Xenharmonic Wiki

30edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Consolidate rank-2 temps and commas sections
ArrowHead294 (talk | contribs)
15,218 edits
mNo edit summary
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|30}}
{{ED intro}}
== Theory ==
== Theory ==
{{Harmonics in equal|30}}
{{Harmonics in equal|30}}
Line 6: Line 6:
Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament.
Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament.
[[File:Plot30.png|alt=plot30.png|thumb|A plot of the Z function around 30.]]
[[File:Plot30.png|alt=plot30.png|thumb|A plot of the Z function around 30.]]
However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.  
However, 5\30 is 200{{c}}, which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.  


Instead of the 18\30 fifth of 720 cents, 30edo also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8.
Instead of the 18\30 fifth of 720 cents, 30edo also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8.
Line 13: Line 13:
30edo has subset edos {{EDOs|1, 2, 3, 5, 6, 10, 15}} and it is a [[largely composite]] edo.
30edo has subset edos {{EDOs|1, 2, 3, 5, 6, 10, 15}} and it is a [[largely composite]] edo.


30edo is the 3rd [[wikipedia:primorial|primorial]] edo, being the product of first three primes and thus the smallest number with three distinct prime factors. As a corollary, 30edo is the smallest EDO that supports [[perfectly balanced]] scales that are minimal and not equally spaced. See the article on perfect balance.
30edo is the 3rd {{w|primorial}} edo, being the product of first three primes and thus the smallest number with three distinct prime factors. As a corollary, 30edo is the smallest EDO that supports [[perfectly balanced]] scales that are minimal and not equally spaced. See the article on perfect balance.


== Intervals ==
== Intervals ==
Line 474: Line 474:


=== Subsets of [[Mavila]][16] ===
=== Subsets of [[Mavila]][16] ===
* Arcade (approximated from [[32afdo]]): 9 3 5 8 5
* Arcade (approximated from [[32afdo]]): 9 3 5 8 5
* [[Blackened skies]] (approximated from [[Compton]] in [[72edo]]): 8 5 2 3 2 8 2
* [[Blackened skies]] (approximated from [[Compton]] in [[72edo]]): 8 5 2 3 2 8 2
Line 491: Line 490:


=== Subsets of [[15edo]] ===
=== Subsets of [[15edo]] ===
* Augmented[6] MOS: 8 2 8 2 8 2
* Augmented[6] MOS: 8 2 8 2 8 2
* Equipentatonic (exact from [[5edo]]): 6 6 6 6 6
* Equipentatonic (exact from [[5edo]]): 6 6 6 6 6
Line 497: Line 495:


=== Other notable scales ===
=== Other notable scales ===
* Approximation of [[Pelog]] lima: 3 4 10 3 10
* Approximation of [[Pelog]] lima: 3 4 10 3 10
* [[Amiot]] scale
* [[Amiot]] scale


== 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 0.001.  
The tables below show chords that approximate 3-integer-limit [[delta-rational]] chords with least-squares error less than 0.001.
 
=== Fully delta-rational triads ===
=== Fully delta-rational triads ===
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
!|chord
!|delta signature
!|error
|-
|-
|0,1,2
! Chord
! Delta signature
! Error
|-
| 0,1,2
| +1+1
| +1+1
|0.00026
| 0.00026
|-
|-
|0,1,3
| 0,1,3
| +1+2
| +1+2
|0.00058
| 0.00058
|-
|-
|0,1,4
| 0,1,4
| +1+3
| +1+3
|0.00094
| 0.00094
|-
|-
|0,2,3
| 0,2,3
| +2+1
| +2+1
|0.00047
| 0.00047
|-
|-
|0,3,4
| 0,3,4
| +3+1
| +3+1
|0.00068
| 0.00068
|-
|-
|0,3,11
| 0,3,11
| +1+3
| +1+3
|0.00064
| 0.00064
|-
|-
|0,4,11
| 0,4,11
| +1+2
| +1+2
|0.00039
| 0.00039
|-
|-
|0,5,8
| 0,5,8
| +3+2
| +3+2
|0.00057
| 0.00057
|-
|-
|0,6,16
| 0,6,16
| +1+2
| +1+2
|0.00042
| 0.00042
|-
|-
|0,7,13
| 0,7,13
| +1+1
| +1+1
|0.00035
| 0.00035
|-
|-
|0,7,23
| 0,7,23
| +1+3
| +1+3
|0.00024
| 0.00024
|-
|-
|0,10,25
| 0,10,25
| +1+2
| +1+2
|0.00072
| 0.00072
|-
|-
|0,11,17
| 0,11,17
| +3+2
| +3+2
|0.00063
| 0.00063
|-
|-
|0,11,27
| 0,11,27
| +1+2
| +1+2
|0.00072
| 0.00072
|-
|-
|0,13,23
| 0,13,23
| +1+1
| +1+1
|0.00030
| 0.00030
|-
|-
|0,14,29
| 0,14,29
| +2+3
| +2+3
|0.00019
| 0.00019
|-
|-
|0,15,19
| 0,15,19
| +3+1
| +3+1
|0.00069
| 0.00069
|-
|-
|0,20,25
| 0,20,25
| +3+1
| +3+1
|0.00085
| 0.00085
|}
|}


