389edo: Difference between revisions

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== Theory ==
== Theory ==
{{Primes in edo|389|columns=13}}
{{Primes in edo|389|columns=8}}
The best subgroup for 389edo is 7.17.31.41.
 
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 ===
=== 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.
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 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.


== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |Subgroup
! rowspan="2" |[[Comma list]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal
8ve stretch (¢)
! colspan="2" |Tuning error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3.5
|{{monzo|20 -17 3}}, {{monzo|-39 -12 25}}
|[{{val|389 617 903}}]
| -0.19
|0.500
|16.2
|-
|2.3.5
|2109375/2097152, {{monzo|-7, 44, -27}}
|[{{val|389 616 903}}]
|0.46
|0.451
|14.6
|-
|2.5.7
|2100875/2097152, {{monzo|0, 52, -43}}
|[{{val|389 903 1092}}]
|0.12
|0.131
|4.2
|}
== Scales ==
== Scales ==



Revision as of 19:11, 13 March 2022

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

Theory

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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.

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]] 0.46 0.451 14.6
2.5.7 2100875/2097152, [0, 52, -43 [389 903 1092]] 0.12 0.131 4.2

Scales

  • Solstice[69]
  • SolsticeDay[94]

Links

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