Orgonia: Difference between revisions

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-__FORCETOC__
+{{Technical data page}}
-Welcome to Orgonia, the commatic realm of the [[orgonisma]], the [[11-limit|11-limit]] [[Comma|comma]] 65536/65219!
+'''Orgonia''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[orgonisma]].
-=Orgonismic temperament=
+== Orgonismic ==
-Comma: 65536/65219
+[[Subgroup]]: 2.3.5.7.11
-[[Eigenmonzo_subgroup|Minimax tuning subgroup]]: 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)^(1/5), which is 1.679 cents, and the [[5-limit|5-limit]] just.
+[[Comma list]]: 65536/65219
-Mapping: &lt;&lt;1 0 0 2 4]
+[[Mapping]]: <br>
+[{{val| 1 0 0 2 4 }}<br>
+{{val| 0 1 0 0 0 }}<br>
+{{val| 0 0 1 0 0 }}<br>
+{{val| 0 0 0 3 -2 }}]
-[0 1 0 0 0]
+[[Minimax tuning]]:
+* [[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.
-[0 0 1 0 0]
+{{Optimal ET sequence|legend=1| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}
-[0 0 0 3 -2]||
+[[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
-EDOs: 15, 19, 22, 37, 41, 89, 111, 130, 152, 282
+== Subgroup temperaments ==
+=== Orgone ===
+{{Main|Orgone}}
+{{See also| Chromatic pairs #Orgone }}
-[[Spectrum_of_a_temperament|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
+[[File:orgone_heptatonic.jpg|thumb|alt=orgone_heptatonic.jpg|Orgone heptatonic]]
-=Subgroup temperaments=
+Orgone, the 4 &amp; 7 temperament in the 2.7.11 subgroup, is related to [[superkleismic]].
-==Orgone==
+[[Subgroup]]: 2.7.11
-Commas:65536/65219
-Subgroup: 2.7.11
+[[Comma list]]: [[65536/65219]]
-POTE generator: ~77/64 = 323.372
+{{Mapping|legend=2| 1 2 4 | 0 3 -2 }}
-Sval mapping: [&lt;1 2 4|, &lt;0 3 -2|]
+{{Mapping|legend=3| 1 0 0 2 4 | 0 0 0 3 -2 }}
-EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc
+: [[gencom]]: [2 77/64; 65536/65219]
-[[File:orgone_heptatonic.jpg|alt=orgone_heptatonic.jpg|orgone_heptatonic.jpg]]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~77/64 = 323.372
-==Oregon==
+{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475, 783 }}
-Commas: 55/54, 64/63, 100/99
-Subgroup: 2.9.15.7.11
+[[Tp tuning #T2 tuning|RMS error]]: 0.1888 cents
-POTE generator: ~6/5 = 326.139
+==== Oregon ====
+{{See also| Chromatic pairs #Oregon }}
-Sval mapping: [&lt;1 1 1 5 2|, &lt;0 3 4 -3 2|]
+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.
-EDOs: 7, 11, 59b, 70bc, 81bcd, 92bcd
+[[Subgroup]]: 2.9.15.7.11
-The subgroup 2.9.15.7.11 is the [[11-limit|11-limit]] [[k*N_subgroups|2*11 subgroup]], the largest subgroup of the 11-limit on which [[11edo|11edo]] acts like [[22edo|22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[Porcupine_family|porcupine temperament]] restricted to this subgroup.
+[[Comma list]]: 55/54, 64/63, 100/99
-===Orca===
+{{Mapping|legend=2| 1 1 1 5 2 | 0 3 4 -3 2 }}
-Commas: 55/54, 64/63, 100/99, 85/84
+{{Mapping|legend=3| 1 2 3 2 4 | 0 -3/2 -5/2 3 -2 }}
+: [[gencom]]: [2 6/5; 55/54 64/63 100/99]
+[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495
+[[Optimal tuning]] (inharmonic [[POTE]]): ~2 = 1\1,  ~6/5 = 326.139
+{{Optimal ET sequence|legend=1| 7, 11, 37b, 48b, 59b }}
+[[Tp tuning #T2 tuning|RMS error]]: 2.550 cents
+===== Orca =====
 Subgroup: 2.9.15.7.11.17
+Comma list: 55/54, 64/63, 100/99, 85/84
+Sval mapping: [{{val| 1 1 1 5 2 7 }}, {{val| 0 3 4 -3 2 -4 }}]
 POTE generator: ~6/5 = 326.644
-Sval mapping: [&lt;1 1 1 5 2 7|, &lt;0 3 4 -3 2 -4|]
+{{Optimal ET sequence|legend=1| 7, 11, 92bcd, 103bcd }}
-EDOs: 7, 11, 92bcd, 103bcd
+===== Ork =====
+Subgroup: 2.9.15.7.11.17
-===Ork===
+Comma list: 99/98, 121/120, 136/135, 256/255
-Commas: 99/98, 121/120, 136/135, 256/255
-Subgroup: 2.9.15.7.11.17
+Sval mapping: [{{val| 1 1 5 2 4 3 }}, {{val| 0 8 -4 3 -2 4 }}]
 POTE generator: ~17/14 = 325.714
-Sval mapping: [&lt;1 1 5 2 4 3|, &lt;0 8 -4 3 -2 4|]
+{{Optimal ET sequence|legend=1| 11, 37, 48, 59, 70c }}
-EDOs: 11, 37, 48, 59, 70c
 [[Category:Orgonia]]
+[[Category:Commatic realms]]