In a nutshell / diatonic destinations. Substitution is simply about replacing one element with another yes? In most songs we have diatonic destinations. The One chord goes to Four. Six, the relative minor of One / major, is a very common destination from any number of angles. Of course there's the dominant V7, keeping track of what's where and motoring things along.

Knowing that these destinations are the same throughout all of our styles and genres, 'how we get there', using chords and melody, and rhythm too, even tempo, all combine to capture a story in a song and style. And part of the how we'll get there can include chord substitution.

Substitution is simply about replacing one element with another yes? And in music theory, as our Americana musics are near all homophonic, we're usually talking about arpeggios and triads, chords and colortones for substitution components. Most times our substitution has some of the same pitches as our written chord. Makes it easier too when it does. Our focus is too on the bass line, how a chord substitution reshapes the bass line and its story. For example, in jazz, the tritone sub' is cool. Thinking Two / Five / One in 'C';

'D-7 G7 C maj 7' becomes 'D-7 Db7 C maj 7.'

Subbing 'Db' root for 'G' and moving from 'D' towards 'C', we energize a chromatic bassline; 'D Db C.' Crazy but chromatic leans sleeker, and sleeker leans faster, for an easy way to jazzing it up.

Chances are it was in a song. And while we substitute a chord for any number of reasons including; variety, create new challenges, to find the right chord for that one particular spot, to build anticipation and then bring mystery, even create surprises to quickly change moods, or to morph between style through rhythms, there always seems to be a historical source of the chord from a song. And often times that song was a hit tune. Often termed a standard', each style has its gems to learn, study and try to master. So we learn tunes too, and have something to play at the show also.

For composers. The composers of these standard songs, found a unique melody note, something in their hook, that had need for a new chord, figured it out and discovered a new way. Well, sometimes it turns out that 'that new chord' also opened up a new area to explore, especially for the improvising musician who is playing this song and on the lookout for their next 'cool', to add in their lines. Sub in a new chord into written changes we've new lines to master; bass, chords and melodies.

And stylewise ? Chord substitution is mostly in the blues and jazz. And while we learn throughout our musics that ...

'anything can be anywhere'

'once we're past the basics, musical substitution revolves around V7, so the dominant chord, our neighborhood traffic cop, and we build from there. We know from our studies that the V7, dominant chord type is the essence of basis of 'blues style harmony', and thus right on into the 12 tone world of jazz.

blues and jazz
blues harmony
12 tones of jazz

Methods. So in the following studies we explore five ways to generate substitute chords and place them into chord progressions. Included are the historically 'tried and true' solutions that still rule modern jazz harmony today. In exploring each method step by step, we can maintain our sense of musical style and its relationship to our Americana historical eras, to better understand where today's 'cliche' substitutions first came from, and our evolutions through using chord substitutions in Americana musics over the decades. These combined theory basics also give us the tools to find or shape new substitutions from scratch, and can help us to find the perfect chord to solve a compositional puzzle.

A rule of thumb for chord substitution. While chord substitution creates variety, new challenges and often a freshness to the 'same old same old', there's an initial guideline or two that helps retain the essence of where we start from and where sub out to.

1) We try to swap chord type for chord type; if we're subbing for a dominant chord such as 'G7', we might first try another V7 chord type, such as 'Db7.'

D-7 G7 C maj 7

D-7 Db7 C maj 7

2) Follow 'thumb one' for all three chord types.

D-7 G7 Db maj 7

F maj 7 G7 C maj 7

Once you're substituting chords and solid with the process, sky's the limit. Cool ?

Author's note. In terms of music style, we find the following diatonic theory in actual practice towards the folk side of our style spectrum, and surely trending towards the wide varieties of pop music.

Also, these audio examples are weak in portraying these colors, so as best you can, when you can, find them at a piano and rote the pitches, triads, theory and resulting sounds. All on the white keys in 'C' major.

