Bird's eye view of temperaments by accuracy: Difference between revisions
m →High or medium accuracy (: improve wording to be less debatable |
m →5-limit focus: add srutal archagall |
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Low or very low accuracy temperaments are of interest to people wanting simple scales and who are fine with high damage. As a result, they tend not to have "higher-limit focus", as the error involved on intervals beyond the [[17-limit]] is too much. A variety of people consider this category to largely or even entirely be composed of exotemperaments, while others argue for various entries in this category being reasonable to consider harmonically based on the temperability of the simplest [[LCJI]] intervals. | Low or very low accuracy temperaments are of interest to people wanting simple scales and who are fine with high damage. As a result, they tend not to have "higher-limit focus", as the error involved on intervals beyond the [[17-limit]] is too much. A variety of people consider this category to largely or even entirely be composed of exotemperaments, while others argue for various entries in this category being reasonable to consider harmonically based on the temperability of the simplest [[LCJI]] intervals. | ||
== 5-limit focus == | == 5-limit focus == | ||
=== [[Srutal archagall]] === | |||
Note counts: | |||
* 10 for {3, 5, 9, 15, 17} ([[2L 8s]]) | |||
* 12 for adding {25} ([[10L 2s]]) | |||
Srutal archagall is the natural extension of 5-limit [[diaschismic]] to prime 17 by interpreting the generator as a near-just [[17/16]] and the period as [[~]][[24/17]][[~]][[17/12]]. | |||
It is notable as preserving a lot of intuitions of 12edo like [[9/8]] as two semitones, [[6/5]] as three semitones, [[5/4]] as a semitone less than [[4/3]] which is itself a semitone less than half an octave. It essentially "doubles up" on familiar categories by: two major seconds, [[~]][[10/9]] and [[~]][[9/8]][[~]][[17/15]], two minor thirds, [[~]][[20/17]] and [[~]][[6/5]], and two major thirds, [[~]][[5/4]] and [[~]][[51/40]][[~]][[32/25]]. The distance between these pairs is an exaggerated syntonic comma ([[81/80]]) making it useful as a slightly more accurate alternative to meantone. Notably the intervals of 5 require using the period offset to reach, so that the minor third reached by the circle of fifths is actually [[20/17]]. | |||
For abundant options, one might prefer a 22-note MOS over a 12-note one, so that srutal archagall can be seen as a detempering of [[22edo]], but the 12-note MOS is likely the easiest and most intuitive to approach for a beginner. [[34edo]] is a good tuning for optimizing the 2.3.5.17 subgroup. | |||
== 7-limit focus == | == 7-limit focus == | ||
== 11-limit focus == | == 11-limit focus == | ||