Garischismic clan: Difference between revisions

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The '''garischismic clan''' of temperaments tempers out the [[garischisma]], {{monzo| 25 -14 0 -1 }} = 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).

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. ~~Trident~~ 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.

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:

* [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] (+225/224)

* ''[[Newt]]'' → [[Breedsmic temperaments #Newt|Breedsmic temperaments]] (+2401/2400)

* ''[[Sextile]]'' → [[Landscape microtemperaments #Sextile|Landscape microtemperaments]] (+250047/250000)

* ''[[Satin]]'' → [[Canousmic temperaments #Satin|Canousmic temperaments]] (+2100875/2097152)

* ''[[~~Trident~~]]'' → [[~~Tricot~~ family #~~Trident~~|~~Tricot~~ family]] (+6144/6125)

* ''[[Alphatrident]]'' → [[Alphatricot family #Alphatrident|Alphatricot family]] (+6144/6125)

* ''[[Vulture]]'' → [[Vulture family #Vulture|Vulture family]] (+4375/4374)

* ''[[Quintagar]]'' → [[Quindromeda family #Quintagar|Quindromeda family]] (+3136/3125)

* ''[[Paramity]]'' → [[Amity family #Paramity|Amity family]] (+65625/65536)

* ''[[Garistearn]]'' → [[Stearnsmic clan #Garistearn|Stearnsmic clan]] (+118098/117649)

Considered below are cotoneum and world calendar.

== Gary ==

@@ Line 1: / Line 1: @@
-The '''garischismic clan''' of temperaments tempers out the [[garischisma]], {{monzo| 25 -14 0 -1 }} = 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).
-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. Trident 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.
+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:
 * [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] (+225/224)
 * ''[[Newt]]'' → [[Breedsmic temperaments #Newt|Breedsmic temperaments]] (+2401/2400)
 * ''[[Sextile]]'' → [[Landscape microtemperaments #Sextile|Landscape microtemperaments]] (+250047/250000)
 * ''[[Satin]]'' → [[Canousmic temperaments #Satin|Canousmic temperaments]] (+2100875/2097152)
-* ''[[Trident]]'' → [[Tricot family #Trident|Tricot family]] (+6144/6125)
+* ''[[Alphatrident]]'' → [[Alphatricot family #Alphatrident|Alphatricot family]] (+6144/6125)
 * ''[[Vulture]]'' → [[Vulture family #Vulture|Vulture family]] (+4375/4374)
 * ''[[Quintagar]]'' → [[Quindromeda family #Quintagar|Quindromeda family]] (+3136/3125)
 * ''[[Paramity]]'' → [[Amity family #Paramity|Amity family]] (+65625/65536)
 * ''[[Garistearn]]'' → [[Stearnsmic clan #Garistearn|Stearnsmic clan]] (+118098/117649)
+Considered below are cotoneum and world calendar.
 == Gary ==