commonly used 5L 3s tuning.
==Standing assumptions==
==Standing assumptions ==
The [[TAMNAMS]] system is used in this article to name 5L 3s<11/5><ref>the rare simplest tuning for a diatonic minor ninth </ref> intervals and step size ratios and step ratio ranges.
The [[TAMNAMS]] system is used in this article to name 5L 3s<11/5><ref>the rare simplest tuning for a diatonic minor ninth </ref> intervals and step size ratios and step ratio ranges.


Line 19: Line 10:
The chain of perfect 4ths becomes: ... Ef Af Qf Ff Bf Df G C E A Q F B D ...
The chain of perfect 4ths becomes: ... Ef Af Qf Ff Bf Df G C E A Q F B D ...


Thus the [[13edIX]] gamut is as follows:
Thus the [[13ed11/5]] gamut is as follows:


'''G/F#''' G#/Af '''A''' A#/Bf '''B/Cf''' '''C/B#''' C#/Qf '''Q''' Q#/Df '''D/Ef E/D#''' E#/Ff '''F/Gf G'''
'''G/F#''' G#/Af '''A''' A#/Bf '''B/Cf''' '''C/B#''' C#/Qf '''Q''' Q#/Df '''D/Ef E/D#''' E#/Ff '''F/Gf G'''


The 18edIX gamut is notated as follows:
The [[18ed11/5]] gamut is notated as follows:


'''G''' F#/Af G# '''A''' Bf A#/Cf '''B''' '''C''' B#/Qf C# '''Q''' Df Q#/Ef '''D E''' D#/Ff E#/Gf '''F G'''
'''G''' F#/Af G# '''A''' Bf A#/Cf '''B''' '''C''' B#/Qf C# '''Q''' Df Q#/Ef '''D E''' D#/Ff E#/Gf '''F G'''


The 21edIX gamut:
The [[21ed11/5]] gamut:


'''G''' G# Af '''A''' A# Bf '''B''' B#/Cf '''C''' C# Qf '''Q''' Q# Df '''D''' D#/Ef '''E''' E# Ff '''F''' F#/Gf '''G'''
'''G''' G# Af '''A''' A# Bf '''B''' B#/Cf '''C''' C# Qf '''Q''' Q# Df '''D''' D#/Ef '''E''' E# Ff '''F''' F#/Gf '''G'''
Line 33: Line 24:
The author suggests the name '''Neapolitan'''-'''oneirotonic'''.
The author suggests the name '''Neapolitan'''-'''oneirotonic'''.
==Intervals==
==Intervals==
The table of Neapolitan-oneirotonic intervals below takes the fourth as the generator. Given the size of the fourth generator ''g'', any oneirotonic 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 1300 (for relative cents) if necessary (so you can use "''k''*''g'' % 1300" for search engines, for plugged-in values of ''k'' and ''g''). For example, since the major third is reached by six fourth generators, 18edIX's major third is 6*505.56 mod 1300 = 3033.33 mod 1300 = 433.33r¢.
The table of Neapolitan-oneirotonic intervals below takes the fourth as the generator. Given the size of the fourth generator ''g'', any oneirotonic 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 11/5.
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
Line 43: Line 34:
!Notation of 2/1 inverse
!Notation of 2/1 inverse
!name
!name
!In L's and s's
! In L's and s's
|-
|-
| colspan="8" |The 8-note MOS has the following intervals (from some root):
| colspan="8" |The 8-note MOS has the following intervals (from some root):
Line 54: Line 45:
|G
|G
|“perfect” minor 9th
|“perfect” minor 9th
|5L + 3s
| 5L + 3s
|-
|-
|1
|1
Line 78: Line 69:
|major 2nd
|major 2nd
|1L + 0s
|1L + 0s
| -3
| -3
|Ff
|Ff
|diminished octave
|diminished octave
Line 102: Line 93:
|-
|-
|6
|6
|B
| B
|major 3rd
|major 3rd
|2L + 0s
|2L + 0s
Line 112: Line 103:
|7
|7
|D
|D
|major 6th
| major 6th
|4L + 1s
|4L + 1s
| -7
| -7
|Cf
|Cf
|diminished 4th
| diminished 4th
|1L + 2s
|1L + 2s
|-
|-
| colspan="8" |The chromatic 13-note MOS (either [[5L 8s (minor ninth equivalent)|5L 8s]], [[8L 5s (minor ninth equivalent)|8L 5s]], or [[13edIX]]) also has the following intervals (from some root):
| colspan="8" |The chromatic 13-note MOS (either [[5L 8s (11/5-equivalent)|5L 8s]], [[8L 5s (11/5-equivalent)|8L 5s]], or [[13ed11/5]]) also has the following intervals (from some root):
|-
|-
|8
|8
Line 125: Line 116:
|augmented unison
|augmented unison
|1L - 1s
|1L - 1s
| -8
| -8
|Gf
|Gf
|diminished 9th
|diminished 9th
|4L + 4s
|4L + 4s
|-
|-
|9
| 9
|C#
|C#
|augmented 4th
| augmented 4th
|3L + 0s
|3L + 0s
| -9
| -9
|Dff
|Dff
|diminished 6th
|diminished 6th
Line 142: Line 133:
|E#
|E#
|augmented 7th
|augmented 7th
|5L + 1s
| 5L + 1s
| -10
| -10
|Bff
|Bff
Line 153: Line 144:
|2L - 1s
|2L - 1s
| -11
| -11
|Fff
| Fff
|doubly diminished octave
|doubly diminished octave
|3L + 4s
|3L + 4s
Line 162: Line 153:
|4L + 0s
|4L + 0s
| -12
| -12
|Qff
| Qff
|doubly diminished 5th
|doubly diminished 5th
