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Created page with "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 pa..." |
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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 == | == Optimal Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
! | ! | ||
! | !Minimum | ||
! | !Maximum | ||
|- | |- | ||
!1 | !1 | ||
! colspan=" | ! colspan="2" |100.2793 | ||
|- | |- | ||
!2 | !2 | ||
! colspan=" | ! colspan="2" |200.5586 | ||
|- | |- | ||
!3 | !3 | ||
! colspan=" | ! colspan="2" |300.8379 | ||
|- | |- | ||
!4 | !4 | ||
! colspan=" | ! colspan="2" |401.1171 | ||
|- | |- | ||
!5 | !5 | ||
! colspan=" | ! colspan="2" |501.3964 | ||
|- | |- | ||
!6 | !6 | ||
! colspan=" | ! colspan="2" |601.6757 | ||
|- | |- | ||
!7 | !7 | ||
! colspan=" | ! colspan="2" |701.955 | ||
|- | |- | ||
|8 | |8 | ||
| | |797.955 | ||
| | |804.8121 | ||
|- | |- | ||
|9 | |9 | ||
| | |893.955 | ||
| | |907.6692 | ||
|- | |- | ||
|10 | |10 | ||
| | |989.955 | ||
| | |1010.5264 | ||
|- | |- | ||
|11 | |11 | ||
| | |1085.955 | ||
| | |1113.3836 | ||
|- | |- | ||
|12 | |12 | ||
| | |1181.955 | ||
| | |1216.2407 | ||
|- | |- | ||
|13 | |13 | ||
| | |1277.955 | ||
| | |1319.0979 | ||
|- | |- | ||
|14 | |14 | ||
| | |1373.955 | ||
| | |1421.955 | ||
|} | |} | ||
Revision as of 05:48, 30 May 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.
Optimal Intervals
| Minimum | Maximum | |
|---|---|---|
| 1 | 100.2793 | |
| 2 | 200.5586 | |
| 3 | 300.8379 | |
| 4 | 401.1171 | |
| 5 | 501.3964 | |
| 6 | 601.6757 | |
| 7 | 701.955 | |
| 8 | 797.955 | 804.8121 |
| 9 | 893.955 | 907.6692 |
| 10 | 989.955 | 1010.5264 |
| 11 | 1085.955 | 1113.3836 |
| 12 | 1181.955 | 1216.2407 |
| 13 | 1277.955 | 1319.0979 |
| 14 | 1373.955 | 1421.955 |