16edo: Difference between revisions
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[[:File:16ed2-001.svg|16ed2-001.svg]] | [[:File:16ed2-001.svg|16ed2-001.svg]] | ||
== | == Octave Theory == | ||
The scale supports the diminished temperament with its 1/4 octave period, though its generator size, equal to its step size of 75 cents, is smaller than ideal. Its very flat 3/2 of 675 cents [[support]]s Mavila temperament, where the mapping of major and minor is reversed. The temperament could be popular for its 150-cent "3/4-tone" equal division of the traditional 300-cent minor third. | The scale supports the diminished temperament with its 1/4 octave period, though its generator size, equal to its step size of 75 cents, is smaller than ideal. Its very flat 3/2 of 675 cents [[support]]s Mavila temperament, where the mapping of major and minor is reversed. The temperament could be popular for its 150-cent "3/4-tone" equal division of the traditional 300-cent minor third. | ||
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[[Easley Blackwood Jr]] writes of 16edo: | [[Easley Blackwood Jr]] writes of 16edo: | ||
"16 notes: This tuning is best thought of as a combination of four intertwined diminished seventh chords. Since 12-note tuning can be regarded as a combination of three diminished seventh chords, it is plain that the two tunings have elements in common. The most obvious difference in the way the two tunings sound and work is that triads in 16-note tuning, although recognizable, are too discordant to serve as the final harmony in cadences. Keys can still be established by successions of altered subdominant and dominant harmonies, however, and the Etude is based mainly upon this property. The fundamental consonant harmony employed is a minor triad with an added minor seventh." | "''16 notes: This tuning is best thought of as a combination of four intertwined diminished seventh chords. Since 12-note tuning can be regarded as a combination of three diminished seventh chords, it is plain that the two tunings have elements in common. The most obvious difference in the way the two tunings sound and work is that triads in 16-note tuning, although recognizable, are too discordant to serve as the final harmony in cadences. Keys can still be established by successions of altered subdominant and dominant harmonies, however, and the Etude is based mainly upon this property. The fundamental consonant harmony employed is a minor triad with an added minor seventh.''" | ||
From a harmonic series perspective, if we take 13\16 as a 7/4 ratio approximation, sharp by 6.174 cents, and take the 300-cent minor third as an approximation of the harmonic 19th ([[19/16]], approximately 297.5 cents), that can combine with the approximation of the harmonic seventh to form a 16:19:28 triad . | From a harmonic series perspective, if we take 13\16 as a 7/4 ratio approximation, sharp by 6.174 cents, and take the 300-cent minor third as an approximation of the harmonic 19th ([[19/16]], approximately 297.5 cents), that can combine with the approximation of the harmonic seventh to form a 16:19:28 triad . | ||
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The interval between the 28th & 19th harmonics, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's "narrow fifth". Another voicing for this chord is 14:16:19, which features 19:14 as the outer interval (528.7 cents just, 525.0 cents in 16edo). A perhaps more consonant open voicing is 7:16:19. | The interval between the 28th & 19th harmonics, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's "narrow fifth". Another voicing for this chord is 14:16:19, which features 19:14 as the outer interval (528.7 cents just, 525.0 cents in 16edo). A perhaps more consonant open voicing is 7:16:19. | ||
== | == Notation == | ||
16edo notation can be easy utilizing Goldsmith's Circle of keys, nominals, and respective notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon additions to A-G. The Armodue model uses a 4-line staff for 16edo. | 16edo notation can be easy utilizing Goldsmith's Circle of keys, nominals, and respective notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon additions to A-G. The Armodue model uses a 4-line staff for 16edo. | ||
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[10]: 2 1 2 1 2 2 1 2 1 2 | [10]: 2 1 2 1 2 2 1 2 1 2 | ||
== Metallic Harmony | == Metallic Harmony == | ||
Because 16edo does not approximate 3/2 well at all, triadic harmony based on heptatonic thirds is not a great option for typical harmonic timbres. | Because 16edo does not approximate 3/2 well at all, triadic harmony based on heptatonic thirds is not a great option for typical harmonic timbres. | ||