|1L + 3s
|1L + 3s
|}
|}
==Tuning ranges==
==Tuning ranges==
===Simple tunings===
=== Simple tunings===
Table of intervals in the simplest Neapolitan-oneirotonic tunings:
Table of intervals in the simplest Neapolitan-oneirotonic tunings:
{| class="wikitable right-2 right-3 right-4 sortable"
{| class="wikitable right-2 right-3 right-4 sortable"
|-
|-
! class="unsortable" |Degree
! class="unsortable" |Degree
!Size in 13edIX (basic)
!Size in 13ed11/5 (basic)
!Size in 18edIX (hard)
!Size in 18ed11/5 (hard)
!Size in 21edIX (soft)
!Size in 21ed11/5 (soft)
! class="unsortable" |Note name on G
! class="unsortable" |Note name on G
!#Gens up
!#Gens up
Line 185: Line 176:
|0
|0
|-
|-
|minor 2nd
| minor 2nd
|1\13, 100.00
|1\13, 105.000
|1\18, 70.59 (72.22)
|1\18, 75.834
|2\21, 126.32 (121.81)
|2\21, 130.000
|Af
|Af
| -5
| -5
|-
|-
|major 2nd
|major 2nd
|2\13, 200.00
|2\13, 210.001
|3\18, 211.765 (216.67)
|3\18, 227.501
|3\21, 189.47 (185.71)
|3\21, 195.001
|A
|A
| +3
| +3
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 3rd
|minor 3rd
|3\13, 300.00
|3\13, 315.001
|4\18, 282.35 (288.89)
|4\18, 303.334
|5\21, 315.79 (309.52)
|5\21, 325.001
|Bf
|Bf
| -2
| -2
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 3rd
|major 3rd
| rowspan="2" |4\13, 400.00
| rowspan="2" |4\13, 420.001
|6\18, 423.53 (433.33)
|6\18, 455.001
|6\21, 378.95 (371.43)
|6\21, 390.001
|B
|B
| +6
| +6
|-
|-
|diminished 4th
| diminished 4th
|5\18, 352.94 (361.11)
|5\18, 379.168
|7\21, 442.105 (433.33)
|7\21, 455.001
|Cf
|Cf
| -7
| -7
|-
|-
|natural 4th
|natural 4th
|5\13, 500.00
| 5\13, 525.002
|7\18, 494.12 (505.56)
|7\18, 530.835
|8\21, 505.26 (495.24)
|8\21, 520.002
|C
|C
| +1
| +1
|-
|-
|augmented 4th
|augmented 4th
| rowspan="2" |6\13, 600.00
| rowspan="2" |6\13, 630.002
|9\18, 635.29 (650.00)
|9\18, 682.502
|9\21, 568.42 (557.14)
|9\21, 585.002
|C#
|C#
| +9
| +9
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|diminished 5th
|diminished 5th
|8\18, 564.71 (577.78)
|8\18, 606.669
|10\21, 631.58 (619.05)
|10\21, 650.002
|Qf
|Qf
| -4
| -4
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect 5th
|perfect 5th
|7\13, 700.00
|7\13, 735.002
|10\18, 705.88 (722.22)
|10\18, 758.336
|11\31, 694.74 (680.95)
| 11\21, 715.002
|Q
|Q
| +4
| +4
|-
|-
|minor 6th
|minor 6th
|8\13, 800.00
|8\13, 840.003
|11\18, 776.47 (794.44)
|11\18, 834.169
|13\21, 821.05 (802.76)
|13\21, 780.002
|Df
|Df
| -1
| -1
|-
|-
|major 6th
|major 6th
| rowspan="2" |9\13, 900.00
| rowspan="2" |9\13, 945.003
|13\18, 917.65 (938.89)
|13\18, 985.836
|14\21, 884.21 (866.67)
|14\21, 845.003
|D
|D
| +7
| +7
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 7th
| minor 7th
|12\18, 847.06 (866.67)
|12\18, 910.003
|15\21, 947.37 (928.57)
|15\21, 910.003
|Ef
|Ef
| -6
| -6
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 7th
|major 7th
|10\13, 1000.00
|10\13, 1050.003
|14\18, 988.235 (1011.11)
|14\18, 1061.670
|16\21, 1017.53 (990.48)
|16\21, 975.003
|E
|E
| +2
| +2
|-
|-
|diminished octave
|diminished octave
|11\13, 1100.00
|11\13, 1155.004
|15\18, 1052.82 (1083.33)
|15\18, 1137.504
|18\21, 1136.84 (1114.29)
|18\21, 1105.003
|Ff
| Ff
| -3
| -3
|-
|-
|perfect octave
|perfect octave
|12\13, 1200.00
|12\13, 1260.004
|17\18, 1200.00 (1227.78)
|17\18, 1289.171
|19\21, 1200.00 (1178.19)
|19\21, 1170.003
|F
|F
| +5
| +5
Line 293: Line 284:
**The large step is near the Pythagorean 9/8 whole tone, somewhere between as in [[12edo]] and as in [[17edo]].
**The large step is near the Pythagorean 9/8 whole tone, somewhere between as in [[12edo]] and as in [[17edo]].
**The major 3rd (made of two large steps) is a near-[[Pythagorean]] to [[Neogothic]] major third.
**The major 3rd (made of two large steps) is a near-[[Pythagorean]] to [[Neogothic]] major third.
EDIXs that are in the hypohard range include [[13edIX]], 18edIX, and 31edIX.
EDIXs that are in the hypohard range include [[13ed11/5]], [[18ed11/5]], and [[31ed11/5]].


The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various hypohard Neapolitan-oneiro tunings.
The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various hypohard Neapolitan-oneiro tunings.
Line 299: Line 290:
|-
|-
!
!
