Xen concepts for beginners: Difference between revisions

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== Basic RTT ==

Assuming several things from common 12edo practice, JI has several disadvantages. To get infinite modulation and have exactly the same chords on every note, we need infinitely many notes unlike the finitely many notes of 12edo. JI with such infinite modulation and regularity also has small intervals that may be undesirable, called commas. This is the problem that [[regular temperament theory]] (RTT) exists to solve. Regular temperaments equate certain intervals by considering the difference between them as a comma and "[[tempering out]]" the difference.

''Assuming several things from common 12edo practice'', JI has several disadvantages. To get infinite modulation and have exactly the same chords on every note, we need infinitely many notes unlike the finitely many notes of 12edo. JI with such infinite modulation and regularity also has small intervals that may be undesirable, called commas. This is the problem that [[regular temperament theory]] (RTT) exists to solve. Regular temperaments equate certain intervals by considering the difference between them as a comma and "[[tempering out]]" the difference. One issue with this criticism is that not all JI composers treat JI like one would an edo, and that some regular temperament tunings are infinite.

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. RTT provides a way of not being overwhelmed with dozens of notes in a scale.

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.

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 == Basic RTT ==
-Assuming several things from common 12edo practice, JI has several disadvantages. To get infinite modulation and have exactly the same chords on every note, we need infinitely many notes unlike the finitely many notes of 12edo. JI with such infinite modulation and regularity also has small intervals that may be undesirable, called commas. This is the problem that [[regular temperament theory]] (RTT) exists to solve. Regular temperaments equate certain intervals by considering the difference between them as a comma and "[[tempering out]]" the difference.
+''Assuming several things from common 12edo practice'', JI has several disadvantages. To get infinite modulation and have exactly the same chords on every note, we need infinitely many notes unlike the finitely many notes of 12edo. JI with such infinite modulation and regularity also has small intervals that may be undesirable, called commas. This is the problem that [[regular temperament theory]] (RTT) exists to solve. Regular temperaments equate certain intervals by considering the difference between them as a comma and "[[tempering out]]" the difference. One issue with this criticism is that not all JI composers treat JI like one would an edo, and that some regular temperament tunings are infinite.
+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. RTT provides a way of not being overwhelmed with dozens of notes in a scale.
 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.