988edo: Difference between revisions
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== Theory == | == 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, | 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 1156/1155, 1275/1274, 1445/1444, 1716/1715, 2080/2079, 2431/2430, 4096/4095. | ||
An alternate mapping for 17 would be the 988g val | An alternate mapping for 17 would be the 988g val, where 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. | 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. | ||
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|988}} | {{Harmonics in equal|988|columns=11}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | !Periods<br>per 8ve | ||
per | ! Generator<br>(Reduced) | ||
!Generator | ! Cents<br>(Reduced) | ||
( | ! Associated<br>Ratio | ||
!Cents | ! Temperaments | ||
( | |||
!Associated | |||
!Temperaments | |||
|- | |- | ||
|52 | | 52 | ||
|325\988 | | 325\988<br>(2\988) | ||
(2\988) | | 394.736<br>(2.429) | ||
|394.736 | | 134560000/107132311<br>(?) | ||
(2.429) | | [[French deck]] | ||
|134560000/107132311 | |} | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | |||
Revision as of 10:26, 2 November 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 1156/1155, 1275/1274, 1445/1444, 1716/1715, 2080/2079, 2431/2430, 4096/4095.
An alternate mapping for 17 would be the 988g val, where 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 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 52 | 325\988 (2\988) |
394.736 (2.429) |
134560000/107132311 (?) |
French deck |