Non-over-1 temperament: Difference between revisions

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== Examples ==

=== 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.

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-2 temperament.

=== Sensi ===

[[Sensi]] is ''effectively'' a non-over-1 temperament provided you restrict yourself to the sensi[8] MOS. The sensi[8] MOS only has a 5:6:7:9:13 chord, but no chord of the form 2:m<sub>1</sub>:...:m<sub>k</sub> (except 2:3). Thus sensi can be viewed as a 2.6/5.7/5.9/5.13/10 or 2.3.6/5.7/5.13/10 temperament. (See [http://x31eq.com/cgi-bin/rt.cgi?limit=2_6%2F5_7%2F5_9%2F5_13%2F10&ets=19_27&tuning=po&subgroup=on x31eq data page].)

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 == Examples ==
 === 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.
+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-2 temperament.
 === Sensi ===
 [[Sensi]] is ''effectively'' a non-over-1 temperament provided you restrict yourself to the sensi[8] MOS. The sensi[8] MOS only has a 5:6:7:9:13 chord, but no chord of the form 2:m<sub>1</sub>:...:m<sub>k</sub> (except 2:3). Thus sensi can be viewed as a 2.6/5.7/5.9/5.13/10 or 2.3.6/5.7/5.13/10 temperament. (See [http://x31eq.com/cgi-bin/rt.cgi?limit=2_6%2F5_7%2F5_9%2F5_13%2F10&ets=19_27&tuning=po&subgroup=on x31eq data page].)