“Tritone Substitutions” article @ All About Jazz

” data-original-title title>Gene Rodgers. The tritone sub is featured prominently in m. 3 as the bassist, William Oscar Smith, plays a D♮ instead of the A♭.

Compare that to the early version of the tune from 1930 by

” data-original-title title>Paul Whiteman:

The differences in the harmonies, particularly in the first four measures of the verse are striking.

What is interesting to note is that in the notated version from the “Real Book,” in the second half of m. 4, there is a G♭7 chord that moves to Fmin7. A tritone away from G♭ is C, which is the dominant of F. Thus, this tritone sub is actually notated in the lead sheet! We also find an example of a tritone sub going to a chord other than the tonic or dominant. Its use must have been so prevalent that the Berklee scribes who put the original Real Book together must have seen it as the standardized chord progression to use.

Here is the tune by the

” data-original-title title>Gene Krupa Trio from 1945:

We can hear the tritone sub appearing in m. 2 as the pianist, ” data-original-title title>Teddy Napoleon, plays a D7 chord instead of the A♭7, but the tritone sub in the second half of m. 3 is not present… yet.

Here is the same tune eleven years later by

” data-original-title title>Sonny Stitt:

In this version, we can hear the pianist,

” data-original-title title>Jimmy Jones, playing the upper structure harmonies of the tritone sub (D7) before the tonic in mm. 2-3. This creates a very colorful chord over the A♭ in the bass —A♭ 7, ♭9, ♭13. We also hear the tritone sub in m. 3 as the G♭7 chord moves to Fmin7 chord in m. 4 Why does it work? Because the 3rd and the 7th of dominant chords are in a somewhat unique intervallic relationship—they are a tritone apart. Since there are only twelve pitches, and since a tritone is six half-steps, it means that the tritone is a dyad (a dyad is two pitches played simultaneously) of “limited transposition”—when transposed, it does not create 12 new versions of itself, like the major and minor chord do. The reason for this “limited transposition” is that there are six half-steps between the pitches, and six divides evenly into 12. Similarly, all chords and scales made up of intervals that divide evenly into twelve are of limited transposition:

• The minor 2nd is one half-step which means that there is only one chromatic scale.
• The major 2nd is two half-steps, which means that there are only two whole-tone scales.
• The minor 3rd is three half-steps, and the diminished chord is made up of four notes that are a minor 3rd apart—thus, there are only three diminished chords.
• Finally, the major 3rd is four half-steps and the augmented chord is made up of three pitches that are a major 3rd apart—thus, there are only four augmented triads.

Here are all of the dyads that are a tritone apart:

Note that after six transpositions going up half a step each time, the original dyad appears again—C and F#.

The tritone, therefore, serves “double duty” as the 3rd and 7th of two different dominant chords. It is this ambiguity that jazz musicians capitalized on to great effect in the implementation of the tritone sub.

Theoretically, the tritone sub can be used as an approach to any chord, but of course, it must be used tastefully. For example, the melody may have notes that clash with the tritone sub, or like any colorful, novel variation, it can become tiresome if overused. Jazz musicians use the tritone sub freely as an approach to many different chords, but the most common is in the approach to the tonic, as described above in “Body and Soul.”

Pedagogical Implications

Classical theorists call dominant 7th chords that do not resolve to their tonic “non-functional dominant 7th.” This doesn’t mean that the chords have no function; it just means that they are used in different ways, mostly as embellishing chords that do not highlight or utilize their powerful “pull” to the tonic. Thus, they are not as structurally important as “functional dominant 7ths,” which are essential as pillars of the form of any piece of tonal music.

Jazz musicians do not use this terminology, but they are certainly aware that not all dominant chords are alike—some indicate new key areas, and some do not. How do these differences affect the improviser’s approach to functional and non-functional dominant 7th chords?

Here are the first 13 measures of the jazz standard “On a Clear Day”:

There are two non-functional dominant 7th chords: C7#11 (mm. 3-4) and F7#11 (mm. 11- 12). They are non-functional because they are not followed by their tonic chord—the tonic of C is F, and the tonic of F is B♭. In this tune, C7 moves down a fourth to Gmaj7 (the tonic of the piece), and F7 moves down a tritone to Bmin7. There is also a functional dominant 7th, E7, in m. 15.

