Non-over-1 temperament: Difference between revisions
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== Examples == | == Examples == | ||
=== Greeley === | === 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¢). | Greeley is a [[23edo|23]]&[[31edo|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. | * One generator represents 12/11 and 11/10. | ||
* Two generators represents 6/5. | * Two generators represents 6/5. | ||
* Four generators represent 10/7. | * Four generators represent 10/7. | ||
* Six generators represent 12/7. | * Six generators represent 12/7. | ||
=== Petrtri === | === 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. | 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. | ||