Extended-diatonic interval names: Difference between revisions

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== Ups and Downs ==

One final interval naming system, associated with the [[Ups and ~~Downs Notation~~]] system, belonging to microtonal theorist and musician [[KiteGiedraitis|Kite Giedraitis]], like Sagittal is based on deviations from pythagorean intervals. In this system however, deviations (from major, minor, perfect, augmented and diminished) are notated simply by the addition of up or down arrows: '^' or 'v', corresponding to raising or lowering of a single step of an edo. In some tunings ([[12edo|12-tET]], 19-tET or 31-tET for example) 5/4 may be a M3, and in others a vM3 (downmajor 3rd) (e.g. [[15edo|15-tET]], [[22edo|22-tET]], 41-tET, 72-tET), or even an up-major 3rd (e.g. [[21edo|21-tET]]). Ups and downs also includes neutrals, which lay exactly in-between major and minor intervals of the same degree, labelled '~' (mid). The mid-4th ~4 is halfway between P4 and A4, and ~5 is likewise half-way diminished. 'Up' and 'down' prefixes may be used before mid also, e.g. 'v~ 3' in 72-tET. P1, P4, P5 and P8 when upped or downed (or midded, in the case of P4 and P5) are simply labelled '1', '4', '5' and '8'. This system benefits from its simplicity as well as its conservation of interval arithmetic. The latter makes possible the naming of chords, e.g. downminor 7th. Rank-2 temperaments may also be described, with the possible addition of an additional pair of qualifiers, lifts and drops - '/' and '\'. A rank-2 scale, such as a MOS scale may appear different than this rank-2 notation when approximated in an equal (rank-1) tuning. Another criticism of Kite's system that does not apply to the others is the fact that when an edo is doubled or multiplied by some simple fraction, and the best fifth is constant across the two edos, the same intervals may be given different names.

One final interval naming system, associated with the [[Ups and downs notation]] system, belonging to microtonal theorist and musician [[KiteGiedraitis|Kite Giedraitis]], like Sagittal is based on deviations from pythagorean intervals. In this system however, deviations (from major, minor, perfect, augmented and diminished) are notated simply by the addition of up or down arrows: '^' or 'v', corresponding to raising or lowering of a single step of an edo. In some tunings ([[12edo|12-tET]], 19-tET or 31-tET for example) 5/4 may be a M3, and in others a vM3 (downmajor 3rd) (e.g. [[15edo|15-tET]], [[22edo|22-tET]], 41-tET, 72-tET), or even an up-major 3rd (e.g. [[21edo|21-tET]]). Ups and downs also includes neutrals, which lay exactly in-between major and minor intervals of the same degree, labelled '~' (mid). The mid-4th ~4 is halfway between P4 and A4, and ~5 is likewise half-way diminished. 'Up' and 'down' prefixes may be used before mid also, e.g. 'v~ 3' in 72-tET. P1, P4, P5 and P8 when upped or downed (or midded, in the case of P4 and P5) are simply labelled '1', '4', '5' and '8'. This system benefits from its simplicity as well as its conservation of interval arithmetic. The latter makes possible the naming of chords, e.g. downminor 7th. Rank-2 temperaments may also be described, with the possible addition of an additional pair of qualifiers, lifts and drops - '/' and '\'. A rank-2 scale, such as a MOS scale may appear different than this rank-2 notation when approximated in an equal (rank-1) tuning. Another criticism of Kite's system that does not apply to the others is the fact that when an edo is doubled or multiplied by some simple fraction, and the best fifth is constant across the two edos, the same intervals may be given different names.

[[Igliashon Jones]] is a supporter of this system, but for the relabeling of 'down' as 'sub' and 'up' as 'super' and 'mid' as 'neutral', so that more common names are used, wherein 'super' infers a raise of 1 step of the edo, and 'sub' a lowering of one step. In this 'Extra-diatonic' system 'super' and 'sub' may be doubly applied, as in Ups and Downs, but they may not be applied before 'neutral' where in Ups and Downs they may be applied before 'mid'.

