Misty: Difference between revisions
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{{Infobox regtemp | |||
| Title = Misty | |||
| Subgroups = 2.3.5, 2.3.5.7, 2.3.5.7.17.19 | |||
| Comma basis = [[67108864/66430125]] (5-limit); <br>[[3136/3125]], [[5120/5103]] (7-limit); <br>[[256/255]], [[324/323]], [[400/399]], [[476/475]]<br>(2.3.5.7.17.19) | |||
| Edo join 1 = 12 | Edo join 2 = 99 | |||
| Mapping = 3; 1 -4 -10 3 1 | |||
| Generators = 3/2 | |||
| Generators tuning = 703.1 | |||
| Optimization method = CWE | |||
| MOS scales = [[3L 9s]], [[12L 3s]] | |||
| Odd limit 1 = 9 | Mistuning 1 = 1.96 | Complexity 1 = 39 | |||
}} | |||
'''Misty''' is the [[regular temperament]] [[tempering out]] the [[misty comma]]. It equates the [[Pythagorean comma]] with the [[diesis]], and splits this interval into three equal parts, one representing the [[schisma]]~[[diaschisma]], and two representing the [[syntonic comma]]. Consequently, the octave is also split into three parts of [[512/405]] each. This temperament, supported by [[12edo|12et]], is notably in the [[schismic–Pythagorean equivalence continuum]], with {{nowrap|''n'' {{=}} 3}}. | '''Misty''' is the [[regular temperament]] [[tempering out]] the [[misty comma]]. It equates the [[Pythagorean comma]] with the [[diesis]], and splits this interval into three equal parts, one representing the [[schisma]]~[[diaschisma]], and two representing the [[syntonic comma]]. Consequently, the octave is also split into three parts of [[512/405]] each. This temperament, supported by [[12edo|12et]], is notably in the [[schismic–Pythagorean equivalence continuum]], with {{nowrap|''n'' {{=}} 3}}. | ||
In the 7-limit, the canonical extension tempers out [[3136/3125]] and [[5120/5103]]. Possible tunings include [[87edo]], [[99edo]] and [[111edo]]. | In the 7-limit, the canonical extension tempers out [[3136/3125]] and [[5120/5103]]. Possible tunings include [[87edo]], [[99edo]] and [[111edo]]. | ||
See [[Misty family]] for technical data. | See [[Misty family #Misty]] and [[Misty family #Septimal misty|#Septimal misty]] for technical data. | ||
== Interval chain == | == Interval chain == | ||
| Line 60: | Line 72: | ||
| '''8/5''' | | '''8/5''' | ||
| 12.2 | | 12.2 | ||
| 126/125, 225/224 | | 126/125, 225/224 | ||
|- | |- | ||
| 5 | | 5 | ||