=== Partially delta-rational tetrads ===
=== Partially delta-rational tetrads ===
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
{| class="mw-collapsible mw-collapsed class="wikitable sortable"
!|chord
!|delta signature
!|error
|-
|-
|0,1,2,3
! Chord
! Delta signature
! Error
|-
| 0,1,2,3
| +1+?+1
| +1+?+1
|0.00064
| 0.00064
|-
|-
|0,1,3,4
| 0,1,3,4
| +1+?+1
| +1+?+1
|0.00097
| 0.00097
|-
|-
|0,1,15,16
| 0,1,15,16
| +2+?+3
| +2+?+3
|0.00097
| 0.00097
|-
|-
|0,1,15,17
| 0,1,15,17
| +1+?+3
| +1+?+3
|0.00098
| 0.00098
|-
|-
|0,1,16,17
| 0,1,16,17
| +2+?+3
| +2+?+3
|0.00060
| 0.00060
|-
|-
|0,1,16,18
| 0,1,16,18
| +1+?+3
| +1+?+3
|0.00050
| 0.00050
|-
|-
|0,1,17,18
| 0,1,17,18
| +2+?+3
| +2+?+3
|0.00021
| 0.00021
|-
|-
|0,1,17,19
| 0,1,17,19
| +1+?+3
| +1+?+3
|0.00002
| 0.00002
|-
|-
|0,1,18,19
| 0,1,18,19
| +2+?+3
| +2+?+3
|0.00018
| 0.00018
|-
|-
|0,1,18,20
| 0,1,18,20
| +1+?+3
| +1+?+3
|0.00047
| 0.00047
|-
|-
|0,1,19,20
| 0,1,19,20
| +2+?+3
| +2+?+3
|0.00058
| 0.00058
|-
|-
|0,1,19,21
| 0,1,19,21
| +1+?+3
| +1+?+3
|0.00098
| 0.00098
|-
|-
|0,1,20,21
| 0,1,20,21
| +2+?+3
| +2+?+3
|0.00099
| 0.00099
|-
|-
|0,1,28,29
| 0,1,28,29
| +1+?+2
| +1+?+2
|0.00086
| 0.00086
|-
|-
|0,2,3,4
| 0,2,3,4
| +2+?+1
| +2+?+1
|0.00094
| 0.00094
|-
|-
|0,2,6,11
| 0,2,6,11
| +1+?+3
| +1+?+3
|0.00036
| 0.00036
|-
|-
|0,2,7,12
| 0,2,7,12
| +1+?+3
| +1+?+3
|0.00063
| 0.00063
|-
|-
|0,2,11,12
| 0,2,11,12
| +3+?+2
| +3+?+2
|0.00089
| 0.00089
|-
|-
|0,2,11,14
| 0,2,11,14
| +1+?+2
| +1+?+2
|0.00084
| 0.00084
|-
|-
|0,2,12,13
| 0,2,12,13
| +3+?+2
| +3+?+2
|0.00044
| 0.00044
|-
|-
|0,2,12,15
| 0,2,12,15
| +1+?+2
| +1+?+2
|0.00005
| 0.00005
|-
|-
|0,2,13,14
| 0,2,13,14
| +3+?+2
| +3+?+2
|0.00002
| 0.00002
|-
|-
|0,2,13,16
| 0,2,13,16
| +1+?+2
| +1+?+2
|0.00095
| 0.00095
|-
|-
|0,2,14,15
| 0,2,14,15
| +3+?+2
| +3+?+2
|0.00049
| 0.00049
|-
|-
|0,2,15,16
| 0,2,15,16
| +3+?+2
| +3+?+2
|0.00098
| 0.00098
|-
|-
|0,2,16,20
| 0,2,16,20
