Non-over-1 temperament: Difference between revisions

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== Examples ==

=== ~~Tridec~~ ===

=== Petrtri ===

~~Tridec is a~~ temperament ~~generated~~ by ~~a generator near 455~~.~~2178¢ (for example~~, [[~~29edo|11\29~~]] or [~~[37edo|14\37~~]]) and ~~has an 8~~-~~note MOS. If you restrict~~ to the ~~8-note MOS, Tridec is an~~ 2.7/5.11/5.13~~/5 temperament that tempers the chord~~ 5:7:11:13~~; one generator represents a 13/~~10~~, three~~ generators ~~represent a~~ 11~~/10, -4 generators represent a 7/5.~~

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.

~~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]]~~.

=== 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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=== Tridec ===

Tridec is a temperament generated by a generator near 455.2178¢ (for example, [[29edo|11\29]] or [[37edo|14\37]]) and has an 8-note MOS. If you restrict to the 8-note MOS, Tridec is an 2.7/5.11/5.13/5 temperament that tempers the chord 5:7:11:13; one generator represents a 13/10, three generators represent a 11/10, -4 generators represent a 7/5.

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]]

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 == Examples ==
-=== Tridec ===
+=== Petrtri ===
-Tridec is a temperament generated by a generator near 455.2178¢ (for example, [[29edo|11\29]] or [[37edo|14\37]]) and has an 8-note MOS. If you restrict to the 8-note MOS, Tridec is an 2.7/5.11/5.13/5 temperament that tempers the chord 5:7:11:13; one generator represents a 13/10, three generators represent a 11/10, -4 generators represent a 7/5.
+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.
-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]].
 === 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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+=== Tridec ===
+Tridec is a temperament generated by a generator near 455.2178¢ (for example, [[29edo|11\29]] or [[37edo|14\37]]) and has an 8-note MOS. If you restrict to the 8-note MOS, Tridec is an 2.7/5.11/5.13/5 temperament that tempers the chord 5:7:11:13; one generator represents a 13/10, three generators represent a 11/10, -4 generators represent a 7/5.
+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]]