~ sharp Four / flat Five ~

~ the tritone blue note ~ #4 / b5 ~

~ augmented (+) 4th / diminished (°) 5th ~

~ the tritone sub ~

'... the octave's midpoint and a two pitch catalyst that energizes the director of Americana harmony ... '

~

In a nutshell. The enharmonic labeling of the #4 / b5 tritone interval provides us with the exact midpoint of our perfect octave span from either direction. As for the 'tri' in tritone, it simply implies three whole tones. As diatonic Four, Five and the octave are perfect intervals, we use the terms to 'augment' up to #4 or 'diminish' down to b5 to find our tritone.

Melodically there's the blues hued lines created by the tritone / #4 within the blues scale. We'll get some whole tone magic too with 'b5' and work these up the octave with the #11 colortone. As a melody pitch in diatonic line, here's one with the #4 / b5 pitch that might ring a bell. In C major, drum roll please ... brrrrr ... example 1.

Who woulda' thunk huh? All diatonic triads and the sharp Four creates the one of a kind melody.

melody

Harmonically, #4 / b5 tritone studies center around its catalyst role in V7 and the 'double tritone' of V7b9. This last ties us into Coltrane's evolution and ascension to Giant Steps and towards today's 'chromatic blur.' Forward on to #15 for a new system of composition etc. Similar theory / pitch paths for the softened melodic minor / Lydian b7 way of grouping the pitches. Expanding basic changes into more jazzier chord substitutions associated with the 12 bar blues is another super exciting area to examine, once the theory here or even just the ability to quickly spell chords is committed to rote memory.

The tritone in scales and chords. We theorists of the American magic should strive to understand and hear this essential spice in two core ways; as a single pitch within a scale or group of pitches and as a two pitch tritone spanning interval that lives in certain chords.

Scale pitch. As a scale pitch, our tritone color is an essential blue note. Initially we can find it added to the pitches of the minor pentatonic color. This simple edition of the one pitch tritone creates our core blues group of pitches. Examine the pitches of C blues. Example 1.

scale degrees
root / 1
.
b3
4
#4
5
.
b7
8
C Blues scale
C
.
Eb
F
F# / Gb
G
.
Bb
C

Nothing really too fancy in this last idea. Just pushing the buttons in order and the blues hue comes forth. In this last idea we follow right along the scale shape and pitches of our primary pattern with the 'x's marking the tritones. Have this one under your fingers? Do learn it here if need be. Example 1a.

This single scale shape is the original one that we inherit from from the earlier G open string banjo tuning.

A tritone melody. I think this next idea goes all the way back. Try it as a vamp behind the soloist. It's also a great start for horn players to head for the jungle. Example 2.

Dig that big tritone vamp. Ought to be able to make that into some sort of 12 bar blues yes?

Additional melodies. Bernstein's "Maria" beloved as noted above. Pianist Kenny Barron's "Voyage" has a very cool tritone lick at the close of the B section. As a passing tone in A section consequent phrase of Billy Strayhorn's "Take The A Train" is an essential jazz classic of course. And lot's and lot's of everyone's blues licks over the last century or so.

blues licks

Tritone focus. We also find tritone interval and pitch used way out in the open in the mix and at very loud volumes with giant distortion through stacks, as the focus point pitch in the melody line. We can find this in metal music and its subgenres. Deep Purple's "Smoke On The Water" is a tritone nuanced melody.

Tritone in a chord. When built into chords as the 3rd and 7th, the presence of the diatonic two pitch tritone creates our dominant family of chords. This is the family of chords that directs our music, is the core of our cadential motions and the core harmonic color we use to back the blues. Examine the pitch letter names locating the diatonic two pitch tritone from within the pitches of C major, then run the changes of a few root position dominant chord shapes for guitar. Example 2a.

scale degrees
root / 1
2
3
4
5
6
7
8
C major scale
C
D
E
F
G
A
B
C

Recognize the evolution of these chords? Surely we can find the dominant / tritone color in all of the American styles we dig. This last sequence of chords evolves our G7 from folk / blues through rock, bossa and pop/ jazz and back to the bluesy V7#9 before resolving to the Hollywood tonic.