| +1+?+3
| +1+?+3
|0.00053
| 0.00053
|-
|-
|0,2,17,19
| 0,2,17,19
| +2+?+3
| +2+?+3
|0.00043
| 0.00043
|-
|-
|0,2,17,21
| 0,2,17,21
| +1+?+3
| +1+?+3
|0.00046
| 0.00046
|-
|-
|0,2,18,20
| 0,2,18,20
| +2+?+3
| +2+?+3
|0.00036
| 0.00036
|-
|-
|0,3,4,8
| 0,3,4,8
| +2+?+3
| +2+?+3
|0.00071
| 0.00071
|-
|-
|0,3,5,9
| 0,3,5,9
| +2+?+3
| +2+?+3
|0.00050
| 0.00050
|-
|-
|0,3,7,12
| 0,3,7,12
| +1+?+2
| +1+?+2
|0.00017
| 0.00017
|-
|-
|0,3,9,16
| 0,3,9,16
| +1+?+3
| +1+?+3
|0.00024
| 0.00024
|-
|-
|0,3,16,22
| 0,3,16,22
| +1+?+3
| +1+?+3
|0.00003
| 0.00003
|-
|-
|0,3,17,18
| 0,3,17,18
| +2+?+1
| +2+?+1
|0.00085
| 0.00085
|-
|-
|0,3,17,19
| 0,3,17,19
| +1+?+1
| +1+?+1
|0.00100
| 0.00100
|-
|-
|0,3,17,20
| 0,3,17,20
| +2+?+3
| +2+?+3
|0.00066
| 0.00066
|-
|-
|0,3,17,21
| 0,3,17,21
| +1+?+2
| +1+?+2
|0.00006
| 0.00006
|-
|-
|0,3,18,19
| 0,3,18,19
| +2+?+1
| +2+?+1
|0.00031
| 0.00031
|-
|-
|0,3,18,20
| 0,3,18,20
| +1+?+1
| +1+?+1
|0.00005
| 0.00005
|-
|-
|0,3,18,21
| 0,3,18,21
| +2+?+3
| +2+?+3
|0.00055
| 0.00055
|-
|-
|0,3,19,20
| 0,3,19,20
| +2+?+1
| +2+?+1
|0.00025
| 0.00025
|-
|-
|0,3,19,21
| 0,3,19,21
| +1+?+1
| +1+?+1
|0.00092
| 0.00092
|-
|-
|0,3,20,21
| 0,3,20,21
| +2+?+1
| +2+?+1
|0.00081
| 0.00081
|-
|-
|0,3,24,29
| 0,3,24,29
| +1+?+3
| +1+?+3
|0.00063
| 0.00063
|-
|-
|0,4,5,15
| 0,4,5,15
| +1+?+3
| +1+?+3
|0.00038
| 0.00038
|-
|-
|0,4,7,12
| 0,4,7,12
| +2+?+3
| +2+?+3
|0.00062
| 0.00062
|-
|-
|0,4,10,19
| 0,4,10,19
| +1+?+3
| +1+?+3
|0.00023
| 0.00023
|-
|-
|0,4,11,17
| 0,4,11,17
| +1+?+2
| +1+?+2
|0.00078
| 0.00078
|-
|-
|0,4,12,13
| 0,4,12,13
| +3+?+1
| +3+?+1
|0.00099
| 0.00099
|-
|-
|0,4,13,14
| 0,4,13,14
| +3+?+1
| +3+?+1
|0.00049
| 0.00049
|-
|-
|0,4,13,15
| 0,4,13,15
| +3+?+2
| +3+?+2
|0.00044
| 0.00044
|-
|-
|0,4,13,16
| 0,4,13,16
| +1+?+1
| +1+?+1
|0.00005
| 0.00005
|-
|-
|0,4,14,15
| 0,4,14,15
| +3+?+1
| +3+?+1
|0.00002
| 0.00002
|-
|-
|0,4,14,16
| 0,4,14,16
| +3+?+2
| +3+?+2
|0.00052
| 0.00052
|-
|-