Diatonic substitution / passing chords. In beginning our studies of chord substitution, we can simply look at the full arpeggio of a key center and gently shift our way between our diatonic chords. Thinking in 'C' major, and exploring the passing chords as three note triads, examine the seven diatonic triads within this key center. Example 1.

arpeggio # degrees
1
3
5
7
9
11
13
15
C major arpeggio
C
E
G
B
D
F
A
C
scale # degrees
1
2
3
4
5
6
7
8
diatonic triads
CEG
DFA
EGB
FAC
GBD
ACE
BDF
CEG

Cool ? Are you hip to spelling triads ?

Diatonic passing chords. So a passing chord is one that we slip in between to two principle songs of a song's chord progression. Thinking One to Four, and all of the chords in root position, compare the three versions in 'C' major. Example 1a.

Measure 1; One to Four, with triads. Measure 2; a clear minor chord on Three passing to Four, which is the next grouping of three pitches in the arpeggio. Example 1b.

arpeggio # degrees
1
3
5
7
9
11
13
15
C major arpeggio
C
E
G
B
D
F
A
C
C major triad
C
E
G
.
.
.
.
.
E minor triad
.
E
G
B
.
.
.
.
F major triad
.
.
F
A
C
.
.
.

In creating diatonic passing chords, between the principle chords of a progression, it is very common to simply moving up to the next group of three in the diatonic arpeggio of a key center. This sort of motion is a piano players dream come true :)

In the last measure, we've used something a bit different, a '1st inversion' chord, passing from One to Four. Inversions of triads function the same way as root position chords, but create a due hue. First inversion is a 'softer' tonic, while second inversion puts Five in the bass, which can make it fairly potent. So, two basic, diatonic ways to fill this gap. Here it is again. Example 1c.

Cool ? First inversion is a 'softer' tonic in most cases, gets us some motion in the bass line too. There's a second inversion with triads, which puts the fifth of the triad in the bass, as the lowest pitch of the voicing. Compare the three ways to configure / invert a 'C' major triad; 'C E G.' Example 1d.

Hear some differences ? It's subtle for certain and each might certainly have a place in your music. Inversions are often the 'chord in between' and knowing how to make them advances our puzzle solving abilities.

Working it all out. In creating your music and finding what you need using these diatonic passing chords, learn how to sift through the pitches looking for your gems. The basics of this for guitar, is to simply start with root position and find the next note of the triad, up in register on the same string. Example 1e.

Sense how the pitches shift in the moves? Cool. This sort of exercise is a way to discover new chords, while keeping them with a context of music you understand. This method will work for finding the inversions and new voicings, for every chord in the book, in theory :)

in theory :)

Passing chord to Four. Motion from One to Four, via a passing chord. Example 1f.

Passing chord to Four. This next idea uses a few more of our colortones, so leans us stylewise towards the jazz horizon of our spectrum of styles. Motion from One to Four and again in 'C' major, in this idea we locate a a passing chord on the dominant chord chord, and add a new colortone along the way. Example 1g.

Sifting the theory to discover new coolness. In the last idea we bumped into a 'half diminished 7th chord' in our motion to Four. Common in the blues as part of a V9 chord, extracted and examined, we discover the diatonic 'Seven' chord, ' E-7b5', in the key of 'F.'

'Sifting' goes like this. Working with the top four strings, simply spell chord and locate the notes in the chord voicing. Then using just these pitches we spell our chord and work it up the neck and along the way locate its 'passing / inversions of the chord' while moving up the neck, and keeping to just the top four strings.

Our chord is spelt; E G Bb D / its voicing is; E Bb D G

Next, we move up to 'G, Bb, D and close back on E.' Run out of frets ? Oh well, either way voila ... three new chords from one, all movable, super useful as quasi V9 chords in all blues hue'd songs too ... ?

And ... half diminished 7th is the 'portal / pivot' diatonic Seven chord employed all through all sorts of jazz songs and musical coolness so in essence ... what ... is ... not ... to ... love ... about this theory and process ? ! :) Hear the magic. Example 1h.