![[13edIX]] (basic)
![[13ed11/5]] (basic)
!18edIX (hard)
![[18ed11/5]] (hard)
!31edIX (semihard)
![[31ed11/5]] (semihard)
|-
|-
|generator (g)
|generator (g)
|5\13, 500.00
|5\13, 525.002
|7\18, 494.12 (505.56)
|10\18, 758.336
|12\31, 496.55 (503.23)
|12\31, 496.55  
|-
|-
|L (3g - minor 9th)
|L (3g - minor 9th)
|2\13, 200.00
|2\13, 210.001
|3\18, 211.765 (216.67)
|3\18, 227.501
|5\31, 206.87 (209.68)
|5\31, 206.87
|-
|-
|s (-5g + 2 minor 9ths)
|s (-5g + 2 minor 9ths)
|1\13, 100.00
|1\13, 105.000
|1\18, 70.59 (72.22)
| 1\18, 75.834
|2\31, 82.76 (83.87)
|2\31, 82.76  
|}
|}
====Intervals====
====Intervals====
Line 323: Line 314:
|-
|-
! class="unsortable" |Degree
! class="unsortable" |Degree
!Size in 13edIX (basic)
!Size in 13ed11/5 (basic)
!Size in 18edIX (hard)
!Size in 18ed11/5 (hard)
!Size in 31edIX (semihard)
!Size in 31ed11/5 (semihard)
! class="unsortable" |Note name on G
! class="unsortable" |Note name on G
! class="unsortable" |Approximate ratios<ref>The ratio interpretations that are not valid for 18edo are italicized.</ref>
! class="unsortable" |Approximate ratios
!#Gens up
!#Gens up
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 335: Line 326:
|0\31, 0.00
|0\31, 0.00
|G
|G
|1/1
| 1/1
|0
|0
|-
|-
|minor 2nd
|minor 2nd
|1\13, 100.00
|1\13, 105.000
|1\18, 70.59 (72.22)
|1\18, 75.834
|2\31, 82.76 (83.87)
|2\31, 88.065
|Af
|Af
|21/20, ''22/21''
|21/20, ''22/21''
Line 347: Line 338:
|-
|-
|major 2nd
|major 2nd
|2\13, 200.00
|2\13, 210.001
|3\18, 211.765 (216.67)
|3\18, 227.501
|5\31, 206.87 (209.68)
|5\31, 220.162
|A
|A
|9/8
|9/8
| +3
| +3
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 3rd
|minor 3rd
|3\13, 300.00
|3\13, 315.001
|4\18, 282.35 (288.89)
|4\18, 303.334
|7\31, 289.655 (293.55)
|7\31, 308.227
|Bf
|Bf
|13/11, 33/28
|13/11, 33/28
Line 363: Line 354:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 3rd
|major 3rd
| rowspan="2" |4\13, 400.00
| rowspan="2" |4\13, 420.001
|6\18, 423.53 (433.33)
|6\18, 455.001
|10\31, 413.79 (419.355)
|10\31, 440.324
|B
|B
|14/11, 33/26
|14/11, 33/26
Line 371: Line 362:
|-
|-
|diminished 4th
|diminished 4th
|5\18, 352.94 (361.11)
|5\18, 379.168
|9\31, 372.41 (377.42)
|9\31, 396.292
|Cf
|Cf
|''5/4, 11/9''
|''5/4, 11/9''
Line 378: Line 369:
|-
|-
|natural 4th
|natural 4th
|5\13, 500.00
|5\13, 525.002
|7\18, 494.12 (505.56)
|7\18, 530.835
|12\31, 496.55 (503.23)
|12\31, 528.389
|C
|C
|4/3
|4/3
| +1
| +1
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|augmented 4th
|augmented 4th
| rowspan="2" |6\13, 600.00
| rowspan="2" |6\13, 630.002
|9\18, 635.29 (650.00)
|9\18, 682.502
|15\31, 620.69 (629.03)
|15\31, 660.486
|C#
|C#
|''10/7, 18/13, 11/8''
|''10/7, 18/13, 11/8''
Line 394: Line 385:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|diminished 5th
|diminished 5th
|8\18, 564.71 (577.78)
| 8\18, 606.669
|14\31, 579.31 (587.10)
|14\31, 616.454
|Qf
|Qf
|''7/5, 13/9'', ''16/11''
|''7/5, 13/9'', ''16/11''
| -4
| -4
|-
|-
|perfect 5th
| perfect 5th
|7\13, 700.00
|7\13, 735.002
|10\18, 705.88 (722.22)
|10\18, 758.336
|17\31, 703.45 (712.90)
| 17\31, 748.551
|Q
|Q
|3/2
|3/2
Line 409: Line 400:
|-
|-
|minor 6th
|minor 6th
|8\13, 800.00
|8\13, 840.003
|11\18, 776.47 (794.44)
|11\18, 834.169
|19\31, 786.21 (796.77)
|19\31, 836.615
|Df
|Df
|52/33, 11/7
| 52/33, 11/7
| -1
| -1
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 6th
| major 6th
| rowspan="2" |9\13, 900.00
| rowspan="2" |9\13, 945.003
|13\18, 917.65 (938.89)
|13\18, 985.836
|22\31, 910.345 (922.58)
|22\31, 968.713
|D
| D
|56/33, 22/17
|56/33, 22/17
| +7
| +7
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 7th
|minor 7th
|12\18, 847.06 (866.67)
|12\18, 910.003
|21\31, 868.97 (880.645)
|21\31, 924.680
|Ef
|Ef
|5/3, 18/11
|5/3, 18/11
| -6
| -6
|-
|-
|major 7th
| major 7th
|10\13, 1000.00
|10\13, 1050.003
|14\18, 988.235 (1011.11)
|14\18, 1061.670
|24\31, 993.13 (1007.45)
|24\31, 1056.778
|E
|E
|16/9
|16/9
Line 440: Line 431:
|-
|-
|diminished octave
|diminished octave
|11\13, 1100.00
|11\13, 1155.004
|15\18, 1052.82 (1083.33)
|15\18, 1137.5035
|26\31, 1075.86 (1090.32)
|26\31, 1144.84
|Ff
|Ff
|11/6, 13/7, 15/8
|11/6, 13/7, 15/8
Line 448: Line 439:
|-
|-
|perfect octave
|perfect octave
|12\13, 1200.00
|12\13, 1260.004
|17\18, 1200.00 (1227.78)
|17\18, 1289.171
|29\31, 1200.00 (1212.13)
|29\31, 1276.939
|F
|F
|2/1
|2/1
Line 465: Line 456:
|-
|-
!
!