|0,4,15,16
| 0,4,15,16
| +3+?+1
| +3+?+1
|0.00054
| 0.00054
|-
|-
|0,4,17,21
| 0,4,17,21
| +2+?+3
| +2+?+3
|0.00089
| 0.00089
|-
|-
|0,4,18,22
| 0,4,18,22
| +2+?+3
| +2+?+3
|0.00074
| 0.00074
|-
|-
|0,4,20,25
| 0,4,20,25
| +1+?+2
| +1+?+2
|0.00030
| 0.00030
|-
|-
|0,4,22,29
| 0,4,22,29
| +1+?+3
| +1+?+3
|0.00041
| 0.00041
|-
|-
|0,5,6,9
| 0,5,6,9
| +3+?+2
| +3+?+2
|0.00051
| 0.00051
|-
|-
|0,5,6,18
| 0,5,6,18
| +1+?+3
| +1+?+3
|0.00011
| 0.00011
|-
|-
|0,5,8,16
| 0,5,8,16
| +1+?+2
| +1+?+2
|0.00028
| 0.00028
|-
|-
|0,5,9,15
| 0,5,9,15
| +2+?+3
| +2+?+3
|0.00030
| 0.00030
|-
|-
|0,5,10,14
| 0,5,10,14
| +1+?+1
| +1+?+1
|0.00027
| 0.00027
|-
|-
|0,5,10,21
| 0,5,10,21
| +1+?+3
| +1+?+3
|0.00084
| 0.00084
|-
|-
|0,5,11,13
| 0,5,11,13
| +2+?+1
| +2+?+1
|0.00017
| 0.00017
|-
|-
|0,5,12,14
| 0,5,12,14
| +2+?+1
| +2+?+1
|0.00078
| 0.00078
|-
|-
|0,5,14,21
| 0,5,14,21
| +1+?+2
| +1+?+2
|0.00095
| 0.00095
|-
|-
|0,5,15,25
| 0,5,15,25
| +1+?+3
| +1+?+3
|0.00006
| 0.00006
|-
|-
|0,5,18,23
| 0,5,18,23
| +2+?+3
| +2+?+3
|0.00093
| 0.00093
|-
|-
|0,5,20,29
| 0,5,20,29
| +1+?+3
| +1+?+3
|0.00014
| 0.00014
|-
|-
|0,5,22,28
| 0,5,22,28
| +1+?+2
| +1+?+2
|0.00093
| 0.00093
|-
|-
|0,5,23,24
| 0,5,23,24
| +3+?+1
| +3+?+1
|0.00073
| 0.00073
|-
|-
|0,5,23,25
| 0,5,23,25
| +3+?+2
| +3+?+2
|0.00075
| 0.00075
|-
|-
|0,5,23,26
| 0,5,23,26
| +1+?+1
| +1+?+1
|0.00020
| 0.00020
|-
|-
|0,5,24,25
| 0,5,24,25
| +3+?+1
| +3+?+1
|0.00009
| 0.00009
|-
|-
|0,5,24,26
| 0,5,24,26
| +3+?+2
| +3+?+2
|0.00045
| 0.00045
|-
|-
|0,5,25,26
| 0,5,25,26
| +3+?+1
| +3+?+1
|0.00057
| 0.00057
|-
|-
|0,6,7,21
| 0,6,7,21
| +1+?+3
| +1+?+3
|0.00086
| 0.00086
|-
|-
|0,6,8,13
| 0,6,8,13
| +1+?+1
| +1+?+1
|0.00079
| 0.00079
|-
|-
|0,6,10,17
| 0,6,10,17
| +2+?+3
| +2+?+3
|0.00091
| 0.00091
|-
|-
|0,6,11,20
| 0,6,11,20
| +1+?+2
| +1+?+2
|0.00026
| 0.00026
|-
|-
|0,6,14,17
| 0,6,14,17
| +3+?+2
| +3+?+2
|0.00003
| 0.00003
|-
|-
|0,6,19,21
| 0,6,19,21
| +2+?+1
| +2+?+1
