Porcupine temperament modal harmony: Difference between revisions

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=Intro To [[Porcupine]]=

Porcupine temperament has a number of significant properties that make it somewhat unique in the universe of temperaments.

Porcupine is one of the few reasonably good 5-limit temperaments, alongside [[meantone]] ~~(and perhaps [[mavila]])~~, which possesses a 7-note MOS scale that is well-supplied with 5-limit major and minor triads (specifically, it has two of each of them). What is perhaps more significant about it is how naturally it extends those triads to involve the 11th harmonic; for instance, the first five consecutive notes of the Lssssss mode approximate the consecutive harmonics 8:9:10:11:12. This makes it a prime candidate for using extended JI-style harmonies in a compact and intuitive scale structure.

Porcupine is one of the few reasonably good 5-limit temperaments, alongside [[meantone]], which possesses a 7-note MOS scale that is well-supplied with 5-limit major and minor triads (specifically, it has two of each of them). What is perhaps more significant about it is how naturally it extends those triads to involve the 11th harmonic; for instance, the first five consecutive notes of the Lssssss mode approximate the consecutive harmonics 8:9:10:11:12. This makes it a prime candidate for using extended JI-style harmonies in a compact and intuitive scale structure.

It is also significant because it is supported by both [[15edo]] and [[22edo]], the smallest ETs which improve on the 11-limit damage of [[12edo]] (other than [[19edo]]). In those ETs, Porcupine is an excellent candidate for providing a 7-nominal notational basis and 7-interval-class categorical framework for those ETs. This is important, because if you want to use 15edo or 22edo in a somewhat "heptatonic" fashion, where 5/4 and 6/5 are types of "third", 3/2 is a type of "fifth," and 5-limit major and minor triads share the same "1-3-5" triad shape, thinking of those ETs in terms of porcupine temperament is, in a certain sense, the natural approach. Furthermore, *any* heptatonic scale in [[15edo]] or [[22edo]] can be viewed as a MODMOS of the porcupine-7 MOS.

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 =Intro To [[Porcupine]]=
+{{Todo|rewrite|inline=1|text=Explain in a non-MOS-centric way}}
 Porcupine temperament has a number of significant properties that make it somewhat unique in the universe of temperaments.
-Porcupine is one of the few reasonably good 5-limit temperaments, alongside [[meantone]] (and perhaps [[mavila]]), which possesses a 7-note MOS scale that is well-supplied with 5-limit major and minor triads (specifically, it has two of each of them). What is perhaps more significant about it is how naturally it extends those triads to involve the 11th harmonic; for instance, the first five consecutive notes of the Lssssss mode approximate the consecutive harmonics 8:9:10:11:12. This makes it a prime candidate for using extended JI-style harmonies in a compact and intuitive scale structure.
+Porcupine is one of the few reasonably good 5-limit temperaments, alongside [[meantone]], which possesses a 7-note MOS scale that is well-supplied with 5-limit major and minor triads (specifically, it has two of each of them). What is perhaps more significant about it is how naturally it extends those triads to involve the 11th harmonic; for instance, the first five consecutive notes of the Lssssss mode approximate the consecutive harmonics 8:9:10:11:12. This makes it a prime candidate for using extended JI-style harmonies in a compact and intuitive scale structure.
 It is also significant because it is supported by both [[15edo]] and [[22edo]], the smallest ETs which improve on the 11-limit damage of [[12edo]] (other than [[19edo]]). In those ETs, Porcupine is an excellent candidate for providing a 7-nominal notational basis and 7-interval-class categorical framework for those ETs. This is important, because if you want to use 15edo or 22edo in a somewhat "heptatonic" fashion, where 5/4 and 6/5 are types of "third", 3/2 is a type of "fifth," and 5-limit major and minor triads share the same "1-3-5" triad shape, thinking of those ETs in terms of porcupine temperament is, in a certain sense, the natural approach. Furthermore, *any* heptatonic scale in [[15edo]] or [[22edo]] can be viewed as a MODMOS of the porcupine-7 MOS.