3042/3025: Difference between revisions
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Created page with "{{Infobox Interval | Name = diagassormisma | Color name = 3oo1uugg2, <br>bitholugu 2nd, <br>Bitholugu comma | Comma = yes }} '''3042/3025''', the '''diagassormisma''' is a ..." |
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== Temperaments == | == Temperaments == | ||
Tempering out this comma leads to the '''diagassormismic temperament''', which splits the octave into two equal parts, each representing 55/39 (small gassormic tritone) and its octave complement, [[78/55]] (large gassormic tritone). Odd EDOs cannot temper it out. | Tempering out this comma leads to the '''diagassormismic temperament''', which splits the octave into two equal parts, each representing 55/39 (small gassormic tritone) and its octave complement, [[78/55]] (large gassormic tritone). Odd-numbered EDOs cannot temper it out. | ||
=== 2.3.5.11.13 diagassormismic === | === 2.3.5.11.13 diagassormismic === | ||
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Optimal tuning (POTE): ~55/39 = 1＼2, ~3/2 = 701.7083, ~5/4 = 387.2538, ~11/8 = 553.2831 | Optimal tuning (POTE): ~55/39 = 1＼2, ~3/2 = 701.7083, ~5/4 = 387.2538, ~11/8 = 553.2831 | ||
{{Optimal ET sequence|legend=1|8, 10, 12e, 12f, 14cf, 16, 22, 24, 34, 58, 72, 96, 130, 282f}} | |||
== See also == | == See also == | ||
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[[Category:Diagassormismic]] | [[Category:Diagassormismic]] | ||
[[Category:Commas named by combining multiple temperament names]]{{todo|add etymology|research|comment=double check, confirm this}} | |||
Latest revision as of 23:54, 15 November 2024
| Interval information |
bitholugu 2nd,
Bitholugu comma
3042/3025, the diagassormisma is a 13-limit interval measuring about 9.7¢. It forms the difference between two 55/39s and an octave.
Temperaments
Tempering out this comma leads to the diagassormismic temperament, which splits the octave into two equal parts, each representing 55/39 (small gassormic tritone) and its octave complement, 78/55 (large gassormic tritone). Odd-numbered EDOs cannot temper it out.
2.3.5.11.13 diagassormismic
Subgroup: 2.3.5.11.13
Comma list: 3042/3025
Mapping: [⟨2 0 0 0 -1], ⟨0 1 0 0 -1], ⟨0 0 1 0 1], ⟨0 0 0 1 1]]
- Mapping generators: ~55/39, ~3, ~5, ~11
Optimal tuning (POTE): ~55/39 = 1＼2, ~3/2 = 701.7083, ~5/4 = 387.2538, ~11/8 = 553.2831
Optimal ET sequence: 8, 10, 12e, 12f, 14cf, 16, 22, 24, 34, 58, 72, 96, 130, 282f