Dominant 7th chords have many options for improvisers in terms of potential scales that work well. In general, the different scales most commonly used as “pitch palettes” are the be-bop scale, the diminished scale, and two different ascending melodic minor scales. Here is each scale as it would be used over C7:

In terms of dissonance with the chord, the scales are markedly different. The bebop scale (#1) and the ascending melodic minor on G (#3) are free of any real dissonances against the chord and its home key of F major. They use diatonic pitches from the home key but introduce one color tone each: In the bebop scale, (B♮ is included as a passing tone between B♭ and C, and in the ascending melodic minor on G, F#, the raised 11th, provides the leading tone to the fifth of the chord and gives it a Lydian flavor.

The other two scales, the diminished scale (#2) and the ascending melodic minor on D♮ (#4) introduce strong dissonances like ♮9, #9, ♮13 (ascending melodic minor on D♮). They both also have the raised 11th, but given the level of dissonance in the other pitches, neither scale has the brightness that the Lydian provides. These strong dissonances work well with a functional dominant, which is such a strong chord that it can withstand all manner of alteration without losing its power as the dominant. The non-functional dominant chord does not enjoy that position of strength, and as such, it is not able to accommodate those dissonances—they introduce pitches that do not resolve satisfactorily because the chord is not moving to its own tonic.

Improvisers have these and other choices as well. Which scales function best on C7 in “On A Clear Day”? The bebop scale and the diminished scale work very well, while the diminished scale and the ascending melodic minor on D♮ do not. This is the case with most, if not all, non-functional dominants—the brighter, consonant scales work best while the darker, more dissonant scales do not.

On the other hand, when we find functional dominant chords, like the E7 in m. 8 which moves to its minor tonic, the situation is reversed—the brighter scales invoke the major key, which does not work as well. The darker scales invoke the minor key, and work much better.

What about the functional dominant, D7—Gmaj7, at the end of the piece in the final cadence?

All four of the primary dominant 7th scale choices can be used with functional dominants.

In terms of pedagogy then, the tendencies are as follows:

• Non-functional dominant 7th chords work best with the ascending melodic minor from the pitch a perfect fifth up from the root, and with the bebop scale and its variations. The diminished scale and the ascending melodic minor built on the pitch a half-step up from the root introduce too much dissonance, which destabilizes the key.
• Functional dominant chords in major keys work well with any of the scales.
• Functional dominant chords in minor keys are the opposite of non-functional dominant 7th chords in terms of scale choice. They work well with the diminished scale and the ascending melodic minor built on the pitch a half-step up from the root of the chord.

So, while jazz musicians may not use the classical theory terminology, they acknowledge the concept and imply it with their choice of scales over the different types of dominant 7th chords.

To wit, here is

” data-original-title title>George Coleman‘s solo on “On A Clear Day,” which uses the scales almost unerringly, precisely as described above:

I have written about this before, asserting that there is a hidden “Schenkerian” in every jazz musician in my article Strange Bedfellows: Jazz and Pop and Heinrich Schenker?:

…I contend that jazz musicians, in particular, engage in Schenkerian analysis as a matter of course in their approach to improvisation and composition. Professional jazz musicians can look at a new chart and instantly see its harmonic “background.” This involves identifying structural chords that denote key areas and modulations while at the same time relegating embellishing chords to the foreground, where they can often be ignored. Indeed, this is difficult for young jazz musicians to understand—there are a lot of chords on the page, and amateur jazz musicians are unable to place them in a structural hierarchy. This is something that jazz teachers regularly do for their students. Identifying the background simplifies the improvisational options for young musicians. Again, professional musicians do this as a matter of course—the applied nature of their work as jazz musicians makes them practicing Schenkerians who immediately see the background structure and work intimately with it, even in their first encounters with new works.

As a truly applied art form, jazz musicians must perform instantaneous theoretical analysis as part of their craft, but they do not need to use the terminology of music theorists to do so—they know what works and what doesn’t work in any given situation, and they know that intuitively from a lifetime of “hands-on” experimentation with the myriad harmonic, melodic, and rhythmic resources available.

Part 3 will look at the classical counterpart of the tritone sub, the Augmented 6th chord.

Endnotes

¹ In truth, F# and G♭ are different pitches—F# is slightly higher than G♭. Non-fixed pitch instruments, like the strings or trombones, are able to play them as different pitches. On the piano and other fixed-pitch instruments, a compromise is made that allows for the pitches to be used enharmonically. This compromise sacrifices some of the piano’s sonorous richness for an ability to play in all of the twelve keys without re-tuning. Bach’s “Well-Tempered Clavier” was somewhat of a musical manifesto for the tuning system that allowed free movement between all of the keys. Prior to the adoption of this tuning system, harpsichords would have to be re-tuned between pieces in different keys.↩

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