Whitewood family: Difference between revisions

m - redundant category
- mujannab (covered in very low accuracy temps)
Line 1: Line 1:
{{Technical data page}}
{{Technical data page}}
The '''whitewood family''' of [[temperament]]s [[tempering out|tempers out]] the 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.
The '''whitewood family''' of [[temperament]]s [[tempering out|tempers out]] the 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.
Temperaments discussed elsewhere include:
* ''[[Jamesbond]]'' → [[7th-octave temperaments#Jamesbond|7th-octave temperaments]]


== Whitewood ==
== Whitewood ==
Line 28: Line 25:


Scales: [[7L 7s in 140edo]]
Scales: [[7L 7s in 140edo]]
=== Overview to extensions ===
Temperaments discussed elsewhere include:
* ''[[Jamesbond]]'' → [[7th-octave temperaments#Jamesbond|7th-octave temperaments]]
* ''[[Sept]]'' → [[Very low accuracy temperaments #Sept|Very low accuracy temperaments]]
Considered below are septimal whitewood, redwood, and greenwood.


== Septimal whitewood ==
== Septimal whitewood ==
Line 109: Line 113:


Badness (Sintel): 2.59
Badness (Sintel): 2.59
== Mujannab ==
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 54/49, 64/63
{{Mapping|legend=1| 7 11 0 20 | 0 0 1 0 }}
[[Optimal tuning]]s:
* [[WE]]: ~9/8 = 170.8233{{c}}, ~5/4 = 393.7921{{c}} (~15/14 = 52.1453{{c}})
: [[error map]]: {{val| -4.236 -22.898 -0.994 +47.642 }}
* [[CWE]]: ~9/8 = 171.4286{{c}}, ~5/4 = 392.7194{{c}} (~15/14 = 49.8622{{c}})
: error map: {{val| 0.000 -16.241 +6.406 +59.746 }}
{{Optimal ET sequence|legend=1| 7, 14d }}
[[Badness]] (Sintel): 2.68
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 45/44, 54/49, 64/63
Mapping: {{mapping| 7 11 0 20 8 | 0 0 1 0 1 }}
Optimal tunings:
* WE: ~11/10 = 170.8171{{c}}, ~5/4 = 393.2529{{c}} (~33/32 = 51.6187{{c}})
* CWE: ~11/10 = 171.4286{{c}}, ~5/4 = 391.8401{{c}} (~33/32 = 48.9830{{c}})
{{Optimal ET sequence|legend=0| 7, 14de }}
Badness (Sintel): 2.02
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 45/44, 52/49, 64/63
Mapping: {{mapping| 7 11 0 20 8 26 | 0 0 1 0 1 0 }}
Optimal tunings:
* WE: ~11/10 = 170.7953{{c}}, ~5/4 = 393.6112{{c}} (~33/32 = 52.0206{{c}})
* CWE: ~11/10 = 171.4286{{c}}, ~5/4 = 392.7250{{c}} (~33/32 = 49.8678{{c}})
{{Optimal ET sequence|legend=0| 7, 14de }}
Badness (Sintel): 1.77


== Greenwood ==
== Greenwood ==