Xen concepts for beginners: Difference between revisions

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From the perspective of an edo user, another problem RTT solves is that there are very few small edos and they do not constitute that wide a palette. Especially in larger edos, RTT provides a way of not being overwhelmed with dozens of notes.

RTT views edos as regular temperaments. To simplify the infinite JI space to a finite set, ~~we need to deform~~ the intervals so that certain chosen intervals vanish. We can also approach simplifying JI ratios from edos themselves, namely how edos approximate each prime. This is a vector called a [[val]]. Vals map primes to a set number of edo steps and thus tell us how many edo steps each interval in JI is mapped to. The usual 12edo val (called the 12edo [[patent val]]) in the 5-limit is {{val| 12 19 28}}, as the 12edo intervals that are closest to 2/1, 3/1 and 5/1 are 12, 19 and 28 steps respectively.

RTT views edos as regular temperaments. Under this view, edos simplify the infinite JI space to a finite set, deforming the intervals so that certain chosen intervals vanish. We can also approach simplifying JI ratios from edos themselves, namely how edos approximate each prime. This is a vector called a [[val]]. Vals map primes to a set number of edo steps and thus tell us how many edo steps each interval in JI is mapped to. The usual 12edo val (called the 12edo [[patent val]]) in the 5-limit is {{val| 12 19 28}}, as the 12edo intervals that are closest to 2/1, 3/1 and 5/1 are 12, 19 and 28 steps respectively.

There are various temperaments in xen with varying levels of practicality. The most important one to know is probably [[Meantone]] temperament, which equates four fifths ((3/2)^4 = 81/16) with a major third plus two octaves (5/4 * 4 = 5 = 80/16), which is encoded by tempering out the syntonic comma [[81/80]] (monzo {{monzo| -4 4 -1 }}).

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 From the perspective of an edo user, another problem RTT solves is that there are very few small edos and they do not constitute that wide a palette. Especially in larger edos, RTT provides a way of not being overwhelmed with dozens of notes.
-RTT views edos as regular temperaments. To simplify the infinite JI space to a finite set, we need to deform the intervals so that certain chosen intervals vanish. We can also approach simplifying JI ratios from edos themselves, namely how edos approximate each prime. This is a vector called a [[val]]. Vals map primes to a set number of edo steps and thus tell us how many edo steps each interval in JI is mapped to. The usual 12edo val (called the 12edo [[patent val]]) in the 5-limit is {{val| 12 19 28}}, as the 12edo intervals that are closest to 2/1, 3/1 and 5/1 are 12, 19 and 28 steps respectively.
+RTT views edos as regular temperaments. Under this view, edos simplify the infinite JI space to a finite set, deforming the intervals so that certain chosen intervals vanish. We can also approach simplifying JI ratios from edos themselves, namely how edos approximate each prime. This is a vector called a [[val]]. Vals map primes to a set number of edo steps and thus tell us how many edo steps each interval in JI is mapped to. The usual 12edo val (called the 12edo [[patent val]]) in the 5-limit is {{val| 12 19 28}}, as the 12edo intervals that are closest to 2/1, 3/1 and 5/1 are 12, 19 and 28 steps respectively.
 There are various temperaments in xen with varying levels of practicality. The most important one to know is probably [[Meantone]] temperament, which equates four fifths ((3/2)^4 = 81/16) with a major third plus two octaves (5/4 * 4 = 5 = 80/16), which is encoded by tempering out the syntonic comma [[81/80]] (monzo {{monzo| -4 4 -1 }}).