Xen concepts for beginners: Difference between revisions

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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).

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 vector called 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).

There are many approaches to JI music: lattice-based JI, constant structure scales, free JI, primodality, tonality diamonds, combination product sets...

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 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).
+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 vector called 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).
 There are many approaches to JI music: lattice-based JI, constant structure scales, free JI, primodality, tonality diamonds, combination product sets...