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'''97.5cET''' is an [[equal-step tuning]] with steps of 97.5 [[cent]]s (or each 13th step of [[160edo]]). | '''97.5cET''' is an [[equal-step tuning]] with steps of 97.5 [[cent]]s (or each 13th step of [[160edo]]). It approximates the 9th harmonic to within 2c, and may alternatively be tuned or conceived of as [[39ed9]]. In contrast to [[12edo]], which is very similar in step size, it is not considered to approximate the octave ([[2/1]]) or perfect fifth ([[3/2]]), and has a workable, but rather (10.5c) flat approximation of their complement, the perfect fourth ([[4/3]]). It excels however in the 4/3.5/3.7/3.11/3.13/3.9 [[Just intonation subgroup|subgroup]], in which it tempers out 64/63, 100/99, 275/273, 325/324, and 572/567, for example. | ||
== Intervals == | == Intervals == | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
! Steps | ! Steps | ||
! [[Cent]]s | ! [[Cent]]s | ||
!Ratio approximated* | |||
|- | |- | ||
| 1 || 97.5 | | 1 || 97.5 | ||
|16/15, 21/20, 35/33, 55/52 | |||
|- | |- | ||
| 2 || 195.0 | | 2 || 195.0 | ||
|28/25 | |||
|- | |- | ||
| 3 || 292.5 | | 3 || 292.5 | ||
|13/11 | |||
|- | |- | ||
| 4 || 390.0 | | 4 || 390.0 | ||
|5/4 | |||
|- | |- | ||
| 5 || 487.5 | | 5 || 487.5 | ||
|4/3 | |||
|- | |- | ||
| 6 || 585.0 | | 6 || 585.0 | ||
|7/5 | |||
|- | |- | ||
| 7 || 682.5 | | 7 || 682.5 | ||
|49/33 | |||
|- | |- | ||
| 8 || 780.0 | | 8 || 780.0 | ||
|11/7 | |||
|- | |- | ||
| 9 || 877.5 | | 9 || 877.5 | ||
|5/3 | |||
|- | |- | ||
| 10 || 975.0 | | 10 || 975.0 | ||
|16/9, 7/4 | |||
|- | |- | ||
| 11 || 1072.5 | | 11 || 1072.5 | ||
|13/7 | |||
|- | |- | ||
| 12 || 1170.0 | | 12 || 1170.0 | ||
|49/25 | |||
|- | |- | ||
| 13 || 1267.5 | | 13 || 1267.5 | ||
|27/13 | |||
|- | |- | ||
| 14 || 1365.0 | | 14 || 1365.0 | ||
|11/5 | |||
|- | |- | ||
| 15 || 1462.5 | | 15 || 1462.5 | ||
|7/3 | |||
|- | |- | ||
| 16 || 1560.0 | | 16 || 1560.0 | ||
|27/11, 49/20 | |||
|- | |- | ||
| 17 || 1657.5 | | 17 || 1657.5 | ||
|13/5 | |||
|- | |- | ||
| 18 || 1755.0 | | 18 || 1755.0 | ||
|11/4 | |||
|- | |- | ||
| 19 || 1852.5 | | 19 || 1852.5 | ||
|35/12 | |||
|- | |- | ||
| 20 || 1950.0 | | 20 || 1950.0 | ||
|49/16 | |||
|- | |||
|21 | |||
|2047.5 | |||
|13/4 | |||
|} | |} | ||
<nowiki>*</nowiki>some simpler ratios, based on treating 97.5cET as a 4/3.5/3.7/3.11/3.13/3.9 subgroup temperament; other approaches are possible. | |||
== Music == | == Music == | ||
* [https://soundcloud.com/ | * [https://soundcloud.com/lillianhearne/strange-waves-1 Strange Waves] by [[Lillian Hearne]] | ||
* [https://soundcloud.com/ | * [https://soundcloud.com/lillianhearne/blues-975 Blues 97.5] by [[Lillian Hearne]] | ||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
Revision as of 17:52, 22 June 2022
97.5cET is an equal-step tuning with steps of 97.5 cents (or each 13th step of 160edo). It approximates the 9th harmonic to within 2c, and may alternatively be tuned or conceived of as 39ed9. In contrast to 12edo, which is very similar in step size, it is not considered to approximate the octave (2/1) or perfect fifth (3/2), and has a workable, but rather (10.5c) flat approximation of their complement, the perfect fourth (4/3). It excels however in the 4/3.5/3.7/3.11/3.13/3.9 subgroup, in which it tempers out 64/63, 100/99, 275/273, 325/324, and 572/567, for example.
Intervals
| Steps | Cents | Ratio approximated* |
|---|---|---|
| 1 | 97.5 | 16/15, 21/20, 35/33, 55/52 |
| 2 | 195.0 | 28/25 |
| 3 | 292.5 | 13/11 |
| 4 | 390.0 | 5/4 |
| 5 | 487.5 | 4/3 |
| 6 | 585.0 | 7/5 |
| 7 | 682.5 | 49/33 |
| 8 | 780.0 | 11/7 |
| 9 | 877.5 | 5/3 |
| 10 | 975.0 | 16/9, 7/4 |
| 11 | 1072.5 | 13/7 |
| 12 | 1170.0 | 49/25 |
| 13 | 1267.5 | 27/13 |
| 14 | 1365.0 | 11/5 |
| 15 | 1462.5 | 7/3 |
| 16 | 1560.0 | 27/11, 49/20 |
| 17 | 1657.5 | 13/5 |
| 18 | 1755.0 | 11/4 |
| 19 | 1852.5 | 35/12 |
| 20 | 1950.0 | 49/16 |
| 21 | 2047.5 | 13/4 |
*some simpler ratios, based on treating 97.5cET as a 4/3.5/3.7/3.11/3.13/3.9 subgroup temperament; other approaches are possible.