Garischismic clan: Difference between revisions

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This clan of temperaments tempers out the [[garischisma]], {{monzo| 25 -14 0 -1 }} = 33554432/33480783, and includes these:
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).
* [[Garibaldi]], {225/224, 3125/3087} → [[Schismatic family #Garibaldi|Schismatic family]]
 
* ''[[Newt]]'', {2401/2400, 33554432/33480783} → [[Breedsmic temperaments #Newt|Breedsmic temperaments]]
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.
* ''[[Quintagar]]'', {3136/3125, 33554432/33480783} → [[Quindromeda family #Quintagar|Quindromeda family]]
 
* ''[[Vulture]]'', {4375/4374, 33554432/33480783} → [[Vulture family #Vulture|Vulture family]]
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.
* ''[[Trident]]'', {6144/6125, 14348907/14336000} → [[Tricot family #Trident|Tricot family]]
 
* [[Cotoneum]], {10976/10935, 823543/819200} → [[Hemimage temperaments #Cotoneum|Hemimage temperaments]]
* [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] (+225/224)
* ''[[Paramity]]'', {65625/65536, 1600000/1594323} → [[Amity family #Paramity|Amity family]]
* [[Cotoneum]] → [[Hemimage temperaments #Cotoneum|Hemimage temperaments]] (+10976/10935)
* ''[[Garistearn]]'', {118098/117649, 33554432/33480783} → [[Stearnsmic clan #Garistearn|Stearnsmic clan]]
* ''[[Newt]]'' → [[Breedsmic temperaments #Newt|Breedsmic temperaments]] (+2401/2400)
* ''[[Sextile]]'', {250047/250000, 33554432/33480783} → [[Landscape microtemperaments #Sextile|Landscape microtemperaments]]
* ''[[Sextile]]'' → [[Landscape microtemperaments #Sextile|Landscape microtemperaments]] (+250047/250000)
* ''[[Satin]]'', {2100875/2097152, 4802000/4782969} → [[Canousmic temperaments #Satin|Canousmic temperaments]]
* ''[[Satin]]'' → [[Canousmic temperaments #Satin|Canousmic temperaments]] (+2100875/2097152)
* ''[[Trident]]'' → [[Tricot family #Trident|Tricot 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)


== Gary ==
== Gary ==
Subgroup: 2.3.7
[[Subgroup]]: 2.3.7


[[Comma list]]: 33554432/33480783
[[Comma list]]: 33554432/33480783


[[Sval]] [[mapping]]: [{{val| 1 2 -3 }}, {{val| 0 -1 14 }}]
{{Mapping|legend=2| 1 2 -3 | 0 -1 14 }}


[[POTE generator]]: ~3/2 = 702.2079
[[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 }}
{{Optimal ET sequence|legend=1| 12, 29, 41, 94, 135, 364, 499, 634, 3035bd, 3669bd, 4303bd, 4937bbdd, 5571bbdd }}
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Comma list: 19712/19683, 41503/41472
Comma list: 19712/19683, 41503/41472


Sval mapping: [{{val| 1 2 -3 13 }}, {{val| 0 -1 14 -23 }}]
Sval mapping: {{mapping| 1 2 -3 13 | 0 -1 14 -23 }}


POTE generator: ~3/2 = 702.2292
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.2292


{{Optimal ET sequence|legend=1| 12e, 41, 94, 135, 716, 851, 986, 1121, 1256 }}
{{Optimal ET sequence|legend=1| 12e, 41, 94, 135, 716, 851, 986, 1121, 1256 }}
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== World calendar ==
== World calendar ==
''World calendar'' tempers out the [[dimcomp comma]] and the garischisma, and can be described as the 12 & 364 temperament. The name derives from a [[wikipedia:World Calendar|certain calendar layout]] by the same name.  
World calendar tempers out the [[dimcomp comma]] and the garischisma, and can be described as the 12 & 364 temperament. The name derives from a [[wikipedia: World Calendar|certain calendar layout]] by the same name.  


