Pentatonic Functional Just System: Difference between revisions
Maybe it's best not to have a purely 11-limit section |
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{{Editable user page| | {{Editable user page|Also feel free to add more content, but please do not delete existing content without my permission.}} | ||
Traditionally, we use a [[5L 2s|diatonic]] system of interval classification. This works well in the [[5-limit]] and in [[meantone]]. However, in other systems like [[superpyth]], a pentatonic system of classification based on the [[2L 3s]] [[MOS scale]] may be preferred, with priority on the [[2.3.7 subgroup|2.3.7-]][[subgroup]]. In this page, we will develop a pentatonic version of the [[FJS]], starting from the [[3-limit]] and using [[formal comma]]s to reach higher limits. | Traditionally, we use a [[5L 2s|diatonic]] system of interval classification. This works well in the [[5-limit]] and in [[meantone]]. However, in other systems like [[superpyth]], a pentatonic system of classification based on the [[2L 3s]] [[MOS scale]] may be preferred, with priority on the [[2.3.7 subgroup|2.3.7-]][[subgroup]]. In this page, we will develop a pentatonic version of the [[FJS]], starting from the [[3-limit]] and using [[formal comma]]s to reach higher limits. | ||
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In full 7-limit superpyth, 10/9 is a subsecond, 6/5 is a supersecond, 5/4 is a sub-subthird (a subthird is 9/7), and 7/5 is a super-superthird (a superthird is [[27/20]]~[[48/35]]). Their [[octave complement]]s can be classified accordingly. | In full 7-limit superpyth, 10/9 is a subsecond, 6/5 is a supersecond, 5/4 is a sub-subthird (a subthird is 9/7), and 7/5 is a super-superthird (a superthird is [[27/20]]~[[48/35]]). Their [[octave complement]]s can be classified accordingly. | ||
== | == The 11- and 13-limits == | ||
We now look at ratios of 11, with [[33/32]] as our formal comma. By pentatonic interval classification, many undecimal ratios fall right between two interval categories, the edges of which are the 5-limit intervals; thus they are called '''interpental''', just like [[interseptimal]] intervals in diatonic classification. | We now look at ratios of 11, with [[33/32]] as our formal comma. By pentatonic interval classification, many undecimal ratios fall right between two interval categories, the edges of which are the 5-limit intervals; thus they are called '''interpental''', just like [[interseptimal]] intervals in diatonic classification. | ||
; Todo<nowiki>:</nowiki> Add the tables | ; Todo<nowiki>:</nowiki> Add the tables | ||