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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|32}}
{{ED intro}}
 
== Theory ==
== Theory ==
32edo is generally the first power-of-2 edo which can be considered to handle [[limit|low-limit]] just intonation at all. It has unambiguous mappings for [[prime]]s up to the [[11-limit]], although [[6/5]] and Pythagorean intervals are especially poorly approximated if going by the [[patent val]] instead of using [[direct approximation|inconsistent approximations]]. Since 32edo is poor at approximating primes and it is a high power of 2, both traditional [[RTT]] and temperament-agnostic [[mos]] theory are of limited usefulness in the system (though it has an [[ultrasoft]] [[smitonic]] with {{nowrap|L/s {{=}} 5/4}}). 32edo's 5:2:1 [[blackdye]] scale {{nowrap|(1 5 2 5 1 5 2 5 1 5)}}, which is melodically comparable to [[31edo]]'s 5:2:1 [[diasem]], is notable for having 412.5¢ neogothic major thirds and 450¢ naiadics in place of the traditional 5-limit and Pythagorean major thirds in 5-limit blackdye, and the 75¢ semitone in place of 16/15. The 712.5¢ sharp fifth and the 675¢ flat fifth correspond to 3/2 and [[40/27]] in 5-limit blackdye, making 5:2:1 blackdye a [[dual-fifth]] scale.
=== As a tuning of other temperaments ===
While even advocates of less-common [[edo]]s can struggle to find something about 32edo worth noting, it does provide an excellent tuning for the [[sixix]] temperament, which [[tempering out|tempers out]] the [[5-limit]] sixix comma, [[3125/2916]], using its 9\32 generator of size 337.5 cents. [[Petr Pařízek]]'s preferred generator for sixix is (128/15)<sup>(1/11)</sup>, which is 337.430 cents and which gives equal error to fifths and major thirds, so 32edo does sixix about as well as sixix can be done. It also can be used (with the 9\32 generator) to tune [[mohavila]], an 11-limit temperament which does not temper out sixix.
While even advocates of less-common [[edo]]s can struggle to find something about 32edo worth noting, it does provide an excellent tuning for the [[sixix]] temperament, which [[tempering out|tempers out]] the [[5-limit]] sixix comma, [[3125/2916]], using its 9\32 generator of size 337.5 cents. [[Petr Pařízek]]'s preferred generator for sixix is (128/15)<sup>(1/11)</sup>, which is 337.430 cents and which gives equal error to fifths and major thirds, so 32edo does sixix about as well as sixix can be done. It also can be used (with the 9\32 generator) to tune [[mohavila]], an 11-limit temperament which does not temper out sixix.


It also tempers out [[2048/2025]] in the 5-limit, and [[50/49]] with [[64/63]] in the [[7-limit]], which means it [[support]]s [[pajara]], with a very sharp fifth of 712.5 cents which could be experimented with by those with a penchant for fifths even sharper than the fifth of [[27edo]]; this fifth is in fact very close to the [[minimax tuning]] of the pajara extension [[Diaschismic family#Pajaro|pajaro]], using the 32f val. In the 11-limit it provides the [[optimal patent val]] for the {{nowrap|15 &amp; 32}} temperament, tempering out [[55/54]], 64/63, and [[245/242]].
It also tempers out [[2048/2025]] in the 5-limit, and [[50/49]] with [[64/63]] in the [[7-limit]], which means it [[support]]s [[pajara]], with a very sharp fifth of 712.5 cents which could be experimented with by those with a penchant for fifths even sharper than the fifth of [[27edo]]; this fifth is in fact very close to the [[minimax tuning]] of the pajara extension [[Diaschismic family #Pajaro|pajaro]], using the 32f val. In the 11-limit it provides the [[optimal patent val]] for the {{nowrap| 15 & 17 }} temperament, tempering out [[55/54]], 64/63, and [[245/242]].


The sharp fifth of 32edo can be used to generate a very unequal [[archy]] (specifically [[subgroup temperaments#Oceanfront|Oceanfront]]) [[5L 2s|diatonic scale]], with a [[diatonic semitone]] of 5 steps and a [[chromatic semitone]] of only 1. The "major third" (which can sound like both a major third and a flat fourth depending on context) is an interseptimal interval of 450¢, approximating [[9/7]] and [[13/10]], and the minor third is 262.5¢, approximating [[7/6]]. Because of the unequalness of the scale, the minor second is reduced to a fifth-tone, but it still strongly resembles "normal" diatonic music, especially for darker [[mode]]s. In addition to the sharp fifth, there is an alternative [[mavila|mavila-like]] flat fifth of 675¢ (inherited from [[16edo]]), but it is much more inaccurate and discordant than the sharp fifth.
The sharp fifth of 32edo can be used to generate a very unequal [[archy]] (specifically [[oceanfront]]) [[5L 2s|diatonic scale]], with a [[diatonic semitone]] of 5 steps and a [[chromatic semitone]] of only 1. The diatonic [[major third]] (which can sound like both a major third and a flat fourth depending on context) is an interseptimal interval of 450¢, approximating [[9/7]] and [[13/10]], and the minor third is 262.5¢, approximating [[7/6]]. Because of the unequalness of the scale, the minor second is reduced to a fifth-tone, but it still strongly resembles "normal" diatonic music, especially for darker [[mode]]s. In addition to the sharp fifth, there is an alternative [[mavila|mavila-like]] flat fifth of 675{{c}} (inherited from [[16edo]]), but it is much more inaccurate and discordant than the sharp fifth.


