Just intonation: Difference between revisions

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; Harmonic limits and subgroups

[[Harmonic limit]]s set a limit for the highest prime number in the factorization of any ratio used; for example, western music is based off the [[5-limit]]. [[Subgroup]]s name a list of allowable prime numbers used.

[[Harmonic limit]]s, also known as ''prime limits'', set a limit for the highest prime number in the factorization of any ratio used; for example, western music is based off the [[5-limit]]. Lower limits tend to be more familiar and consonant, while higher limits contain more exotic harmony. [[Subgroup]]s name a list of allowable prime numbers used. For example, the [[2.3.7 subgroup|2.3.7-subgroup]] consists of all intervals with only primes 2, 3, and 7 in the numerator and denominator. (A harmonic limit is also a type of subgroup, though they are less commonly stated as such.) Different subgroups each contain their own unique structures, including commas, temperaments, [[scale form]]s, etc.

; Restrictions on the denominator or numerator

Some approaches restrict "the denominator to one or very few values"<ref name=":0">From Jacques Dudon, "Differential Coherence", ''1/1'' vol. 11, no. 2: p.1).</ref> (the [[harmonic series]], [[isoharmonic chord]]s, [[AFDO]]s/[[overtone scale]]s, [[primodality]], [[Ringer scale|ringer scales]]), the "numerator to one or very few values" (the [[subharmonic series]], [[IFDO]]s/undertone scales), or both ([[Tonality diamond|tonality diamonds]])

Some approaches restrict "the denominator to one or very few values"<ref name=":0">From Jacques Dudon, "Differential Coherence", ''1/1'' vol. 11, no. 2: p.1).</ref> (the [[harmonic series]], [[isoharmonic chord]]s, [[AFDO]]s/[[overtone scale]]s, [[primodality]], [[Ringer scale|ringer scales]]), the "numerator to one or very few values" (the [[subharmonic series]], [[IFDO]]s/undertone scales), or both ([[Tonality diamond|tonality diamonds]]).

; Mediants

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== Notation ==

There are various [[Musical notation|notation systems]] for just intonation.

There are various [[Musical notation|notation systems]] for just intonation, for example [[Helmholtz-Ellis notation]] and the [[Functional Just System]].

==See also==

@@ Line 33: / Line 33: @@
 ; Harmonic limits and subgroups
-[[Harmonic limit]]s set a limit for the highest prime number in the factorization of any ratio used; for example, western music is based off the [[5-limit]]. [[Subgroup]]s name a list of allowable prime numbers used.
+[[Harmonic limit]]s, also known as ''prime limits'', set a limit for the highest prime number in the factorization of any ratio used; for example, western music is based off the [[5-limit]]. Lower limits tend to be more familiar and consonant, while higher limits contain more exotic harmony. [[Subgroup]]s name a list of allowable prime numbers used. For example, the [[2.3.7 subgroup|2.3.7-subgroup]] consists of all intervals with only primes 2, 3, and 7 in the numerator and denominator. (A harmonic limit is also a type of subgroup, though they are less commonly stated as such.) Different subgroups each contain their own unique structures, including commas, temperaments, [[scale form]]s, etc.
 ; Restrictions on the denominator or numerator
-Some approaches restrict "the denominator to one or very few values"<ref name=":0">From Jacques Dudon, "Differential Coherence", ''1/1'' vol. 11, no. 2: p.1).</ref> (the [[harmonic series]], [[isoharmonic chord]]s, [[AFDO]]s/[[overtone scale]]s, [[primodality]], [[Ringer scale|ringer scales]]), the "numerator to one or very few values" (the [[subharmonic series]],  [[IFDO]]s/undertone scales), or both ([[Tonality diamond|tonality diamonds]])
+Some approaches restrict "the denominator to one or very few values"<ref name=":0">From Jacques Dudon, "Differential Coherence", ''1/1'' vol. 11, no. 2: p.1).</ref> (the [[harmonic series]], [[isoharmonic chord]]s, [[AFDO]]s/[[overtone scale]]s, [[primodality]], [[Ringer scale|ringer scales]]), the "numerator to one or very few values" (the [[subharmonic series]],  [[IFDO]]s/undertone scales), or both ([[Tonality diamond|tonality diamonds]]).
 ; Mediants
@@ Line 60: / Line 60: @@
 == Notation ==
-There are various [[Musical notation|notation systems]] for just intonation.
+There are various [[Musical notation|notation systems]] for just intonation, for example [[Helmholtz-Ellis notation]] and the [[Functional Just System]].
+{{Todo|expand|inline=1}}
 ==See also==
 {{todo|cleanup|inline=1}}