Tritone catalyst, in V7 it's the 3rd and 7th. Any dominant 7th chord, used in any and all of our musical styles or situations, has a tritone interval in it. Usually along with a root and 5th, it's makes Five seven V7 :) Examine letter name, notation and sound of the diatonic pitches of G7, the dominant V7 chord in the key of C major. Example 3.

scale degrees
root / 1
2
3
4
5
6
7
8
G7
G
A
B
C
D
E
F
G
arpeggio degrees
root / 1
3
5
7
9
11
13
15
arpeggio pitches
G
B
D
F
A
C
E
G
G7 pitches
G
B
D
F
.
.
.
.
3~7 tritone interval
.
B
.
F
.
.
.
.

Resolving the tritone / leading tone. The resolution of the tritone interval pitches in the Five to One cadential motion is based on key two aspects. First is that our pitch B is the leading tone to C. Second, that we follow the age old voice leading idea that if we move each of our pitches in one chord to the closest pitches available in the next chord in our progression, chances are we'll be groovy in sound and theory.

So just like our physical gravity, proximity of pitch creates a tonal pull or gravity, i.e., the leading tone resolves by ascending by half step. Thus, our B to F tritone interval within G 7, following the 'closest rule', resolves to C major in the following manner. Ex. 3a.

Tension / resolution. Sense the tension / release dynamic in the pitches? Yes ? Cool. After hearing the music a few times, can you predict what'll happen next? Developing a sense of this aural predictability becomes a key aspect of our artistic evolution.

No? Not sensing the tension / release dynamic? Then ya might want to just stop right here until you do. Get out your guitar and jam along. Just keep clicking to hear the sound of the above resolutions, find the pitches and chords and stretch the time to create additional tension. This basic artistic dynamic is sort of a big deal as it lives nearly everywhere in our Americana music.

Update our DNA. 'Feeling' this release of the G7 chord's tritone tension, upon the sounding of the tonic C major chord, is surely one of the keys to better understanding the theory of our local American musical universe. This Five 7 to One cadential motion is simply everywhere in our American music and has been for the last couple of hundred years. So if need be take the time to get it in your DNA here and now and you're good to go for evermore :)

What about the flip side? In this tritone pitch pairing of the pitches B and F, can we make F the leading tone? Absolutely. And F is the leading tone pitch to what key center? Examine the pitches of the two possible resolutions for the pitches B and F. Do note the enharmonic spelling shift of the B / Cb when F is the leading tone. Example 3b.

B is the leading tone
or ...
F is the leading tone
tritone pitches
resolves by half step to
chords
tritone pitches
resolves by half step to
chords
B up
C
G7 to C
B (Cb) down
Bb
Db7 to Gb
F down
E
F up
Gb
 

Here we've simply reversed the direction of the resolutions of the B (Cb) and F pitches. F becomes the leading tone and resolves upward, as all leading tones tend to do, while now the B (Cb) goes down. Examine the pitches. Example 3c.

Ever been to Gb major? It's the other side of the universe from where we normally hang out. We can change which pitch of our tritone interval is the leading tone and consequently change the direction of the resolution? Yes indeed. Of course the different leading tones take us to different key centers. So if it's the same tritone, can we swap the chords around?

~ super theory game changer ~ the tritone sub ~

Tritone substitution. Surely a most common chord substitution in American jazz is working with V7 and its tritone substitution potentials. If your thing doesn't really swing yet there might be a reason. And this theory just might be the newly found key to unlock swing for you. In this next idea we simply add to the cadential motion just above by including a diatonic Two chord. Examine the following Two / Five / One motions into C major. Example 3d.

Two / Five / One
C major diatonic chords
tritone substitute
ii / V / I
ii / b II / I

We're going to Gb major. Same ideas as above but simply going to the other key center as provided by the tritone / leading tone theory examined above. The following voicings are solid core jazz guitar shapes. Examine the following Two / Five One motions into Gb major. Example 3e.

Gb major diatonic chords
tritone substitute
ii / V / I
ii / b II / I

Rather sweet n'est-ce pas? Notice how much sleeker the tritone cadential motions are due to their chromatic bass lines? In our American music, sleekness is one sure way to encourage acceleration. Of what? Well two things that American jazz players love to do. Play in brighter tempos and change keys more often.