It is generally the first power-of-2 edo which can be considered to handle [[low-limit JI]] at all. It has unambiguous mappings for primes up to the [[11-limit]], although [[6/5]] and Pythagorean intervals are especially poorly approximated if going by the [[patent val]] instead of using [[direct approximation|inconsistent approximations]]. Since 32edo is poor at approximating primes and it is a high power of 2, both traditional [[RTT]] and temperament-agnostic [[mos]] theory are of limited usefulness in the system (though it has an [[ultrasoft]] [[smitonic]] with {{nowrap|L/s {{=}} 5/4}}). 32edo's 5:2:1 [[blackdye]] scale {{nowrap|(1 5 2 5 1 5 2 5 1 5)}}, which is melodically comparable to [[31edo]]'s 5:2:1 [[diasem]], is notable for having 412.5¢ neogothic major thirds and 450¢ naiadics in place of the traditional 5-limit and Pythagorean major thirds in 5-limit blackdye, and the 75¢ semitone in place of 16/15. The 712.5¢ sharp fifth and the 675¢ flat fifth correspond to 3/2 and [[40/27]] in 5-limit blackdye, making 5:2:1 blackdye a [[dual-fifth]] scale.
=== Odd harmonics ===
{{Harmonics in equal|32}}


=== Harmonics ===
=== Subsets and supersets ===
{{Harmonics in equal|32}}
Since 32 factors into primes as 2<sup>5</sup>, 32edo contains subset edos {{EDOs| 2, 4, 8, and 16 }}.


== Intervals ==
== Intervals ==
Line 18: Line 23:
! Degree
! Degree
! Cents
! Cents
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and downs notation]]
! 13-limit Ratios
! 13-limit Ratios
! Other
! Other
Line 285: Line 290:


== Notation ==
== Notation ==
===Sagittal notation===
=== Ups and downs notation ===
This notation uses the same sagittal sequence as [[25edo#Sagittal notation|25-EDO]], and is a subset of the notation for [[64edo#Sagittal notation|64b]].
32edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
====Evo flavor====
{{Sharpness-sharp5a}}
 
Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
 
{{Sharpness-sharp5}}
 
If the arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best denoted using triple arrows.


=== Sagittal notation ===
This notation uses the same sagittal sequence as [[25edo#Sagittal notation|25-EDO]], and is a subset of the notation for [[64edo#Second-best fifth notation|64b]].
==== Evo flavor ====
<imagemap>
<imagemap>
File:32-EDO_Evo_Sagittal.svg
File:32-EDO_Evo_Sagittal.svg
Line 298: Line 313:
</imagemap>
</imagemap>


====Revo flavor====
==== Revo flavor ====
 
<imagemap>
<imagemap>
File:32-EDO_Revo_Sagittal.svg
File:32-EDO_Revo_Sagittal.svg
Line 310: Line 324:


== Approximation to JI ==
== Approximation to JI ==
=== Zeta function ===
{{Q-odd-limit intervals|32}}
 
=== Zeta properties ===
Below is a plot of the [[Zeta]] function, showing how its peak (ie most negative) value is shifted above 32, corresponding to a zeta tuning with octaves flattened to 1197.375 cents. This will improve the fifth, at the expense of the third.
Below is a plot of the [[Zeta]] function, showing how its peak (ie most negative) value is shifted above 32, corresponding to a zeta tuning with octaves flattened to 1197.375 cents. This will improve the fifth, at the expense of the third.


