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=== Harmonics ===
=== Harmonics ===
It 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.
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.
{{Harmonics in equal|32}}
{{Harmonics in equal|32}}


Line 284: Line 284:


== Notation ==
== Notation ==
===Sagittal notation===
=== 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]].
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====


==== Evo flavor ====
<imagemap>
<imagemap>
File:32-EDO_Evo_Sagittal.svg
File:32-EDO_Evo_Sagittal.svg
Line 297: Line 297:
</imagemap>
</imagemap>


====Revo flavor====
==== Revo flavor ====
 
<imagemap>
<imagemap>
File:32-EDO_Revo_Sagittal.svg
File:32-EDO_Revo_Sagittal.svg
Line 309: Line 308:


== 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]]


== Zeta properties ==
==== Zeta peak index ====
===Zeta peak index===
{| class="wikitable"
{| class="wikitable"
! colspan="3" |Tuning
! colspan="3" |Strength
! colspan="2" |Closest EDO
! colspan="2" |Integer limit
|-
|-
!ZPI
! colspan="3" | Tuning
!Steps per octave
! colspan="3" | Strength
!Step size (cents)
! colspan="2" | Closest EDO
!Height
! colspan="2" | Integer limit
!Integral
!Gap
!EDO
!Octave (cents)
!Consistent
!Distinct
|-
|-
|[[133zpi]]
! ZPI
|32.0701500181780
! Steps per octave
|37.4179727665700
! Step size (cents)
|4.471728
! Height
|0.689412
! Integral
|12.537826
! Gap
|32edo
! EDO
|1197.37512853024
! Octave (cents)
|4
! Consistent
|4
! Distinct
|-
| [[133zpi]]
| 32.0701500181780
| 37.4179727665700
| 4.471728
| 0.689412
| 12.537826
| 32edo
| 1197.37512853024
| 4
| 4
|}
|}
== 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 ===
=== Fully delta-rational triads ===
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
!|Steps
!|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 ===
=== Partially delta-rational tetrads ===
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
!|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
|}
|}


Retrieved from "https://en.xen.wiki/w/32edo"