Bird's eye view of temperaments by accuracy: Difference between revisions
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=== Father === | === Father === | ||
[[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. | [[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. | ||
=== Bug === | |||
[[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. | |||
== 7-limit focus == | == 7-limit focus == | ||
=== Dominant === | === Dominant === | ||
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. | 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. | ||
=== Decimal === | |||
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 5/4). The period is treated as 7/5~10/7 (tempering out 50/49). | |||
== 11-limit focus == | == 11-limit focus == | ||
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== No-3's focus == | == No-3's focus == | ||
== No-5's focus == | == No-5's focus == | ||
=== Semaphore === | |||
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. | |||
= '''Low or very low accuracy (<~18c)''' = | = '''Low or very low accuracy (<~18c)''' = | ||