[[File:plot32.png|alt=plot32.png|plot32.png]]
[[File:plot32.png|alt=plot32.png|plot32.png]]
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{Monzo| 51 -32 }}
| {{Mapping| 32 51 }}
| -3.327
| 3.32
| 8.87
|-
| 2.3.7
| 64/63, 46118408/43046721
| {{Mapping| 32 51 90 }}
| -2.950
| 2.76
| 7.38
|- style="border-top: double;"
| 2.3.5
| 648/625, 20480/19683
| {{Mapping| 32 51 75 }} (32c)
| -5.965
| 4.61
| 12.3
|-
| 2.3.5.7
| 64/63, 245/243, 392/375
| {{Mapping| 32 51 75 90 }} (32c)
| -5.027
| 4.31
| 11.5
|- style="border-top: double;"
| 2.3.5
| 2048/2025, 3125/2916
| {{Mapping| 32 51 74 }} (32)
| +0.177
| 4.72
| 12.6
|-
| 2.3.5.7
| 50/49, 64/63, 3125/2916
| {{Mapping| 32 51 75 90 }} (32)
| -1.008
| 4.15
| 11.1
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>ratio*
! Temperaments
|-
| 1
| 1\32
| 37.5
| 49/48
| [[Slender]] (32)
|-
| 1
| 9\32
| 262.5
| 7/6
| [[Septimin]] (32f)
|-
| 1
| 9\32
| 337.5
| 6/5
| [[Sixix]] (32f)
|-
| 1
| 13\32
| 487.5
| 4/3
| [[Superpyth]] (32c, 7-limit) / [[ultrapyth]] (32) / [[quasiultra]] (32)
|-
| 1
| 15\32
| 562.5
| 7/5
| [[Progress]] (32cf)
|-
| 2
| 13\32
| 487.5
| 4/3
| [[Pajara]] (32, 7-limit)
|-
| 8
| 14\33<br>(1\32)
| 487.5<br>(37.5)
| 4/3<br>(36/35)
| [[Octonion]] (32cf)
|-
| 16
| 14\33<br>(1\32)
| 487.5<br>(37.5)
| 4/3<br>(45/44)
| [[Sedecic]] (32)
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct


== Delta-rational harmony ==
== Delta-rational harmony ==
The tables below show chords that approximate 3-integer-limit [[delta-rational]] chords with least-squares error less than 0.0015.  
The tables below show chords that approximate 3-integer-limit [[delta-rational]] chords with least-squares error less than 0.0015.  
=== Fully delta-rational triads ===
 
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
{| class="wikitable mw-collapsible mw-collapsed sortable"
!|Steps
|+ style="font-size: 105%; white-space: nowrap;" | Fully delta-rational triads
!|Delta signature
!|Least-squares error
|-
|-
|0,1,2
! Steps
! Delta signature
! Least-squares error
|-
| 0,1,2
| +1+1
| +1+1
|0.00023
| 0.00023
|-
|-
|0,1,3
| 0,1,3
| +1+2
| +1+2
|0.00051
| 0.00051
|-
|-
|0,1,4
| 0,1,4
| +1+3
| +1+3
|0.00083
| 0.00083
|-
|-
|0,2,3
| 0,2,3
| +2+1
| +2+1
|0.00041
| 0.00041
|-
|-
|0,2,4
| 0,2,4
| +1+1
| +1+1
|0.00092
| 0.00092
|-
|-
|0,3,4
| 0,3,4
| +3+1
| +3+1
|0.00060
| 0.00060
|-
|-
|0,3,11
| 0,3,11
| +1+3
| +1+3
|0.00014
| 0.00014
|-
|-
|0,4,11
| 0,4,11
| +1+2
| +1+2
|0.00087
| 0.00087
|-
|-
|0,5,8
| 0,5,8
| +3+2
| +3+2
|0.00076
| 0.00076
|-
|-
|0,6,16
| 0,6,16
| +1+2
| +1+2
|0.00076
| 0.00076
|-
|-
|0,8,26
| 0,8,26
| +1+3
| +1+3
|0.00016
| 0.00016
|-
|-
|0,9,23
| 0,9,23
| +1+2
| +1+2
|0.00000
| 0.00000
|-
|-
|0,12,17
| 0,12,17
| +2+1
| +2+1
|0.00004
| 0.00004
|-
|-
|0,13,20
| 0,13,20
| +3+2
| +3+2
|0.00008
| 0.00008
|-
|-
|0,15,21
| 0,15,21
| +2+1
| +2+1
|0.00007
| 0.00007
|-
|-
|0,18,27
| 0,18,27
| +3+2
| +3+2
|0.00000
| 0.00000
|-
|-
|0,22,30
| 0,22,30
| +2+1
| +2+1
|0.00030
| 0.00030
|-
|-
|0,25,31
| 0,25,31
| +3+1
| +3+1
|0.00062
| 0.00062
|}
|}


