988edo
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Theory
988edo provides excellent tuning for the 2, 3, 5, 11, 13, 19, 37, 43, 47, 53, 59th harmonics and a reasonable tuning for 23, 29, 31, 41st harmonics, making a strong higher-limit system. In lower limits, it is enfactored in the 17-limit, with the same tuning as 494edo, which is notable for being a zeta edo. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. The comma basis for 988edo in the 19-limit 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. In addition, in the 988ccd val it is a tuning for quadritikleismic temperament in the 7-limit.
Higher limits
In the 2.5.11.13.19.29.31 it supports period-52 temperament called french deck, with the tempering out of 6656/6655 inherited from 494edo.
988edo is similar to 2016edo in the fact that both tune well the 2.5.11.13.19.41.47 subgroup. The result is the 988 & 2016 temperament, which reaches 13/8 in four generators and has a comma basis {7943/7942, 322465/322373, 16777475/16777216, 22151168/22150865, 12998046875/12994428928}.
Subsets and supersets
988edo has subset edos 1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494.
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.
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
Note: temperaments represented by 494edo are not included.
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 4 | 261\988 (14\988) |
317.004 (17.004) |
6/5 (126/125) |
Quadritikleismic (988ccd) |
| 19 | 141\988 (37\988) |
171.255 (44.939) |
6545/5928 (?) |
Kalium |
| 52 | 325\988 (2\988) |
394.736 (2.429) |
134560000/107132311 (?) |
French deck |