User:Moremajorthanmajor/14wtn: Difference between revisions

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The best '''well-tempered divisions of nonets into 14 parts''' (14WTNs) are related to classical well temperaments, but with a nonet rather than the 2/1 being constant. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.
The best '''well-tempered divisions of nonets into 14 parts''' (14WTNs) are related to classical well temperaments, but with a nonet rather than the 2/1 being constant. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.  


== Intervals ==
== Patent Intervals ==
{| class="wikitable"
{| class="wikitable"
|+
|+
!
!
!''“fifth” 2 = 600¢''
!Target a
!“nonet” = 1351.429¢
!Target b
!“nonet” = 1460¢
!Alternating [[EDO|edo]] and *ed(9/8)
!''“fifth” 2 = 800¢''
|-
|-
!1
! colspan="4" |100.2793
|-
!2
! colspan="4" |200.5586
|-
!3
! colspan="4" |300.8379
|-
!4
! colspan="4" |401.1171
|-
!5
! colspan="4" |501.3964
|-
!6
! colspan="4" |601.6757
|-
!7
! colspan="4" |701.955
|-
|8
|''787.6692''
|794.7369
|810.2471
|''816.2407''
|-
|9
|''873.3835''
|887.5189
|918.5393
|''930.5264''
|-
|10
|''959.0979''
|980.3008
|1026.8314
|''1044.8121''
|-
|11
|''1044.8121''
|1073.0828
|1135.1236
|''1159.0979''
|-
|12
|''1130.5264''
|1165.8647
|1243.4157
|''1273.3835''
|-
|13
|''1216.2407''
|1258.6466
|1351.7079
|''1387.6693''
|-
|14
|''1301.955''
|1351.429
|1460
|''1501.955''
|}
== Common Tuning ==
{| class="wikitable"
|+
|1
|1
|100.2793
! colspan="2" |100.2793
|100
|-
|-
|2
|2
|200.5586
! colspan="2" |200.5586
|200
|-
|-
|3
|3
|300.8379
! colspan="2" |300.8379
|300
|-
|-
|4
|4
|401.1171
! colspan="2" |401.1171
|400
|-
|-
|5
|5
|501.3964
! colspan="2" |501.3964
|500
|-
|-
|6
|6
|601.6757
! colspan="2" |601.6757
|600
|-
|-
|7
|7
|701.955
! colspan="2" |701.955
|700
|-
|-
|8
|8
|801.955
|801.564
|784.9625
|800
|-
|-
|9
|9
|901.955
|901.173
|867.97
|900
|-
|-
|10
|10
|1001.955
|1000.782
|950.9775
|1000
|-
|-
|11
|11
|1101.955
|1101.391
|1033.985
|1100
|-
|-
|12
|12
|1201.955
|1200
|1116.9925
|1200
|-
|-
|13
|13
|1299.609
|1200
|1301.955
|1301.955
|-
|-
|14
|14
|1401.955
|1398.218
|-
|1283.0075
!
|1403.91
!Fifths
|-
|1
|701.6757
|-
|2
|701.3964
|-
|3
|701.1171
|-
|4
|700.8379
|-
|5
|700.5586
|-
|6
|700.2793
|-
|7
|700
|-
|8
|700.2793
|-
|9
|700.5586
|-
|10
|700.8379
|-
|11
|701.1171
|-
|12
|701.3964
|-
|13
|701.6757
|-
|14
|701.955
|}
|}
[[Category:Well tempered nonet]]

Latest revision as of 09:31, 1 September 2025

The best well-tempered divisions of nonets into 14 parts (14WTNs) are related to classical well temperaments, but with a nonet rather than the 2/1 being constant. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.

Patent Intervals

Target a Target b Alternating edo and *ed(9/8)
1 100.2793 100
2 200.5586 200
3 300.8379 300
4 401.1171 400
5 501.3964 500
6 601.6757 600
7 701.955 700
8 801.564 784.9625 800
9 901.173 867.97 900
10 1000.782 950.9775 1000
11 1101.391 1033.985 1100
12 1200 1116.9925 1200
13 1299.609 1200 1301.955
14 1398.218 1283.0075 1403.91
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