The rule of thumb for tritone subs. In theory we substitute dominant chords with dominant chords, whose root is a tritone interval away from our written or starting chord i.e., G / Db ~ Db / G.

And that's all there is to it. At least in terms of the initial theory of the thing. So we can change which pitch of our tritone interval is the leading tone and thus change the direction of the resolution? Yes indeed. Of course the different leading tones take us to different key centers, both relatives of the diatonic. This expands of course with 'double tritone' of V7b9.

V7b9

Where in the music. Dig the sounds of the above cadential possibilities? Do realize we are starting to move out of the diatonic realm of most things American music. While this sort of substitution is very common in American jazz, it's rather rare anywhere else. Hen's teeth rare ...? Yes pretty much.

We just do not find tritone substitute chords in folk, rock, pop or their myriad genres. Even the blues? Yes for the most part even the blues, unless we call the 'half step lead in' motion a tritone sub. Of course the blues plays a giant role in jazz. And while at the core a jazz blues and a delta blues have identical elements, in practice they become two distinctly different animals.

Evolving our thought process. A core philosophy of this "Essentials" work is based on the idea that an artist will consciously choose to create greater challenges as they mature in their work. Being a studier of jazz music, I know this to be the norm. Each of our musical styles has its own unique challenges that the pro players strive to master. The theory is all one of the same.

The next level. So how does an artist create the next level of challenge for themselves artistically? In theory we can simply expand our numbers / pitches one by one more note. For example; V7 to V9, ii-7 to ii-9 etc., adding a pitch to make Four into Two, add b9 to V7. Warm up on a pentatonic folk melody and gradually add new pitches towards all 12. See where these new colors take us artistically. Change to a higher number on your time generator.

Using the theory to evolve. As in the above tritone sub discussions, we used the theory to evolve a new chord progression. Of course, originally someone 'discovered' this process, and we theorists came along after and figured out their coolness. So our theoretical evolution encourages our artistic evolution. Which was initially prompted by someone's artistic evolution or discovery. So hand and hand and round and round it goes. With this organic evolutionary process in mind, the following philosophy and core basis of this text emerges.

A double tritone / V7b5 chords. There is common way we can bring a double tritone to the lower part of our dominant harmony. In this new color we retain the major 3 and blue 7 which together create the essential core tritone of V7 and add a second tritone by simply lowering the 5th of the chord by half step. This creates a tritone interval between our root pitch and our lowered or diminished 5th, opening up the 'whole tone' universe. Examine the pitches and their sound. Example 5.

arpeggio degrees
1
3
b5
7
.
.
.
.
G 7b5 pitches
G
B
Db
F
.
.
.
.
whole tones
G
A
B
Db
.
.
.
.

Surely not an everyday color, these V7b5 chords find their way into rather select spots. Unless you're a jazz artist, where the whole tone colors are right at hand.

 

So where in the music? Bossa nova artists dig this chord V7b5. The last example is similar to Jobim's "Desafinado." As the Five of Five is almost standard changes, any alteration is within bounds. Jazz players will of course find all sorts of places for this color. It is also a common last chord / final hold in arrangements for a splash of dissonance, especially in the blues.

In more modern playing today, players will also use the lowered 5th on their tonic major 7th chord type, further reducing the center of tonal gravity of their tonic function chords. Jazz pianist Bill Evans is said to have been quite fond of this color.

wiki ~ Bill Evans

A double tritone / V7b9 chords. We do get another very common jazzy dominant chord with a double tritone in its pitches / intervals. This occurs in the V7b9 chord. While it is a bit outside of this realm #4 / b5 realm, these two chords as dominant V7 types will function pretty much the same ways and both are very cool setting up minor tonic chords and key centers. V7b9 is unuque in that it has the perfect minor 3rd symmetry of a fully diminished 7th chord in its DNA. This symmetry of leading tones opens up the entire Americana harmony for its evolutions towards the chromatical 12 tone sounds of the 'tres modernes' (my term) from the late 1950's and forward till this day.

wiki ~ free jazz tres modernes

Up an octave to #11. In thinking of our numerical designations that #4 = b5, which of course it does, we can simply expand this root / tritone pairing by moving the #4 / b5 up one octave in the arpeggio to #11. Examine the pitches in C major. Example 5a.

scale degrees
1
2
3
#4
5
6
7
8
C major
C
D
E
F#
G
A
B
C
arpeggio degrees
1
3
5
7
9
#11
13
15
pitches
C
E
G
B
D
F#
A
C

This next idea features the back and forth between the 5th of the chord to the #11, designated by the triangle in the #11 chord grid. Example 5a.

