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| == No-3's focus == | | == No-3's focus == |
| == No-5's focus == | | == No-5's focus == |
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| = '''Exotemperaments (>~18c)''' =
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| Exotemperaments are useful as targets for [[detempering]], as they often underly the logic of various [[JI]] [[scale]]s. They are also explored for novelty.
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| == 5-limit focus ==
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| === Dicot ===
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| [[Dicot]] equates 5/4 with 6/5 into a generic neutral third, so that 3/2 is found at 2 generators. It is most notable as appearing commonly as an underlying logic of JI scales which do not find both 5/4 and 6/5 relative to the same scale degree anywhere, but for which 5/4 and 6/5 [[subtend]] the same number of scalesteps.
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| === Father ===
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| [[Father]] equates 4/3 with 5/4, so that 3/2 and 5/4 are made into octave-complements. Thus it is extremely simple (and extremely high damage). If one detempers father into a JI scale, one must ensure 5/4 and 4/3 do not appear relative to the same scale degree anywhere and that they [[subtend]] the same number of scalesteps, which rules out most 5-limit JI scales people usually consider.
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| === Bug ===
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| [[Bug]] equates 5/3 with 9/5, so that two semi-twelfth intervals can be made into a twelfth. It can be useful for creating 5-limit pentatonic scales, along with father. In addition, it is tempered out by [[14edo]], which in a sense might be the largest 5-limit exotemperament EDO.
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| == 7-limit focus ==
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| === Dominant ===
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| Dominant makes a generic minor third of 7/6~6/5 and major third of 5/4~9/7. It is the result of attempting to temper both [[64/63]] and [[81/80]]. An especially notable detempering is 14:16:18:20:21:24:27:28, a low-complexity, 7-note, 7-limit, over-7 diatonic JI scale, which has [[10/9]], [[9/8]] and [[8/7]] as whole tones, and [[21/20]] and [[28/27]] as small semitones, thus fulfilling the [[5L 2s]] diatonic pattern.
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| === Decimal ===
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| Decimal makes many semi-closely-related intervals equivalent, which can be useful at times when one wants to create low-cardinality scales or use it as an analysis system. For example, the generator can be an 8/7~7/6 (tempering out 49/48) or 6/5~5/4 (tempering out 25/24). The period is treated as 7/5~10/7 (tempering out 50/49).
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| == 11-limit focus ==
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| == ~17-limit focus ==
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| == Higher-limit focus ==
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| == No-2's focus ==
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| == No-3's focus ==
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| == No-5's focus ==
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| === Semaphore ===
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| Semaphore and bug are quite similar in that they have semi-twelfths (or semi-fourths). However, unlike bug, semaphore's semi-twelfths have a ratio of 12/7~7/4.
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