|0.00066
| 0.00066
|-
|-
|0,6,19,23
| 0,6,19,23
| +1+?+1
| +1+?+1
|0.00086
| 0.00086
|-
|-
|0,6,20,22
| 0,6,20,22
| +2+?+1
| +2+?+1
|0.00048
| 0.00048
|-
|-
|0,7,8,11
| 0,7,8,11
| +2+?+1
| +2+?+1
|0.00095
| 0.00095
|-
|-
|0,7,8,12
| 0,7,8,12
| +3+?+2
| +3+?+2
|0.00035
| 0.00035
|-
|-
|0,7,9,11
| 0,7,9,11
| +3+?+1
| +3+?+1
|0.00020
| 0.00020
|-
|-
|0,7,9,12
| 0,7,9,12
| +2+?+1
| +2+?+1
|0.00039
| 0.00039
|-
|-
|0,7,10,12
| 0,7,10,12
| +3+?+1
| +3+?+1
|0.00074
| 0.00074
|-
|-
|0,7,11,19
| 0,7,11,19
| +2+?+3
| +2+?+3
|0.00075
| 0.00075
|-
|-
|0,7,13,23
| 0,7,13,23
| +1+?+2
| +1+?+2
|0.00005
| 0.00005
|-
|-
|0,7,14,28
| 0,7,14,28
| +1+?+3
| +1+?+3
|0.00034
| 0.00034
|-
|-
|0,7,16,21
| 0,7,16,21
| +1+?+1
| +1+?+1
|0.00097
| 0.00097
|-
|-
|0,7,18,27
| 0,7,18,27
| +1+?+2
| +1+?+2
|0.00030
| 0.00030
|-
|-
|0,7,21,24
| 0,7,21,24
| +3+?+2
| +3+?+2
|0.00028
| 0.00028
|-
|-
|0,7,27,29
| 0,7,27,29
| +2+?+1
| +2+?+1
|0.00032
| 0.00032
|-
|-
|0,8,10,27
| 0,8,10,27
| +1+?+3
| +1+?+3
|0.00088
| 0.00088
|-
|-
|0,8,12,21
| 0,8,12,21
| +2+?+3
| +2+?+3
|0.00022
| 0.00022
|-
|-
|0,8,14,18
| 0,8,14,18
| +3+?+2
| +3+?+2
|0.00099
| 0.00099
|-
|-
|0,8,15,17
| 0,8,15,17
| +3+?+1
| +3+?+1
|0.00054
| 0.00054
|-
|-
|0,8,15,18
| 0,8,15,18
| +2+?+1
| +2+?+1
|0.00001
| 0.00001
|-
|-
|0,8,16,18
| 0,8,16,18
| +3+?+1
| +3+?+1
|0.00053
| 0.00053
|-
|-
|0,8,22,27
| 0,8,22,27
| +1+?+1
| +1+?+1
|0.00033
| 0.00033
|-
|-
|0,9,10,15
| 0,9,10,15
| +3+?+2
| +3+?+2
|0.00013
| 0.00013
|-
|-
|0,9,10,29
| 0,9,10,29
| +1+?+3
| +1+?+3
|0.00029
| 0.00029
|-
|-
|0,9,12,19
| 0,9,12,19
| +1+?+1
| +1+?+1
|0.00028
| 0.00028
|-
|-
|0,9,12,25
| 0,9,12,25
| +1+?+2
| +1+?+2
|0.00000
| 0.00000
|-
|-
|0,9,16,28
| 0,9,16,28
| +1+?+2
| +1+?+2
|0.00005
| 0.00005
|-
|-
|0,9,19,25
| 0,9,19,25
| +1+?+1
| +1+?+1
|0.00028
| 0.00028
|-
|-
|0,9,20,24
| 0,9,20,24
| +3+?+2
| +3+?+2
|0.00025
| 0.00025
|-
|-
|0,9,21,23
| 0,9,21,23
| +3+?+1
| +3+?+1
|0.00015
| 0.00015
|-
|-
|0,9,21,24
