5-limit: Difference between revisions

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[[File:Lattice 5lim.png|alt=The lattice is a grid with 60 degree triangles and intervals at the vertices. The center vertex is 1/1, moving right is multiplication by 3/2, up-right is multiplication by 5/4, and up-left is multiplication by 5/3. Everything is octave-reduced.|thumb|5-limit hexagonal lattice]]

The '''5-limit''' (a.k.a. ''ya'' in [[color notation]]) consists of all [[just intonation]] intervals whose [[ratio|numerators and denominators]] are both products of the primes 2, 3, and 5~~; these are sometimes called {{w|regular number}}s~~. The 5-limit is the third prime limit and is a superset of the [[3-limit]] and a subset of the [[7-limit]]. Some examples of 5-limit intervals are [[5/4]], [[6/5]], [[10/9]] and [[81/80]].

The '''5-limit''' (a.k.a. ''ya'' in [[color notation]]) consists of all [[just intonation]] intervals whose [[ratio|numerators and denominators]] are both products of the primes 2, 3, and 5. The 5-limit is the third prime limit and is a superset of the [[3-limit]] and a subset of the [[7-limit]]. Some examples of 5-limit intervals are [[5/4]], [[6/5]], [[10/9]] and [[81/80]].

These things are contained by the 5-limit, but not the 3-limit:

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 {{Wikipedia|Five-limit tuning}}
 [[File:Lattice 5lim.png|alt=The lattice is a grid with 60 degree triangles and intervals at the vertices. The center vertex is 1/1, moving right is multiplication by 3/2, up-right is multiplication by 5/4, and up-left is multiplication by 5/3. Everything is octave-reduced.|thumb|5-limit hexagonal lattice]]
-The '''5-limit''' (a.k.a. ''ya'' in [[color notation]]) consists of all [[just intonation]] intervals whose [[ratio|numerators and denominators]] are both products of the primes 2, 3, and 5; these are sometimes called {{w|regular number}}s. The 5-limit is the third prime limit and is a superset of the [[3-limit]] and a subset of the [[7-limit]]. Some examples of 5-limit intervals are [[5/4]], [[6/5]], [[10/9]] and [[81/80]].
+The '''5-limit''' (a.k.a. ''ya'' in [[color notation]]) consists of all [[just intonation]] intervals whose [[ratio|numerators and denominators]] are both products of the primes 2, 3, and 5. The 5-limit is the third prime limit and is a superset of the [[3-limit]] and a subset of the [[7-limit]]. Some examples of 5-limit intervals are [[5/4]], [[6/5]], [[10/9]] and [[81/80]].
 These things are contained by the 5-limit, but not the 3-limit: