Orgonia: Difference between revisions

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~~Welcome to~~ Orgonia, ~~the commatic realm of~~ the [[orgonisma]]~~, the [[11-limit]] [[comma]] 65536/65219!~~

'''Orgonia''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[orgonisma]].

== Orgonismic ==

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* [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)<sup>1/5</sup>, which is 1.679 cents, and the [[5-limit]] just.

{{~~Val list~~|legend=1| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}

{{Optimal ET sequence|legend=1| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}

[[Complexity spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11

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== Subgroup temperaments ==

=== Orgone ===

[[File:orgone_heptatonic.jpg|thumb|alt=orgone_heptatonic.jpg|Orgone heptatonic]]

Orgone, the 4 & 7 temperament in the 2.7.11 subgroup, is related to [[superkleismic]].

[[Subgroup]]: 2.7.11

[[Comma list]]: 65536/65219

[[Comma list]]: [[65536/65219]]

: [[gencom]]: [2 77/64; 65536/65219]

[[~~Sval~~]] [[~~mapping~~]]: ~~[{{val|~~ 1 ~~2 4 }}~~, ~~{{val| 0 3 -2 }}]~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~77/64 = 323.372

~~[[POTE generator]]: ~77/64~~ = ~~323.372~~

{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475, 783 }}

~~{{Val list~~|~~legend=1| 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc }}~~

[[Tp tuning #T2 tuning|RMS error]]: 0.1888 cents

==== Oregon ====

The subgroup 2.9.15.7.11 is the [[11-limit]] [[k*N_subgroups|2*11 subgroup]], the largest subgroup of the 11-limit on which [[11edo]] acts like [[22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[porcupine]] restricted to this subgroup.

Subgroup: 2.9.15.7.11

[[Subgroup]]: 2.9.15.7.11

[[Comma list]]: 55/54, 64/63, 100/99

~~Comma list~~: 55/54, 64/63, 100/99

: [[gencom]]: [2 6/5; 55/54 64/63 100/99]

~~Sval mapping:~~ [~~{{val~~| 1 1 1 5 2 }}, ~~{{val|0 3 4 -3 2 }}]~~

[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495

[[Optimal tuning]] (inharmonic [[POTE]]): ~2 = 1\1, ~6/5 = 326.139

~~POTE generator: ~6/5~~ = ~~326.139~~

~~Optimal GPV sequence~~: ~~{{val list| 7, 11, 59b, 70bc, 81bcd, 92bcd }}~~

[[Tp tuning #T2 tuning|RMS error]]: 2.550 cents

===== Orca =====

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POTE generator: ~6/5 = 326.644

Optimal ~~GPV~~ sequence~~: {{val list~~| 7, 11, 92bcd, 103bcd }}

===== Ork =====

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POTE generator: ~17/14 = 325.714

Optimal ~~GPV~~ sequence~~: {{val list~~| 11, 37, 48, 59, 70c }}

[[Category:Orgonia]]

[[Category:Commatic realms]]

@@ Line 1: / Line 1: @@
-Welcome to Orgonia, the commatic realm of the [[orgonisma]], the [[11-limit]] [[comma]] 65536/65219!
+{{Technical data page}}
+'''Orgonia''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[orgonisma]].
 == Orgonismic ==
@@ Line 15: / Line 16: @@
 * [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)<sup>1/5</sup>, which is 1.679 cents, and the [[5-limit]] just.
-{{Val list|legend=1| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}
+{{Optimal ET sequence|legend=1| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}
 [[Complexity spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11
@@ Line 21: / Line 22: @@
 == Subgroup temperaments ==
 === Orgone ===
+{{Main|Orgone}}
+{{See also| Chromatic pairs #Orgone }}
 [[File:orgone_heptatonic.jpg|thumb|alt=orgone_heptatonic.jpg|Orgone heptatonic]]
+Orgone, the 4 &amp; 7 temperament in the 2.7.11 subgroup, is related to [[superkleismic]].
 [[Subgroup]]: 2.7.11
-[[Comma list]]: 65536/65219
+[[Comma list]]: [[65536/65219]]
+{{Mapping|legend=2| 1 2 4 | 0 3 -2 }}
+{{Mapping|legend=3| 1 0 0 2 4 | 0 0 0 3 -2 }}
+: [[gencom]]: [2 77/64; 65536/65219]
-[[Sval]] [[mapping]]: [{{val| 1 2 4 }}, {{val| 0 3 -2 }}]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~77/64 = 323.372
-[[POTE generator]]: ~77/64 = 323.372
+{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475, 783 }}
-{{Val list|legend=1| 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc }}
+[[Tp tuning #T2 tuning|RMS error]]: 0.1888 cents
 ==== Oregon ====
+{{See also| Chromatic pairs #Oregon }}
 The subgroup 2.9.15.7.11 is the [[11-limit]] [[k*N_subgroups|2*11 subgroup]], the largest subgroup of the 11-limit on which [[11edo]] acts like [[22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[porcupine]] restricted to this subgroup.
-Subgroup: 2.9.15.7.11
+[[Subgroup]]: 2.9.15.7.11
+[[Comma list]]: 55/54, 64/63, 100/99
+{{Mapping|legend=2| 1 1 1 5 2 | 0 3 4 -3 2 }}
+{{Mapping|legend=3| 1 2 3 2 4 | 0 -3/2 -5/2 3 -2 }}
-Comma list: 55/54, 64/63, 100/99
+: [[gencom]]: [2 6/5; 55/54 64/63 100/99]
-Sval mapping: [{{val| 1 1 1 5 2 }}, {{val|0 3 4 -3 2 }}]
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495
+[[Optimal tuning]] (inharmonic [[POTE]]): ~2 = 1\1,  ~6/5 = 326.139
-POTE generator: ~6/5 = 326.139
+{{Optimal ET sequence|legend=1| 7, 11, 37b, 48b, 59b }}
-Optimal GPV sequence: {{val list| 7, 11, 59b, 70bc, 81bcd, 92bcd }}
+[[Tp tuning #T2 tuning|RMS error]]: 2.550 cents
 ===== Orca =====
@@ Line 55: / Line 76: @@
 POTE generator: ~6/5 = 326.644
-Optimal GPV sequence: {{val list| 7, 11, 92bcd, 103bcd }}
+{{Optimal ET sequence|legend=1| 7, 11, 92bcd, 103bcd }}
 ===== Ork =====
@@ Line 66: / Line 87: @@
 POTE generator: ~17/14 = 325.714
-Optimal GPV sequence: {{val list| 11, 37, 48, 59, 70c }}
+{{Optimal ET sequence|legend=1| 11, 37, 48, 59, 70c }}
 [[Category:Orgonia]]
 [[Category:Commatic realms]]