389edo

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389edo, divides the octave into parts of 3.0848c each.

Theory

Approximation of prime intervals in 389 EDO
Prime number 2 3 5 7 11 13 17 19
Error absolute (¢) +0.00 +1.39 -0.71 -0.19 +0.87 -1.45 -0.07 -1.37
relative (%) +0 +45 -23 -6 +28 -47 -2 -44
Steps (reduced) 389 (0) 617 (228) 903 (125) 1092 (314) 1346 (179) 1439 (272) 1590 (34) 1652 (96)

389edo has two mappings for 3, which makes it a dual-fifth system. The best approach to this tuning is through a 2.5.7.11.17 subgroup.

Relation to a calendar reform

389edo represents the north solstice (summer in the northern hemisphere) leap year cycle 69/389 as devised by Sym454 inventor Irvin Bromberg. The outcome scale uses 327\389, or 62\389 as its generator. The solstice leap day scale with 94 notes uses 269\389 as a generator. Since this is a maximum evenness scale, temperament can be generated by simply merging the numerator and the denominator.

Solstice Leap Day (94 & 295)

295 seems to precede 389.

Subgroup: 2.5.7.11.17

POTE generator: 370.1796c

Comma list: 250000/248897, 2100875/2097152, 4096000/4092529

Regular temperament properties

Subgroup Comma list Mapping Optimal

8ve stretch (¢)

Tuning error
Absolute (¢) Relative (%)
2.3.5 [20 -17 3, [-39 -12 25 [389 617 903]] -0.19 0.500 16.2
2.3.5 2109375/2097152, [-7, 44, -27 [389 616 903]] (389b) 0.46 0.451 14.6
2.5.7 2100875/2097152, [0, 52, -43 [389 903 1092]] 0.12 0.131 4.2
2.5.7.11.17 6664/6655, 156250/155771, 180625/180224, 184960/184877 [389 903 1092 1346 1590]] 0.03 0.177 5.7

Scales

  • Solstice[69]
  • SolsticeDay[94]

Links

https://individual.utoronto.ca/kalendis/leap/index.htm#mod