User:Moremajorthanmajor/24wtn: Difference between revisions

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A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. It alternates [[EDF|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.


==Optimal Intervals==
==Patent Intervals==
{| class="wikitable"
{| class="wikitable"
|+
|+
!
!
!Minimum a
!Target a
!Maximum a
!Target b
!Minimum b
!Alternating [[edo]] and *ed(9/8) a
!Maximum b
!Alternating edo and *ed(9/8) b
|-
|-
!1
!1
! colspan="4" |58.49625
! colspan="2" |58.49625
|60
|57.1429
|-
|-
!2
!2
! colspan="4" |116.9925
! colspan="2" |116.9925
|120
|114.2857
|-
|-
!3
!3
! colspan="4" |175.48875
! colspan="2" |175.48875
|180
|171.4286
|-
|-
!4
!4
! colspan="4" |233.985
! colspan="2" |233.985
|240
|228.5714
|-
|-
!5
!5
! colspan="4" |292.48125
! colspan="2" |292.48125
|300
|285.7143
|-
|-
!6
!6
! colspan="4" |350.9775
! colspan="2" |350.9775
|360
|342.8571
|-
|-
!7
!7
! colspan="4" |409.47375
! colspan="2" |409.47375
|420
|400.00
|-
|-
!8
!8
! colspan="4" |467.97
! colspan="2" |467.97
|480
|457.1429
|-
|-
!9
!9
! colspan="4" |526.46625
! colspan="2" |526.46625
|540
|514.2857
|-
|-
!10
!10
! colspan="4" |584.9625
! colspan="2" |584.9625
|600
|571.4286
|-
|-
!11
!11
! colspan="4" |643.45875
! colspan="2" |643.45875
|660
|628.5714
|-
|-
!12
!12
! colspan="4" |701.955
! colspan="2" |701.955
|720
|685.7143
|-
|-
|13
|13
|761.955
|764.2106
|766.2407
|757.2933
|755.2883
|780
|759.0979
|742.8571
|-
|-
|14
|14
|821.955
|826.466
|830.5264
|812.6317
|808.6117
|840
|816.2407
|800.00
|-
|-
|15
|15
|881.955
|888.7219
|894.8121
|867.97
|861.955
|900
|873.3836
|857.1429
|-
|-
|16
|16
|941.955
|950.9775
|959.0979
|923.3083
|915.2883
|960
|930.5264
|914.285
|-
|-
|17
|17
|1001.955
|1013.2331
|1023.3836
|978.6467
|968.6117
|1020
|987.6693
|971.4286
|-
|-
|18
|18
|1061.955
|1075.48875
|1087.6693
|1033.985
|1021.955
|1080
|1044.8121
|1028.5714
|-
|-
|19
|19
|1121.955
|1137.7444
|1151.955
|1089.3233
|1075.2883
|1140
|1101.955
|1085.7143
|-
|-
|20
|20
|1181.955
|1200
|1216.2407
|1144.6617
|1128.6117
|1200.000
|1159.0979
|1142.8571
|-
|-
|21
|21
|1241.955
|1262.2556
|1280.5264
|1200
|1181.955
|1250.9775
|1216.2407
|1200.000
|-
|-
|22
|22
|1324.511
|1255.3383
|1301.955
|1301.955
|1344.8121
|1267.97
|1235.2883
|1273.3836
|-
|-
|23
|23
|1361.955
|1386.7669
|1409.0907
|1310.6767
|1288.6117
|1352.9325
|1330.5264
|1333.94
|-
|-
|24
|24
|1441.955
|1449.0225
|1473.3836
|1366.015
|1341.955
! colspan="2" |1403.91
|1387.6693
|}
|}
[[Category:Well tempered nonet]]

Latest revision as of 09:31, 1 September 2025

A 24 tone well tempered nonet (24WTN) is related to well temperaments of 20edo and 21edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

Patent Intervals

Target a Target b Alternating edo and *ed(9/8) a Alternating edo and *ed(9/8) b
1 58.49625 60 57.1429
2 116.9925 120 114.2857
3 175.48875 180 171.4286
4 233.985 240 228.5714
5 292.48125 300 285.7143
6 350.9775 360 342.8571
7 409.47375 420 400.00
8 467.97 480 457.1429
9 526.46625 540 514.2857
10 584.9625 600 571.4286
11 643.45875 660 628.5714
12 701.955 720 685.7143
13 764.2106 757.2933 780 742.8571
14 826.466 812.6317 840 800.00
15 888.7219 867.97 900 857.1429
16 950.9775 923.3083 960 914.285
17 1013.2331 978.6467 1020 971.4286
18 1075.48875 1033.985 1080 1028.5714
19 1137.7444 1089.3233 1140 1085.7143
20 1200 1144.6617 1200.000 1142.8571
21 1262.2556 1200 1250.9775 1200.000
22 1324.511 1255.3383 1301.955 1267.97
23 1386.7669 1310.6767 1352.9325 1333.94
24 1449.0225 1366.015 1403.91
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