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. | ||
== | == Patent Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
! | ! | ||
!Target | !Target a | ||
!Target | !Target b | ||
!Alternating [[EDO|edo]] and *ed(9/8) | |||
! | |||
|- | |- | ||
|1 | |||
! colspan=" | ! colspan="2" |100.2793 | ||
|100 | |||
|- | |- | ||
|2 | |||
! colspan=" | ! colspan="2" |200.5586 | ||
|200 | |||
|- | |- | ||
|3 | |||
! colspan=" | ! colspan="2" |300.8379 | ||
|300 | |||
|- | |- | ||
|4 | |||
! colspan=" | ! colspan="2" |401.1171 | ||
|400 | |||
|- | |- | ||
|5 | |||
! colspan=" | ! colspan="2" |501.3964 | ||
|500 | |||
|- | |- | ||
|6 | |||
! colspan=" | ! colspan="2" |601.6757 | ||
|600 | |||
|- | |- | ||
|7 | |||
! colspan=" | ! colspan="2" |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 | |13 | ||
| | |1299.609 | ||
| | |1200 | ||
|1301.955 | |||
|- | |- | ||
|14 | |14 | ||
| | |1398.218 | ||
| | |1283.0075 | ||
| | |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 |