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. This temperament, supported by [[12edo|12et]], is notably in the [[schismic-Pythagorean equivalence continuum]], with ''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]].
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 See [[Misty family]] for more technical data.
-{{IoT}}
+== Interval chain ==
-[[Category:Misty| ]] <-- main article -->
+{| class="wikitable center-1 right-2"
+|-
+! rowspan="2" | #
+! colspan="2" | Period 0
+! colspan="2" | Period 1
+! colspan="2" | Period 2
+|-
+! Cents*
+! Approximate Ratios
+! Cents*
+! Approximate Ratios
+! Cents*
+! Approximate Ratios
+|-
+| 0
+| 0.0
+| '''1/1'''
+| 400.0
+| 63/50
+| 800.0
+| 100/63
+|-
+| 1
+| 96.9
+| 135/128
+| 496.9
+| '''4/3'''
+| 896.9
+| 42/25
+|-
+| 2
+| 193.7
+| 28/25
+| 593.7
+| 45/32
+| 993.7
+| 16/9
+|-
+| 3
+| 290.6
+| 32/27
+| 690.6
+| 112/75
+| 1090.6
+| 15/8
+|-
+| 4
+| 387.4
+| '''5/4'''
+| 787.4
+| 63/40
+| 1187.4
+| 125/63, 448/225
+|}
+<nowiki />* In 7-limit CTE tuning
+== Tunings ==
+* 7-limit POTE tuning: ~3/2 = 703.0212
+* 7-limit CTE tuning: ~3/2 = 703.1448
+=== Tuning spectrum ===
+{| class="wikitable center-all left-4"
+|-
+! Edo<br>Generator
+! [[Eigenmonzo|Eigenmonzo<br>(rnchanged-interval)]]
+! Generator<br>(¢)
+! Comments
+|-
+| 7\12
+|
+| 700.000
+| Lower bound of 9-odd-limit diamond monotone
+|-
+|
+| 3/2
+| 701.955
+|
+|-
+|
+| 81/80
+| 702.688
+|
+|-
+| 65\111
+|
+| 702.703
+|
+|-
+|
+| 15/14
+| 702.778
+|
+|-
+|
+| 7/5
+| 702.915
+|
+|-
+|
+| 9/7
+| 702.924
+|
+|-
+|
+| 9/5
+| 702.933
+| 9-odd-limit minimax (error = 1.955¢)
+|-
+|
+| 7/6
+| 703.012
+|
+|-
+| 58\99
+|
+| 703.030
+|
+|-
+|
+| 35/18
+| 703.048
+|
+|-
+|
+| 49/48
+| 703.062
+|
+|-
+|
+| 21/20
+| 703.107
+|
+|-
+|
+| 7/4
+| 703.117
+| 7-odd-limit minimax (error = 1.217¢)
+|-
+|
+| 5/3
+| 703.128
+| 5-odd-limit minimax (error = 1.173¢)
+|-
+|
+| 21/16
+| 703.247
+|
+|-
+|
+| 25/24
+| 703.259
+|
+|-
+|
+| 63/32
+| 703.408
+|
+|-
+|
+| 5/4
+| 703.422
+|
+|-
+| 51\87
+|
+| 703.448
+|
+|-
+|
+| 15/8
+| 703.910
+|
+|-
+| 44\75
+|
+| 704.000
+|
+|-
+| 37\63
+|
+| 704.762
+| Upper bound of 9-odd-limit diamond monotone
+|}
+[[Category:Misty| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
 [[Category:Misty family]]
 [[Category:Hemimean clan]]
 [[Category:Hemifamity temperaments]]