Modern Latin vamp. This last idea is fairly common these days among jazz players looking for extended solo sections with an almost static or non changing harmony. The voicing above, a true Doc Miller Hollywood chord, easily phases back and forth with the #11 and Lydian based color. If we're skilled enough to make the bar lines go away in the Latin groove, this type of extended soloing just might go on for a couple of days while all dancers will rejoice :)

Whole tone qualities. Well anytime we get three consecutive whole steps we gain the whole tone color potential. The wholetone grouping of pitches holds the same symmetrical properties as the diminished color. It has the multiple resolution to assigned tonics from one set group of pitches commonly arranged as a scale, arpeggio or chord. Like the diminished shapes, all can be moved as a constant structure by whole step, major third tritone etc., all the while retaining core pitches and overall musical direction of the composition.

Whole tone resolving qualities. In examining our whole tone, double tritone V7b5 chord, we can easily fill in the rest of the pitches generated by the whole tone scale formula and create the complete whole tone scale. From this we can diatonically build our altered dominant chords and see the possible resolutions based on our Five / One cadential motion. Example 6.

scale degrees
1
2
3
#4 / b5
#5
b7
G whole tone scale
G
A
B
C# / Db
Eb
F
arpeggio degrees
1
3
5
7
.
.
G 7b5 pitches
G
B
Db
F
.
.
V7b5 chords
G7b5
A7b5
B7b5
Db7b5
Eb7b5
F7b5
V7b5 chord pitches
G B Db F
A C# Eb G
B D# F A
Db F G B
Eb G A Db
F A B Eb
resolution maj / min
C / A-
D / B-
E / G#-
Gb / Eb-
Ab / F-
Bb / D-

Common V7b5 motions. In this next idea we put some of the above color to work with resolutions to major tonic One chords. Example 6a.

To the minor key center. The b5 dominant color into the minor tonality can get pretty tangled up as the b5 can be a half step above our tonic / root pitch. Note in the next idea that we briefly move up to the b9 before resolving to C minor. Of the augmented / whole tone colors, the V7+5 is possibly more common into the minor tonality as the +5 is the blue 3rd of our tonic. Example 6b.

b9

Whole tone chord resolving magic. Turns out from the same group we'll get the V7+5 chords also. This augmented dominant color is a bit more common, especially into the minor key centers. Examine the pitches with a careful eye towards enharmonic pitches as the chords are spelt. Same set of resolution key centers. Example 6c.

scale degrees
1
2
3
#4 / b5
#5
b7
G whole tone scale
G
A
B
C# / Db
Eb
F
arpeggio degrees
1
3
5
7
.
.
G 7#5 pitches
G
B
Db
F
.
.
V7#5 chords
G7#5
A7#5
B7#5
Db7#5
Eb7#5
F7#5
V7#5 chord pitches
G B Eb F
A C# E# G
B D# G A
Db F A# B
Eb G B Db
F A C# Eb
resolution maj / min
C / A-
D / B-
E / G#-
Gb / Eb-
Ab / F-
Bb / D-

A key diminished chord built on sharp Four. This penultimate entry in covering our sharp Four position within the local chromatic universe is a rather common event in the blues especially when jazz players get a hold of the 12 bar form. Turns out in the 6th bar the harmony begs to go to the #iv dim 7 chord. Really? Yep, very common with jazz players. Just yet another way to accelerate the sense of forward motion while getting a wee bit more mileage out of the thing. Here are the basic changes, thinking C Blues. Example 7.

forward motion

Taking it out. This last idea for sharp Four is quite common in certain circles, it's one of the 'arrangements while you wait' type endings that players often will improvise together. It's cool in that we use the tonic pitch as a common tone to link all of the chords together in progression as we take it out. Thinking F major. Example 8.

take it out

Wheel of tritones / cycle of fifths. The tritone interval enjoys a rather distinctive status on our wheel of pitches. It's curious how this all shakes loose but it is what it is. Examine the location of our tritone intervals on our 12 pitch keyclock. Example 9.

keyclock

tritone interval pitches
C
G
D
A
E
B
F#
Db
Ab
Eb
Bb
F
F# / Gb
Db
Ab
Eb
Bb
F
C
Gb
D
A
E
B

Really? Directly across the clock face? We can locate any pitch's tritone interval by locating the pitch directly across the circle? That is indeed the case mon ami. Crazy huh but very handy :) So knowing this, check this out. Example 9b.

