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101edo: Difference between revisions

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autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
+todo: Please don't add trailing 5 digits! (rounding doesn't really harm and it's not really hard to calculate the "correct" values for everyone)
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Line 11: Line 11:
! Steps
! Steps
! Cents
! Cents
!Difference from 8edo
|-
|-
|13
|13
|154.455
|154.455
| +4.455¢
|-
|-
| '''25'''
|'''25'''
| '''297.030'''
|'''297.030'''
| -2.97¢
|-
|-
| '''38'''
|'''38'''
| '''451.485'''
|'''451.485'''
| +1.485¢
|-
|-
|51
|51
|605.9405
|605.9405
| +5.9405¢
|-
|-
| '''63'''
|'''63'''
| '''748.515'''
|'''748.515'''
| -1.485¢
|-
|-
|75
|75
|891.089
|891.089
| -8.911¢
|-
|-
| '''88'''
|'''88'''
| '''1045.5445'''
| '''1045.5445'''
| -4.5555¢
|}
|}


Line 37: Line 45:


{| class="wikitable"
{| class="wikitable"
! Steps
!Steps
! Cents
!Cents
!Difference from 12edo
|-
|-
|9
|9
|106.059
|106.059
| +6.059¢
|-
|-
| '''17'''
|'''17'''
| '''201.980'''
|'''201.980'''
| +1.98¢
|-
|-
|26
|26
|308.911
| 308.911
| +8.911¢
|-
|-
| '''34'''
|'''34'''
| '''403.960'''
|'''403.960'''
| +3.96¢
|-
|-
| '''42'''
|'''42'''
| '''499.010'''
|'''499.010'''
| -.99¢
|-
|-
|51
|51
|605.940
|605.9405
| +5.9405¢
|-
|-
| '''59'''
|'''59'''
| '''700.990'''
|'''700.990'''
| +.99¢
|-
|-
|68
|68
|807.921
|807.921
| +7.921¢
|-
|-
| '''76'''
|'''76'''
| '''902.970'''
|'''902.970'''
| +2.97¢
|-
|-
|85
| 85
|1009.901
|1009.901
| +9.901¢
|-
|-
| '''93'''
| '''93'''
| '''1104.950'''
|'''1104.950'''
| +4.95¢
|}
|}


Line 77: Line 97:


{| class="wikitable"
{| class="wikitable"
! Steps
!Steps
! Cents
!Cents
|-
|-
|10
|10
|118.812
|118.812
|-
|-
| '''13'''
|'''13'''
| '''154.455'''
|'''154.455'''
|-
|-
|23
|23
|273.267
|273.267
|-
|-
| '''26'''
|'''26'''
| '''308.911'''
|'''308.911'''
|-
|-
|36
|36
|427.723
|427.723
|-
|-
| '''39'''
|'''39'''
| '''463.366'''
|'''463.366'''
|-
|-
|49
|49
|582.178
|582.178
|-
|-
| '''52'''
|'''52'''
| '''617.822'''
|'''617.822'''
|-
|-
|62
|62
|736.337
|736.337
|-
|-
| '''65'''
|'''65'''
| '''772.277'''
|'''772.277'''
|-
|-
|75
|75
|891.089
|891.089
|-
|-
| '''78'''
|'''78'''
| '''926.733'''
|'''926.733'''
|-
|-
|88
| 88
|1045.5445
| 1045.5445
|-
|-
| '''91'''
| '''91'''
| '''1081.188'''
|'''1081.188'''
|}
|}


Line 126: Line 146:


{| class="wikitable"
{| class="wikitable"
! Steps
!Steps
! Cents
!Cents
|-
|-
|8
|8
|95.0495
|95.0495
|-
|-
| '''13'''
|'''13'''
| '''154.455'''
|'''154.455'''
|-
|-
|21
|21
|249.505
|249.505
|-
|-
| '''26'''
|'''26'''
| '''308.911'''
|'''308.911'''
|-
|-
|34
|34
|403.960
| 403.960
|-
|-
| '''39'''
|'''39'''
| '''463.366'''
|'''463.366'''
|-
|-
| '''44'''
|'''44'''
| '''522.772'''
|'''522.772'''
|-
|-
|52
|52
|617.822
|617.822
|-
|-
| '''57'''
|'''57'''
| '''677.228'''
|'''677.228'''
|-
|-
|65
|65
|772.277
|772.277
|-
|-
| '''70'''
|'''70'''
| '''831.683'''
|'''831.683'''
|-
|-
|78
|78
|926.733
|926.733
|-
|-
| '''83'''
|'''83'''
| '''986.139'''
|'''986.139'''
|-
|-
|91
|91
Line 172: Line 192:
|-
|-
| '''96'''
| '''96'''
| '''1045.545'''
|'''1045.545'''
|}
|}


