Garischismic clan: Difference between revisions
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The '''garischismic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[garischisma]] ({{monzo|legend=1| 25 -14 0 -1 }}, [[ratio]]: 33554432/33480783). The head of this clan is gary, which is generated by a perfect fifth. Two apotomes i.e. 14 fifths octave reduced make a [[8/7|septimal major second (8/7)]]. Equivalently stated, the [[7/4|harmonic seventh (7/4)]] is found at the double-diminished octave (C–Cbb). | The '''garischismic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[garischisma]] ({{monzo|legend=1| 25 -14 0 -1 }}, [[ratio]]: 33554432/33480783). The head of this clan is gary, which is generated by a perfect fifth. Two apotomes i.e. 14 fifths octave reduced make a [[8/7|septimal major second (8/7)]]. Equivalently stated, the [[7/4|harmonic seventh (7/4)]] is found at the double-diminished octave (C–Cbb). | ||
== Gary == | |||
[[Subgroup]]: 2.3.7 | |||
[[Comma list]]: 33554432/33480783 | |||
{{Mapping|legend=2| 1 0 25 | 0 1 -14 }} | |||
: sval mapping generators: ~2, ~3 | |||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.2079 | |||
{{Optimal ET sequence|legend=1| 12, 29, 41, 94, 135, 364, 499, 634, 3035bd, 3669bd, 4303bd, 4937bbdd, 5571bbdd }} | |||
[[Badness]]: 0.0135 | |||
=== Overview to extensions === | |||
The second comma of the comma list determines which full 7-limit family member we are looking at. Garibaldi adds the [[schisma]], or equivalently [[225/224]] and finds 5/4 at the diminished fourth. Cotoneum adds [[10976/10935]] and finds 5/4 at the septuple-diminished octave. These are generated by the fifth as is gary. | The second comma of the comma list determines which full 7-limit family member we are looking at. Garibaldi adds the [[schisma]], or equivalently [[225/224]] and finds 5/4 at the diminished fourth. Cotoneum adds [[10976/10935]] and finds 5/4 at the septuple-diminished octave. These are generated by the fifth as is gary. | ||
Newt adds [[2401/2400]], slicing the fifth in two. Sextile adds [[250047/250000]] with a 1/3-octave period. Alphatrident adds [[6144/6125]], slicing the twelfth in three. Satin adds [[2100875/2097152]], slicing the fourth in three. Vulture adds [[4375/4374]], slicing the twelfth in four. World calendar adds [[390625/388962]] with a 1/4-octave period as well as a bisect generator. Quintagar adds [[3136/3125]], slicing the fourth in five. Paramity adds [[65625/65536]], slicing the eleventh in five | Gariwizmic adds the [[wizma]] with a 1/2-octave period. Newt adds [[2401/2400]], slicing the fifth in two. Sextile adds [[250047/250000]] with a 1/3-octave period. Alphatrident adds [[6144/6125]], slicing the twelfth in three. Satin adds [[2100875/2097152]], slicing the fourth in three. Vulture adds [[4375/4374]], slicing the twelfth in four. World calendar adds [[390625/388962]] with a 1/4-octave period as well as a bisect generator. Quintagar adds [[3136/3125]], slicing the fourth in five. Paramity adds [[65625/65536]], slicing the eleventh in five. | ||
Temperaments discussed elsewhere are: | Temperaments discussed elsewhere are: | ||
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* ''[[Paramity]]'' → [[Amity family #Paramity|Amity family]] (+65625/65536) | * ''[[Paramity]]'' → [[Amity family #Paramity|Amity family]] (+65625/65536) | ||
* ''[[Garistearn]]'' → [[Stearnsmic clan #Garistearn|Stearnsmic clan]] (+118098/117649) | * ''[[Garistearn]]'' → [[Stearnsmic clan #Garistearn|Stearnsmic clan]] (+118098/117649) | ||
* ''[[Wizmic microtemperaments#Gariwizmic|Gariwizmic]]'' → [[Wizmic microtemperaments]] (+420175/419904) | * ''[[Wizmic microtemperaments #Gariwizmic|Gariwizmic]]'' → [[Wizmic microtemperaments #Gariwizmic|Wizmic microtemperaments]] (+420175/419904) | ||
Considered below are cotoneum and world calendar. | Considered below are cotoneum and world calendar. | ||
=== 2.3.7.11 subgroup === | === 2.3.7.11 subgroup === | ||