988edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 987edo988edo989edo →
Prime factorization 22 × 13 × 19
Step size 1.21457¢
Fifth 578\988 (702.024¢) (→289\494)
Semitones (A1:m2) 94:74 (114.2¢ : 89.88¢)
Consistency limit 15
Distinct consistency limit 15

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, 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 provides a good correction for the 19th harmonic over 494edo. 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

Approximation of prime harmonics in 988edo
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

Periods
per 8ve
Generator
(Reduced)
Cents
(Reduced)
Associated
Ratio
Temperaments
52 325\988
(2\988)
394.736
(2.429)
134560000/107132311
(?)
French deck