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.  


== Optimal Intervals ==
== Patent Intervals ==
{| class="wikitable"
{| class="wikitable"
|+
|+
!
!
!Minimum
!Target a
!Maximum
!Target b
![7\12 99.609¢]
!Alternating [[EDO|edo]] and *ed(9/8)
|-
|-
!1
|1
! colspan="3" |100.2793
! colspan="2" |100.2793
|100
|-
|-
!2
|2
! colspan="3" |200.5586
! colspan="2" |200.5586
|200
|-
|-
!3
|3
! colspan="3" |300.8379
! colspan="2" |300.8379
|300
|-
|-
!4
|4
! colspan="3" |401.1171
! colspan="2" |401.1171
|400
|-
|-
!5
|5
! colspan="3" |501.3964
! colspan="2" |501.3964
|500
|-
|-
!6
|6
! colspan="3" |601.6757
! colspan="2" |601.6757
|600
|-
|-
!7
|7
! colspan="3" |701.955
! colspan="2" |701.955
|700
|-
|-
|8
|8
|797.955
|804.8121
|801.564
|801.564
|784.9625
|800
|-
|-
|9
|9
|893.955
|907.6692
|901.173
|901.173
|867.97
|900
|-
|-
|10
|10
|989.955
|1010.5264
|1000.782
|1000.782
|950.9775
|1000
|-
|-
|11
|11
|1085.955
|1113.3836
|1101.391
|1101.391
|1033.985
|1100
|-
|-
|12
|12
|1181.955
|1200
|1216.2407
|1116.9925
|1200
|1200
|-
|-
|13
|13
|1277.955
|1299.609
|1319.0979
|1200
|1300.9775
|1301.955
|-
|-
|14
|14
|1373.955
|1398.218
|1421.955
|1283.0075
|1401.955
|1403.91
|}
|}
[[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