Run out of frets ? Yea that happens, luckily everything loops back to where we started and in this case we six stringers get two more strings below from where we started this time. Hmm ... try the same process on the middle four strings ? Put bass notes on the low string ?

This method of finding passing chords , inversions and substitution harmonies works perfectly the same on all the chords, same for any chord. And just as easy at the piano :) Pick a key, pick a scale, morph it into its arpeggio, spell the triads, and run the chords up and down. It's all built right in.

Shedding vs. practicing. Find some coolness? Did you build out and around the new shapes with other chords too ? Finding a local V7 chord, creating 'mini' chord progressions, which contain passing chords too ?

Cool, this is more shedding than practicing, using the theory to generate new coolness. And practice ? Well, practice makes permanent, so we reserve it for those 'rote' sessions where we work out the physics of a lick, by going note by note, then build it up, play it slowly with clicks, then bring it up to tempo = practicing :)

Make your notes as you go, as everything is movable from this last exercise, easy to run the pattern up and down the fingerboard, working over your favorite key centers. And with two lower strings to explore in a similar manner, our shedding fun has just begun :)

Swapping chords. Substitution is simple about replacing one element with another. So with chords in a song, we can swap one chord with another. Near always, swaps last a few beats to a bar or two. This is true of the following chord swaps. While there's a few common chord swaps, most often we're borrowing an idea from another song, using its chord choice in a similar spot in a different song. We find the ones we like and write them into our own musics. For example, here's four common chord swaps. Example 2.

One and Six, are the relatives for major and minor and are a common swap of chords in folk, country and pop musics. When Four becomes Two, we get closer bass line pitches, a different chord type and the beginnings of a Two / Five cell. This gets us moving in jazz direction. The tritone sub is THE initial portal to points beyond as its theory is tricky and its tonic proximity can really bring the swing, again leans jazz. The montuno Latin is pure refreshment and is often the first lick to learn how to make the bar line sounds in the music go away.

This last idea somehow makes a nice chord progression too, and each of the 'cells' easily extract into energizing their own grooves, in all manner of genres and tempos. Pick one out an loop it.

Quick review. Substitution is simple about replacing one element with another. We've a few ways to diatonically generate some possibilities; most common might be to shift up a note in key center's arpeggio, creating passing chords. Or borrowing an idea from another song, and swap out its chord and putting it into a similar place in another song. They're are style 'swaps' too, to bring in some special flavor and jazz things up a bit.

Cool ? Now, the heavy lifting as we chart a course of chord substitution on the V7b9 and onto the Coltrane pioneered 'sheets of sound.' But first a ... :)

~ super theory game changer ~

Common tone diminished / tonic One. In all the theory of chord substitution in this discussion, which is very soon to go fully diminished 7th chord complicated and then stay there for a spell as we sort through its options towards 'sheets of sound', we've the true blue organic Americana source for this color in our musics. Here's an original lick of blues guitar lifted from the 1930's. 'Blues in A', tonic One chord to tonic diminished 7th. Ex 3.

Only takes this much. In our history and evolutions, it might only take this sort of one or two beat 'invention' to spark innovation. Which in our studies of chord substitution here, means projecting this diminished color from other spots within our songs. And as we exhaust the depth of what is potentially there, we'll discover a handful of 'super keeper gems' that fix themselves historically into our Americana weave of magics. This last idea is one of them, the core of it all diminished.

And while mostly incorporated into jazz, these 'gems' can jazz it up in any of our styles and genres, judiciously added of course :) Easy way to loose the folk gig ? Overdue it with the diminished chords, V7b9's and various related 'outside' colors.

Same idea but as an intro / turnaround. In 'C' major, same basic idea extended, tonic V7 to passing diminished 7th chord to One, then the "Muddy walkdown" lick as the turnaround, setting up the top of the form. Example 3.

That's the start. Sound as if you know where the music is going ? Cool, yea that sense of predictability created by the motion of the bass, melody and chords anchors Americana. Begin to master your own version of it, and find yourself a mojo lick or two if need be.

