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 }}. This has the effect of equating the [[33/32|undecimal quartertone (33/32)]] with a stack of two [[64/63|septimal commas (64/63)]].

The '''olympic clan''' of [[rank-3 temperament|rank-3]] [[temperament]]s [[tempering out|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)]].

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

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[[Comma list]]: 131072/130977

~~[[Sval]] [[mapping]]: [~~{{~~val~~| 1 0 0 17 ~~}}, {{val~~| 0 1 0 -5 ~~}}, {{val~~| 0 0 1 -2 }}]

: sval mapping generators: ~2, ~3, ~7

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Temperaments discussed elsewhere are:

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

* ''[[Akea]]'' (+385/384) → [[Hemifamity family #Akea|Hemifamity family]]

* ''[[Pessoal]]'' → [[Kalismic temperaments #Pessoal|Kalismic temperaments]]

* ''[[Pessoal]]'' (+9801/9800) → [[Kalismic temperaments #Pessoal|Kalismic temperaments]]

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

* ''[[Lux]]'' (+3025/3024) → [[Lehmerismic temperaments #Lux|Lehmerismic temperaments]]

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

* ''[[Hera]]'' (+6144/6125) → [[Porwell family #Hera|Porwell family]]

Considered below are baffin and sophia.

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[[Comma list]]: 67108864/66976875

~~[[Mapping]]: [~~{{~~val~~| 1 0 0 13 ~~}}, {{val~~| 0 2 0 -7 ~~}}, {{val~~| 0 0 1 -2 }}]

: mapping generators: ~2, ~8192/4725, ~5

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[[Comma list]]: 5632/5625, 131072/130977

~~[[Mapping]]: [~~{{~~val~~| 1 0 0 13 -9 ~~}}, {{val~~| 0 2 0 -7 4 ~~}}, {{val~~| 0 0 1 -2 4 }}]

[[Optimal tuning]] ([[POTE]]): ~400/231 = 951.0585, ~5/4 = 386.7912

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Comma list: 676/675, 1001/1000, 4096/4095

Mapping: [{{~~val~~| 1 0 0 13 -9 1 ~~}}, {{val~~| 0 2 0 -7 4 3 ~~}}, {{val~~| 0 0 1 -2 4 1 }}]

Mapping: {{mapping| 1 0 0 13 -9 1 | 0 2 0 -7 4 3 | 0 0 1 -2 4 1 }}

Optimal tuning (POTE): ~26/15 = 951.0882, ~5/4 = 386.7507

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[[Comma list]]: 42875/42768, 131072/130977

~~[[Mapping]]: [~~{{~~val~~| 1 0 2 3 11 ~~}}, {{val~~| 0 1 0 0 -5 ~~}}, {{val~~| 0 0 5 -3 6 }}]

[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.3024, ~256/245 = 77.1952

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Comma list: 2080/2079, 4096/4095, 13720/13689

Mapping: [{{~~val~~| 1 0 2 3 11 7 ~~}}, {{val~~| 0 1 0 0 -5 -2 ~~}}, {{val~~| 0 0 5 -3 6 -2 }}]

Mapping: {{mapping| 1 0 2 3 11 7 | 0 1 0 0 -5 -2 | 0 0 5 -3 6 -2 }}

Optimal tuning (POTE): ~3/2 = 702.3319, ~117/112 = 77.2152

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Comma list: 595/594, 833/832, 1156/1155, 4096/4095

Mapping: [{{~~val~~| 1 0 2 3 11 7 7 ~~}}, {{val~~| 0 1 0 0 -5 -2 -2 ~~}}, {{val~~| 0 0 5 -3 6 -2 4 }}]

Mapping: {{mapping| 1 0 2 3 11 7 7 | 0 1 0 0 -5 -2 -2 | 0 0 5 -3 6 -2 4 }}

Optimal tuning (POTE): ~3/2 = 702.3205, ~68/65 = 77.2255

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[[Category:Temperament clans]]

[[Category:Olympic clan| ]]

[[Category:Olympic| ]]

[[Category:Rank 3]]