| 0,9,21,24
| +2+?+1
| +2+?+1
|0.00068
| 0.00068
|-
|-
|0,10,13,17
| 0,10,13,17
| +2+?+1
| +2+?+1
|0.00052
| 0.00052
|-
|-
|0,10,13,24
| 0,10,13,24
| +2+?+3
| +2+?+3
|0.00042
| 0.00042
|-
|-
|0,10,15,20
| 0,10,15,20
| +3+?+2
| +3+?+2
|0.00006
| 0.00006
|-
|-
|0,10,17,24
| 0,10,17,24
| +1+?+1
| +1+?+1
|0.00005
| 0.00005
|-
|-
|0,10,25,29
| 0,10,25,29
| +3+?+2
| +3+?+2
|0.00048
| 0.00048
|-
|-
|0,10,26,28
| 0,10,26,28
| +3+?+1
| +3+?+1
|0.00028
| 0.00028
|-
|-
|0,10,26,29
| 0,10,26,29
| +2+?+1
| +2+?+1
|0.00061
| 0.00061
|-
|-
|0,11,13,16
| 0,11,13,16
| +3+?+1
| +3+?+1
|0.00032
| 0.00032
|-
|-
|0,11,17,21
| 0,11,17,21
| +2+?+1
| +2+?+1
|0.00085
| 0.00085
|-
|-
|0,11,20,25
| 0,11,20,25
| +3+?+2
| +3+?+2
|0.00095
| 0.00095
|-
|-
|0,12,14,23
| 0,12,14,23
| +1+?+1
| +1+?+1
|0.00005
| 0.00005
|-
|-
|0,12,17,20
| 0,12,17,20
| +3+?+1
| +3+?+1
|0.00014
| 0.00014
|-
|-
|0,12,22,26
| 0,12,22,26
| +2+?+1
| +2+?+1
|0.00081
| 0.00081
|-
|-
|0,12,24,29
| 0,12,24,29
| +3+?+2
| +3+?+2
|0.00014
| 0.00014
|-
|-
|0,13,18,27
| 0,13,18,27
| +1+?+1
| +1+?+1
|0.00000
| 0.00000
|-
|-
|0,13,21,24
| 0,13,21,24
| +3+?+1
| +3+?+1
|0.00013
| 0.00013
|-
|-
|0,14,16,23
| 0,14,16,23
| +3+?+2
| +3+?+2
|0.00035
| 0.00035
|-
|-
|0,14,19,24
| 0,14,19,24
| +2+?+1
| +2+?+1
|0.00067
| 0.00067
|-
|-
|0,14,25,28
| 0,14,25,28
| +3+?+1
| +3+?+1
|0.00040
| 0.00040
|-
|-
|0,15,23,28
| 0,15,23,28
| +2+?+1
| +2+?+1
|0.00083
| 0.00083
|-
|-
|0,16,19,23
| 0,16,19,23
| +3+?+1
| +3+?+1
|0.00076
| 0.00076
|-
|-
|0,17,20,28
| 0,17,20,28
| +3+?+2
| +3+?+2
|0.00099
| 0.00099
|-
|-
|0,17,21,27
| 0,17,21,27
| +2+?+1
| +2+?+1
|0.00067
| 0.00067
|-
|-
|0,17,22,26
| 0,17,22,26
| +3+?+1
| +3+?+1
|0.00042
| 0.00042
|-
|-
|0,18,25,29
| 0,18,25,29
| +3+?+1
| +3+?+1
|0.00042
| 0.00042
|-
|-
|0,19,20,29
| 0,19,20,29
| +3+?+2
| +3+?+2
|0.00033
| 0.00033
|-
|-
|0,21,23,28
| 0,21,23,28
| +3+?+1
| +3+?+1
|0.00012
| 0.00012
|}
|}


Retrieved from "https://en.xen.wiki/w/30edo"