35th-octave temperaments: Difference between revisions

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[[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 ==

This is the comma that identifies [[51/50]] with 1 step of 35edo.

Subgroup: 2.3.5.7.11.13.17

Comma list: [36 -35 70 0 0 0 -~~35⟩~~

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 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}}, ...

{{#switch: 1 | 1 = [[Mapping]]:  | 2 = [[Sval]] [[mapping]]:  | 3 = [[Gencom]] [[mapping]]:  }}<span class="left-delim">[</span>{{bra| 35 0 0 0 0 0 36 }}{{#if: 0 1 0 0 0 0 -1|, {{bra| 0 1 0 0 0 0 -1 }} }}{{#if: 0 0 1 0 0 0 2|, {{bra| 0 0 1 0 0 0 2 }} }}{{#if: 0 0 0 1 0 0 0|, {{bra| 0 0 0 1 0 0 0 }} }}<span class="right-delim">]</span>

== Bromine ==

Bromine is named after the 35th chemical element.

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Optimal tuning (CTE): ~5/4 = 386.174

[[Category:35edo]]

~~[[Category:Temperament collections]]~~

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-{{Fractional-octave navigation|35}}
+{{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.
 == 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: [36 -35 70 0 0 0 -35⟩
+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}}, ...
-{{#switch: 1 | 1 = [[Mapping]]:&nbsp; | 2 = [[Sval]] [[mapping]]:&nbsp; | 3 = [[Gencom]] [[mapping]]:&nbsp; }}<span class="left-delim">&#91;</span>{{bra| 35 0 0 0 0 0 36 }}{{#if: 0 1 0 0 0 0 -1|, {{bra| 0 1 0 0 0 0 -1 }} }}{{#if: 0 0 1 0 0 0 2|, {{bra| 0 0 1 0 0 0 2 }} }}{{#if: 0 0 0 1 0 0 0|, {{bra| 0 0 0 1 0 0 0 }} }}<span class="right-delim">&#93;</span>
 == Bromine ==
 Bromine is named after the 35th chemical element.
@@ Line 111: / Line 132: @@
 Optimal tuning (CTE): ~5/4 = 386.174
+{{Navbox fractional-octave}}
 [[Category:35edo]]
-[[Category:Temperament collections]]