=== Partially delta-rational tetrads ===
{| class="wikitable mw-collapsible mw-collapsed sortable"
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
|+ style="font-size: 105%; white-space: nowrap;" | Partially delta-rational tetrads
!|Steps
!|Delta signature
!|Least-squares error
|-
|-
|0,1,2,3
! Steps
! Delta signature
! Least-squares error
|-
| 0,1,2,3
| +1+?+1
| +1+?+1
|0.00056
| 0.00056
|-
|-
|0,1,2,4
| 0,1,2,4
| +1+?+2
| +1+?+2
|0.00100
| 0.00100
|-
|-
|0,1,3,4
| 0,1,3,4
| +1+?+1
| +1+?+1
|0.00085
| 0.00085
|-
|-
|0,1,16,17
| 0,1,16,17
| +2+?+3
| +2+?+3
|0.00091
| 0.00091
|-
|-
|0,1,16,18
| 0,1,16,18
| +1+?+3
| +1+?+3
|0.00093
| 0.00093
|-
|-
|0,1,17,18
| 0,1,17,18
| +2+?+3
| +2+?+3
|0.00058
| 0.00058
|-
|-
|0,1,17,19
| 0,1,17,19
| +1+?+3
| +1+?+3
|0.00051
| 0.00051
|-
|-
|0,1,18,19
| 0,1,18,19
| +2+?+3
| +2+?+3
|0.00025
| 0.00025
|-
|-
|0,1,18,20
| 0,1,18,20
| +1+?+3
| +1+?+3
|0.00009
| 0.00009
|-
|-
|0,1,19,20
| 0,1,19,20
| +2+?+3
| +2+?+3
|0.00010
| 0.00010
|-
|-
|0,1,19,21
| 0,1,19,21
| +1+?+3
| +1+?+3
|0.00034
| 0.00034
|-
|-
|0,1,20,21
| 0,1,20,21
| +2+?+3
| +2+?+3
|0.00045
| 0.00045
|-
|-
|0,1,20,22
| 0,1,20,22
| +1+?+3
| +1+?+3
|0.00078
| 0.00078
|-
|-
|0,1,21,22
| 0,1,21,22
| +2+?+3
| +2+?+3
|0.00081
| 0.00081
|-
|-
|0,1,30,31
| 0,1,30,31
| +1+?+2
| +1+?+2
|0.00076
| 0.00076
|-
|-
|0,2,3,4
| 0,2,3,4
| +2+?+1
| +2+?+1
|0.00082
| 0.00082
|-
|-
|0,2,6,11
| 0,2,6,11
| +1+?+3
| +1+?+3
|0.00077
| 0.00077
|-
|-
|0,2,7,12
| 0,2,7,12
| +1+?+3
| +1+?+3
|0.00009
| 0.00009
|-
|-
|0,2,8,13
| 0,2,8,13
| +1+?+3
| +1+?+3
|0.00097
| 0.00097
|-
|-
|0,2,12,13
| 0,2,12,13
| +3+?+2
| +3+?+2
|0.00072
| 0.00072
|-
|-
|0,2,12,15
| 0,2,12,15
| +1+?+2
| +1+?+2
|0.00060
| 0.00060
|-
|-
|0,2,13,14
| 0,2,13,14
| +3+?+2
| +3+?+2
|0.00032
| 0.00032
|-
|-
|0,2,13,16
| 0,2,13,16
| +1+?+2
| +1+?+2
|0.00018
| 0.00018
|-
|-
|0,2,14,15
| 0,2,14,15
| +3+?+2
| +3+?+2
|0.00009
| 0.00009
|-
|-
|0,2,14,17
| 0,2,14,17
| +1+?+2
| +1+?+2
|0.00097
| 0.00097
|-
|-
|0,2,15,16
| 0,2,15,16
| +3+?+2
| +3+?+2
|0.00050
| 0.00050
|-
|-
|0,2,16,17
| 0,2,16,17
| +3+?+2
| +3+?+2
|0.00093
| 0.00093
|-
|-
|0,2,17,21
| 0,2,17,21
| +1+?+3
| +1+?+3
|0.00061
| 0.00061
|-
|-
|0,2,18,20
| 0,2,18,20
| +2+?+3
| +2+?+3
|0.00050
| 0.00050
|-
|-
|0,2,18,22
| 0,2,18,22
| +1+?+3
| +1+?+3
|0.00025
| 0.00025
|-
|-
|0,2,19,21
| 0,2,19,21
| +2+?+3
| +2+?+3
|0.00020
| 0.00020
|-
|-
|0,2,20,22
| 0,2,20,22
| +2+?+3
| +2+?+3
|0.00091
| 0.00091
|-
|-
|0,3,4,8
| 0,3,4,8
| +2+?+3
| +2+?+3
|0.00098
| 0.00098
|-
|-
|0,3,5,9
| 0,3,5,9
| +2+?+3
| +2+?+3
|0.00007
| 0.00007
|-
|-
|0,3,7,12
