SHEFKHED interval names: Difference between revisions

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31-tET: P1 tai-1/vai-1 tao-m2 m2 vai-m2/vao-M2 M2 tai-M2 tao-m3 m3 vai-m3/vao-M3 M3 tai-M3 tao-4 P4 vai-4 A4 d5 vao-5 P5 tai-5 tao-m6 m6 vai-m6/vao-M6 M6 tai-M6 tao-m7 m7 vai-m7.vao-M7 M7 tai-M7 vao-8/tao-8 P8

===Dave Keenan's most recent system===

[[File:Dave Keenan edo interval names prefix diagram.png|thumb|~~580.99x580.99px~~|Prefix diagram from ''One way to name the interval of any EDO from 5 to 72'', Keenan, 2016, pg. 4.]]

[[File:Dave Keenan edo interval names prefix diagram.png|thumb|434x581px|Prefix diagram from ''One way to name the interval of any EDO from 5 to 72'', Keenan, 2016, pg. 4.]]

In 2016 Dave Keenan proposed an alternative generalised [http://dkeenan.com/Music/EdoIntervalNames.pdf microtonal interval naming system for edos]. In what might be understood as a generalisation of his extended-diatonic interval-naming system described above onto any equal tuning. Employing as prefixes the familiar 'sub', 'super', and 'neutral'. His scheme is based on the diatonic scale, however the diatonic interval names are not defined by their position in a cycle of fifths like is Sagispeak. In Keenan's system the ET's best 3/2 is first labelled P5, and the fourth P4. The interval half-way between the tonic and fifth is labelled the neutral third, or 'N3', and halfway between the fourth and the octave N6. Then the interval a perfect fifth larger than N3 is labelled N7, and the interval a fifth smaller than N6 labelled N2. The neutral intervals then lie either at a step of the ET, or between two steps. After this the remaining interval names are decided based on the distance they lie in pitch from the 7 labelled intervals, which make up the ''Neutral scale'', P1 N2 N3 P4 P5 N6 N7, which, like the diatonic, is an MOS scale, which may be labelled [[Neutral7|Neutral[7]]] 3|3 using [[Modal UDP Notation|Modal UPD notation]]. To name an interval in an ET, the number of steps of 72-tET that most closely approximate the size of the interval difference from a note of the neutral scale is first found. Then the prefix corresponding to that number of steps of 72-tET is applied to the interval name. The diagram to the right details this process. An interval just smaller than a major third in Keenan's system is labelled a ''narrow major third'', and an interval just wider than a 6/5 minor third a ''wide minor third'', however he notes that 'narrow' and 'wide' are only necessary in edos greater than 31. This system is equivalent to the Fokker/Keenan Extended-diatonic interval-naming system and Miracle interval naming when applied to any of the ETs they were able to cover.

@@ Line 417: / Line 417: @@
 -tET: P1 tai-1/vai-1 tao-m2 m2 vai-m2/vao-M2 M2 tai-M2 tao-m3 m3 vai-m3/vao-M3 M3 tai-M3 tao-4 P4 vai-4 A4 d5 vao-5 P5 tai-5 tao-m6 m6 vai-m6/vao-M6 M6 tai-M6 tao-m7 m7 vai-m7.vao-M7 M7 tai-M7 vao-8/tao-8 P8
 ===Dave Keenan's most recent system===
-[[File:Dave Keenan edo interval names prefix diagram.png|thumb|580.99x580.99px|Prefix diagram from ''One way to name the interval of any EDO from 5 to 72'', Keenan, 2016, pg. 4.]]
+[[File:Dave Keenan edo interval names prefix diagram.png|thumb|434x581px|Prefix diagram from ''One way to name the interval of any EDO from 5 to 72'', Keenan, 2016, pg. 4.]]
 In 2016 Dave Keenan proposed an alternative generalised [http://dkeenan.com/Music/EdoIntervalNames.pdf microtonal interval naming system for edos]. In what might be understood as a generalisation of his extended-diatonic interval-naming system described above onto any equal tuning. Employing as prefixes the familiar 'sub', 'super', and 'neutral'. His scheme is based on the diatonic scale, however the diatonic interval names are not defined by their position in a cycle of fifths like is Sagispeak. In Keenan's system the ET's best 3/2 is first labelled P5, and the fourth P4. The interval half-way between the tonic and fifth is labelled the neutral third, or 'N3', and halfway between the fourth and the octave N6. Then the interval a perfect fifth larger than N3 is labelled N7, and the interval a fifth smaller than N6 labelled N2. The neutral intervals then lie either at a step of the ET, or between two steps. After this the remaining interval names are decided based on the distance they lie in pitch from the 7 labelled intervals, which make up the ''Neutral scale'', P1 N2 N3 P4 P5 N6 N7, which, like the diatonic, is an MOS scale, which may be labelled [[Neutral7|Neutral[7]]] 3|3 using [[Modal UDP Notation|Modal UPD notation]]. To name an interval in an ET, the number of steps of 72-tET that most closely approximate the size of the interval difference from a note of the neutral scale is first found. Then the prefix corresponding to that number of steps of 72-tET is applied to the interval name. The diagram to the right details this process. An interval just smaller than a major third in Keenan's system is labelled a ''narrow major third'', and an interval just wider than a 6/5 minor third a ''wide minor third'', however he notes that 'narrow' and 'wide' are only necessary in edos greater than 31. This system is equivalent to the Fokker/Keenan Extended-diatonic interval-naming system and Miracle interval naming when applied to any of the ETs they were able to cover.