Misty: Difference between revisions
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'''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 [[ | '''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]]. | ||
| Line 7: | Line 7: | ||
== Interval chain == | == Interval chain == | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
|- | |||
! rowspan="2" | # | ! rowspan="2" | # | ||
! colspan="2" | Period 0 | ! colspan="2" | Period 0 | ||
| Line 59: | Line 60: | ||
| 125/63, 448/225 | | 125/63, 448/225 | ||
|} | |} | ||
<nowiki>* | <nowiki />* In 7-limit CTE tuning | ||
== | == Tunings == | ||
* 7-limit POTE tuning: ~3/2 = 703.0212 | * 7-limit POTE tuning: ~3/2 = 703.0212 | ||
* 7-limit CTE tuning: ~3/2 = 703.1448 | * 7-limit CTE tuning: ~3/2 = 703.1448 | ||
=== Tuning spectrum === | |||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |||
! Edo<br>Generator | ! Edo<br>Generator | ||
! [[Eigenmonzo|Eigenmonzo<br>( | ! [[Eigenmonzo|Eigenmonzo<br>(rnchanged-interval)]] | ||
! Generator<br>(¢) | ! Generator<br>(¢) | ||
! Comments | ! Comments | ||
| Line 77: | Line 81: | ||
|- | |- | ||
| | | | ||
| | | 3/2 | ||
| 701.955 | | 701.955 | ||
| | |||
|- | |||
| | |||
| 81/80 | |||
| 702.688 | |||
| | | | ||
|- | |- | ||
| Line 89: | Line 98: | ||
| 15/14 | | 15/14 | ||
| 702.778 | | 702.778 | ||
| | | | ||
|- | |- | ||
| Line 107: | Line 111: | ||
|- | |- | ||
| | | | ||
| | | 9/5 | ||
| 702.933 | | 702.933 | ||
| 9-odd-limit minimax (error = 1.955¢) | | 9-odd-limit minimax (error = 1.955¢) | ||
| Line 122: | Line 126: | ||
|- | |- | ||
| | | | ||
| | | 35/18 | ||
| 703.048 | | 703.048 | ||
| | | | ||
| Line 134: | Line 138: | ||
| 21/20 | | 21/20 | ||
| 703.107 | | 703.107 | ||
| | | | ||
|- | |- | ||
| | | | ||
| | | 7/4 | ||
| 703.117 | | 703.117 | ||
| 7-odd-limit minimax (error = 1.217¢) | | 7-odd-limit minimax (error = 1.217¢) | ||
|- | |- | ||
| | | | ||
| | | 5/3 | ||
| 703.128 | | 703.128 | ||
| 5-odd-limit minimax (error = 1.173¢) | | 5-odd-limit minimax (error = 1.173¢) | ||
|- | |||
| | |||
| 21/16 | |||
| 703.247 | |||
| | |||
|- | |- | ||
| | | | ||
| 25/24 | | 25/24 | ||
| 703.259 | | 703.259 | ||
| | |||
|- | |||
| | |||
| 63/32 | |||
| 703.408 | |||
| | | | ||
|- | |- | ||
| Line 162: | Line 176: | ||
|- | |- | ||
| | | | ||
| | | 15/8 | ||
| 703.910 | | 703.910 | ||
| | | | ||
| Line 177: | Line 191: | ||
|} | |} | ||
[[Category:Misty| ]] <!-- main article --> | [[Category:Misty| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | |||
[[Category:Misty family]] | [[Category:Misty family]] | ||
[[Category:Hemimean clan]] | [[Category:Hemimean clan]] | ||
[[Category:Hemifamity temperaments]] | [[Category:Hemifamity temperaments]] | ||