| 0,3,7,12
| +1+?+2
| +1+?+2
|0.00048
| 0.00048
|-
|-
|0,3,8,13
| 0,3,8,13
| +1+?+2
| +1+?+2
|0.00071
| 0.00071
|-
|-
|0,3,9,16
| 0,3,9,16
| +1+?+3
| +1+?+3
|0.00074
| 0.00074
|-
|-
|0,3,10,17
| 0,3,10,17
| +1+?+3
| +1+?+3
|0.00057
| 0.00057
|-
|-
|0,3,17,23
| 0,3,17,23
| +1+?+3
| +1+?+3
|0.00026
| 0.00026
|-
|-
|0,3,18,19
| 0,3,18,19
| +2+?+1
| +2+?+1
|0.00082
| 0.00082
|-
|-
|0,3,18,21
| 0,3,18,21
| +2+?+3
| +2+?+3
|0.00075
| 0.00075
|-
|-
|0,3,18,22
| 0,3,18,22
| +1+?+2
| +1+?+2
|0.00025
| 0.00025
|-
|-
|0,3,19,20
| 0,3,19,20
| +2+?+1
| +2+?+1
|0.00035
| 0.00035
|-
|-
|0,3,19,21
| 0,3,19,21
| +1+?+1
| +1+?+1
|0.00019
| 0.00019
|-
|-
|0,3,19,22
| 0,3,19,22
| +2+?+3
| +2+?+3
|0.00030
| 0.00030
|-
|-
|0,3,19,23
| 0,3,19,23
| +1+?+2
| +1+?+2
|0.00094
| 0.00094
|-
|-
|0,3,20,21
| 0,3,20,21
| +2+?+1
| +2+?+1
|0.00013
| 0.00013
|-
|-
|0,3,20,22
| 0,3,20,22
| +1+?+1
| +1+?+1
|0.00066
| 0.00066
|-
|-
|0,3,21,22
| 0,3,21,22
| +2+?+1
| +2+?+1
|0.00063
| 0.00063
|-
|-
|0,3,26,31
| 0,3,26,31
| +1+?+3
| +1+?+3
|0.00016
| 0.00016
|-
|-
|0,4,5,12
| 0,4,5,12
| +1+?+2
| +1+?+2
|0.00059
| 0.00059
|-
|-
|0,4,5,15
| 0,4,5,15
| +1+?+3
| +1+?+3
|0.00060
| 0.00060
|-
|-
|0,4,8,13
| 0,4,8,13
| +2+?+3
| +2+?+3
|0.00013
| 0.00013
|-
|-
|0,4,11,20
| 0,4,11,20
| +1+?+3
| +1+?+3
|0.00049
| 0.00049
|-
|-
|0,4,12,18
| 0,4,12,18
| +1+?+2
| +1+?+2
|0.00042
| 0.00042
|-
|-
|0,4,13,14
| 0,4,13,14
| +3+?+1
| +3+?+1
|0.00079
| 0.00079
|-
|-
|0,4,13,16
| 0,4,13,16
| +1+?+1
| +1+?+1
|0.00088
| 0.00088
|-
|-
|0,4,14,15
| 0,4,14,15
| +3+?+1
| +3+?+1
|0.00035
| 0.00035
|-
|-
|0,4,14,16
| 0,4,14,16
| +3+?+2
| +3+?+2
|0.00024
| 0.00024
|-
|-
|0,4,14,17
| 0,4,14,17
| +1+?+1
| +1+?+1
|0.00024
| 0.00024
|-
|-
|0,4,15,16
| 0,4,15,16
| +3+?+1
| +3+?+1
|0.00009
| 0.00009
|-
|-
|0,4,15,17
| 0,4,15,17
| +3+?+2
| +3+?+2
|0.00060
| 0.00060
|-
|-
|0,4,16,17
| 0,4,16,17
| +3+?+1
| +3+?+1
|0.00055
| 0.00055
|-
|-
|0,4,17,25
| 0,4,17,25
| +1+?+3
| +1+?+3
|0.00058
| 0.00058
|-
|-
|0,4,19,23
| 0,4,19,23
| +2+?+3
| +2+?+3
|0.00040
| 0.00040
|-
|-
|0,4,21,26
| 0,4,21,26
| +1+?+2
| +1+?+2
|0.00030
| 0.00030
|-
|-
|0,4,23,30
| 0,4,23,30
| +1+?+3
| +1+?+3
|0.00062
| 0.00062
|-
|-
|0,5,6,9
| 0,5,6,9
| +3+?+2
| +3+?+2
|0.00013
| 0.00013
|-
|-
|0,5,7,19
| 0,5,7,19
| +1+?+3
| +1+?+3
|0.00069
| 0.00069
|-
|-
|0,5,9,17
| 0,5,9,17
| +1+?+2
| +1+?+2
|0.00047
| 0.00047
|-
|-
|0,5,10,16
| 0,5,10,16
| +2+?+3
| +2+?+3
|0.00038
| 0.00038
|-
|-
|0,5,11,13
| 0,5,11,13
| +2+?+1
| +2+?+1
|0.00067
| 0.00067
|-
|-
|0,5,11,15
| 0,5,11,15
| +1+?+1
| +1+?+1
|0.00027
| 0.00027
|-
|-
|0,5,11,22
| 0,5,11,22
