35th-octave temperaments: Difference between revisions
→Bromine: expand to 11-limit and 19-limit via 2730edo's consistency, also can't keep the "normal" matrix due to limitations of the sintel's finder so 152 and -7 for 19-limit in the mapping |
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{{Infobox fractional-octave|35}} | |||
[[35edo]] is a tuning system that's not remarkable in its own right from a regular temperament theory perspective, but some of its multiples are either [[zeta]] edos like [[3395edo]], have an exceptionally precise perfect fifth like [[665edo]], or have high consistency limits like [[525edo]]. In addition, one step of 35edo is close to [[50/49]] in low limits and [[51/50]] in the higher limits. | [[35edo]] is a tuning system that's not remarkable in its own right from a regular temperament theory perspective, but some of its multiples are either [[zeta]] edos like [[3395edo]], have an exceptionally precise perfect fifth like [[665edo]], or have high consistency limits like [[525edo]]. In addition, one step of 35edo is close to [[50/49]] in low limits and [[51/50]] in the higher limits. | ||
== Insanobromismic == | |||
{{Main|Insanobromisma}} | |||
This is the comma that identifies [[51/50]] with 1 step of 35edo. | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: {{monzo|36 -35 70 0 0 0 -35}} | |||
Mapping: [{{val|35 0 0 0 0 0 36}}, {{val|0 1 0 0 0 0 -1}}, {{val|0 0 1 0 0 0 2}}, {{val|0 0 0 1 0 0 0}}, {{val|0 0 0 0 1 0 0}}, {{val|0 0 0 0 0 1 0}}] | |||
: mapping generators: ~51/50 = 1\35, ~3, ~5, ~7, ~11, ~13, ~17 | |||
[[Support]]ing [[ET]]s: {{EDOs|140, 525, 665, 2730, 3395, 3920, 7980, 11375, 15960, 16625, 24605, 28000, 32585}}, ... | |||
=== Insanobromic === | |||
Subgroup: 2.3.5.17 | |||
Comma list: {{monzo|36 -35 70 -35}} | |||
{{Mapping|legend=2|35 0 0 36|0 1 0 -1|0 0 1 2}} | |||
: mapping generators: ~51/50 = 1\35, ~3, ~5, | |||
[[Support]]ing [[ET]]s: {{EDOs|140, 525, 665, 2730, 3395, 3920, 7980, 11375, 15960, 16625, 24605, 28000, 32585}}, ... | |||
== Bromine == | == Bromine == | ||
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While 665edo still tunes bromine in the 11-limit, it is not recommended due to error on the 11th harmonic. [[2730edo]] or [[3395edo]] are better tunings. Alternately, considering bromine as a no-11s temperament keeps it within the realm of [[very high accuracy temperaments]], having [[TE error]] of less than 0.005 cents per octave. | While 665edo still tunes bromine in the 11-limit, it is not recommended due to error on the 11th harmonic. [[2730edo]] or [[3395edo]] are better tunings. Alternately, considering bromine as a no-11s temperament keeps it within the realm of [[very high accuracy temperaments]], having [[TE error]] of less than 0.005 cents per octave. | ||
If a strong 11th harmonic is needed, [[6125edo]] is the tuning for that. | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Optimal tuning (CTE): ~3/2 = 701.975 | Optimal tuning (CTE): ~3/2 = 701.975 | ||
{{Optimal ET sequence|legend=1|665, 2730, 3395, 6125, 9520}} | |||
=== 13-limit === | === 13-limit === | ||
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Optimal tuning (CTE): ~5/4 = 386.174 | Optimal tuning (CTE): ~5/4 = 386.174 | ||
{{Navbox fractional-octave}} | |||
[[Category:35edo]] | [[Category:35edo]] | ||