'''7 3 7 3 7 7 3 7 3 7 3 7 7 3 7 3 7 3 7:''' ''8L3s MOS'' (Improper Sensi-11)
'''4 3 3 4 3 3 4 3 4 3 3 4 3 3 4 3 3 4 3 4 3 3 4 3 3 4 3 3 4 3:''' ''11L19s MOS'' (Improper Sensi-30, a 30-tone circulating temperament)


{| class="wikitable"
{| class="wikitable"
! Steps
!Steps
! Cents
!Cents
!Difference from 30edo
|-
|-
|7
|4
|83.168
|47.525
| +7.525¢
|-
|'''7'''
|'''83.168'''
| +3.168¢
|-
|'''10'''
|'''118.812'''
| -1.188¢
|-
|14
|166.336
| +6.336¢
|-
|'''17'''
| '''201.980'''
| +1.98¢
|-
|'''20'''
|'''237.624'''
| +7.624¢
|-
|'''24'''
|'''285.1485'''
| +5.1485¢
|-
|'''27'''
|'''320.792'''
| +.792¢
|-
|31
|368.317
| +8.317¢
|-
|'''34'''
|'''403.960'''
| +3.96¢
|-
|'''37'''
|'''439.604'''
| -.396¢
|-
|41
|487.129
| +7.129¢
|-
|-
| '''10'''
|'''44'''
| '''118.812'''
|'''527.772'''
| +7.772¢
|-
|-
|17
|'''47'''
|201.980
|'''558.416'''
| +8.416¢
|-
|-
| '''20'''
|51
| '''237.624'''
|605.9405
| +5.9405¢
|-
|-
| '''27'''
|'''54'''
| '''320.792'''
| '''641.584'''
| +1.584¢
|-
|-
|34
|'''57'''
|403.960
|'''677.228'''
| +7.228¢
|-
|-
| '''37'''
|61
| '''439.604'''
|724.7525
| +4.7525¢
|-
|-
|44
|'''64'''
|527.772
|'''760.396'''
| +.396¢
|-
|-
| '''47'''
|68
| '''558.416'''
|807.921
| +7.921¢
|-
|-
|54
|'''71'''
|641.584
|'''843.564'''
| +3.564¢
|-
|-
| '''57'''
|'''74'''
| '''677.228'''
|'''879.218'''
| -.792¢
|-
|-
| '''64'''
|78
| '''760.396'''
|926.733
| +6.733¢
|-
|-
|71
|'''81'''
|843.564
|'''962.376'''
| +2.376¢
|-
|-
| '''74'''
|'''84'''
| '''879.218'''
|'''998.020'''
| -1.98¢
|-
|-
|81
|88
|962.376
|1045.5445
| +5.5445¢
|-
|-
| '''84'''
|'''91'''
| '''998.020'''
|'''1081.188'''
| +1.188¢
|-
|-
|91
|'''94'''
|1081.188
|'''1116.842'''
| -3.158¢
|-
|-
| '''94'''
|98
| '''1116.842'''
|1164.3564
| +4.356¢
|}
|}


Line 239: Line 322:


