Olympic clan: Difference between revisions

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The '''olympic clan''' of [[rank-3 temperament]]s tempers out the [[olympia]], 131072/130977 = {{monzo| 17 -5 0 -2 -1 }}.

The '''olympic clan''' of [[rank-3 temperament]]s tempers out the [[olympia]], 131072/130977 = {{monzo| 17 -5 0 -2 -1 }}. This has the effect of equating the [[33/32|undecimal quartertone (33/32)]] with a stack of two [[64/63|septimal commas (64/63)]].

~~Temperaments discussed elsewhere are:~~

* ''[[~~Akea]]'', {385~~/~~384, 2200~~/~~2187} → [[Hemifamity family #Akea|Hemifamity family~~]]

* ''[[~~Lux]]'', {3025~~/~~3024, 131072/130977} → [[Lehmerismic temperaments #Lux~~|~~Lehmerismic temperaments]]~~

* ''[[Hera]]'', {6144/~~6125, 8019/8000} → [[Porwell family #Hera|Porwell family~~]]

~~Considered below are olympian, no-5 subgroup temperament, in addition to baffin and sophia~~.

For the rank-4 olympic temperament, see [[Rank-4 temperament #Olympic (131072/130977)]].

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[[Badness]]: 0.0183 × 10<sup>-3</sup>

=== Overview to extensions ===

The second comma in the comma list determines how we extend olympian to include the harmonic 5. Akea adds [[385/384]], and finds harmonics 5 by equating the [[81/80|syntonic comma (81/80)]] with the septimal comma. Baffin adds [[5632/5625]], splitting the perfect twelfth into two. Lux adds [[3025/3024]], splitting the ~21/16 into two. Hera adds [[6144/6125]] or [[8019/8000]], splitting the ~21/16 into three. Finally, sophia adds 42875/42768, splitting the ~8/7 into three. These all have neat extensions to the 13-limit via tempering out both [[2080/2079]] and [[4096/4095]].

Temperaments discussed elsewhere are:

* ''[[Akea]]'' → [[Hemifamity family #Akea|Hemifamity family]]

* ''[[Lux]]'' → [[Lehmerismic temperaments #Lux|Lehmerismic temperaments]]

* ''[[Hera]]'' → [[Porwell family #Hera|Porwell family]]

Considered below are baffin and sophia.

== Baffin ==

=== 7-limit (decovulture) ===

[[Subgroup]]: 2.3.5.7~~.11~~

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 67108864/66976875

@@ Line 1: / Line 1: @@
-The '''olympic clan''' of [[rank-3 temperament]]s tempers out the [[olympia]], 131072/130977 = {{monzo| 17 -5 0 -2 -1 }}.
+The '''olympic clan''' of [[rank-3 temperament]]s tempers out the [[olympia]], 131072/130977 = {{monzo| 17 -5 0 -2 -1 }}. This has the effect of equating the [[33/32|undecimal quartertone (33/32)]] with a stack of two [[64/63|septimal commas (64/63)]].
-Temperaments discussed elsewhere are:
-* ''[[Akea]]'', {385/384, 2200/2187} → [[Hemifamity family #Akea|Hemifamity family]]
-* ''[[Lux]]'', {3025/3024, 131072/130977} → [[Lehmerismic temperaments #Lux|Lehmerismic temperaments]]
-* ''[[Hera]]'', {6144/6125, 8019/8000} → [[Porwell family #Hera|Porwell family]]
-Considered below are olympian, no-5 subgroup temperament, in addition to baffin and sophia.
 For the rank-4 olympic temperament, see [[Rank-4 temperament #Olympic (131072/130977)]].
@@ Line 24: / Line 17: @@
 [[Badness]]: 0.0183 × 10<sup>-3</sup>
+=== Overview to extensions ===
+The second comma in the comma list determines how we extend olympian to include the harmonic 5. Akea adds [[385/384]], and finds harmonics 5 by equating the [[81/80|syntonic comma (81/80)]] with the septimal comma. Baffin adds [[5632/5625]], splitting the perfect twelfth into two. Lux adds [[3025/3024]], splitting the ~21/16 into two. Hera adds [[6144/6125]] or [[8019/8000]], splitting the ~21/16 into three. Finally, sophia adds 42875/42768, splitting the ~8/7 into three. These all have neat extensions to the 13-limit via tempering out both [[2080/2079]] and [[4096/4095]].
+Temperaments discussed elsewhere are:
+* ''[[Akea]]'' → [[Hemifamity family #Akea|Hemifamity family]]
+* ''[[Lux]]'' → [[Lehmerismic temperaments #Lux|Lehmerismic temperaments]]
+* ''[[Hera]]'' → [[Porwell family #Hera|Porwell family]]
+Considered below are baffin and sophia.
 == Baffin ==
 === 7-limit (decovulture) ===
-[[Subgroup]]: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 67108864/66976875