7th-octave temperaments: Difference between revisions
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Optimal tuning (CTE): ~1157625/1048576 = 1\7, ~1029/1024 = 8.531 | Optimal tuning (CTE): ~1157625/1048576 = 1\7, ~1029/1024 = 8.531 | ||
{{Optimal ET sequence|legend=1|140, 1407, 1547}}, ... | |||
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[[Category:Rank 2]] | [[Category:Rank 2]] | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
Revision as of 21:59, 8 May 2023
7th octave temperament occurs through temperament merging any two edos whose greatest common divisor is 7. A comma that frequently appears in 7th-octave temps is akjaysma, which sets 105/64 to be equal to 5\7.
Temperaments discussed elsewhere include:
- Septant → Schismatic family
- Brahmagupta → Ragismic microtemperaments
- Absurdity → Syntonic chromatic equivalence continuum
Nitrogen
Described as 140 & 1407 temperament in the 7-limit, named after the 7th element for being period-7 and also because 140 and 1407 only contain numbers 7 and 14, atomic number and atomic weight of nitrogen respectively. On top of this connection to the number 7, it also reaches 7th harmonic 7 generators down.
Subgroup: 2.3.5.7
Comma list: 3955078125/3954653486, 140737488355328/140710042265625
Mapping: [⟨7 10 17 20], ⟨0 22 -15 -7]]
Mapping generators: ~1157625/1048576, ~1029/1024
Optimal tuning (CTE): ~1157625/1048576 = 1\7, ~1029/1024 = 8.531
Optimal ET sequence: 140, 1407, 1547, ...