Bird's eye view of temperaments by accuracy: Difference between revisions
→~17-limit focus: briefly discuss genchain, add odd 19 as a target of the larger MOS scales, discuss 48edo as structurally related but damaged, note mapping of 19 simplifies for 48edo and 53edo to help justify its inclusion/notability, note interseptimals of 48edo to help justify its notability, but in brackets due to its damage and following a different mapping |
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Godzilla is a very coarse temperament, where we use context to suggest ~4:5:6:7(:8). It admits a natural extension to prime 13 based on interpreting its semifourth of [[~]][[8/7]][[~]][[7/6]] much more accurately as [[15/13]], though if you specifically want 15/13 as the semifourth, there is much more accurate temperaments available that don't require interpreting it inaccurately as ~8/7~7/6, such as [[#Immunity]], or if you don't need a semifourth as the generator, [[#Cata]]. Nonetheless, insofar as it makes sense, it's notable for providing a usefully-small 9-note scale for the entire [[9-odd-limit]] (insofar as it is capable of approximating its sound with context). Due to its inaccuracy, it is recommended to use a sharp octave-tempering for this temperament, such as [[30edt]] instead of [[19edo]], in which case you also improve various intervals of 13 as well. Doing this means that you can use voicing across octaves to improve the accuracy and hence psychoacoustic convincingness of godzilla. | Godzilla is a very coarse temperament, where we use context to suggest ~4:5:6:7(:8). It admits a natural extension to prime 13 based on interpreting its semifourth of [[~]][[8/7]][[~]][[7/6]] much more accurately as [[15/13]], though if you specifically want 15/13 as the semifourth, there is much more accurate temperaments available that don't require interpreting it inaccurately as ~8/7~7/6, such as [[#Immunity]], or if you don't need a semifourth as the generator, [[#Cata]]. Nonetheless, insofar as it makes sense, it's notable for providing a usefully-small 9-note scale for the entire [[9-odd-limit]] (insofar as it is capable of approximating its sound with context). Due to its inaccuracy, it is recommended to use a sharp octave-tempering for this temperament, such as [[30edt]] instead of [[19edo]], in which case you also improve various intervals of 13 as well. Doing this means that you can use voicing across octaves to improve the accuracy and hence psychoacoustic convincingness of godzilla. | ||
=== [[Negri]] === | |||
Note count: 9 for {1, 3, 5, 7} ([[1L 8s]]) | |||
Negri is a temperament that stands out because of its relative simplicity. It divides the 4/3 into four equal semitone-like steps that more closely resemble steps of 10edo, and anyone familiar with either 9 or 10edo might be able to understand the structure of this temperament. | |||
== 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 == | ||
= '''Exotemperaments (>~18c)''' = | = '''Exotemperaments (>~18c)''' = | ||