WOW ! Now the compass points show us four key centers, each of which is the major / relative minor tonic of each other. I'll have to add this into the mix. This visualization of the major / minor key centers from within the cycle of fifth's is new for me. I just discovered this :) Maybe print and tack these two up for reference.

First review; so where's the tritone in our music? Well anytime we're grooving on anything with a hint of the blues, chances are there's a tritone in the local neighborhood; in both melodies and chords. So in thinking of the Americans sounds, in a word, everywhere. Well, probably not in children's songs of course, unless they're very spooky Halloween tunes.

In folk, never ( did I just say that ... yet another first :) in the melody but always of course in any standard type of V7 / G7 / D7 chord etc. The blues influence in any of the folk or rock styles of course needs the tritone pitch for chords and melody intervals.

The metalists love the tritone interval. It's kind of all over their music and used to very cool dramatic effect. In pop, again any V7 chord is going to have the tritone within. Rare in pop melodies, although one of America's favorite melodies from 1957 "Maria" is classic tritone color. For jazz and beyond, like everything else we jazz theorists can conjure, the tritone is a super catalyst for coolness, a building block to new horizons where it often loses its bristly edge and becomes a key step in the stairway to the musical stars and beyond.

Where in history. Well, early history was not overly kind to our tritone. Known at one point as the 'diablo de musica', big tritone players probably have had a bit of a rough going all along. Yet once the American blues took hold, its clarion call of attention to our commonly shared human sensibilities has shook the globe over and over. Somewhere in every style imaginable. Still does. For as a cherished member of the melting pot of our Americana music family, even when more quietly encapsulated within V7, tritone is always there.

wiki ~ tritone historical Diablo de Musica

Expansive thoughts. When the jazz harmony started to evolve in the later 30's toward bebop with guitarist Charlie Christian, the double tritone fully diminished 7th chord color found a way into what was then known as a "Sears Roebuck Bridge." This organic 'double tritone' opened up a new way to look at things. As artists got hipper, through V7b9 theory they created a new, totally inside and legit way 'out' with the same old pitches.

Within twenty five years or so of Mr. Christian and his contemporaries adventurous work, John Coltrane shedded, wrote and released "Giant Steps", a landmark composition which even today sits as the crown jewel atop the new theory / shedding challenges that guitarist Mr. Christian helped initiate which Mr. Coltrane then developed, conquered and evolved.

bebop
Charlie Christian
wiki ~ rhythm changes / Sears Roebuck bridge

Second review. Perhaps needless to say the tritone has come quite a ways since its days as "el diablo." A core component in American blues from earliest times, the root of all things American music, the tritone and its related activities plays an essential role in anything blues and beyond.

Our tritone comes in two basic varieties. As a single note interval measured from another or as a two pitch, pre-made tritone, that we slip into existing structures. Our single pitch, octave splitter is the crucial pitch to evolve the blues scale from its minor pentatonic core. While the two pitch tritone evolves the major pentatonic grouping of pitches into the diatonic major / relative minor scales.

In our harmony, the tritone color creates the basis of aural tension that makes our dominant Five seven chord a dominant V7 chord. We'll find this basic chord generally within all of our American musical styles. From V7 forward, at least within the jazz language, artists have added the tritone's symmetrical theory properties to find new ways to create the tension and release of their art.

"I’m not accustomed to talking about myself, “I talk in the studio with musicians. Or through my songs."
Allen Toussanthttp://www.nytimes.com; 11/11/15
1
#1
b2
2
b3
3
4
#4
b5
5
#5
b6
6
b7
7
8
b9
9
#9
-10
10
11
#11
12
b13
13
b14
14
15
#15
Footnotes:

Russell, George. The Lydian Chromatic Concept Of Tonal Organization. USA Concept Publishing Company, Cambridge, Mass. 1982