719edo

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← 718edo 719edo 720edo →
Prime factorization 719 (prime)
Step size 1.66898¢ 
Fifth 421\719 (702.643¢)
Semitones (A1:m2) 71:52 (118.5¢ : 86.79¢)
Dual sharp fifth 421\719 (702.643¢)
Dual flat fifth 420\719 (700.974¢)
Dual major 2nd 122\719 (203.616¢)
Consistency limit 3
Distinct consistency limit 3

719 equal divisions of the octave (abbreviated 719edo or 719ed2), also called 719-tone equal temperament (719tet) or 719 equal temperament (719et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 719 equal parts of about 1.67 ¢ each. Each step represents a frequency ratio of 21/719, or the 719th root of 2.

Theory

719edo is only consistent to the 3-odd-limit and the error of its harmonic 3 is quite large. Its harmonics 5 and 7 are also about halfway its steps. It can be used in the 2.9.15.21.11.17.19.23.29 subgroup, tempering out 1701/1700, 3025/3024, 2376/2375, 8625/8624, 21888/21875, 72171/72128, 2001/2000 and 116127/116000. It supports marfifths.

Odd harmonics

Approximation of odd harmonics in 719edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.688 -0.778 -0.815 -0.294 -0.553 +0.641 -0.091 +0.191 -0.434 -0.127 -0.736
Relative (%) +41.2 -46.6 -48.8 -17.6 -33.1 +38.4 -5.4 +11.4 -26.0 -7.6 -44.1
Steps
(reduced)
1140
(421)
1669
(231)
2018
(580)
2279
(122)
2487
(330)
2661
(504)
2809
(652)
2939
(63)
3054
(178)
3158
(282)
3252
(376)

Subsets and supersets

719edo is the 128th prime EDO. 1438edo, which doubles it, gives a good correction to the harmonics 3, 5 and 7.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [-2279 719 [719 2279]] 0.0464 0.0464 2.78