Hemimage temperaments: Difference between revisions

Switch to Sintel's badness, WE & CWE tunings
- classical squarschmidt (addressed in the 3et equivalence continuum)
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== Squarschmidt ==
== Squarschmidt ==
A generator for the squarschimidt temperament is the fourth root of [[5/2]], (5/2)<sup>1/4</sup>, tuned around 396.6 cents. The squarschimidt temperament can be described as {{nowrap| 118 & 239 }} temperament, tempering out the hemimage comma and quasiorwellisma, 29360128/29296875 in the 7-limit. In the 11-limit, it tempers out 3025/3024, 5632/5625, and 12005/11979, and the generator represents ~44/35.
: ''For the 5-limit version, see [[Father–3 equivalence continuum #Squarschmidt (5-limit)]].''


[[Subgroup]]: 2.3.5
Squarschimidt may be described as {{nowrap| 118 & 121 }} temperament. The extension here is a less accurate 7-limit interpretation, tempering out the hemimage comma and quasiorwellisma, 29360128/29296875. In the 11-limit, it tempers out 3025/3024, 5632/5625, and 12005/11979, and the generator represents ~44/35.  
 
[[Comma list]]: {{monzo| 61 4 -29 }}
 
{{Mapping|legend=1| 1 -8 1 | 0 29 4 }}
: mapping generators: ~2, ~98304/78125
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9653{{c}}, ~98304/78125 = 396.6094{{c}}
: [[error map]]: {{val| -0.099 +0.543 +0.029 -0.719 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~98304/78125 = 396.6201{{c}}
: error map: {{val| 0.000 +0.653 +0.253 -0.552 }}
 
{{Optimal ET sequence|legend=1| 118, 593, 711, 829, 947, 9588cc, 10535cc, 11482ccc }}
 
[[Badness]] (Sintel): 5.12


=== 7-limit ===
=== 7-limit ===