No-twos subgroup temperaments: Difference between revisions

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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.

* Arcturus, Aldebaran and Polaris have a 3/1 period and ~5/3 generator. There is one-to-one correspondence between the 3.5 subgroup and mapped intervals.

* BPS ~~is with~~ a ~9/7 generator, two of which give the ~5/3.

* BPS has 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.

* Sirius has 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.

* Deneb has 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 up a tritave).

* Canopus has a ~7/5 generator, five of which give the ~27/5 (9/5 up a tritave).

* Alnilam ~~is with~~ a ~81/55 generator, ten of which give the ~243/5 (9/5 up three tritaves).

* Alnilam has a ~81/55 generator, ten of which give the ~243/5 (9/5 up three tritaves).

* Izar ~~is with~~ a ~16807/10125 generator, twelve of which give the ~2187/5 (9/5 up five tritaves).

* Izar has a ~16807/10125 generator, twelve of which give the ~2187/5 (9/5 up five tritaves).

* Mintaka does not include the 5th harmonic, and has an ~11/7 generator, two of which give the ~27/11, and three of which give the ~27/7 (9/7 and a tritave).

* Antipyth and Juggernaut use 5/1 as a period, and have a ~7/5 generator. There is one-to-one correspondence between the 5.7 subgroup and mapped intervals.

== 3.5.7 subgroup temperaments ==

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 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.
+* Arcturus, Aldebaran and Polaris have a 3/1 period and ~5/3 generator. There is one-to-one correspondence between the 3.5 subgroup and mapped intervals.
-* BPS is with a ~9/7 generator, two of which give the ~5/3.
+* BPS has 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.
+* Sirius has 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.
+* Deneb has 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 up a tritave).
+* Canopus has a ~7/5 generator, five of which give the ~27/5 (9/5 up a tritave).
-* Alnilam is with a ~81/55 generator, ten of which give the ~243/5 (9/5 up three tritaves).
+* Alnilam has a ~81/55 generator, ten of which give the ~243/5 (9/5 up three tritaves).
-* Izar is with a ~16807/10125 generator, twelve of which give the ~2187/5 (9/5 up five tritaves).
+* Izar has a ~16807/10125 generator, twelve of which give the ~2187/5 (9/5 up five tritaves).
 * Mintaka does not include the 5th harmonic, and has an ~11/7 generator, two of which give the ~27/11, and three of which give the ~27/7 (9/7 and a tritave).
+* Antipyth and Juggernaut use 5/1 as a period, and have a ~7/5 generator. There is one-to-one correspondence between the 5.7 subgroup and mapped intervals.
 == 3.5.7 subgroup temperaments ==