{| class="wikitable"
{| class="wikitable"
! Steps
!Steps
! Cents
!Cents
|-
|-
| '''7'''
|
| '''83.168'''
'''7'''
|'''83.168'''
|-
|-
| '''14'''
|'''14'''
| '''166.337'''
|'''166.337'''
|-
|-
|21
|21
|249.505
| 249.505
|-
|-
| '''22'''
|'''22'''
| '''261.386'''
|'''261.386'''
|-
|-
| '''29'''
|'''29'''
| '''344.554'''
|'''344.554'''
|-
|-
| '''36'''
|'''36'''
| '''427.723'''
|'''427.723'''
|-
|-
| '''43'''
|'''43'''
| '''510.891'''
|'''510.891'''
|-
|-
| '''50'''
|'''50'''
| '''594.059'''
|'''594.059'''
|-
|-
|57
|57
|677.278
| 677.278
|-
|-
| '''58'''
|'''58'''
| '''689.119'''
|'''689.119'''
|-
|-
| '''65'''
|'''65'''
| '''772.287'''
|'''772.287'''
|-
|-
| '''72'''
|'''72'''
| '''855.446'''
|'''855.446'''
|-
|-
| '''79'''
|'''79'''
| '''938.614'''
|'''938.614'''
|-
|-
| '''86'''
|'''86'''
| '''1021.782'''
|'''1021.782'''
|-
|-
| '''93'''
|'''93'''
| '''1104.950'''
|'''1104.950'''
|-
|-
|100
|100
|1188.119
|1188.119
|}Since 101edo has a step of 11.881 cents, it also allows one to use its MOS scales as circulating temperaments. It is the first edo which truly allows one to use an 80 tone or larger MOS scale as a circulating temperament.
{| class="wikitable"
|+Circulating temperaments in 101edo
!Tones
!Pattern
!L:s
|-
|5
|[[1L 4s]]
|21:20
|-
|6
|[[5L 1s]]
|17:16
|-
|7
|[[3L 4s]]
|15:14
|-
|8
|[[5L 3s]]
|13:12
|-
|9
|[[2L 7s]]
|12:11
|-
|10
|[[1L 9s]]
|11:10
|-
|11
|2L 9s
|10:9
|-
|12
|[[4L 8s]]
|9:8
|-
|13
|[[9L 4s]]
| rowspan="2" |8:7
|-
|14
|[[2L 12s]]
|-
|15
|[[11L 4s]]
| rowspan="2" |7:6
|-
|16
|[[5L 11s]]
|-
|17
|16L 1s
| rowspan="4" |6:5
|-
|18
|11L 7s
|-
|19
|[[6L 13s]]
|-
|20
|1L 19s
|-
|21
|17L 4s
| rowspan="5" |5:4
|-
|22
|13L 9s
|-
|23
|9L 14s
|-
|24
|[[5L 19s]]
|-
|25
|1L 24s
|-
|26
|23L 3s
| rowspan="8" |4:3
|-
|27
|20L 7s
|-
|28
|17L 11s
|-
|29
|14L 15s
|-
|30
|11L 19s
|-
|31
|8L 23s
|-
|32
|5L 27s
|-
|33
|2L 31s
|-
|34
|33L 1s
| rowspan="17" |3:2
|-
|35
|31L 4s
|-
|36
|29L 7s
|-
|37
|27L 10s
|-
|38
|25L 13s
|-
|39
|23L 16s
|-
|40
|21L 19s
|-
|41
|19L 22s
|-
|42
|17L 25s
|-
|43
|15L 28s
|-
|44
|13L 31s
|-
|45
|11L 34s
|-
|46
|9L 37s
|-
|47
|7L 40s
|-
|48
|5L 43s
|-
|49
|3L 49s
|-
|50
|1L 49s
|-
|51
|50L 1s
| rowspan="30" |2:1
|-
|52
|49L 3s
|-
|53
|48L 5s
|-
|54
|47L 7s
|-
|55
|46L 9s
|-
|56
|45L 11s
|-
|57
|44L 13s
|-
|58
|43L 15s
|-
|59
|42L 17s
|-
|60
|41L 19s
|-
|61
|40L 21s
|-
|62
|39L 23s
|-
|63
|38L 25s
|-
|64
|37L 27s
|-
|65
|36L 29s
|-
|66
|35L 31s
|-
|67
|34L 33s
|-
|68
|33L 35s
|-
|69
|32L 37s
|-
|70
|31L 39s
|-
|71
|30L 41s
|-
|72
|29L 43s
|-
|73
|28L 45s
|-
|74
|27L 47s
|-
|75
|26L 49s
|-
|76
|25L 51s
|-
|77
|24L 53s
|-
|78
|23L 55s
|-
|79
|22L 57s
|-
|80
|21L 59s
|}
|}
 
==Links==
== Links ==
[http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal]
[http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal]


Retrieved from "https://en.xen.wiki/w/101edo"