User:Moremajorthanmajor/20wtn: Difference between revisions

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A '''20 tone well tempered none'''t (20WTN) is related to well temperaments of [[17edo|17 edo]], but with a nonet rather than the 2/1 being constant. It  alternates [[EDF|division of the just perfect fifth]] into 10 equal parts (10EDF) with sequences of ten equal steps of 60 to 80 cents each. This will create ten equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''20 tone well tempered none'''t (20WTN) is related to well temperaments of [[17edo|17 edo]], but with a nonet rather than the 2/1 being constant. It  alternates [[EDF|division of the just perfect fifth]] into 10 equal parts (10EDF) with sequences of ten equal steps of 60 to 80 cents each. This will create ten equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.


== Intervals ==
== Optimal Intervals ==
{| class="wikitable"
{| class="wikitable"
|+
|+
!
!
!''“fifth” 2 = 600¢''
!Minimum a
!“nonet” = 1351.429¢
!Maximum a
!“nonet” = 1460¢
!Minimum b
!''“fifth” 2 = 800¢''
!Maximum b
|-
|-
!1
!1
Line 41: Line 41:
|-
|-
|11
|11
|''761.955''
|770.526
|766.902
|775.424
|777.7595
|761.955
|''781.955''
|766.241
|-
|-
|12
|12
|''821.955''
|839.098
|831.85
|848.893
|853.564
|821.955
|''861.955''
|830.526
|-
|-
|13
|13
|''881.955''
|907.669
|896.797
|921.363
|929.3685
|881.955
|''941.955''
|894.812
|-
|-
|14
|14
|''941.955''
|976.241
|961.744
|995.833
|1005.173
|941.955
|''1021.955''
|959.098
|-
|-
|15
|15
|''1001.955''
|1044.812
|1026.692
|1069.302
|1080.9775
|1001.955
|''1101.955''
|1023.384
|-
|-
|16
|16
|''1061.955''
|1113.384
|1091.639
|1142.771
|1156.782
|1061.955
|''1181.955''
|1087.669
|-
|-
|17
|17
|''1121.955''
|1181.955
|1156.5865
|1216.241
|1232.5865
|1121.955
|''1261.955''
|1151.955
|-
|-
|18
|18
|''1181.955''
|1250.526
|1221.534
|1289.71
|1308.391
|1181.955
|''1341.955''
|1216.241
|-
|-
|19
|19
|''1241.955''
|1319.098
|1286.481
|1363.2245
|1384.1955
|1241.955
|''1421.955''
|1280.526
|-
|-
|20
|20
|''1301.955''
|1387.669
|1351.429
|1467.912
|1460
|1301.955
|''1501.955''
|''1501.955''
|}
== Common Tuning ==
{| class="wikitable"
|1
|70.1955
|-
|2
|140.391
|-
|3
|210.5865
|-
|4
|280.782
|-
|5
|350.9775
|-
|6
|421.173
|-
|7
|491.3685
|-
|8
|561.564
|-
|9
|631.7595
|-
|10
|701.955
|-
|11
|772.543
|-
|12
|843.1315
|-
|13
|913.72
|-
|14
|984.308
|-
|15
|1054.896
|-
|16
|1125.484
|-
|17
|1196.073
|-
|18
|1266.661
|-
|19
|1337.245
|-
|20
|1407.837
|-
!
!Fifths
|-
|1
|702.3475
|-
|2
|702.741
|-
|3
|703.1335
|-
|4
|703.526
|-
|5
|703.9185
|-
|6
|704.311
|-
|7
|704.7115
|-
|8
|705.097
|-
|9
|705.4805
|-
|10
|705.882
|-
|11
|705.4805
|-
|12
|705.097
|-
|13
|704.7115
|-
|14
|704.311
|-
|15
|703.9185
|-
|16
|703.526
|-
|17
|703.1335
|-
|18
|702.741
|-
|19
|702.3475
|-
|20
|701.955
|}
|}

Revision as of 18:18, 30 May 2021

A 20 tone well tempered nonet (20WTN) is related to well temperaments of 17 edo, but with a nonet rather than the 2/1 being constant. It alternates division of the just perfect fifth into 10 equal parts (10EDF) with sequences of ten equal steps of 60 to 80 cents each. This will create ten equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

Optimal Intervals

Minimum a Maximum a Minimum b Maximum b
1 70.1955
2 140.391
3 210.5865
4 280.782
5 350.9775
6 421.173
7 491.3685
8 561.564
9 631.7595
10 701.955
11 770.526 775.424 761.955 766.241
12 839.098 848.893 821.955 830.526
13 907.669 921.363 881.955 894.812
14 976.241 995.833 941.955 959.098
15 1044.812 1069.302 1001.955 1023.384
16 1113.384 1142.771 1061.955 1087.669
17 1181.955 1216.241 1121.955 1151.955
18 1250.526 1289.71 1181.955 1216.241
19 1319.098 1363.2245 1241.955 1280.526
20 1387.669 1467.912 1301.955 1501.955
Retrieved from "https://en.xen.wiki/index.php?title=User:Moremajorthanmajor/20wtn&oldid=71121"