988edo

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Revision as of 10:27, 18 October 2022 by Eliora (talk | contribs) (Theory: rank 2 temp)
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← 987edo 988edo 989edo →
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

Template:EDO intro

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

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 (%) +0.0 +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