Xenharmonic Wiki

Meantone family: Difference between revisions

← Older editNewer edit →

CompactStar (talk | contribs)

1 user group
5,894 edits
VisualWikitext
CompactStar (talk | contribs)
autopatrolled
5,894 edits
moving mohair and the other one to rastmic clan because the other mohaha extensions are there
Tag: Reverted
CompactStar (talk | contribs)
autopatrolled
5,894 edits
reverting everything back because I forgot that Mohajira is 2.3.5.7
Tag: Manual revert
Line 1,231: Line 1,231:


Badness (Sintel): 1.67
Badness (Sintel): 1.67
== Mohajira ==
{{Main| Mohajira }}
Mohajira can be viewed as derived from [[mohaha]] which maps the interval half a [[chromatic semitone|chroma]] flat of the minor seventh to ~7/4 so that 7/4 is mapped to a semidiminished seventh (C–Bdb), although mohajira really makes more sense as an 11-limit temperament. It tempers out 6144/6125, the [[porwell comma]]. It can be described as {{nowrap| 24 & 31 }}; its ploidacot is dicot. [[31edo]] makes for an excellent mohajira tuning, with generator 9\31. Note that while 24 + 31 = [[55edo]] doesn't apear in the optimal ET sequence, it is a [[patent val]] tuning and recommendable if you prefer a light meantone tempering.
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 81/80, 6144/6125
{{Mapping|legend=1| 1 1 0 6 | 0 2 8 -11 }}
: mapping generators: ~2, ~128/105
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.8160{{c}}, ~128/105 = 348.6518{{c}}
: [[error map]]: {{val| +0.816 -3.835 +2.901 +0.900 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 348.4194{{c}}
: error map: {{val| 0.000 -5.116 +1.041 -1.439 }}
[[Minimax tuning]]:
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~128/105 = {{monzo| 0 0 1/8 }}
: [[projection map]]: {{monzo list| 1 0 0 0 | 1 0 1/4 0 | 0 0 1 0 | 6 0 -11/8 0 }}
: [[eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.5
[[Tuning ranges]]:
* 7- and 9-odd-limit [[diamond monotone]]: ~128/105 = [347.368, 350.000] (11\38 to 7\24)
* 7-odd-limit [[diamond tradeoff]]: ~128/105 = [347.393, 350.978]
* 9-odd-limit diamond tradeoff: ~128/105 = [345.601, 350.978]
[[Algebraic generator]]: Mohabis, real root of 3''x''<sup>3</sup> - 3''x''<sup>2</sup> - 1, 348.6067 cents. Corresponding recurrence converges quickly.
{{Optimal ET sequence|legend=1| 7, 24, 31 }}
[[Badness]] (Sintel): 1.41
Scales: [[mohaha7]], [[mohaha10]]
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 81/80, 121/120, 176/175
{{Mapping|legend=0| 1 1 0 6 2 | 0 2 8 -11 5 }}
Optimal tunings:
* WE: ~2 = 1201.1562{{c}}, ~11/9 = 348.8124{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 348.4910{{c}}
Minimax tuning:
* 11-odd-limit: ~11/9 = {{monzo| 0 0 1/8 }}
: projection map: [{{Monzo| 1 0 0 0 0 }}, {{monzo| 1 0 1/4 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 6 0 -11/8 0 0 }}, {{monzo| 2 0 5/8 0 0 }}]
: unchanged-interval (eigenmonzo) basis: 2.5
Tuning ranges:
* 11-odd-limit diamond monotone: ~11/9 = [348.387, 350.000] (9\31 to 7\24)
* 11-odd-limit diamond tradeoff: ~11/9 = [344.999, 350.978]
{{Optimal ET sequence|legend=0| 7, 24, 31 }}
Badness (Sintel): 0.862
Scales: [[mohaha7]], [[mohaha10]]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 81/80, 105/104, 121/120
{{Mapping|legend=0| 1 1 0 6 2 4 | 0 2 8 -11 5 -1 }}
Optimal tunings:
* WE: ~2 = 1200.4256{{c}}, ~11/9 = 348.6819{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 348.5622{{c}}
{{Optimal ET sequence|legend=0| 7, 24, 31 }}
Badness (Sintel): 0.966
Scales: [[mohaha7]], [[mohaha10]]
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 66/65, 81/80, 105/104, 121/120, 154/153
{{Mapping|legend=0| 1 1 0 6 2 4 7 | 0 2 8 -11 5 -1 -10 }}
Optimal tunings:
* WE: ~2 = 1200.0382{{c}}, ~11/9 = 348.7471{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 348.7360{{c}}
{{Optimal ET sequence|legend=0| 7, 24, 31 }}
Badness (Sintel): 1.05
Scales: [[mohaha7]], [[mohaha10]]
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 66/65, 77/76, 81/80, 96/95, 105/104, 153/152
{{Mapping|legend=0| 1 1 0 6 2 4 7 6 | 0 2 8 -11 5 -1 -10 -6 }}
Optimal tunings:
* WE: ~2 = 1199.7469{{c}}, ~11/9 = 348.7367{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 348.8117{{c}}
{{Optimal ET sequence|legend=0| 7, 24, 31, 55 }}
Badness (Sintel): 1.05
Scales: [[mohaha7]], [[mohaha10]]
== Mohamaq ==
Mohamaq is a lower-accuracy alternative to mohajira that favors tunings sharp of 24edo. It may be described as {{nowrap| 17c & 24 }}; its ploidacot is dicot, the same as mohajira. [[7/4]] is mapped to the semi-augmented sixth (C–A{{demisharp2}}), extending [[hemif]].
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 81/80, 392/375
{{Mapping|legend=1| 1 1 0 -1 | 0 2 8 13 }}
: mapping generators: ~2, ~25/21
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.0661{{c}}, ~25/21 = 350.3127{{c}}
: [[error map]]: {{val| -0.934 -2.264 +16.188 -13.827 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~25/21 = 350.4856{{c}}
: error map: {{val| 0.000 -0.984 +17.571 -12.513 }}
{{Optimal ET sequence|legend=1| 7d, 17c, 24 }}
[[Badness]] (Sintel): 1.97
Scales: [[mohaha7]], [[mohaha10]]
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 56/55, 77/75, 243/242
{{Mapping|legend=0| 1 1 0 -1 2 | 0 2 8 13 5 }}
Optimal tunings:
* WE: ~2 = 1199.1924{{c}}, ~11/9 = 350.3286{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.4821{{c}}
{{Optimal ET sequence|legend=0| 7d, 17c, 24 }}
Badness (Sintel): 1.20
Scales: [[mohaha7]], [[mohaha10]]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 66/65, 77/75, 243/242
{{Mapping|legend=0| 1 1 0 -1 2 4 | 0 2 8 13 5 -1 }}
Optimal tunings:
* WE: ~2 = 1198.5986{{c}}, ~11/9 = 350.3353{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.6459{{c}}
{{Optimal ET sequence|legend=0| 7d, 17c, 24, 41c }}
Badness (Sintel): 1.19
Scales: [[mohaha7]], [[mohaha10]]


== Liese ==
== Liese ==
Retrieved from "https://en.xen.wiki/w/Meantone_family"