User:Hotcrystal0/Temperaments: Difference between revisions

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=== Tridecapyth ===
=== Tridecapyth ===
Tridecapyth equates a stack of twenty [[3/2]] octave-reduced with [[13/8]], or alternatively two [[pythagorean comma]]s with [[1053/1024]].


[[Subgroup]]: 2.3.13
See [[Tridecapyth comma#Tridecapyth]].
 
[[Comma list]]: 3489660928/3486784401
 
{{Mapping|legend=2| [unfinished] | }}
: mapping generators: ~2, ~3/2
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.978{{c}}, ~3/2 = 702.017{{c}}
: [[error map]]: {{val| -0.022, +0.040, -0.011 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.028{{c}}
: error map: {{val| 0.000, +0.073, +0.039 }}
 
{{Optimal ET sequence|legend=1| 12, 29f, 41, 53, 94, 147, 494, 641, 788, 2217, 3005 }}
 
[[Badness]] (Sintel): 0.211


==Rank-3==
==Rank-3==

Revision as of 00:28, 24 June 2026

This page is for hotcrystal0's temperament research.

Rank-2

Tridecapyth

See Tridecapyth comma#Tridecapyth.

Rank-3

Unnamed 159 & 166 & 171

Subgroup: 2.3.5.7

Comma list: 10763703445887/10737418240000

Mapping: [⟨1 0 0], ⟨1 1 0], ⟨3 1 -3], ⟨8 -6 -4]]

Optimal tunings:

  • WE: ~2 = 1200.057 ¢, ~3/2 = 701.806 ¢, ~20480/15309 = 505.209 ¢
error map: ⟨+0.057 -0.093 +0.036 -0.040]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 701.777 ¢, ~20480/15309 = 505.167 ¢
error map: ⟨0.000 -0.178 -0.039 -0.155]

Optimal ET sequence: [to be finished]

Badness (Sintel): [to be finished]

Rank-4

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