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

Revision as of 04:14, 2 June 2021

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