!21edIX (soft)
! 21ed11/5 (soft)
!34edIX (semisoft)
!34ed11/5 (semisoft)
|-
|-
|generator (g)
| generator (g)
|8\21, 505.26 (495.24)
|8\21, 520.002
|13\34, 458.82
|13\34, 521.913
|-
|-
|L (3g - minor 9th)
|L (3g - minor 9th)
|3\21, 189.47 (185.71)
| 3\21, 195.001
|5\34, 193.55 (191.18)
|5\34, 200.736
|-
|-
|s (-5g + 2 minor 9ths)
|s (-5g + 2 minor 9ths)
|2\31, 82.76 (83.87)
|2\21, 130.000
|3\34, 116.19 (114.71)
|3\34, 120.442
|}
|}
====Intervals====
====Intervals====
Sortable table of major and minor intervals in hyposoft tunings (13edIX not shown):
Sortable table of major and minor intervals in hyposoft tunings (13ed11/5 not shown):
{| class="wikitable right-2 right-3 sortable"
{| class="wikitable right-2 right-3 sortable"
|-
|-
! class="unsortable" |Degree
! class="unsortable" |Degree
!Size in 21edIX (soft)
!Size in 21ed11/5 (soft)
!Size in 34edo (semisoft)
!Size in 34ed11/5 (semisoft)
! class="unsortable" |Note name on G
! class="unsortable" |Note name on G
! class="unsortable" |Approximate ratios
! class="unsortable" |Approximate ratios
Line 499: Line 490:
|-
|-
|minor 2nd
|minor 2nd
|2\21, 126.32 (121.81)
| 2\21, 130.000
|3\34, 116.19 (114.71)
|3\34, 120.442
|Af
|Af
|16/15
|16/15
Line 506: Line 497:
|-
|-
|major 2nd
|major 2nd
|3\21, 189.47 (185.71)
|3\21, 195.001
|5\34, 193.55 (191.18)
|5\34, 200.736
|A
|A
|10/9, 9/8
|10/9, 9/8
| +3
| +3
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 3rd
|minor 3rd
|5\21, 315.79 (309.52)
|5\21, 325.001
|8\34, 309.68 (305.88)
|8\34, 321.177
|Bf
|Bf
|6/5
|6/5
Line 520: Line 511:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 3rd
|major 3rd
|6\21, 378.95 (371.43)
|6\21, 390.001
|10\34, 387.10 (382.35)
|10\34, 401.472
|B
|B
|5/4
|5/4
Line 527: Line 518:
|-
|-
|diminished 4th
|diminished 4th
|7\21, 442.105 (433.33)
|7\21, 455.001
|11\34, 425.81 (420.59)
|11\34, 441.619
|Cf
|Cf
|9/7
|9/7
Line 534: Line 525:
|-
|-
|natural 4th
|natural 4th
|8\21, 505.26 (495.24)
|8\21, 520.002
|13\34, 503.23 (497.06)
|13\34, 521.913
|C
|C
|4/3
| 4/3
| +1
| +1
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|augmented 4th
| augmented 4th
|9\21, 568.42 (557.14)
|9\21, 585.002
|15\34, 580.645 (573.53)
|15\34, 602.208
|C#
| C#
|7/5
|7/5
| +9
| +9
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|diminished 5th
|diminished 5th
|10\21, 631.58 (619.05)
|10\21, 650.002
|16\34, 619.355 (611.765)
| 16\34, 642.355
|Qf
|Qf
|10/6
|10/6
Line 555: Line 546:
|-
|-
|perfect 5th
|perfect 5th
|11\31, 694.74 (680.95)
|11\21, 715.002
|18\34, 696.77 (688.235)
| 18\34, 722.649
|Q
|Q
|3/2
|3/2
Line 562: Line 553:
|-
|-
|minor 6th
|minor 6th
|13\21, 821.05 (802.76)
|13\21, 780.002
|21\34, 812.90 (802.94)
|21\34, 843.091
|Df
|Df
|8/5
|8/5
Line 569: Line 560:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 6th
|major 6th
|14\21, 884.21 (866.67)
|14\21, 845.003
|23\34, 890.32 (879.41)
|23\34, 923.385
|D
|D
|5/3
|5/3
| +7
| +7
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 7th
|minor 7th
|15\21, 947.37 (928.57)
|15\21, 910.003
|24\34, 929.03 (917.65)
|24\34, 963.532
|Ef
|Ef
|12/7
|12/7
Line 583: Line 574:
|-
|-
|major 7th
|major 7th
|16\21, 1017.53 (990.48)
|16\21, 975.003
|26\34, 1006.45 (995.12)
|26\34, 1043.826
|E
|E
|9/5, 16/9
|9/5, 16/9
Line 590: Line 581:
|-
|-
|diminished octave
|diminished octave
|18\21, 1136.84 (1114.29)
|18\21, 1105.003
|29\34, 1122.58 (1109.88)
|29\34, 1164.268
|Ff
|Ff
|27/14, 48/25
|27/14, 48/25
Line 597: Line 588:
|-
|-
|perfect octave
|perfect octave
|19\21, 1200.00 (1178.19)
|19\21, 1170.003
|31\34, 1200.00 (1185.29)
|31\34, 1244.563
|F
|F
|2/1
|2/1
Line 610: Line 601:
|-
|-
!
!
!29edIX (supersoft)
!29ed11/5 (supersoft)
!37edIX
!37ed11/5
|-
|-
|generator (g)
| generator (g)
|11\29, 507.69 (493.10)
|11\29, 517.760
|14\37, 509.09 (491.89)
|14\37, 516.488
|-
|-
|L (3g - minor 9th)
|L (3g - minor 9th)
|4\29, 184.615 (179.31)
|4\29, 188.276
|5\37, 181.82 (175.68)
| 5\37, 184.460
|-
|-
|s (-5g + 2 minor 9ths)
|s (-5g + 2 minor 9ths)
|3\29, 138.46 (134.49)
|3\29, 141.207
|4\37, 145.455 (140.54)
|4\37, 147.568
|}
|}
====Intervals====
====Intervals====
Line 630: Line 621:
|-
|-
! class="unsortable" |Degree
! class="unsortable" |Degree
!Size in 29edIX (supersoft)
!Size in 29ed11/5 (supersoft)
! class="unsortable" |Note name on G
! class="unsortable" |Note name on G
! class="unsortable" |Approximate ratios
! class="unsortable" |Approximate ratios
Line 642: Line 633:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|chroma
|chroma
|1\29, 46.15 (44.83)
|1\29, 47.069
|G#
|G#
|[[33/32]], [[49/48]], [[36/35]], [[25/24]]
|[[33/32]], [[49/48]], [[36/35]], [[25/24]]
Line 648: Line 639:
|-
|-
|diminished 2nd
|diminished 2nd
|2\29, 92.31 (89.655)
|2\29, 94.138
|Aff
|Aff
|[[21/20]], [[22/21]], [[26/25]]
|[[21/20]], [[22/21]], [[26/25]]
Line 654: Line 645:
|-
|-
|minor 2nd
|minor 2nd
|3\29, 138.46 (134.49)
|3\29, 141.207
|Af
|Af
|[[12/11]], [[13/12]], [[14/13]], [[16/15]]
|[[12/11]], [[13/12]], [[14/13]], [[16/15]]
| -5
| -5
|-
|-
|major 2nd
| major 2nd
|4\29, 184.615 (179.31)
|4\29, 188.276
|A
|A
|[[9/8]], [[10/9]], [[11/10]]
