Xen concepts for beginners: Difference between revisions

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The easiest way to get concordance (blending, buzzing chords) is to use low-numbered JI ratios in your interval or chord, for example 3/2 the just perfect fifth, 5/4 a just major third, and 7/5 a just tritone. When pure JI ratios are used, the acoustic effect called JI buzz occurs. When the overall chord is low number JI, such as 8:9:10:11:12:13:14, the result is very concordant.

No edo interval except for the octave (2/1) is exact JI. A JI ratio might be far from a 12edo interval; for example 7/4 is 969 cents. This is another reason why JI is a common approach to xen.

No edo interval except for the octave (2/1) and stacks of it is exact JI. A JI ratio might be far from a 12edo interval; for example 7/4 is 969 cents. This is another reason why JI is a common approach to xen.

As stacking JI ratios involves multiplying, primes are important as the simplest building blocks of arbitrary JI ratios. So we can write every ratio as a monzo, a list of powers for primes. 81/80's monzo is [-4 4 -1>. We can visualize each ratio as living in some JI lattice (the set of all intervals built by stacking a finite set of basic intervals).

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 The easiest way to get concordance (blending, buzzing chords) is to use low-numbered JI ratios in your interval or chord, for example 3/2 the just perfect fifth, 5/4 a just major third, and 7/5 a just tritone. When pure JI ratios are used, the acoustic effect called JI buzz occurs. When the overall chord is low number JI, such as 8:9:10:11:12:13:14, the result is very concordant.
-No edo interval except for the octave (2/1) is exact JI. A JI ratio might be far from a 12edo interval; for example 7/4 is 969 cents. This is another reason why JI is a common approach to xen.
+No edo interval except for the octave (2/1) and stacks of it is exact JI. A JI ratio might be far from a 12edo interval; for example 7/4 is 969 cents. This is another reason why JI is a common approach to xen.
 As stacking JI ratios involves multiplying, primes are important as the simplest building blocks of arbitrary JI ratios. So we can write every ratio as a monzo, a list of powers for primes. 81/80's monzo is [-4 4 -1>. We can visualize each ratio as living in some JI lattice (the set of all intervals built by stacking a finite set of basic intervals).