Xenharmonic Wiki

Orgonia: Difference between revisions

← Older edit
VisualWikitext
Cleanup
m Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"
 
(6 intermediate revisions by 4 users not shown)
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 ==
== Orgonismic ==
Line 13: Line 14:


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[Eigenmonzo 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.
* [[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
[[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 ==
== Subgroup temperaments ==
=== Orgone ===
=== Orgone ===
{{Main|Orgone}}
{{See also| Chromatic pairs #Orgone }}
[[File:orgone_heptatonic.jpg|thumb|alt=orgone_heptatonic.jpg|Orgone heptatonic]]
[[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
[[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 ====
==== 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.
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 =====
===== Orca =====
Line 55: Line 76:
POTE generator: ~6/5 = 326.644
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 =====
===== Ork =====
Line 66: Line 87:
POTE generator: ~17/14 = 325.714
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:Orgonia]]
[[Category:Commatic realms]]
[[Category:Commatic realms]]
Retrieved from "https://en.xen.wiki/w/Orgonia"