Non-over-1 temperament: Difference between revisions

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== Examples ==

=== Greeley ===

Greeley is a 23&31 temperament on the 2.5/3.7/3.11/3 subgroup, with a MOS generator size close to [[porcupine]] but smaller (the POL2 generator is around 155.7756¢).

* One generator represents 12/11 and 11/10.

* Two generators represents 6/5.

* Four generators represent 10/7.

* Six generators represent 12/7.

=== Petrtri ===

Define petrtri as the 2.9/5.11/5.13/5 subgroup temperament supported by 13edo and 21edo. Then petrtri mainly approximates 5:9:11:13, and this chord is found twice in the [[oneirotonic]] MOS petrtri[8]. Both 13edo and 21edo support the -7 generators = 5/4 mapping, so petrtri extends to the 2.5.9.11.13 subgroup; however, a 4:5:9:11:13 chord must span 10 generators (11 notes) thus must go outside the 8-note MOS. Thus it is fair to say that approximations of 5:9:11:13 in the 8-note MOS use this non-over-1 temperament.

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Tridec essentially contains all the notes of 2.3.5 [[porcupine]] temperament and satisfies all its relations; hence it is essentially the same as 13-limit [[Ammonite]].

[[Category:Temperament]]

[[Category:Regular temperament theory]]

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 == Examples ==
+=== Greeley ===
+Greeley is a 23&31 temperament on the 2.5/3.7/3.11/3 subgroup, with a MOS generator size close to [[porcupine]] but smaller (the POL2 generator is around 155.7756¢).
+* One generator represents 12/11 and 11/10.
+* Two generators represents 6/5.
+* Four generators represent 10/7.
+* Six generators represent 12/7.
 === Petrtri ===
 Define petrtri as the 2.9/5.11/5.13/5 subgroup temperament supported by 13edo and 21edo. Then petrtri mainly approximates 5:9:11:13, and this chord is found twice in the [[oneirotonic]] MOS petrtri[8]. Both 13edo and 21edo support the -7 generators = 5/4 mapping, so petrtri extends to the 2.5.9.11.13 subgroup; however, a 4:5:9:11:13 chord must span 10 generators (11 notes) thus must go outside the 8-note MOS. Thus it is fair to say that approximations of 5:9:11:13 in the 8-note MOS use this non-over-1 temperament.
@@ Line 56: / Line 62: @@
 Tridec essentially contains all the notes of 2.3.5 [[porcupine]] temperament and satisfies all its relations; hence it is essentially the same as 13-limit [[Ammonite]].
 [[Category:Temperament]]
+[[Category:Regular temperament theory]]