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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


Map: &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 map: [&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 map: [&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
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
POTE generator: ~6/5 = 326.644


Sval map: [&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
POTE generator: ~17/14 = 325.714


Sval map: [&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:Orgonia]]
[[Category:Commatic realms]]

Latest revision as of 13:45, 13 April 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

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

Orgonismic

Subgroup: 2.3.5.7.11

Comma list: 65536/65219

Mapping:
[⟨1 0 0 2 4]
⟨0 1 0 0 0]
⟨0 0 1 0 0]
⟨0 0 0 3 -2]]

Minimax tuning:

Optimal ET sequence: 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

Subgroup temperaments

Orgone

Main article: Orgone
See also: Chromatic pairs § Orgone
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

Sval mapping: [⟨1 2 4], ⟨0 3 -2]]

Gencom mapping: [⟨1 0 0 2 4], ⟨0 0 0 3 -2]]

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

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

Optimal ET sequence: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475, 783

RMS error: 0.1888 cents

Oregon

See also: Chromatic pairs § Oregon

The subgroup 2.9.15.7.11 is the 11-limit 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

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

Sval mapping: [⟨1 1 1 5 2], ⟨0 3 4 -3 2]]

Gencom mapping: [⟨1 2 3 2 4], ⟨0 -3/2 -5/2 3 -2]]

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

Optimal tuning (subgroup POTE): ~2 = 1\1, ~6/5 = 325.495 Optimal tuning (inharmonic POTE): ~2 = 1\1, ~6/5 = 326.139

Optimal ET sequence: 7, 11, 37b, 48b, 59b

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: [⟨1 1 1 5 2 7], ⟨0 3 4 -3 2 -4]]

POTE generator: ~6/5 = 326.644

Optimal ET sequence: 7, 11, 92bcd, 103bcd

Ork

Subgroup: 2.9.15.7.11.17

Comma list: 99/98, 121/120, 136/135, 256/255

Sval mapping: [⟨1 1 5 2 4 3], ⟨0 8 -4 3 -2 4]]

POTE generator: ~17/14 = 325.714

Optimal ET sequence: 11, 37, 48, 59, 70c

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