~ super theory game changer ~

The puzzle of V7b9. The whole tamale theory basis of this super theory game changer is that there's a four pitch, fully diminished 7th chord within the V7b9 modern chord color. Initially built from the 3rd of it's major triad, the symmetry of the intervals in the upper diminished 7 color create the potential kaboom, even to superkaboom levels, for the modern evolving guitarist.

Thinking we'll have a bass player on the gig, we extract just the four pitch shape puzzle that lives above the root note. It's this puzzle piece that contains the chord substitution magic. On guitar it looks like this. Thinking in 'C' major, our V7b9 is guilt on the note 'G', the Five chord. Examine the pitches. Example z.

C D E F G A B C

C E G B D F A

G B D F Ab

B D F Ab

diminished 7th chord / diminished scale

Cool with the pitches and shapes ? Not familiar yet ? No worries for blues leaning to jazz it up artists of all the Americana stripes ! Know there's mucho coolness ahead discovering new spots through the styles of our music for each of the 12 unique pitches :)

In this e-book's main theories of chord substitution, it's a jazz harmony study. It's complex, trying and tricky at times to understand and make sense of let alone aural coolness. With a fair degree of enharmonic pitch spellings, which in themselves can create challenges, it's a can of worms mostly. Luckily, each new discovery brings another of the 12 pitches into the fold thus another nuance of emotional colors for our stories.

There's multiple key centers involved, and once we've the chords we want for substitute chords, we'll build back from them diatonically within each key center. From this perspective we will create parent scales for creating melodic lines over and through the substitute chords, all in relation to a tonal center.

Know that in this complexity of elements, that this theory has the same perfect closure properties of all our music theory. For just as following the formula for creating a major scale will return us to our start point, and every time from any of our 12 pitches, so does the V7b9 / diminished 7th chord theories for chord substitution. Perfect closure every time. And if not, then we've made a mistake in our calculations and we can go back and locate and correct our errors.

Know that any loop we create, or sequence, or when we run out of frets and have to go to the other end of the instrument, and on whatever instrument, if we get the pitches right, then our corresponding sounds will always be 'correct', in theory. Then we each choose what parts of the substitution puzzle that our own ears tell us are cool and thus may have an 'art' potential. These we extract, shed deeply and add into our own musics as our own muse directs.

this e-book
enharmonic
key center
parent scales
soloing over changes
soloing through changes

Unraveling the V7b9 puzzle. Our first step in unraveling our puzzle is to decipher the chord symbol; V7b9. This we do by simply extracting the 'V7 from the b9.' For all during our theory explorations, we need to keep in mind that our dominant to tonic cadential motion, so V7 to I, is what creates and energizes that sense of direction to a point of resolution in our music.

We find this 'V to I' motion in all of our styles and storytelling. Just as 'motion to Four' is a part of every story, a destination our our song's journey, equally important is our Five to One motion, which brings us home and to a sense of rest. Examine the stepwise motion from One to Four, then Five to One and a sense of being at rest. Thinking in 'C' major. Example 3.

Cool ? Yea, very straight forward and with some gospel gets us to Four then a pause, then to V7 to energize our motion to One. So it is in this 'energy' of V7, the tritone within, that is resolved on sounding our One / tonic chord, bringing our line and chord progression to rest.

~ advanced theory ~

V7b9 ~ creates four unique V7 chords. Thus V7 empowered, we now add back its 'b9' to the stack. And what we create from one perspective is a fully diminished 7th chord sitting atop our root note. Thinking in 'C' major, our V7 dominant chord is rooted on the pitch 'G.' We spell this chord as 'G B D F Ab.' Examine this evolution. Example 3a.

A fairly bristly character huh ? Not your average folk chord no :) Now for the magic and the basis of our chord substitution theory. It goes like this. Once we remove the root pitch 'G', we've the four note fully diminished 7th chord. These pitches are spelt; 'B D F Ab.' And in the key of 'C', that 'B' natural is our leading tone yes ? Example 3a.

