988edo: Difference between revisions
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988edo provides excellent tuning for the 2, 3, 5, 11, 13, 19, 37, 43, 47, 53, and 59th harmonics, making a strong higher-limit system. It is double the famous [[494edo]], and with the same mapping for the 17-limit. If considered in the 19-limit, it is basically a spicy 494edo with the 19th harmonic. The comma basis for such regular temperament is 1445/1444, 1716/1715, 2601/2600, 3025/3024, 4225/4224, 10830/10829, 297440/297381. | 988edo provides excellent tuning for the 2, 3, 5, 11, 13, 19, 37, 43, 47, 53, and 59th harmonics, making a strong higher-limit system. It is double the famous [[494edo]], and with the same mapping for the 17-limit. If considered in the 19-limit, it is basically a spicy 494edo with the 19th harmonic. The comma basis for such regular temperament is 1445/1444, 1716/1715, 2601/2600, 3025/3024, 4225/4224, 10830/10829, 297440/297381. | ||
An alternate mapping for 17 would be the 988g val. In it, it tempers out 2025/2023, 13013/13005, 15625/15606, 31213/31212. | |||
One step of 988edo is named '''semisqub''', given the strong relation to 494edo and the fact that 1 step of 494edo is called a squb. | |||
In the 2.5.11.13.19.41.47 it supports a 988 & [[2016edo|2016]] temperament.<!-- why is it notable? --> | In the 2.5.11.13.19.41.47 it supports a 988 & [[2016edo|2016]] temperament.<!-- why is it notable? --> | ||
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{{Harmonics in equal|988}} | {{Harmonics in equal|988}} | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
!Periods | |||
per octave | |||
!Generator | |||
(reduced) | |||
!Cents | |||
(reduced) | |||
!Associated | |||
ratio | |||
!Temperaments | |||
|- | |||
|52 | |||
|325\988 | |||
(2\988) | |||
|394.736 | |||
(2.429) | |||
|134560000/107132311 | |||
(?) | |||
|[[French deck]] | |||
|}<!-- 3-digit number --> | |||
Revision as of 10:27, 18 October 2022
| ← 987edo | 988edo | 989edo → |
Theory
988edo provides excellent tuning for the 2, 3, 5, 11, 13, 19, 37, 43, 47, 53, and 59th harmonics, making a strong higher-limit system. It is double the famous 494edo, and with the same mapping for the 17-limit. If considered in the 19-limit, it is basically a spicy 494edo with the 19th harmonic. The comma basis for such regular temperament is 1445/1444, 1716/1715, 2601/2600, 3025/3024, 4225/4224, 10830/10829, 297440/297381.
An alternate mapping for 17 would be the 988g val. In it, it tempers out 2025/2023, 13013/13005, 15625/15606, 31213/31212.
One step of 988edo is named semisqub, given the strong relation to 494edo and the fact that 1 step of 494edo is called a squb.
In the 2.5.11.13.19.41.47 it supports a 988 & 2016 temperament.
In the 2.5.11.13.29.31 it supports period-52 temperament called french deck.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.069 | -0.079 | +0.405 | +0.099 | -0.042 | -0.502 | +0.058 | -0.339 | +0.382 | +0.309 |
| Relative (%) | +0.0 | +5.7 | -6.5 | +33.3 | +8.2 | -3.4 | -41.3 | +4.8 | -27.9 | +31.5 | +25.4 | |
| Steps (reduced) |
988 (0) |
1566 (578) |
2294 (318) |
2774 (798) |
3418 (454) |
3656 (692) |
4038 (86) |
4197 (245) |
4469 (517) |
4800 (848) |
4895 (943) | |
Regular temperament properties
Rank-2 temperaments
| Periods
per octave |
Generator
(reduced) |
Cents
(reduced) |
Associated
ratio |
Temperaments |
|---|---|---|---|---|
| 52 | 325\988
(2\988) |
394.736
(2.429) |
134560000/107132311
(?) |
French deck |