No-twos subgroup temperaments: Difference between revisions
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This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 2. Because of the absence of octaves, these are all [[nonoctave]] scales using a period of a [[tritave]], or if harmonic 3 is also excluded, [[5/1]]. | This is a collection of [[subgroup temperament]]s which omit the prime harmonic of 2. Because of the absence of octaves, these are all [[nonoctave]] scales using a period of a [[tritave]], or if harmonic 3 is also excluded, [[5/1]]. | ||
== Overview by mapping of 5 == | |||
Classified by focusing on the mapping of 5th harmonic, similar to [[Rank-2 temperaments by mapping of 3]]. | |||
* Arcturus, Aldebaran and Polaris are with 3/1 period and ~5/3 generator. There is one-to-one correspondence between 3.5 subgroup and mapped intervals. | |||
* BPS is with a ~9/7 generator, two of which give the ~5/3. | |||
* Sirius is with a ~25/21 generator, three of which give the ~5/3. | |||
* Deneb is with a ~11/9 generator, three of which give the ~9/5. | |||
* Canopus is with a ~7/5 generator, five of which give the ~27/5 (9/5 and an tritave). | |||
* Alnilam is with a ~81/55 generator, ten of which give the ~243/5 (9/5 and three tritave). | |||
* Izar is with a ~16807/10125 generator, twelve of which give the ~2187/5 (9/5 and five tritave). | |||
== Arcturus == | == Arcturus == | ||