16edo: Difference between revisions

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"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 ~~adds another overtone which~~ 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 .

The interval between the 28th & 19th ~~overtones~~, 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.

==Hexadecaphonic Notation==

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 "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 adds another overtone which 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 .
-The interval between the 28th &amp; 19th overtones, 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 &amp; 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.
 ==Hexadecaphonic Notation==