User:Ganaram inukshuk/7L 3s: Difference between revisions
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{{MOS intro|Scale Signature=7L 3s}} | {{MOS intro|Scale Signature=7L 3s}} | ||
7L 3s represents temperaments such as [[mohajira]]/[[mohaha]]/[[mohoho]], whose generators are around a neutral 3rd. Mohaha and mohoho form a [[Chromatic pairs|chromatic pair]] consisting of a [[Mohaha7|seven]] and [[Mohaha10|ten-note scale]]. | |||
==Name== | ==Name== | ||
TAMNAMS suggests the temperament-agnostic name '''dicoid''' (from dicot, an exotemperament) for the name of this scale. | TAMNAMS suggests the temperament-agnostic name '''dicoid''' (from dicot, an exotemperament) for the name of this scale. | ||
==Intervals== | ==Intervals and degrees== | ||
:''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees.'' | :''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees.'' | ||
Names for this scale's [[degrees]], the positions of the scale's tones, are called '''mosdegrees'''. Its [[Interval|intervals]], the pitch difference between any two tones, are based on the number of large and small steps between the two tones and are thus called '''mossteps'''. Per TAMNAMS, both mosdegrees and mossteps are ''0-indexed'', and may be referred to as '''dicodegrees''' and '''dicosteps'''. Ordinal names, such as mos-1st instead of 0-mosstep, are discouraged for non-diatonic MOS scales. | Names for this scale's [[degrees]], the positions of the scale's tones, are called '''mosdegrees'''. Its [[Interval|intervals]], the pitch difference between any two tones, are based on the number of large and small steps between the two tones and are thus called '''mossteps'''. Per TAMNAMS, both mosdegrees and mossteps are ''0-indexed'', and may be referred to as '''dicodegrees''' and '''dicosteps'''. Ordinal names, such as mos-1st instead of 0-mosstep, are discouraged for non-diatonic MOS scales. | ||
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== Theory == | == Theory == | ||
=== Quartertone and tetrachordal analysis === | === Quartertone and tetrachordal analysis === | ||
Due to the presence of quartertone-like intervals, Graham Breed has proposed the terms ''tone'' (abbreviated as ''t'') and ''quartertone'' (abbreviated as ''q'') as alternatives for large and small steps. This interpretation only makes sense for step ratios in which the small step approximates a quartertone. Additionally, Breed has also proposed a larger tone size, abbreviated using a capital ''T'', to refer to the combination of ''t'' and ''q''. Through this addition of a larger step, 7-note subsets of 7L 3s can be constructed. Some of these subsets are identical to that of 3L 4s, such as ''T-t-T-t-T-t-t'', but | Due to the presence of quartertone-like intervals, Graham Breed has proposed the terms ''tone'' (abbreviated as ''t'') and ''quartertone'' (abbreviated as ''q'') as alternatives for large and small steps. This interpretation only makes sense for step ratios in which the small step approximates a quartertone. Additionally, Breed has also proposed a larger tone size, abbreviated using a capital ''T'', to refer to the combination of ''t'' and ''q''. Through this addition of a larger step, 7-note subsets of 7L 3s can be constructed. Some of these subsets are identical to that of 3L 4s, such as ''T-t-T-t-T-t-t'', but Breed states that non-MOS patterns are possible, such as ''T-t-t-T-t-t-T''. | ||
Additionally, due to the presence of fourth and fifth-like intervals, 7L 3s can be analyzed as a [[tetrachord|tetrachordal scale]]. Since the major 4-dicostep, the fourth-like interval, is reached using 4 steps rather than 3 (3 tones and 1 quartertone), Andrew Heathwaite offers an additional step ''A'', for ''augmented second'', to refer to the combination of two tones (''t''). Thus, the possible tetrachords can be built as a combination of a (large) tone and two (regular) tones (''T''-''t''-''t''), or an augmented step, small tone, and quartertone (''A''-''t''-''q''). | Additionally, due to the presence of fourth and fifth-like intervals, 7L 3s can be analyzed as a [[tetrachord|tetrachordal scale]]. Since the major 4-dicostep, the fourth-like interval, is reached using 4 steps rather than 3 (3 tones and 1 quartertone), Andrew Heathwaite offers an additional step ''A'', for ''augmented second'', to refer to the combination of two tones (''t''). Thus, the possible tetrachords can be built as a combination of a (large) tone and two (regular) tones (''T''-''t''-''t''), or an augmented step, small tone, and quartertone (''A''-''t''-''q''). | ||
==Scale tree == | ==Scale tree == | ||
{{Scale tree|7L 3s | {{Scale tree|7L 3s|Comments=6/5: Restles ↑; | ||
7/5: Beatles; | |||
3/2: Suhajira / ringo; | |||
12/5: Hemif / hemififths; | |||
5/2: Mohaha / neutrominant; | |||
13/5: Hemif / salsa / karadeniz; | |||
8/3: Mohaha / mohamaq; | |||
4/1: Mohaha / migration / mohajira; | |||
6/1: Mohaha / ptolemy; | |||
13/8: Golden suhajira}} | |||
== See also == | == See also == | ||
* Graham Breed's page on 7L 3s | * Graham Breed's page on 7L 3s (and 3L 7s to an extent) | ||