Porcupine rank-3 family: Difference between revisions

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These are the rank three temperaments tempering out the porcupine comma or maximal diesis, 250/243. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.  
{{Technical data page}}
The '''porcupine rank-3 family''' of [[temperament]]s [[tempering out|tempers out]] the porcupine comma or maximal diesis, [[250/243]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.  


==Sonic==
== Rank-3 porcupine ==
Commas: 55/54, 100/99
[[Subgroup]]: 2.3.5.7


Map: [<1 2 3 0 4|, <0 -3 -5 0 -4|, <0 0 0 1 0|]
[[Comma list]]: [[250/243]]


Generators: ~10/9 = 164.078, ~7 = 3367.841
{{Mapping|legend=1| 1 2 3 0 | 0 -3 -5 0 | 0 0 0 1 }}


EDOs: 7, 14c, 15, 22, 37, 44d, 51, 66, 73ce, 139bce, 212bce
: mapping generators: ~2, ~10/9, ~7


Badness: 0.000523
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.5444{{c}}, ~10/9 = 163.8881{{c}}, ~7/4 = 969.6868{{c}}
: [[error map]]: {{val| -0.456 +5.469 -7.121 -0.050 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.0621{{c}}, ~7/4 = 969.4180{{c}}
: error map: {{val| 0.000 +5.859 -6.624 +0.592 }}


==Tikal==
{{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}
Commas: 56/55, 250/243


Map: [<1 2 3 0 0], <0 -3 -5 0 5|, <0 0 0 1 1|]
[[Badness]] (Sintel): 2.36


POTE generators: ~10/9 = 161.519, ~7 = 3371.046
== Sonic ==
[[Subgroup]]: 2.3.5.7.11


EDOs: 15, 37e, 52be
[[Comma list]]: 55/54, 100/99


Badness: 0.001973
{{Mapping|legend=1| 1 2 3 0 4 | 0 -3 -5 0 -4 | 0 0 0 1 0 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}, ~7/4 = 968.1067{{c}}
: [[error map]]: {{val| +0.329 +6.335 -5.940 -0.061 -6.492 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}, ~7/4 = 968.2673{{c}}
: error map: {{val| 0.000 +6.060 -6.289 -0.559 -7.298 }}
 
{{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}
 
[[Badness]] (Sintel): 0.629
 
== Tikal ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 56/55, 250/243
 
{{Mapping|legend=1| 1 2 3 0 0 | 0 -3 -5 0 5 | 0 0 0 1 1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1195.9857{{c}}, ~11/10 = 160.9790{{c}}, ~7/4 = 967.7973{{c}}
: [[error map]]: {{val| -4.014 +7.079 -3.252 -9.057 +13.346 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 162.1977{{c}}, ~7/4 = 964.6202{{c}}
: error map: {{val| 0.000 +11.452 +2.698 -4.206 +24.291 }}
 
{{Optimal ET sequence|legend=1| 7d, 8d, 15, 30dee, 37ee, 52bee }}
 
[[Badness]] (Sintel): 2.37
 
[[Category:Porcupine rank-3 family| ]] <!-- main article -->
[[Category:Porcupine| ]] <!-- key article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-3 temperaments]]

Latest revision as of 11:48, 16 August 2026

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.

The porcupine rank-3 family of temperaments tempers out the porcupine comma or maximal diesis, 250/243. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

Rank-3 porcupine

Subgroup: 2.3.5.7

Comma list: 250/243

Mapping: [⟨1 2 3 0], ⟨0 -3 -5 0], ⟨0 0 0 1]]

mapping generators: ~2, ~10/9, ~7

Optimal tunings:

  • WE: ~2 = 1199.5444 ¢, ~10/9 = 163.8881 ¢, ~7/4 = 969.6868 ¢
error map: ⟨-0.456 +5.469 -7.121 -0.050]
  • CWE: ~2 = 1200.0000 ¢, ~10/9 = 164.0621 ¢, ~7/4 = 969.4180 ¢
error map: ⟨0.000 +5.859 -6.624 +0.592]

Optimal ET sequence: 7d, 8d, 14c, 15, 22, 37, 51, 73c

Badness (Sintel): 2.36

Sonic

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99

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

Optimal tunings:

  • WE: ~2 = 1200.3290 ¢, ~11/10 = 164.1227 ¢, ~7/4 = 968.1067 ¢
error map: ⟨+0.329 +6.335 -5.940 -0.061 -6.492]
  • CWE: ~2 = 1200.0000 ¢, ~11/10 = 163.9951 ¢, ~7/4 = 968.2673 ¢
error map: ⟨0.000 +6.060 -6.289 -0.559 -7.298]

Optimal ET sequence: 7d, 8d, 14c, 15, 22, 37, 51, 88b

Badness (Sintel): 0.629

Tikal

Subgroup: 2.3.5.7.11

Comma list: 56/55, 250/243

Mapping: [⟨1 2 3 0 0], ⟨0 -3 -5 0 5], ⟨0 0 0 1 1]]

Optimal tunings:

  • WE: ~2 = 1195.9857 ¢, ~11/10 = 160.9790 ¢, ~7/4 = 967.7973 ¢
error map: ⟨-4.014 +7.079 -3.252 -9.057 +13.346]
  • CWE: ~2 = 1200.0000 ¢, ~11/10 = 162.1977 ¢, ~7/4 = 964.6202 ¢
error map: ⟨0.000 +11.452 +2.698 -4.206 +24.291]

Optimal ET sequence: 7d, 8d, 15, 30dee, 37ee, 52bee

Badness (Sintel): 2.37

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