988edo
| ← 987edo | 988edo | 989edo → |
988 equal divisions of the octave (988edo), or 988-tone equal temperament (988tet), 988 equal temperament (988et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 988 equal parts of about 1.21 ¢ each.
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}.
As an interval size measure
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 | +6 | -6 | +33 | +8 | -3 | -41 | +5 | -28 | +31 | +25 | |
| 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 |