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 390625/388962, 33554432/33480783
[[Comma list]]: 390625/388962, 33554432/33480783


[[Mapping]]: [{{val| 4 1 -44 86 }}, {{val| 0 2 -13 -28 }}]
{{Mapping|legend=1| 4 1 -44 86 | 0 2 -13 -28 }}


Mapping generators: ~25/21, ~91125/57344
: mapping generators: ~25/21, ~91125/57344


[[POTE generator]]: ~91125/57344 = 801.0947
[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~91125/57344 = 801.0947


{{Optimal ET sequence|legend=1| 12, …, 352, 364 }}
{{Optimal ET sequence|legend=1| 12, …, 352, 364 }}
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Comma list: 2025/2023, 24576/24565, 390625/388962
Comma list: 2025/2023, 24576/24565, 390625/388962


Sval mapping: [{{val| 4 1 -44 86 3 }}, {{val| 0 2 -13 -28 5 }}]
Sval mapping: {{mapping| 4 1 -44 86 3 | 0 2 -13 -28 5 }}


POTE generator: ~27/17 = 801.0908
Optimal tuning (POTE): ~25/21 = 1\4, ~27/17 = 801.0908


{{Optimal ET sequence|legend=1| 12, …, 352, 364 }}
{{Optimal ET sequence|legend=1| 12, …, 352, 364 }}
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Comma list: 1216/1215, 2025/2023, 8075/8064, 48013/48000
Comma list: 1216/1215, 2025/2023, 8075/8064, 48013/48000


Sval mapping: [{{val| 4 1 -44 86 3 25 }}, {{val| 0 2 -13 -28 5 -3 }}]
Sval mapping: {{mapping| 4 1 -44 86 3 25 | 0 2 -13 -28 5 -3 }}


POTE generator: ~27/17 = 801.0945
Optimal tuning (POTE): ~25/21 = 1\4, ~27/17 = 801.0945


{{Optimal ET sequence|legend=1| 12, …, 352, 364 }}
{{Optimal ET sequence|legend=1| 12, …, 352, 364 }}

Revision as of 08:48, 5 July 2023

The garischismic clan of temperaments tempers out the garischisma, [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 septimal major second (8/7). Equivalently stated, the 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.

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.

Gary

Subgroup: 2.3.7

Comma list: 33554432/33480783

Sval mapping: [⟨1 2 -3], ⟨0 -1 14]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.2079

Optimal ET sequence: 12, 29, 41, 94, 135, 364, 499, 634, 3035bd, 3669bd, 4303bd, 4937bbdd, 5571bbdd

Badness: 0.0135

2.3.7.11 subgroup

Subgroup: 2.3.7.11

Comma list: 19712/19683, 41503/41472

Sval mapping: [⟨1 2 -3 13], ⟨0 -1 14 -23]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.2292

Optimal ET sequence: 12e, 41, 94, 135, 716, 851, 986, 1121, 1256

Badness: 0.00731

World calendar

World calendar tempers out the dimcomp comma and the garischisma, and can be described as the 12 & 364 temperament. The name derives from a certain calendar layout by the same name.

Subgroup: 2.3.5.7

Comma list: 390625/388962, 33554432/33480783

Mapping: [⟨4 1 -44 86], ⟨0 2 -13 -28]]

mapping generators: ~25/21, ~91125/57344

Optimal tuning (POTE): ~25/21 = 1\4, ~91125/57344 = 801.0947

Optimal ET sequence: 12, …, 352, 364

Badness: 0.292

2.3.5.7.17 subgroup

Subgroup: 2.3.5.7.17

Comma list: 2025/2023, 24576/24565, 390625/388962

Sval mapping: [⟨4 1 -44 86 3], ⟨0 2 -13 -28 5]]

Optimal tuning (POTE): ~25/21 = 1\4, ~27/17 = 801.0908

Optimal ET sequence: 12, …, 352, 364

Badness: 0.0743

2.3.5.7.17.19 subgroup

Subgroup: 2.3.5.7.17.19

Comma list: 1216/1215, 2025/2023, 8075/8064, 48013/48000

Sval mapping: [⟨4 1 -44 86 3 25], ⟨0 2 -13 -28 5 -3]]

Optimal tuning (POTE): ~25/21 = 1\4, ~27/17 = 801.0945

Optimal ET sequence: 12, …, 352, 364

Badness: 0.0378

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