Some strong pitches and tension yes and the leading tone is pulled up to the tonic; 'C.'

Back to where we started. So we started with a 'G7' chord; 'G7 = G B D F', and comparing its pitches to the diminished chord of 'B D F Ab', just the one pitch which is different. And if we lower 'Ab' by half step to 'G', then we're right back where we started yes ? Exactly; at 'G7';

'B D F Ab'

'B D F G'

Imagine that. Sounds like this. Example 3c.

Cool ? Sure our V7 chord is inverted a bit, first inversion, so the 3rd of the chord as the lowest note of the voicing. Common, cool, first inversion is bit lighter in hue and frees up the bass line a bit too :)

So ... if we can lower one of the four pitches of a fully diminished 7th chord and create a V7 chord, why not try to do that with the three other pitches, and create three more chords. Example 3d.

Cool ? We started with 'G7' and now have three more 'V7' chords which include some of the same pitches. Here's the last idea with stronger bass notes. Ex. 3e.

Sounds better yes ? Big root notes help make a lot more sense of these things. We started with 'G7' and now have three more 'V7' chords with some of the same pitches. Might these three new chords be the generally accepted, the most common substitution chords for 'G7 ?' Yep. And while they're the Five chord of other keys, as dominant chords they can also work just fine getting us back to 'C' major too. As their bass notes have tonic proximity. Examine the resolutions. Example 3f.

jazz it up

Cool huh ? And while they're the Five chord of other keys, as dominant chords they can also work just fine getting us back to 'C' major too.

'G7 to C' is diatonic.

'Bb7 to C' is b7, so bluesy and Mixolydian flavored.

'Db to C' is by half step above, the tritone sub stgc.

'E7 to C is a square peg but E7 to A minor ?' V ~ I :)

So there we have it :)

Quick review. So with the one fully diminished 7th chord, each of its four pitches are a leading tone, a Seven scale degree, to it's own tonic and key center. We now also know from the above study, that by lowering each pitch by half step, we get the root pitches to create four dominant, V7 chords. And in the blues, and more in the jazz world, and as these chords share pitches, we substitute them into chord progressions to create variety, better support a melody note, and open up new tonal convergence vectors for resolving to a chosen tonic.

diminished 7th pitches: B D F Ab

dominant 7th chords; Bb7 Db7 E7 and G7

All of these are common throughout our Americana literature, some in the blues but mostly in jazz songs and 'jazz it up' versions of songs in any style.

In relationship to our chosen key center, 'C' major, we've the following positions;

G7 ~ Bb7 ~ Db7 ~ E7

V ~ bVII ~ bII ~ III

For advancing players, pair these V7's with their Two;

(D- 7 / G7) ~ (F-7 / Bb7) ~ (Ab-7 / Db7) ~ (B-7 / E7)

And use these as 'cells' to initiate the building of your own sense of sheets of sound, as founded on this basis of multiple leading tones of the fully diminished 7th chord.

Here's an old time chart of Two / Five / One resolving motion shapes for guitar, via a primary diminished scale shape. Start with an arpeggio on Two, starting off a line ? Into the tension of the V7b9 / diminished color, and then find a way out to resolve to One. There's the four key centers, presented here in major, but these diminished shapes hold the tension and will resolve to minor tonal centers / keys too. Example 3g.

Cool huh ? And this will all sort out at the piano also.

Quick review. V7 to One and its tritone sub. These are the two basic cadential motions we get with taking apart the V7b9 and its diminished 7th chord within. The most common; V7 to One, for both the relative pairing tonics of major and minor.

'G to C / E to A'

And the 'tritone sub', which moves us by half step root motion to our tonal center from a half step above.

'Db to C / Bb to A'

~ the other five pitches ~

By the numbers / passing diminished 7th chords. In this next part of our discussion we'll name our particular substitution chords by where they fall within the diatonic number system; 1 through 8. We will also borrow the 'other five pitches' theorem from the bop leaning jazz git wizard monster Jimmy Bruno.