| +1+?+3
| +1+?+3
|0.00052
| 0.00052
|-
|-
|0,5,12,14
| 0,5,12,14
| +2+?+1
| +2+?+1
|0.00015
| 0.00015
|-
|-
|0,5,13,15
| 0,5,13,15
| +2+?+1
| +2+?+1
|0.00099
| 0.00099
|-
|-
|0,5,15,22
| 0,5,15,22
| +1+?+2
| +1+?+2
|0.00090
| 0.00090
|-
|-
|0,5,16,26
| 0,5,16,26
| +1+?+3
| +1+?+3
|0.00034
| 0.00034
|-
|-
|0,5,19,24
| 0,5,19,24
| +2+?+3
| +2+?+3
|0.00051
| 0.00051
|-
|-
|0,5,23,29
| 0,5,23,29
| +1+?+2
| +1+?+2
|0.00015
| 0.00015
|-
|-
|0,5,24,25
| 0,5,24,25
| +3+?+1
| +3+?+1
|0.00090
| 0.00090
|-
|-
|0,5,24,27
| 0,5,24,27
| +1+?+1
| +1+?+1
|0.00085
| 0.00085
|-
|-
|0,5,25,26
| 0,5,25,26
| +3+?+1
| +3+?+1
|0.00034
| 0.00034
|-
|-
|0,5,25,27
| 0,5,25,27
| +3+?+2
| +3+?+2
|0.00011
| 0.00011
|-
|-
|0,5,25,28
| 0,5,25,28
| +1+?+1
| +1+?+1
|0.00058
| 0.00058
|-
|-
|0,5,26,27
| 0,5,26,27
| +3+?+1
| +3+?+1
|0.00023
| 0.00023
|-
|-
|0,5,26,28
| 0,5,26,28
| +3+?+2
| +3+?+2
|0.00096
| 0.00096
|-
|-
|0,5,27,28
| 0,5,27,28
| +3+?+1
| +3+?+1
|0.00081
| 0.00081
|-
|-
|0,6,9,14
| 0,6,9,14
| +1+?+1
| +1+?+1
|0.00013
| 0.00013
|-
|-
|0,6,11,18
| 0,6,11,18
| +2+?+3
| +2+?+3
|0.00020
| 0.00020
|-
|-
|0,6,12,21
| 0,6,12,21
| +1+?+2
| +1+?+2
|0.00064
| 0.00064
|-
|-
|0,6,15,18
| 0,6,15,18
| +3+?+2
| +3+?+2
|0.00025
| 0.00025
|-
|-
|0,6,18,26
| 0,6,18,26
| +1+?+2
| +1+?+2
|0.00075
| 0.00075
|-
|-
|0,6,19,25
| 0,6,19,25
| +2+?+3
| +2+?+3
|0.00062
| 0.00062
|-
|-
|0,6,20,22
| 0,6,20,22
| +2+?+1
| +2+?+1
|0.00074
| 0.00074
|-
|-
|0,6,20,24
| 0,6,20,24
| +1+?+1
| +1+?+1
|0.00046
| 0.00046
|-
|-
|0,6,20,31
| 0,6,20,31
| +1+?+3
| +1+?+3
|0.00043
| 0.00043
|-
|-
|0,6,21,23
| 0,6,21,23
| +2+?+1
| +2+?+1
|0.00025
| 0.00025
|-
|-
|0,6,24,31
| 0,6,24,31
| +1+?+2
| +1+?+2
|0.00091
| 0.00091
|-
|-
|0,7,8,12
| 0,7,8,12
| +3+?+2
| +3+?+2
|0.00097
| 0.00097
|-
|-
|0,7,8,14
| 0,7,8,14
| +1+?+1
| +1+?+1
|0.00076
| 0.00076
|-
|-
|0,7,8,24
| 0,7,8,24
| +1+?+3
| +1+?+3
|0.00043
| 0.00043
|-
|-
|0,7,9,11
| 0,7,9,11
| +3+?+1
| +3+?+1
|0.00053
| 0.00053
|-
|-
|0,7,9,12
| 0,7,9,12
| +2+?+1
| +2+?+1
|0.00018
| 0.00018
|-
|-
|0,7,9,13
| 0,7,9,13
| +3+?+2
| +3+?+2
|0.00054
| 0.00054
|-
|-
|0,7,9,20
| 0,7,9,20
| +1+?+2
| +1+?+2
|0.00020
| 0.00020
|-
|-
|0,7,10,12
| 0,7,10,12
| +3+?+1
| +3+?+1
|0.00028
| 0.00028
|-
|-
|0,7,12,20
| 0,7,12,20
| +2+?+3
| +2+?+3
|0.00010
| 0.00010
|-
|-
|0,7,14,24
| 0,7,14,24
| +1+?+2
| +1+?+2
|0.00004
| 0.00004
|-
|-
|0,7,15,29
| 0,7,15,29
| +1+?+3
| +1+?+3
|0.00028
| 0.00028
|-
|-
|0,7,17,22
| 0,7,17,22
| +1+?+1
| +1+?+1
|0.00091
| 0.00091
|-
|-
|0,7,19,26
| 0,7,19,26
| +2+?+3
| +2+?+3
|0.00073
| 0.00073
|-
|-
|0,7,22,25
| 0,7,22,25
| +3+?+2