|[[9/8]], [[10/9]], [[11/10]]
Line 666: Line 657:
|-
|-
|augmented 2nd
|augmented 2nd
|5\29, 230.77 (224.14)
|5\29, 235.346
|A#
| A#
|[[8/7]], [[15/13]]
|[[8/7]], [[15/13]]
| +11
| +11
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|diminished 3rd
|diminished 3rd
|6\29, 276.92 (268.97)
|6\29, 282.415
|Bff
|Bff
|[[7/6]], [[13/11]], [[33/28]]
|[[7/6]], [[13/11]], [[33/28]]
Line 678: Line 669:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 3rd
|minor 3rd
|7\29, 323.08 (313.79)
|7\29, 329.483
|Bf
|Bf
|[[135/112]], [[6/5]]
|[[135/112]], [[6/5]]
Line 684: Line 675:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 3rd
|major 3rd
|8\29, 369.23 (358.21)
|8\29, 376.553
|B
|B
|[[5/4]], [[11/9]], [[16/13]]
|[[5/4]], [[11/9]], [[16/13]]
| +6
| +6
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|augmented 3rd
| augmented 3rd
|9\29, 415.385 (403.45)
|9\29, 423.622
|B#
| B#
|[[9/7]], [[14/11]], [[33/26]]
|[[9/7]], [[14/11]], [[33/26]]
| +14
| +14
|-
|-
|diminished 4th
|diminished 4th
|10\29, 461.54 (448.28)
|10\29, 470.691
|Cf
|Cf
|[[21/16]], [[13/10]]
|[[21/16]], [[13/10]]
Line 702: Line 693:
|-
|-
|natural 4th
|natural 4th
|11\29, 507.69 (493.10)
|11\29, 517.760
|C
|C
|[[75/56]], [[4/3]]
|[[75/56]], [[4/3]]
Line 708: Line 699:
|-
|-
|augmented 4th
|augmented 4th
|12\29, 553.85 (537.93)
|12\29, 564.829
|C#
|C#
|[[11/8]], [[18/13]]
|[[11/8]], [[18/13]]
| +9
| +9
|-
|-
|doubly augmented 4th, doubly diminished 5th
|doubly augmented 4th, doubly diminished 5th
|13\29, 600.00 (582.76)
|13\29, 611.898
|Cx, Qff
|Cx, Qff
|[[7/5]], [[10/7]]
|[[7/5]], [[10/7]]
Line 720: Line 711:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|diminished 5th
|diminished 5th
|14\29, 646.15 (627.59)
|14\29, 658.968
|Qf
|Qf
|[[16/11]], [[13/9]]
|[[16/11]], [[13/9]]
Line 726: Line 717:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect 5th
|perfect 5th
|15\29, 692.31 (672.41)
|15\29, 706.037
|Q
|Q
|[[112/75]], [[3/2]]
|[[112/75]], [[3/2]]
| +4
| +4
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|augmented 5th
|augmented 5th
|16\29, 738.46 (717.24)
|16\29, 753.106
|Q#
|Q#
|[[32/21]], [[20/13]]
|[[32/21]], [[20/13]]
Line 738: Line 729:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|diminished 6th
|diminished 6th
|17\29, 784.615 (762.07)
|17\29, 800.175
|Dff
|Dff
|[[11/7]], [[14/9]]
|[[11/7]], [[14/9]]
Line 744: Line 735:
|-
|-
|minor 6th
|minor 6th
|18\29, 830.77 (806.90)
|18\29, 847.244
|Df
|Df
|[[13/8]], [[8/5]]
|[[13/8]], [[8/5]]
Line 750: Line 741:
|-
|-
|major 6th
|major 6th
|19\29, 876.92 (851.725)
|19\29, 894.313
|D
|D
|[[5/3]], [[224/135]]
|[[5/3]], [[224/135]]
Line 756: Line 747:
|-
|-
|augmented 6th
|augmented 6th
|20\29, 923.08 (896.55)
| 20\29, 941.382
|D#
|D#
|[[12/7]], [[22/13]]
|[[12/7]], [[22/13]]
Line 762: Line 753:
|-
|-
|minor 7th
|minor 7th
|21\29, 969.23 (941.38)
|21\29, 988.451
|Ef
|Ef
|[[7/4]], [[26/15]]
|[[7/4]], [[26/15]]
Line 768: Line 759:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 7th
|major 7th
|22\29, 1015.385 (982.21)
|22\29, 1035.520
|E
|E
|[[9/5]], [[16/9]], [[20/11]]
|[[9/5]], [[16/9]], [[20/11]]
Line 774: Line 765:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|augmented 7th
|augmented 7th
|23\29, 1061.54 (1031.03)
|23\29, 1082.590
|E#
|E#
|[[11/6]], [[13/7]], [[15/8]], [[24/13]]
|[[11/6]], [[13/7]], [[15/8]], [[24/13]]
Line 780: Line 771:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|doubly augmented 7th, doubly diminished octave
|doubly augmented 7th, doubly diminished octave
|24\29, 1107.69 (1075.86)
|24\29, 1129.659
|Ex, Fff
|Ex, Fff
|[[21/11]], [[25/13]], [[40/21]]
|[[21/11]], [[25/13]], [[40/21]]
Line 786: Line 777:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|diminished octave
|diminished octave
|25\29, 1153.85 (1120.69)
|25\29, 1176.728
|Ff
| Ff
|[[64/33]], [[96/49]], [[35/18]], [[48/25]]
|[[64/33]], [[96/49]], [[35/18]], [[48/25]]
| -3
| -3
|-
|-
|perfect octave
|perfect octave
|26\29, 1200.00 (1165.52)
|26\29, 1223.797
|F
|F
|2/1
|2/1
Line 798: Line 789:
|-
|-
|augmented octave
|augmented octave
|27\29, 1246.15 (1210.345)
|27\29, 1270.866
|F#
|F#
|33/16, 49/24, 72/35, 25/12
|33/16, 49/24, 72/35, 25/12
Line 804: Line 795:
|-
|-
|doubly augmented octave, diminished 9th
|doubly augmented octave, diminished 9th
|28\29, 1292.31 (1255.13)
|28\29, 1317.935
|Fx, Gf
|Fx, Gf
|21/10, 44/21, 52/25
|21/10, 44/21, 52/25
Line 810: Line 801:
|}
|}
===Parahard===
===Parahard===
23edIX Neapolitan-oneiro combines the sound of the 32/15 minor ninth and the [[8/7]] whole tone. This is because 23edIX Neapolitan-oneirotonic  a large step of 218.2¢, 22edIX's superpythagorean major second, which is both a warped Pythagorean [[9/8]] whole tone and a warped [[8/7]] septimal whole tone.  
23ed11/5 Neapolitan-oneiro combines the sound of the 32/15 minor ninth and the [[8/7]] whole tone. This is because 23edIX Neapolitan-oneirotonic  a large step of 218.2¢, 22edIX's superpythagorean major second, which is both a warped Pythagorean [[9/8]] whole tone and a warped [[8/7]] septimal whole tone.  