@@ Line 1: / Line 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)]].
+The '''olympic clan''' of [[rank-3 temperament|rank-3]] [[temperament]]s [[tempering out|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)]].
 For the rank-4 olympic temperament, see [[Rank-4 temperament #Olympic (131072/130977)]].
@@ Line 8: / Line 8: @@
 [[Comma list]]: 131072/130977
-[[Sval]] [[mapping]]: [{{val| 1 0 0 17 }}, {{val| 0 1 0 -5 }}, {{val| 0 0 1 -2 }}]
+{{Mapping|legend=2| 1 0 0 17 | 0 1 0 -5 | 0 0 1 -2 }}
 : sval mapping generators: ~2, ~3, ~7
@@ Line 22: / Line 22: @@
 Temperaments discussed elsewhere are:
-* ''[[Akea]]'' → [[Hemifamity family #Akea|Hemifamity family]]
+* ''[[Akea]]'' (+385/384) → [[Hemifamity family #Akea|Hemifamity family]]
-* ''[[Pessoal]]'' → [[Kalismic temperaments #Pessoal|Kalismic temperaments]]
+* ''[[Pessoal]]'' (+9801/9800) → [[Kalismic temperaments #Pessoal|Kalismic temperaments]]
-* ''[[Lux]]'' → [[Lehmerismic temperaments #Lux|Lehmerismic temperaments]]
+* ''[[Lux]]'' (+3025/3024) → [[Lehmerismic temperaments #Lux|Lehmerismic temperaments]]
-* ''[[Hera]]'' → [[Porwell family #Hera|Porwell family]]
+* ''[[Hera]]'' (+6144/6125) → [[Porwell family #Hera|Porwell family]]
 Considered below are baffin and sophia.
@@ Line 35: / Line 35: @@
 [[Comma list]]: 67108864/66976875
-[[Mapping]]: [{{val| 1 0 0 13 }}, {{val| 0 2 0 -7 }}, {{val| 0 0 1 -2 }}]
+{{Mapping|legend=1| 1 0 0 13 | 0 2 0 -7 | 0 0 1 -2 }}
 : mapping generators: ~2, ~8192/4725, ~5
@@ Line 50: / Line 50: @@
 [[Comma list]]: 5632/5625, 131072/130977
-[[Mapping]]: [{{val| 1 0 0 13 -9 }}, {{val| 0 2 0 -7 4 }}, {{val| 0 0 1 -2 4 }}]
+{{Mapping|legend=1| 1 0 0 13 -9 | 0 2 0 -7 4 | 0 0 1 -2 4 }}
 [[Optimal tuning]] ([[POTE]]): ~400/231 = 951.0585, ~5/4 = 386.7912
@@ Line 63: / Line 63: @@
 Comma list: 676/675, 1001/1000, 4096/4095
-Mapping: [{{val| 1 0 0 13 -9 1 }}, {{val| 0 2 0 -7 4 3 }}, {{val| 0 0 1 -2 4 1 }}]
+Mapping: {{mapping| 1 0 0 13 -9 1 | 0 2 0 -7 4 3 | 0 0 1 -2 4 1 }}
 Optimal tuning (POTE): ~26/15 = 951.0882, ~5/4 = 386.7507
@@ Line 78: / Line 78: @@
 [[Comma list]]: 42875/42768, 131072/130977
-[[Mapping]]: [{{val| 1 0 2 3 11 }}, {{val| 0 1 0 0 -5 }}, {{val| 0 0 5 -3 6 }}]
+{{Mapping|legend=1| 1 0 2 3 11 | 0 1 0 0 -5 | 0 0 5 -3 6 }}
 [[Optimal tuning]] ([[POTE]]): ~3/2 = 702.3024, ~256/245 = 77.1952
@@ Line 91: / Line 91: @@
 Comma list: 2080/2079, 4096/4095, 13720/13689
-Mapping: [{{val| 1 0 2 3 11 7 }}, {{val| 0 1 0 0 -5 -2 }}, {{val| 0 0 5 -3 6 -2 }}]
+Mapping: {{mapping| 1 0 2 3 11 7 | 0 1 0 0 -5 -2 | 0 0 5 -3 6 -2 }}
 Optimal tuning (POTE): ~3/2 = 702.3319, ~117/112 = 77.2152
@@ Line 104: / Line 104: @@
 Comma list: 595/594, 833/832, 1156/1155, 4096/4095
-Mapping: [{{val| 1 0 2 3 11 7 7 }}, {{val| 0 1 0 0 -5 -2 -2 }}, {{val| 0 0 5 -3 6 -2 4 }}]
+Mapping: {{mapping| 1 0 2 3 11 7 7 | 0 1 0 0 -5 -2 -2 | 0 0 5 -3 6 -2 4 }}
 Optimal tuning (POTE): ~3/2 = 702.3205, ~68/65 = 77.2255
@@ Line 114: / Line 114: @@
 [[Category:Temperament clans]]
 [[Category:Olympic clan| ]] <!-- main article -->
+[[Category:Olympic| ]] <!-- key article -->
 [[Category:Rank 3]]