| +3+?+2
|0.00065
| 0.00065
|-
|-
|0,7,23,26
| 0,7,23,26
| +3+?+2
| +3+?+2
|0.00086
| 0.00086
|-
|-
|0,7,27,31
| 0,7,27,31
| +1+?+1
| +1+?+1
|0.00074
| 0.00074
|-
|-
|0,7,28,30
| 0,7,28,30
| +2+?+1
| +2+?+1
|0.00044
| 0.00044
|-
|-
|0,7,29,31
| 0,7,29,31
| +2+?+1
| +2+?+1
|0.00074
| 0.00074
|-
|-
|0,8,11,23
| 0,8,11,23
| +1+?+2
| +1+?+2
|0.00070
| 0.00070
|-
|-
|0,8,11,28
| 0,8,11,28
| +1+?+3
| +1+?+3
|0.00080
| 0.00080
|-
|-
|0,8,13,22
| 0,8,13,22
| +2+?+3
| +2+?+3
|0.00070
| 0.00070
|-
|-
|0,8,14,20
| 0,8,14,20
| +1+?+1
| +1+?+1
|0.00072
| 0.00072
|-
|-
|0,8,15,19
| 0,8,15,19
| +3+?+2
| +3+?+2
|0.00057
| 0.00057
|-
|-
|0,8,16,18
| 0,8,16,18
| +3+?+1
| +3+?+1
|0.00031
| 0.00031
|-
|-
|0,8,16,19
| 0,8,16,19
| +2+?+1
| +2+?+1
|0.00023
| 0.00023
|-
|-
|0,8,16,27
| 0,8,16,27
| +1+?+2
| +1+?+2
|0.00085
| 0.00085
|-
|-
|0,8,17,19
| 0,8,17,19
| +3+?+1
| +3+?+1
|0.00063
| 0.00063
|-
|-
|0,8,19,27
| 0,8,19,27
| +2+?+3
| +2+?+3
|0.00084
| 0.00084
|-
|-
|0,8,23,28
| 0,8,23,28
| +1+?+1
| +1+?+1
|0.00055
| 0.00055
|-
|-
|0,9,10,15
| 0,9,10,15
| +3+?+2
| +3+?+2
|0.00092
| 0.00092
|-
|-
|0,9,11,30
| 0,9,11,30
| +1+?+3
| +1+?+3
|0.00012
| 0.00012
|-
|-
|0,9,13,20
| 0,9,13,20
| +1+?+1
| +1+?+1
|0.00100
| 0.00100
|-
|-
|0,9,13,26
| 0,9,13,26
| +1+?+2
| +1+?+2
|0.00021
| 0.00021
|-
|-
|0,9,17,29
| 0,9,17,29
| +1+?+2
| +1+?+2
|0.00062
| 0.00062
|-
|-
|0,9,19,28
| 0,9,19,28
| +2+?+3
| +2+?+3
|0.00096
| 0.00096
|-
|-
|0,9,20,26
| 0,9,20,26
| +1+?+1
| +1+?+1
|0.00070
| 0.00070
|-
|-
|0,9,21,25
| 0,9,21,25
| +3+?+2
| +3+?+2
|0.00055
| 0.00055
|-
|-
|0,9,22,24
| 0,9,22,24
| +3+?+1
| +3+?+1
|0.00031
| 0.00031
|-
|-
|0,9,22,25
| 0,9,22,25
| +2+?+1
| +2+?+1
|0.00034
| 0.00034
|-
|-
|0,9,23,25
| 0,9,23,25
| +3+?+1
| +3+?+1
|0.00077
| 0.00077
|-
|-
|0,10,13,17
| 0,10,13,17
| +2+?+1
| +2+?+1
|0.00066
| 0.00066
|-
|-
|0,10,14,25
| 0,10,14,25
| +2+?+3
| +2+?+3
|0.00076
| 0.00076
|-
|-
|0,10,16,21
| 0,10,16,21
| +3+?+2
| +3+?+2
|0.00034
| 0.00034
|-
|-
|0,10,18,25
| 0,10,18,25
| +1+?+1
| +1+?+1
|0.00004
| 0.00004
|-
|-
|0,10,27,29
| 0,10,27,29
| +3+?+1
| +3+?+1
|0.00080
| 0.00080
|-
|-
|0,10,27,30
| 0,10,27,30
| +2+?+1
| +2+?+1
|0.00029
| 0.00029
|-
|-
|0,10,27,31
| 0,10,27,31
| +3+?+2
| +3+?+2
|0.00077
| 0.00077
|-
|-
|0,10,28,30
| 0,10,28,30
| +3+?+1
| +3+?+1
|0.00040
| 0.00040
|-
|-
|0,11,12,18
| 0,11,12,18
| +3+?+2
| +3+?+2
|0.00040
| 0.00040
|-
|-
|0,11,12,28
| 0,11,12,28
| +1+?+2
| +1+?+2
|0.00038
| 0.00038
|-
|-
|0,11,13,16
| 0,11,13,16
| +3+?+1
| +3+?+1
|0.00049
| 0.00049
|-
|-
|0,11,14,17
| 0,11,14,17
| +3+?+1
| +3+?+1
|0.00085
| 0.00085
|-
|-