====Intervals====
====Intervals ====
The intervals of the extended generator chain (-12 to +12 generators) are as follows in various Neapolitan-oneirotonic tunings close to 23edIX.
The intervals of the extended generator chain (-12 to +12 generators) are as follows in various Neapolitan-oneirotonic tunings close to 23edIX.
{| class="wikitable right-2 right-3 sortable"
{| class="wikitable right-2 right-3 sortable"
|-
|-
! class="unsortable" |Degree
! class="unsortable" |Degree
!Size in 23edIX
!Size in 23ed11/5
(superhard)
(superhard)
! class="unsortable" |Note name on G
! class="unsortable" |Note name on G
Line 825: Line 816:
|0\23, 0.00
|0\23, 0.00
|G
|G
|1/1
| 1/1
|0
|0
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|chroma
|chroma
|3\23, 163.63 (169.565)
|3\23, 178.044
|G#
|G#
|12/11, 11/10, 10/9
|12/11, 11/10, 10/9
Line 835: Line 826:
|-
|-
|minor 2nd
|minor 2nd
|1\23, 54.545 (56.52)
| 1\23, 59.348
|Af
|Af
|[[36/35]], [[34/33]], [[33/32]], [[32/31]]
|[[36/35]], [[34/33]], [[33/32]], [[32/31]]
| -5
| -5
|-
|-
|major 2nd
|major 2nd
|4\23, 218.18 (226.09)
| 4\23, 237.392
|A
|A
|[[9/8]], [[17/15]], [[8/7]]
|[[9/8]], [[17/15]], [[8/7]]
Line 847: Line 838:
|-
|-
|aug. 2nd
|aug. 2nd
|7\23, 381.82 (395.65)
|7\23, 415.436
|A#
|A#
|5/4
|5/4
Line 853: Line 844:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|dim. 3rd
|dim. 3rd
|2\23, 109.09 (113.04)
|2\23, 118.696
|Bf
|Bf
|16/15
|16/15
Line 859: Line 850:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 3rd
|minor 3rd
|5\23, 272.73 (282.61)
|5\23, 296.740
|B
|B
|7/6
| 7/6
| -2
| -2
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 3rd
|major 3rd
|8\23, 436.36 (452.17)
|8\23, 474.784
|B#
|B#
|9/7, 14/11
|9/7, 14/11
Line 871: Line 862:
|-
|-
|dim. 4th
|dim. 4th
|6\23, 327.27 (339.13)
|6\23, 356.088
|Cf
|Cf
|6/5
|6/5
| -7
| -7
|-
|-
|nat. 4th
| nat. 4th
|9\23, 490.91 (508.70)
|9\23, 534.132
|C
|C
|4/3
|4/3
Line 883: Line 874:
|-
|-
|aug. 4th
|aug. 4th
|12\23, 654.545 (678.26)
|12\23, 712.176
|C#
|C#
|[[16/11]], [[22/15]]
|[[16/11]], [[22/15]]
Line 889: Line 880:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|double dim. 5th
|double dim. 5th
|7\23, 381.82 (395.65)
|7\23, 415.436
|Qff
|Qff
|5/4
|5/4
Line 895: Line 886:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|dim. 5th
|dim. 5th
|10\23, 545.455 (565.22)
|10\23, 593.480
|Qf
|Qf
|[[15/11]], [[11/8]]
|[[15/11]], [[11/8]]
Line 901: Line 892:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perf. 5th
|perf. 5th
|13\23, 709.09 (734.78)
|13\23, 771.524
|Q
|Q
|3/2
| 3/2
| +4
| +4
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|aug. 5th
|aug. 5th
|16\23, 872.73 (904.35)
|16\23, 949.568
|Q#
|Q#
|5/3
|5/3
| +12
| +12
|-
|-
|dim. 6th
|dim. 6th
|11\23, 600.00 (621.74)
|11\23, 652.828
|Dff
|Dff
|[[7/5]], [[24/17]], [[17/12]], [[10/7]]
|[[7/5]], [[24/17]], [[17/12]], [[10/7]]
Line 919: Line 910:
|-
|-
|minor 6th
|minor 6th
|14\23, 763.64 (791.30)
|14\23, 830.872
|Df
|Df
|14/9, 11/7
|14/9, 11/7
| -1
| -1
|-
|-
|major 6th
| major 6th
|17\23, 927.27 (960.87)
|17\23, 1008.916
|D
|D
|12/7
| 12/7
| +7
| +7
|-
|-
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 7th
|minor 7th
|15\23, 818.18  (847.83)
|15\23, 890.220
|Ef
|Ef
|8/5
|8/5
Line 938: Line 929:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 7th
|major 7th
|18\23, 981.82 (1017.39)
|18\23, 1068.264
|E
|E
|[[7/4]], [[30/17]], [[16/9]]
|[[7/4]], [[30/17]], [[16/9]]
Line 944: Line 935:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|aug. 7th
|aug. 7th
|21\23, 1145.455 (1186.96)
|21\23, 1246.308
|E#
|E#
|[[31/16]], [[64/33]], [[33/17]], [[35/18]]
|[[31/16]], [[64/33]], [[33/17]], [[35/18]]
| +10
| +10
|-
|-
|dim. octave
| dim. octave
|19\23, 1036.36 (1073.91)
|19\23, 1127.612
|Ff
|Ff
|11/6, 20/11, 9/5
| 11/6, 20/11, 9/5
| -11
| -11
|-
|-
|perf. octave
|perf. octave
|22\23, 1200.00 (1243.48)
|22\23, 1305.656
|F
|F
|2/1
|2/1
| -3
| -3
|-
|-
|aug. octave
| aug. octave
|25\23, 1363.64 (1413.04)
|25\23, 1483.700
|F#
|F#
|24/11, 11/5, 20/9
|24/11, 11/5, 20/9
Line 969: Line 960:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|dim. 8-step
|dim. 8-step
|20\23, 1090.91 (1130.435)
|20\23, 1186.960
|Gf
|Gf
|15/8
|15/8
| -8
| -8
|}
|}
===Ultrahard===
===Ultrahard===
[[Archytas clan#Ultrapyth|Ultrapythagorean]] Neapolitan-oneirotonic is a rank-2 temperament in the [[Step ratio|pseudopaucitonic]] range. It represents the [[harmonic entropy]] minimum of the Neapolitan-oneirotonic spectrum where [[7/4]] is the major seventh.