And while Bruno's version of the other 'five' is more towards color tones and blue notes, which are also the 'other five pitches', we borrow the math and use the 'other five pitches' label to designate the five spaces between the seven pitches of the diatonic scale.

Knowing there's only 12 pitches, and that 7 + 5 = 12, we're 'theory golden', as said academic circles globally.

Five spaces. Turns out that each of the five spaces in between so each of these passing chords, each has ONE MAIN FUNCTION. And while there's always more, knowing these moves, and mastering the one or two U need fro your immediate musics, keeps it simple and brings a nice new color to our palette.

Examine the five substitutions, and their 'space', while thinking in 'C' major root to root pitch.

C D E F G A B C

C# D# F# G# A#

#i dim 7 ~ C# between C and D

# ii dim 7 ~ D# between D and E

# iv dim 7 ~ F# between F and G

# v dim 7 ~ G# between G and A

# vi dim 7 ~ A# between A and B

Cool ? Rote learning the theory in the one key center, then numerically transpose it as similar spots in songs come along in the other keys, major or minor.

wiki ~ Jimmy Bruno
12 pitches
color tones

What's in a name. Of these, only two are common; the '#i' and '#iv.' The '#i' is jazz. The '#iv' is common in jazz leaning blues songs. We love the #v going to Six, as it forms up a 'V7b9 to i' we also bumped into just above.

Ying / Yang = relative major / minor

Of the remaining two, it's a toss up really and they're rare in the literature. For we get the original tonic / One diminished 7th = # ii, from the old blues. Relating these chords to the root pitch 'C.' Example 4.

Chord substitution / passing chord palette. In the following discussion, we simply take the theory properties of the fully diminished 7th chord's capabilities, same as we discussed just above, and build the same theory up from each of the five 'pitches' that exist between the pitches of the diatonic major scale. These five spots become the root notes of these 'passing diminished 7th chords.' For they 'pass' us smoothly (chromatically) between the diatonic positions of the major scale. We then do the math to find the four V7 chords associated with each one.

Near hen's teeth rare in any place but jazz, passing diminished 7th chords are historically part of the 'great accelerators' of Americana musics, reflective of the quickening 'speed of life' that shook 20th century Americana all characterized in its musics. Thinking 'C' major, examine the following letter name pitches of the the five spaces between the diatonic seven pitches. Example 4a.

scale degrees
1
.
2
.
3
4
.
5
.
6
.
7
8
C major scale pitches
C
.
D
.
E
F
.
G
.
A
.
B
C
spaces in between
.
#1
.
#2
.
.
#4
.
#5
#6
other five pitches
.
C#
.
D#
.
.
F#
.
G#
.
A#
.
.

Cool ? Ya that's probably as rocket science music theory as we might ever get here :) For in adding in these passing chords we make our bass line more chromatic, half step motion. So sleeker in shape can mean faster in motion. Add atop the bristly, double tritone bearing fully diminished 7th chord, to each of the passing bass notes and the harmonic elements are in place for hair raising, fill the dance floor on Saturday night excitements.

Sub in a V7 before each chord. This next idea advances chord substitution to a level of complexity that is reserved for the more jazz leaning artist. For as tempos quicken, making improvisational sense of the changes, i.e., playing through the changes, especially with arpeggios, becomes a monumental task. Need a new mountain to climb ?

Here's Two / Five / One in 'C', with a dominant 7th chord 'subbed' in before each. Example 5.

Jazzy ? U bet :) For when the tempos quicken, and the spaces between the chords fill in, with substitutions like V7, we lean towards the sleeker, chromatic blurring of the tonality. Which can open a new realms of art. Dimensions in art; as in pictures, or paintings moving from three to four dimensional representations, might be similar to Picasso's evolution towards cubeism.

"Learn the rules like a pro so you can break them like an artist."
wiki ~ Pablo Picasso

In this next idea, an improvised 'realization' of these last changes; 'soloing through the changes.' Example 5a.

