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69edo: Difference between revisions

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69edo approximation list is about 1/4-1/3 complete. I'm just saving to make sure I don't lose any progress.
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In the [[7-limit]] it is a [[mohajira]] system, tempering out 6144/6125, but not a septimal meantone system, as [[126/125]] maps to one step. It also supports the 12&69 temperament tempering out 3125/3087 along with [[81/80]]. In the 11-limit it tempers out [[99/98]], and supports the 31&69 variant of mohajira, identical to the standard 11-limit mohajira in [[31edo|31EDO]] but not in 69.
In the [[7-limit]] it is a [[mohajira]] system, tempering out 6144/6125, but not a septimal meantone system, as [[126/125]] maps to one step. It also supports the 12&69 temperament tempering out 3125/3087 along with [[81/80]]. In the 11-limit it tempers out [[99/98]], and supports the 31&69 variant of mohajira, identical to the standard 11-limit mohajira in [[31edo|31EDO]] but not in 69.
 
{| class="wikitable center-1 right-3"
|-
!Degree
!Name and Abbreviation
!Cents
!Approximate Ratios*
!Error (abs, [[cent|¢]])
|-
|0
|Natural Unison, 1
|0.000
|[[1/1]]
|0.000
|-
|1
|
|17.391
|
|
|-
|2
|
|34.783
|
|
|-
|3
|
|52.174
|20/19
| -1.844
|-
|4
|
|69.565
|
|
|-
|5
|
|86.957
|
|
|-
|6
|
|104.348
|17/16
| -0.608
|-
|7
|
|121.739
|15/14
|2.296
|-
|8
|
|139.130
|13/12
|0.558
|-
|9
|
|156.522
|
|
|-
|10
|
|173.913
|
|
|-
|11
|
|191.304
|19/17
| -1.253
|-
|12
|
|208.696
|9/8
|4.786
|-
|13
|
|226.087
|8/7
| -5.087
|-
|14
|
|243.478
|23/20
|1.518
|-
|15
|
|260.870
|7/6, 29/25
| -6.001, 3.920
|-
|16
|
|278.261
|27/23
|0.670
|-
|17
|
|295.652
|32/27
|1.517
|-
|18
|
|313.043
|[[6/5]]
| -2.598
|-
|19
|
|330.435
|23/19
| -0.327
|-
|20
|
|347.826
|[[11/9]]
|0.418
|-
|21
|
|365.217
|21/17
| -0.608
|-
|22
|
|382.609
|[[5/4]]
| -3.705
|-
|23
|
|400.000
|
|
|-
|24
|
|417.391
|14/11
| -0.117
|-
|25
|
|434.783
|9/7
| -0.301
|-
|26
|
|452.174
|13/10
| -2.040
|-
|27
|
|469.565
|21/16
| -1.216
|-
|28
|
|486.957
|
|
|-
|29
|
|504.348
|[[4/3]]
|6.303
|-
|30
|
|521.739
|23/17
| -1.580
|-
|31
|
|539.130
|15/11
|2.180
|-
|32
|
|556.522
|11/8, 29/21
|5.204, -2.275
|-
|33
|
|573.913
|7/5, 25/18
| -8.600, 5.196
|-
|34
|
|591.304
|31/22
| -2.413
|-
|35
|
|608.696
|10/7, 27/19
| -8.792, 0.344
|-
|36
|
|626.087
|33/23
|1.088
|-
|37
|
|643.478
|29/20
|0.215
|-
|38
|
|660.870
|19/13, 22/15
|3.884, -2.180
|-
|39
|
|678.261
|34/23, 37/25
|1.580, -0.456
|-
|40
|
|695.652
|[[3/2]]
| -6.303
|-
|41
|
|713.043
|
|
|-
|42
|
|730.435
|
|
|-
|43
|
|747.826
|
|
|-
|44
|
|765.217
|
|
|-
|45
|
|782.609
|
|
|-
|46
|
|800.000
|
|
|-
|47
|
|817.391
|
|
|-
|48
|
|834.783
|
|
|-
|49
|
|852.174
|
|
|-
|50
|
|869.565
|
|
|-
|51
|
|886.957
|
|
|-
|52
|
|904.348
|
|
|-
|53
|
|921.739
|
|
|-
|54
|
|939.130
|
|
|-
|55
|
|956.522
|
|
|-
|56
|
|973.913
|
|
|-
|57
|
|991.304
|
|
|-
|58
|
|1008.696
|
|
|-
|59
|
|1026.087
|
|
|-
|60
|
|1043.478
|
|
|-
|61
|
|1060.870
|
|
|-
|62
|
|1078.261
|
|
|-
|63
|
|1095.652
|
|
|-
|64
|
|1113.043
|
|
|-
|65
|
|1130.435
|
|
|-
|66
|
|1147.826
|
|
|-
|67
|
|1165.217
|
|
|-
|68
|
|1182.609
|
|
|-
|69
|Octave, 8
|1200.000
|[[2/1]]
|0.000
|}
<nowiki>*</nowiki>some simpler ratios listed
[[Category:meantone]]
[[Category:meantone]]
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
Retrieved from "https://en.xen.wiki/w/69edo"