[[Archytas clan#Ultrapyth|Ultrapythagorean]] Neapolitan-oneirotonic is a rank-2 temperament in the [[Step ratio|pseudopaucitonic]] range. It represents the [[harmonic entropy]] minimum of the Neapolitan-oneirotonic spectrum where [[7/4]] is the major seventh.


In the broad sense, Ultrapyth can be viewed as any tuning that divides a 16/7 into 2 equal parts. 23edIX, 28edIX and 33edIX can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18edIX and true Buzzard in terms of harmonies. 38edIX & 43edIX are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but 48edIX is where it really comes into its own in terms of harmonies, providing not only excellent 7:8:9 melodies, but also [[5/4]] and [[The_Archipelago|archipelago]] harmonies, as by shifting one whole tone done a comma, it shifts from [[The Archipelago|archipelago]] to septimal harmonies.
In the broad sense, Ultrapyth can be viewed as any tuning that divides a 16/7 into 2 equal parts. 23ed11/5, 28ed11/5 and 33ed11/5 can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18ed11/5 and true Buzzard in terms of harmonies. 38ed11/5 & 43ed11/5 are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but 48ed11/5 is where it really comes into its own in terms of harmonies, providing not only excellent 7:8:9 melodies, but also [[5/4]] and [[The_Archipelago|archipelago]] harmonies, as by shifting one whole tone done a comma, it shifts from [[The Archipelago|archipelago]] to septimal harmonies.


Beyond that, it's a question of which intervals you want to favor. 53edIX has an essentially perfect [[7/4]], 58edIX also gives three essentially perfect chains of third-comma meantone, while 63edIX has a double chain of essentially perfect quarter-comma meantone and gives about as low overall error as 83edIX does for the basic 4:6:7 triad. But beyond 83edIX, general accuracy drops off rapidly and you might as well be playing equal pentatonic.
Beyond that, it's a question of which intervals you want to favor. 53ed11/5 has an essentially perfect [[7/4]], 58ed11/5 also gives three essentially perfect chains of third-comma meantone, while 63ed11/5 has a double chain of essentially perfect quarter-comma meantone and gives about as low overall error as 83edIX does for the basic 4:6:7 triad. But beyond 83ed11/5, general accuracy drops off rapidly and you might as well be playing equal pentatonic.


The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various ultrapyth tunings.
The sizes of the generator, large step and small step of Neapolitan-oneirotonic are as follows in various ultrapyth tunings.
Line 985: Line 976:
|-
|-
!
!
!38edIX
!38ed11/5
!53edIX
!53ed11/5
!63edIX
!63ed11/5
!Optimal ([[POTE|PNTE]]) Ultrapyth tuning
!Optimal ([[POTE|PNTE]]) Ultrapyth tuning
!JI intervals represented (2.3.5.7.13 subgroup)
!JI intervals represented (2.3.5.7.13 subgroup)
|-
|-
|generator (g)
|generator (g)
|15\38, 486.49  (513.16)
|15\38, 538.817
|21\53, 484.615 (515.09)
| 21\53, 540.850
|25\63, 487.87 (515.87)
|25\63, 541.668
|484.07 (515.52)
|484.07
|4/3
|4/3
|-
|-
|L (3g - minor 9th)
|L (3g - 11/5)
|7/38, 227.03 (239,47)
|7/38, 251.448
|10/53, 230.77 (245.28)
|10/53, 257.548
|12/63, 232.26 (247.62)
|12/63, 260.001
|231.51 (246.55)
|231.51
|8/7
|8/7
|-
|-
|s (-5g + 2 minor 9ths)
|s (-5g + 2 11/5s)
|1/38, 32.43 (34.21)
|1/38, 35.921
|1/53, 23.08 (24.53)
|1/53, 25.755
|1/63, 19.355 (20.635)
|1/63, 21.667
|21.05 (22.41)
|21.05
|50/49 81/80 91/90
|50/49 81/80 91/90
|}
|}
Line 1,017: Line 1,008:
|-
|-
!Degree
!Degree
!Size in 38edIX
!Size in 38ed11/5
!Size in 53edIX
!Size in 53ed11/5
!Size in 63edIX
!Size in 63ed11/5
!Size in PNTE tuning
!Size in PNTE tuning
!Note name on G
!Note name on G
Line 1,034: Line 1,025:
|0
|0
|-
|-
|2
| 2
|7/38, 227.03 (239.47)
|7/38, 251.448
|10/53, 230.77 (245.28)
|10/53, 257.548
|12/63, 232.26 (247.62)
|12/63, 260.001
|231.51 (246.55)
|231.51
|A
|A
|8/7
|8/7
| +3
| +3
|-
|-
|3
|3
|14\38, 454.05 (478.95)
|14\38, 502.896
|20\53, 461.54 (490.57)
|20\53, 515.096
|24\63, 464.52 (495.24)
|24\63, 520.002
|463.03 (293.10)
|463.03
|B
|B
|13/10, 21/16
|13/10, 21/16
Line 1,053: Line 1,044:
|-
|-
|4
|4
|15\38, 486.49  (513.16)
|15\38, 538.817
|21\53, 484.615 (515.09)
|21\53, 540.850
|25\63, 483.87 (515.87)
|25\63, 541.668
|484.07 (515.52)
|484.07
|C
|C
|4/3
|4/3
Line 1,062: Line 1,053:
|-
|-
|5
|5
|22\38, 713.51 (752.63)
|22\38, 754.344
|31\53, 715.385 (760.38)
|31\53, 798.399
|37\63, 716.13 (763.49)
|37\63, 801.669
|715.59 (762.07)
|715.59
|Q
|Q
|3/2
|3/2
Line 1,071: Line 1,062:
|-
|-
|6
|6
