Whitewood family: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The '''whitewood family''' of [[temperament]] | The '''whitewood family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the Pythagorean apotome, [[2187/2048]]. Consequently the [[3/2|fifth]]s are always 4/7 of an [[octave]], a distinctly flat 685.714 [[cent]]s. While quite flat, this is close enough to a just fifth to serve as one, and some people are fond of it. | ||
== Whitewood == | == Whitewood == | ||
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[[Badness]] (Sintel): 3.63 | [[Badness]] (Sintel): 3.63 | ||
Scales: [[7L 7s | Scales: [[7L 7s/13:7]] (140edo) | ||
=== Overview to extensions === | === Overview to extensions === | ||
Temperaments discussed elsewhere include: | Temperaments discussed elsewhere include: | ||
* ''[[Sept]]'' → [[Very low accuracy temperaments #Sept|Very low accuracy temperaments]] | * ''[[Sept]]'' → [[Very low accuracy temperaments #Sept|Very low accuracy temperaments]] | ||
Considered below are septimal whitewood, redwood, and | Considered below are septimal whitewood, redwood, greenwood, and jamesbond. | ||
== Septimal whitewood == | == Septimal whitewood == | ||
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Badness (Sintel): 2.23 | Badness (Sintel): 2.23 | ||
== 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=0| 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=0| 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=0| 7(df), 14cf }} | |||
Badness (Sintel): 0.933 | |||
[[Category:Whitewood family| ]] <!-- main article --> | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category: | [[Category:Catalogs of rank-2 temperaments]] | ||