V7 from above

V7 from below

Beginning to loose the sense of tonic center ? No surprise, as that's what tends to happen as we chromaticize our music; we loose the sense of one pitch as a diatonic center. It's an evolution in tonality, one that we can historically trace through the harmony in both our 'Amer jazz' and 'Euro classical' musics. Good to know that arpeggios can always tell the tale of any changes, substitutions, progressions etc.

Sub all chords V7. Okay, seems as if we are back to right where we started, well almost. Thinking chords, while our Americana blues from the banjo is initially triad based, it wasn't long before the V7 chord on a six string guitar found a true home as THE TONIC CHORD of its own style of music. In the blues ? Yes Sir. The plot thickens ! Example 6.

Where to begin. The song "Dock Of The Bay, composed by Bill Withers in 1964, is a soulful story of a 'day at a time' way of life. All the chords are major triads through a mostly gospel / diatonic chord progressions.

Coda V7b9 ~ Has four leading tones. A way into this whole tamale is created by thinking of the fully diminished 7th chord as a symmetrical group whose four pitches each are potential leading tones to four key centers. Eight actually, as each resolving root can be major or minor. Diminished makes no distinction. And that three minor thirds gets us to major 6, home of the relative minor can also open up some new space.

half step
leading tones
major and minor

Full diminished ~ a perfect symmetry. As the fully diminished color is created exclusively with the interval of a minor third, its perfect symmetry opens up doors not fully available to its diatonic half diminished cousin. Advancing modernes moving in an improv and jazz direction, can use this bold color today just as so many have in the past; as a catalyst to create pathways for new challenges and explorations in their musics.

A one pitch change and voila. This next idea baselines a lot of the fully diminished 7th chords theory. Dig its evolutions as we alter the 7th. Example 7.

 

G 7b9 / fully diminished 7th chord pitches

B D F Ab

 
ii -7b5
raise any one note
.
lower any one note
V7
B -7b5
B
D
F
A
B
Bb
D
F
Ab
Bb7
D -7b5
D
F
Ab
C
D
Db
F
Ab
B(Cb)
Db7
F -7b5
F
Ab
B(Cb)
Eb
F
E
Ab(G#)
B
D
E7
Ab-7b5
Ab
B(Cb)
D(Ebb)
Gb
Ab
G
B
D
F
G7

Diminished evolutions. Thanks to the closeness of these two diminished colors, we can evolve any of our fully diminished chord's four pitches into four half diminished chords simply by raising any one pitch of the arpeggio by half step. Note enharmonic spellings. Example 7a.

diminished 7th arpeggio
B
D
F
Ab
D -7b5
C
D
F
Ab
F -7b5
B (Cb)
Eb
F
Ab
Ab / G# -7b5
B (Cb)
D (Ebb)
F# (Gb)
Ab
B -7b5
B
D
F
A

Another evolution from the fully diminished 7th is by lowering any one of its pitches by half step to create V7. Examine these evolutions with letter name pitches. Example 7b.

diminished arpeggio
B
D
F
Ab
G7
B
D
F
G
Bb 7
Bb
D
F
Ab
Db7
B(Cb)
Db
F
Ab
E7
B
D
E
Ab(G#)

Just more theory magic. From the above charts did you notice that each of the four half diminished chords which evolved from the fully diminished neatly pair up with one of the four V7 chords into a the cool and common Two / Five cadential cell? And that the tritone sub / V7 chord for each -7b5 is available also? Here are the pairings. Example 7c.

ii-7b5
V7
D -7b5
G7
F -7b5
Bb 7
Ab / G# -7b5
Db7
B -7b5
E7

The diminished catalyst. The diminished colors end up having multiple resolving properties / leading tones found in our fully diminished seventh chords and related diminished scales, we use the theory to generate new ideas for chord progressions and melodic support.