|29\38, 940.54 (992.105)
|29\38, 1005.793
|41\53, 946.15 (1005.66)
|41\53, 1055.947
|49\63, 948.39 (1011.11)
|49\63, 1061.670
|947.10 (1008.63)
|947.10
|D
|D
|26/15
|26/15
Line 1,080: Line 1,071:
|-
|-
|7
|7
|30\38, 972.97 (1026.32)
| 30\38, 1077.635
|42\53, 969.23 (1030.19)
| 42\53, 1081.701
|50\63, 967.74 (1031.75)
|50\63, 1083.337
|968.15 (1031.03)
|968.15
|E
|E
|7/4
|7/4
| +2
| +2
|-
|-
|8
| 8
|37\38, 1200.00 (1265.57)
|37\38, 1329.083
|52\53, 1200.00 (1275.47)
|52\53, 1339.249
|62\63, 1200.00 (1280.645)
|62\63, 1343.337
|1199.66 (1277.59)
|1199.66
|F
|F
|2/1
|2/1
Line 1,138: Line 1,129:
|}
|}
==Scale tree==
==Scale tree==
{| class="wikitable center-all"
{{MOS tuning spectrum|Scale Signature=5L 3s<11/5>}}
! colspan="12" |Normalized Generator
!Cents
!Relative Cents
!L
!s
!L/s
!Comments
|-
| colspan="3" |3\(8\7)|| || || || ||
|
|
|
| ||514.286
|487.5||1||1||1.000||
|-
|
|
| || || || colspan="3" |17\(45\40)
|
|
|
| ||510
|491.111||6||5||1.200||
|-
|
|
| || || colspan="3" |14\(37\33)||
|
|
|
| ||509.091
|491.892||5||4||1.250||
|-
|
|
| || || || colspan="3" |25\(66\59)
|
|
|
| ||508.475
|492.424||9||7||1.286||
|-
|
|
| || colspan="3" |11\(29\26)|| ||
|
|
|
| ||507.692
|493.103||4||3||1.333||
|-
|
|
| || || || colspan="3" |30\(79\71)
|
|
|
| ||507.042
|493.671||11||8||1.375||
|-
|
|
| || || colspan="3" |19\(50\45)||
|
|
|
| ||506.667
|494||7||5||1.400||
|-
|
|
| || || || colspan="3" |27\(71\64)
|
|
|
| ||506.25
|494.366||10||7||1.429||
|-
|
|
| colspan="3" |8\(21\19)|| || ||
|
|
|
| ||505.263
|495.238||3||2||1.500||L/s = 3/2
|-
|
|
| || || || colspan="3" |29\(76\69)
|
|
|
| ||504.348
|496.053||11||7||1.571||
|-
|
|
| || || colspan="3" |21\(55\50)||
|
|
|
| ||504
|496.364||8||5||1.600||
|-
|
|
| || || || colspan="3" |34\(89\81)
|
|
|
| ||503.704
|496.629||13||8||1.625||Golden Neapolitan-oneirotonic
|-
|
|
| || colspan="3" |13\(34\31)|| ||
|
|
|
| ||503.226
|497.059||5||3||1.667||
|-
|
|
| || || || colspan="3" |31\(81\74)
|
|
|
| ||502.703
|497.531||12||7||1.714||
|-
|
|
| || || colspan="3" |18\(47\43)||
|
|
|
| ||502.326
|497.872||7||4||1.750||
|-
|
|
| || || || colspan="3" |23\(60\55)
|
|
|
| ||501.818
|498.333||9||5||1.800||
|-
|
|
|
|
|
|
| colspan="3" |28\(73/67)
|
|
|
|501.4925
|498.63
|11
|6
|1.833
|
|-
|
|
|
|
|
|
|
| colspan="3" |33\(86\79)
|
|
|501.265
|498.837
|13
|7
|1.857
|
|-
|
|
|
|
|
|
|
|
| colspan="3" |38\(99\91)
|
|501.099
|498.99
|15
|8
|1.875
|
|-
|
|
|
|
|
|
|
|
|
| colspan="3" |43\(112\103)
|500.971
|499.107
|17
|9
|1.889
|
|-
|
| colspan="3" |5\(13\12)|| || || ||
|
|
|
| ||500
|500||2||1||2.000||Basic Neapolitan-oneirotonic
(generators smaller than this are proper)
|-
|
|
|
|
|
|
|
|
|
| colspan="3" |42\(109\101)
|499.01
|500.917
|17
|8
|2.125
|
|-
|
|
|
|
|
|
|
|
| colspan="3" |37\(96\89)
|
|498.876
|501.041
|15
|7
|2.143
|
|-
|
|
|
|
|
|
|
| colspan="3" |32\(83\77)
|
|
|498.701
|501.205
|13
|6
|2.167
|
|-
|
|
|
|
|
|
| colspan="3" |27\(70\65)
|
|
|
|498.4615
|501.429
|11
|5
|2.200
|
|-
|
|
| || || || colspan="3" |22\(57\53)
|
|
|
| ||498.113
|501.754||9||4||2.250||
|-
|
|
| || || colspan="3" |17\(44\41)||
|
|
|
| ||497.561
|502.273||7||3||2.333||
|-
|
|
| || || || colspan="3" |29\(75\70)
|
|
|
| ||497.143
|502.667||12||5||2.400||
|-
|
|
| || colspan="3" |12\(31\29)|| ||
|
|
|
| ||496.552
|503.226||5||2||2.500||
|-
|
|
| || || || colspan="3" |31\(80\75)
|
|
|
| ||496
|503.75||13||5||2.600||
|-
|
|
| || || colspan="3" |19\(49\46)||
|
|
|
| ||495.652
|504.082||8||3||2.667||
|-
|
|
| || || || colspan="3" |26\(67\63)
|
|
|
| ||495.238
|504.478||11||4||2.750||
|-
|
|
| colspan="3" |7\(18\17)|| || ||
|
|
|
| ||494.118
|505.556||3||1||3.000||L/s = 3/1
|-
|
|
|
|
|
|
| colspan="3" |30\(77\73)
|
|
|
|493.151
|506.4935
|13
|4
|3.250
|
|-
|
|
| || || || colspan="3" |23\(59\56)
|
|
|
| ||492.857
|506.78||10||3||3.333||
|-
|
|
| || || colspan="3" |16\(41\39)||
|
|
|
| ||492.308
|507.317||7||2||3.500||
|-
|
|
| || || || colspan="3" |25\(64\61)
|
|
|
| ||491.803
|507.8125||11||3||3.667||
|-
|
|
| || colspan="3" |9\(23\22)|| ||
|
|
|
| ||490.909
|508.696||4||1||4.000||
|-
|
|
| || || || colspan="3" |20\(51\49)
|
|
|
| ||489.796
|509.804||9||2||4.500||
|-
|
|
| || || colspan="3" |11\(28\27)||
|
|
|
| ||488.889
|510.714||5||1||5.000||
|-
|
|
|
|
|
|
| colspan="3" |24\(61\59)
|
|
|
|488.136
|511.475
|11
|2
|5.500
|
|-
|
|
| || || || colspan="3" |13\(33\32)
|
|
|
| ||487.5
|512.121||6||1||6.000||
|-
| colspan="3" |2\5|| || || || ||
|
|
|
| ||480.000
|520||1||0||→ inf||
|}
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/5L_3s_(11/5-equivalent)"