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 == Ups and Downs ==
-One final interval naming system, associated with the [[Ups and Downs Notation]] system, belonging to microtonal theorist and musician [[KiteGiedraitis|Kite Giedraitis]], like Sagittal is based on deviations from pythagorean intervals. In this system however, deviations (from major, minor, perfect, augmented and diminished) are notated simply by the addition of up or down arrows: '^' or 'v', corresponding to raising or lowering of a single step of an edo. In some tunings ([[12edo|12-tET]], 19-tET or 31-tET for example) 5/4 may be a M3, and in others a vM3 (downmajor 3rd) (e.g. [[15edo|15-tET]], [[22edo|22-tET]], 41-tET, 72-tET), or even an up-major 3rd (e.g. [[21edo|21-tET]]). Ups and downs also includes neutrals, which lay exactly in-between major and minor intervals of the same degree, labelled '~' (mid). The mid-4th ~4 is halfway between P4 and A4, and ~5 is likewise half-way diminished. 'Up' and 'down' prefixes may be used before mid also, e.g. 'v~ 3' in 72-tET. P1, P4, P5 and P8 when upped or downed (or midded, in the case of P4 and P5) are simply labelled '1', '4', '5' and '8'. This system benefits from its simplicity as well as its conservation of interval arithmetic. The latter makes possible the naming of chords, e.g. downminor 7th. Rank-2 temperaments may also be described, with the possible addition of an additional pair of qualifiers, lifts and drops - '/' and '\'. A rank-2 scale, such as a MOS scale may appear different than this rank-2 notation when approximated in an equal (rank-1) tuning. Another criticism of Kite's system that does not apply to the others is the fact that when an edo is doubled or multiplied by some simple fraction, and the best fifth is constant across the two edos, the same intervals may be given different names.
+One final interval naming system, associated with the [[Ups and downs notation]] system, belonging to microtonal theorist and musician [[KiteGiedraitis|Kite Giedraitis]], like Sagittal is based on deviations from pythagorean intervals. In this system however, deviations (from major, minor, perfect, augmented and diminished) are notated simply by the addition of up or down arrows: '^' or 'v', corresponding to raising or lowering of a single step of an edo. In some tunings ([[12edo|12-tET]], 19-tET or 31-tET for example) 5/4 may be a M3, and in others a vM3 (downmajor 3rd) (e.g. [[15edo|15-tET]], [[22edo|22-tET]], 41-tET, 72-tET), or even an up-major 3rd (e.g. [[21edo|21-tET]]). Ups and downs also includes neutrals, which lay exactly in-between major and minor intervals of the same degree, labelled '~' (mid). The mid-4th ~4 is halfway between P4 and A4, and ~5 is likewise half-way diminished. 'Up' and 'down' prefixes may be used before mid also, e.g. 'v~ 3' in 72-tET. P1, P4, P5 and P8 when upped or downed (or midded, in the case of P4 and P5) are simply labelled '1', '4', '5' and '8'. This system benefits from its simplicity as well as its conservation of interval arithmetic. The latter makes possible the naming of chords, e.g. downminor 7th. Rank-2 temperaments may also be described, with the possible addition of an additional pair of qualifiers, lifts and drops - '/' and '\'. A rank-2 scale, such as a MOS scale may appear different than this rank-2 notation when approximated in an equal (rank-1) tuning. Another criticism of Kite's system that does not apply to the others is the fact that when an edo is doubled or multiplied by some simple fraction, and the best fifth is constant across the two edos, the same intervals may be given different names.
 [[Igliashon Jones]] is a supporter of this system, but for the relabeling of 'down' as 'sub' and 'up' as 'super' and 'mid' as 'neutral', so that more common names are used, wherein 'super' infers a raise of 1 step of the edo, and 'sub' a lowering of one step. In this 'Extra-diatonic' system 'super' and 'sub' may be doubly applied, as in Ups and Downs, but they may not be applied before 'neutral' where in Ups and Downs they may be applied before 'mid'.