7th-octave temperaments: Difference between revisions

- akjaysmic (addressed in very high accuracy temps)
- jamesbond (more properly addressed in whitewood family)
Line 6: Line 6:


Temperaments discussed elsewhere include:
Temperaments discussed elsewhere include:
* ''Septant '' [[Schismatic family#Septant|Schismatic family]]
* ''[[Septant]]'' [[Schismatic family #Septant|Schismatic family]]
* ''Brahmagupta '' [[Ragismic microtemperaments#Brahmagupta|Ragismic microtemperaments]]
* ''[[Brahmagupta]]'' [[Ragismic microtemperaments #Brahmagupta|Ragismic microtemperaments]]
* ''Absurdity'' ''→'' [[Syntonic–chromatic equivalence continuum#Absurdity|Syntonic–chromatic equivalence continuum]]
* ''[[Absurdity]]'' → [[Porwell temperaments #Absurdity|Porwell temperaments]]
 
== Jamesbond ==
This temperament uses exactly the same 5-limit as 7et, but the harmonic 7 is mapped to an independent generator. It is so named because its "[[wedgie]]" (a kind of mathematical object representing the temperament) starts with {{multival| 0 0 7 … }} (in fact, it is {{multival| 0 0 7 0 11 16 }})
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 25/24, 81/80
 
{{Mapping|legend=1| 7 11 16 0 | 0 0 0 1 }}
: mapping generators: ~10/9, ~7
 
[[Optimal tuning]]s:
* [[WE]]: ~10/9 = 172.790{{c}}, ~7/4 = 949.343{{c}}
: [[error map]]: {{val| +9.533 -1.261 -21.668 -0.418 }}
* [[CWE]]: ~10/9 = 171.429{{c}}, ~7/4 = 948.499{{c}}
: error map: {{val| -0.000 -16.241 -43.457 -20.327 }}
 
{{Optimal ET sequence|legend=1| 7(d), 14c }}
 
[[Badness]] (Sintel): 1.06
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 25/24, 33/32, 45/44
 
Mapping: {{mapping| 7 11 16 0 24 | 0 0 0 1 0 }}
 
Optimal tunings:
* WE: ~10/9 = 172.830{{c}}, ~7/4 = 948.784{{c}}
* CWE: ~10/9 = 171.429{{c}}, ~7/4 = 946.554{{c}}
 
{{Optimal ET sequence|legend=1| 7(d), 14c }}
 
Badness (Sintel): 0.778
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 25/24, 27/26, 33/32, 40/39
 
Mapping: {{mapping| 7 11 16 0 24 26 | 0 0 0 1 0 0 }}
 
Optimal tunings:
* WE: ~10/9 = 172.390{{c}}, ~7/4 = 954.559{{c}}
* CWE: ~10/9 = 171.429{{c}}, ~7/4 = 952.367{{c}}
 
{{Optimal ET sequence|legend=1| 7(d), 14c }}
 
Badness (Sintel): 0.951
 
==== Austinpowers ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 25/24, 33/32, 45/44, 65/63
 
Mapping: {{mapping| 7 11 16 0 24 6 | 0 0 0 1 0 1 }}
 
Optimal tunings:
* WE: ~10/9 = 172.873{{c}}, ~7/4 = 960.581{{c}}
* CWE: ~10/9 = 171.429{{c}}, ~7/4 = 958.793{{c}}
 
{{Optimal ET sequence|legend=1| 7(df), 14cf }}
 
Badness (Sintel): 0.933


== Nitrogen ==
== Nitrogen ==