Ragismic microtemperaments: Difference between revisions

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== Palladium ==

The name of ''palladium ~~temperament~~'' comes from ~~Palladium~~, the 46th element.

The name of the ''palladium'' temperament comes from palladium, the 46th element. Palladium has a period of 1/46 octave. It tempers out the 46-9/5-comma, {{monzo| -39 92 -46 }}, by which 46 minortones (10/9) fall short of seven octaves. This temperament can be described as 46&414 temperament, which tempers out {{monzo| -51 8 2 12 }} as well as the ragisma.

Palladium temperament has a period of 1/46 octave. It tempers out the 46-9/5-comma, {{monzo|-39 92 -46}}, by which 46 minortones (10/9) fall short of seven octaves. This temperament can be described as 46&414 temperament, which tempers out {{monzo|-51 8 2 12}} as well as the ragisma.

[[Subgroup]]: 2.3.5.7

Subgroup: 2.3.5.7

[[Comma list]]: 4375/4374, 2270317133144025/2251799813685248

[[Mapping]]: [{{val|46 73 107 129}}, {{val|0 -1 -2 1}}]

[[Mapping]]: [{{val| 46 73 107 129 }}, {{val| 0 -1 -2 1 }}]

~~[[Wedgie]]:~~ {{~~multival~~|46 92 -46 39 -202 -365}}

[[POTE ~~generator~~]]: ~3/2 = 701.6074

[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.6074

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Subgroup: 2.3.5.7.11

Comma list: 3025/3024, ~~9801~~/~~9800~~, 134775333/134217728

Comma list: 3025/3024, 4375/4374, 134775333/134217728

Mapping: [{{val|46 73 107 129 159}}, {{val|0 -1 -2 1 1}}]

Mapping: [{{val| 46 73 107 129 159 }}, {{val| 0 -1 -2 1 1 }}]

POTE ~~generator~~: ~3/2 = 701.5951

Optimal tuning (POTE): ~3/2 = 701.5951

Optimal GPV sequence: {{Val list| 46, 368, 414, 460, 874de }}

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Comma list: 3025/3024, 4225/4224, 4375/4374, 26411/26364

Mapping: [{{val|46 73 107 129 159 170}}, {{val|0 -1 -2 1 1 2}}]

Mapping: [{{val| 46 73 107 129 159 170 }}, {{val| 0 -1 -2 1 1 2 }}]

POTE ~~generator~~: ~3/2 = 701.6419

Optimal tuning (POTE): ~3/2 = 701.6419

Optimal GPV sequence: {{Val list| 46, 368, 414, 460, 874de, 1334de }}

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Comma list: 833/832, 1089/1088, 1225/1224, 1701/1700, 4225/4224

Mapping: [{{val|46 73 107 129 159 170 188}}, {{val|0 -1 -2 1 1 2 0}}]

Mapping: [{{val| 46 73 107 129 159 170 188 }}, {{val| 0 -1 -2 1 1 2 0 }}]

POTE ~~generator~~: ~3/2 = 701.6425

Optimal tuning (POTE): ~3/2 = 701.6425

Optimal GPV sequence: {{Val list| 46, 368, 414, 460, 874de, 1334deg }}

@@ Line 1,956: / Line 1,956: @@
 == Palladium ==
-The name of ''palladium temperament'' comes from Palladium, the 46th element.
+The name of the ''palladium'' temperament comes from palladium, the 46th element. Palladium has a period of 1/46 octave. It tempers out the 46-9/5-comma, {{monzo| -39 92 -46 }}, by which 46 minortones (10/9) fall short of seven octaves. This temperament can be described as 46&amp;414 temperament, which tempers out {{monzo| -51 8 2 12 }} as well as the ragisma.
-Palladium temperament has a period of 1/46 octave. It tempers out the 46-9/5-comma, {{monzo|-39 92 -46}}, by which 46 minortones (10/9) fall short of seven octaves. This temperament can be described as 46&amp;414 temperament, which tempers out {{monzo|-51 8 2 12}} as well as the ragisma.
+[[Subgroup]]: 2.3.5.7
-Subgroup: 2.3.5.7
 [[Comma list]]: 4375/4374, 2270317133144025/2251799813685248
-[[Mapping]]: [{{val|46 73 107 129}}, {{val|0 -1 -2 1}}]
+[[Mapping]]: [{{val| 46 73 107 129 }}, {{val| 0 -1 -2 1 }}]
-[[Wedgie]]: {{multival|46 92 -46 39 -202 -365}}
+{{Multival|legend=1| 46 92 -46 39 -202 -365 }}
-[[POTE generator]]: ~3/2 = 701.6074
+[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.6074
 {{Val list|legend=1| 46, 368, 414, 460, 874d }}
@@ Line 1,977: / Line 1,975: @@
 Subgroup: 2.3.5.7.11
-Comma list: 3025/3024, 9801/9800, 134775333/134217728
+Comma list: 3025/3024, 4375/4374, 134775333/134217728
-Mapping: [{{val|46 73 107 129 159}}, {{val|0 -1 -2 1 1}}]
+Mapping: [{{val| 46 73 107 129 159 }}, {{val| 0 -1 -2 1 1 }}]
-POTE generator: ~3/2 = 701.5951
+Optimal tuning (POTE): ~3/2 = 701.5951
 Optimal GPV sequence: {{Val list| 46, 368, 414, 460, 874de }}
@@ Line 1,992: / Line 1,990: @@
 Comma list: 3025/3024, 4225/4224, 4375/4374, 26411/26364
-Mapping: [{{val|46 73 107 129 159 170}}, {{val|0 -1 -2 1 1 2}}]
+Mapping: [{{val| 46 73 107 129 159 170 }}, {{val| 0 -1 -2 1 1 2 }}]
-POTE generator: ~3/2 = 701.6419
+Optimal tuning (POTE): ~3/2 = 701.6419
 Optimal GPV sequence: {{Val list| 46, 368, 414, 460, 874de, 1334de }}
@@ Line 2,005: / Line 2,003: @@
 Comma list: 833/832, 1089/1088, 1225/1224, 1701/1700, 4225/4224
-Mapping: [{{val|46 73 107 129 159 170 188}}, {{val|0 -1 -2 1 1 2 0}}]
+Mapping: [{{val| 46 73 107 129 159 170 188 }}, {{val| 0 -1 -2 1 1 2 0 }}]
-POTE generator: ~3/2 = 701.6425
+Optimal tuning (POTE): ~3/2 = 701.6425
 Optimal GPV sequence: {{Val list| 46, 368, 414, 460, 874de, 1334deg }}