User:Pailiaq/Tritone substitution: Difference between revisions
No edit summary |
No edit summary |
||
| (3 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
==Tritone Substitution== | ==Tritone Substitution== | ||
'''Tritone substitution''' is a chord substitution technique from jazz harmony in which a dominant seventh chord is replaced by another dominant seventh chord whose root is a tritone (600¢) away. The substitution works because both chords share the same tritone interval between their third and seventh, allowing these chord tones to swap roles while maintaining smooth voice leading to the tonic. | A '''Tritone substitution''' is a chord substitution technique from jazz harmony in which a dominant seventh chord is replaced by another dominant seventh chord whose root is a tritone (600¢) away. The substitution works because both chords share the same tritone interval between their third and seventh, allowing these chord tones to swap roles while maintaining smooth voice leading to the tonic. | ||
In 12n-EDOs, tritone substitution works seamlessly with the diatonic dominant seventh chord. However, in most other tuning systems, the diatonic tritone does not equal the semioctave (half-octave, 600¢), requiring either nondiatonic chord construction or an acceptance of "fudged" approximations. | In 12n-EDOs, tritone substitution works seamlessly with the diatonic dominant seventh chord. However, in most other tuning systems, the diatonic tritone does not equal the semioctave (half-octave, 600¢), requiring either nondiatonic chord construction or an acceptance of "fudged" approximations. | ||
| Line 26: | Line 26: | ||
In all other EDOs, the diatonic augmented fourth deviates from 600¢. | In all other EDOs, the diatonic augmented fourth deviates from 600¢. | ||
== | ==In even-numbered EDOs== | ||
Even-numbered EDOs always contain an exact semioctave at n/2 steps. As stated, this semioctave typically does not align with the diatonic augmented fourth. | Even-numbered EDOs always contain an exact semioctave at n/2 steps. As stated, this semioctave typically does not align with the diatonic augmented fourth. | ||
=== Examples === | === Examples === | ||
In 26-EDO, | In 26-EDO, 13\26 = 600¢, but the diatonic augmented fourth is only 12\26 ≈ 554¢. A diatonic dominant seventh chord ((0, 8, 15, 22)\26) therefore lacks a true tritone, breaking the substitution mechanism of the 3rd and 7th swapping. | ||
The solution is to use the '''harmonic seventh chord''' ((0, 8, 15, 21)\26 | The solution is to use the '''harmonic seventh chord''' ((0, 8, 15, 21)\26) as your dominant V. In 26-EDO, the harmonic seventh (7/4) lands at 21\26 ≈ 969¢, which is ~0.4¢ from just. With a major third at 8\26, the interval from third to seventh is exactly 13 steps = 600¢. This nondiatonic chord produces a perfect tritone substitution, with the caveat that you must step outside your scale (playing a downminor 7) when playing a V-I progression if you want consistency in sound for when also using tritone substitutions. | ||
Howewever, using the diatonic, tritoneless dominant 7th chord also can work; the only difference being that the third and 7ths don't perfectly swap positions, as one of them will drift up or down by an edostep. | Howewever, using the diatonic, tritoneless dominant 7th chord also can work; the only difference being that the third and 7ths don't perfectly swap positions, as one of them will drift up or down by an edostep. | ||
== | ==In odd-numbered EDOs== | ||
Odd-numbered EDOs | Odd-numbered EDOs lack a semioctave entirely. Instead, they contain a small tritone and large tritone that straddle 600¢. | ||
This split creates an unavoidable inconsistency when attempting tritone substitution. Composers must make a choice: | |||
Let's look at 31edo as an example, where 15\31 ≈ 581¢ (approximating 7/5) and 16\31 ≈ 619¢ (approximating 10/7), differing by ~39¢. | |||
* '''Preserve the common tones''' | |||
Keep the literal pitches of the third and seventh identical between both chords. If G7 contains B–F (a small tritone), the sub chord Db also uses B and F. Voice leading stays identical—the same pitches resolve to the same destinations. However, B is now a harmonic seventh (~969¢) above Db rather than a minor seventh (~1000¢), so the chord quality shifts from dom7 to harmonic 7th. | |||
*Preserve the chord quality | |||
Build a standard dom7 on Db, giving Db–F–Ab–Cb. This chord contains the large tritone (F–Cb) rather than the small tritone (B–F) of the original G7. The root moves by one tritone size, but the chord contains the other—so Cb ≠ B, and the common tones drift by an edostep. Chord quality stays consistent, but voice leading shifts. | |||
The availability of two tritone sizes also means access to multiple dominant chord types, so long as the intervals fall within the right regions of interval space. This can be generalized to create many different chords with dominant function. | |||
== Structural definition of tritone-substitutable dominant chords== | == Structural definition of tritone-substitutable dominant chords== | ||
A '''tritone-substitutable dominant chord''' is any seventh chord where | A '''tritone-substitutable dominant chord''' is any seventh chord where | ||
* the third and seventh | * two intervals (the third and the seventh OR the root and the fifth) are a tritone apart | ||
* either of the two intervals functions as a leading tone to your target chord (as a dominant 5 chord or as a tritone sub). | |||
Ideally every interval should stay a third apart so as to construct tertian tetrads and avoid sounding like clusters, though following this simple requirement is surprisingly effective at creating smooth voice leading dominant function even in the extreme cases. | |||
What qualifies as a leading tone also is up for debate - generally intervals between 1050¢ and 1150¢ are used as leading tones. | |||
==Tritone complements== | ==Tritone complements== | ||
| Line 81: | Line 89: | ||
* The leading tone resolves by a smaller step (~50¢) to the tonic—a tighter, more chromatic pull | * The leading tone resolves by a smaller step (~50¢) to the tonic—a tighter, more chromatic pull | ||
* The | * The fourth now sits ~550¢ above the tonic, requiring a ~150¢ descent to reach the mediant at 400¢ | ||
* The small leading tone at extremes starts to feel weaker, becoming more like a comma adjustment of the tonic rather than a melodic step | * The small leading tone at extremes starts to feel weaker, becoming more like a comma adjustment of the tonic rather than a melodic step | ||
| Line 87: | Line 95: | ||
* The leading tone resolves by ~150¢—a wider, more whole-tone-like motion | * The leading tone resolves by ~150¢—a wider, more whole-tone-like motion | ||
* The | * The fourth tone at ~450¢ resolves down by ~50¢ to the 400c major third, though may also voicelead more smoothly to the neutral or minor third, letting you target different tonic chords besides major different major | ||
* The upward resolution feels less urgent | * The upward resolution feels less urgent | ||
This balancing act means that dominant function in xenharmonic systems can take on different characters depending on where the leading tone sits. | This balancing act means that dominant function in xenharmonic systems can take on different characters depending on where the leading tone sits. If using a wider tritone, like 630c, with the leading tone at 1050c, the fourth tone will then be located at 420c, which will lead very cleanly to a minor or neutral chord. So tritone size as well as its position in the leading tone interval region gives it different properties. | ||
==Summary== | ==Summary== | ||