Xen concepts for beginners: Difference between revisions

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[[Just intonation]] (JI) is the set of intervals that are tuned to rational frequency ratios, ones can be written as fractions of whole numbers.

The easiest way to get concordance (smoothness, blending and buzzing) is to use low-numbered JI ratios in your interval or chord, for example [[3/2]] the just ~~perfect fifth,~~ [[5/4]] ~~the just major third~~, and [[7/5]] ~~the lesser septimal tritone~~. When pure JI ratios are used, a psychoacoustic 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.

The easiest way to get concordance (smoothness, blending and buzzing) is to use low-numbered JI ratios in your interval or chord, for example the just perfect fifth [[3/2]], the just major third [[5/4]], and the lesser septimal tritone [[7/5]]. When pure JI ratios are used, a psychoacoustic 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) 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.

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There are two ways the term ''[[limit]]'' is used.

* The ''[[harmonic limit|p-prime-limit]]'' is the lattice built by multiplying the primes at most ''p'', possibly multiple times. We write a JI lattice by writing the basic intervals separated by periods. For example, 6/5 = 2 × 3 / 5 is in the 5-limit, or the 2.3.5 subgroup, and so is 45/32 = (3 × 3 × 5) / (2 × 2 × 2 × 2 × 2).

* The ''[[odd limit|n-odd-limit]]'' is the set of all JI ratios where the larger of the numerator and denominator after removing factors of 2 from the JI ratios is at most the odd number ''n''. For example, 7/6, 13/5, 11/10, and 16/15 are all in the 15-odd-limit.

* The ''[[odd limit|q-odd-limit]]'' is the set of all JI ratios where the larger of the numerator and denominator after removing factors of 2 from the JI ratios is at most the odd number ''q''. For example, 7/6, 13/5, 11/10, and 16/15 are all in the 15-odd-limit.

== Basic RTT ==

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 [[Just intonation]] (JI) is the set of intervals that are tuned to rational frequency ratios, ones can be written as fractions of whole numbers.
-The easiest way to get concordance (smoothness, blending and buzzing) is to use low-numbered JI ratios in your interval or chord, for example [[3/2]] the just perfect fifth, [[5/4]] the just major third, and [[7/5]] the lesser septimal tritone. When pure JI ratios are used, a psychoacoustic 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.
+The easiest way to get concordance (smoothness, blending and buzzing) is to use low-numbered JI ratios in your interval or chord, for example the just perfect fifth [[3/2]], the just major third [[5/4]], and the lesser septimal tritone [[7/5]]. When pure JI ratios are used, a psychoacoustic 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) 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.
@@ Line 42: / Line 42: @@
 There are two ways the term ''[[limit]]'' is used.
 * The ''[[harmonic limit|p-prime-limit]]'' is the lattice built by multiplying the primes at most ''p'', possibly multiple times. We write a JI lattice by writing the basic intervals separated by periods. For example, 6/5 = 2 × 3 / 5 is in the 5-limit, or the 2.3.5 subgroup, and so is 45/32 = (3 × 3 × 5) / (2 × 2 × 2 × 2 × 2).
-* The ''[[odd limit|n-odd-limit]]'' is the set of all JI ratios where the larger of the numerator and denominator after removing factors of 2 from the JI ratios is at most the odd number ''n''. For example, 7/6, 13/5, 11/10, and 16/15 are all in the 15-odd-limit.
+* The ''[[odd limit|q-odd-limit]]'' is the set of all JI ratios where the larger of the numerator and denominator after removing factors of 2 from the JI ratios is at most the odd number ''q''. For example, 7/6, 13/5, 11/10, and 16/15 are all in the 15-odd-limit.
 == Basic RTT ==