|0,11,14,26
| 0,11,14,26
| +2+?+3
| +2+?+3
|0.00077
| 0.00077
|-
|-
|0,11,16,24
| 0,11,16,24
| +1+?+1
| +1+?+1
|0.00085
| 0.00085
|-
|-
|0,11,18,22
| 0,11,18,22
| +2+?+1
| +2+?+1
|0.00057
| 0.00057
|-
|-
|0,11,21,26
| 0,11,21,26
| +3+?+2
| +3+?+2
|0.00058
| 0.00058
|-
|-
|0,11,23,30
| 0,11,23,30
| +1+?+1
| +1+?+1
|0.00023
| 0.00023
|-
|-
|0,12,15,24
| 0,12,15,24
| +1+?+1
| +1+?+1
|0.00060
| 0.00060
|-
|-
|0,12,18,21
| 0,12,18,21
| +3+?+1
| +3+?+1
|0.00014
| 0.00014
|-
|-
|0,12,21,29
| 0,12,21,29
| +1+?+1
| +1+?+1
|0.00078
| 0.00078
|-
|-
|0,12,23,27
| 0,12,23,27
| +2+?+1
| +2+?+1
|0.00036
| 0.00036
|-
|-
|0,12,25,30
| 0,12,25,30
| +3+?+2
| +3+?+2
|0.00084
| 0.00084
|-
|-
|0,13,16,21
| 0,13,16,21
| +2+?+1
| +2+?+1
|0.00057
| 0.00057
|-
|-
|0,13,19,28
| 0,13,19,28
| +1+?+1
| +1+?+1
|0.00023
| 0.00023
|-
|-
|0,13,22,25
| 0,13,22,25
| +3+?+1
| +3+?+1
|0.00019
| 0.00019
|-
|-
|0,13,27,31
| 0,13,27,31
| +2+?+1
| +2+?+1
|0.00012
| 0.00012
|-
|-
|0,14,15,30
| 0,14,15,30
| +2+?+3
| +2+?+3
|0.00004
| 0.00004
|-
|-
|0,14,17,24
| 0,14,17,24
| +3+?+2
| +3+?+2
|0.00028
| 0.00028
|-
|-
|0,14,20,25
| 0,14,20,25
| +2+?+1
| +2+?+1
|0.00048
| 0.00048
|-
|-
|0,14,26,29
| 0,14,26,29
| +3+?+1
| +3+?+1
|0.00012
| 0.00012
|-
|-
|0,15,16,20
| 0,15,16,20
| +3+?+1
| +3+?+1
|0.00002
| 0.00002
|-
|-
|0,15,24,29
| 0,15,24,29
| +2+?+1
| +2+?+1
|0.00028
| 0.00028
|-
|-
|0,16,20,31
| 0,16,20,31
| +1+?+1
| +1+?+1
|0.00042
| 0.00042
|-
|-
|0,16,24,31
| 0,16,24,31
| +3+?+2
| +3+?+2
|0.00051
| 0.00051
|-
|-
|0,17,21,29
| 0,17,21,29
| +3+?+2
| +3+?+2
|0.00090
| 0.00090
|-
|-
|0,17,22,28
| 0,17,22,28
| +2+?+1
| +2+?+1
|0.00062
| 0.00062
|-
|-
|0,17,23,27
| 0,17,23,27
| +3+?+1
| +3+?+1
|0.00039
| 0.00039
|-
|-
|0,18,25,31
| 0,18,25,31
| +2+?+1
| +2+?+1
|0.00007
| 0.00007
|-
|-
|0,18,26,30
| 0,18,26,30
| +3+?+1
| +3+?+1
|0.00001
| 0.00001
|-
|-
|0,19,21,30
| 0,19,21,30
| +3+?+2
| +3+?+2
|0.00014
| 0.00014
|-
|-
|0,20,21,26
| 0,20,21,26
| +3+?+1
| +3+?+1
|0.00032
| 0.00032
|-
|-
|0,21,24,29
| 0,21,24,29
| +3+?+1
| +3+?+1
|0.00026
| 0.00026
|}
|}


Line 1,139: Line 1,273:
; [[Petr Pařízek]]
; [[Petr Pařízek]]
* [http://micro.soonlabel.com/petr_parizek/3125_2916_temp_q32.ogg ''Sixix'']
* [http://micro.soonlabel.com/petr_parizek/3125_2916_temp_q32.ogg ''Sixix'']
; [[Billy Stiltner]]
* [https://billystiltner.bandcamp.com/album/1332 ''1332'']


; [[Chris Vaisvil]]
; [[Chris Vaisvil]]
Line 1,149: Line 1,286:
[[Category:Listen]]
[[Category:Listen]]
[[Category:Sixix]]
[[Category:Sixix]]
{{todo|add rank 2 temperaments table}}
Retrieved from "https://en.xen.wiki/w/32edo"