In energizing this process, we examine what the diminished color is capable of doing and find new pathways to follow, then disguise its distinctive color by filtering it through various more diatonic sounding softening techniques, and yet still follow the pathways its theories has shown us. 'Sheets of sound'? Maybe.

wiki ~ sheets of sound

A double tritone / V7b9 chords. In one swift, bold move, we can double the leading tone possibilities discussed with the tritone / V7 chord above simply by adding the flat Nine pitch. Thinking C major, examine the pitches of its dominant chord G7b9 and its two pairs of tritone pitches. Example 7d.

spelling chords
arpeggio degree
1
3
5
7
9
11
13
15
G7b9
G
B
D
F
Ab
.
.
.
1st tritone interval
.
B
.
F
.
.
.
.
2nd tritone interval
.
.
D
.
Ab
.
.
.

Where in the music. The V7b9 is a jazz color. On occasion we hear it in pop music. And within the pop library, b9 is probably more often used in a minor key, as the b9 pitch is diatonic to the natural minor grouping of pitches, its effect can be said to be muted or softened in contrast to major. Examine the pitches of C natural minor / G7b9. Example 7e.

C natural minor
C
D
Eb
F
G
Ab
Bb
C
G7b9 pitches
G
B
D
F
Ab
.
.
.

Major or minor. So the V7b9 color works as a cadential chord in both in the major and minor tonalities? Yes it sure can. While Flat Nine is diatonic in the harmonic minor grouping of pitches, we have to borrow the pitch to create the chord in the major key. Is there any concern with this? Nope. Welcome to the world of the altered dominant chords.

So we borrow pitches all the time in creating the American sounds? Yep. Anytime there's a Blue hue in the scene, chances are it's borrowed. The idea of a diatonic exclusivity simply provides the essential perspective for we theorists who like to know the organic source of all things.

Desert Island flat nine shape. If I had to be on a desert island with just a trusty D'Angelico New Yorker with flat wounds, and only could have one b9 chord shape, it just might be this one. Surely the first one I learned when I finally needed one, Ted Greene might have quipped, "quite a solid little chunk of harmony." It's just one of those movable chord voicings that works like every time, in a major or minor tonality. Example 7f.

G 7b9
one fingering

Know this chord shape? Cool. Oddly enough we call this critter an incomplete dominant 7th chord. It's incomplete in that it has no fifth in its voicing. Usual? No. Happens all the time in lots of our chords. Examine the four pitches included in the chord shape just above. Ex. 7g.

arpeggio degrees
1
3
5
7
9
11
13
15
V7 arpeggio pitches
G
B
D
F
A
C
E
G
V 7b9 pitches
G
B
?
F
Ab
.
.
.

No 5th. Oh well, we can always add one in right? When we do add a perfect 5th interval into this V7b9 chord's pitches, and that's next, the theory, and of course consequently all of its artistic potential in all things dominant, i.e., V, V7, V7b9 / #9 / b5 / #11 / 13 / b13 / sus 4 / and their mix and match substitutions, all advance dramatically.

chord pitches
mix and match

Adding the 5th. Examine the following pitches as we add in the perfect 5th. Example 7h.

arpeggio degrees
1
3
5
7
9
11
13
15
G7 arpeggio pitches
G
B
D
F
A
C
E
G
G 7b9 pitches
G
B
D
F
Ab
.
.
.

Easy do. Now with the addition of the 5th we create a symmetrical arpeggio within our G 7b9 chord whose pitches are a minor third apart. Symmetrical in this context simply means we use only one interval to build the chord, all the chord's intervals are the same, thus symmetrical. This stacking of four pitches by minor third interval we consistently term a fully diminished 7th chord. Example 7i.

G 7b9 pitches
G
B
D
F
Ab
G 7b9
fully diminished 7th chord
finger solution

Fully diminished 7th chord / a circle in the chord symbol. So it turns out that in the upper part of the G7b9 chord we have a fully diminished 7th chord. Once we're cool with jettisoning the root pitch G, we can often leave that to the bass player, the perfectly symmetrical diminished color is capable of infinite hues of nuance and shading by filtering its organic properties through our various musical filters.

While its core shape and resulting sound can be a bit of a rough diamond initially, its potential when cut and polished is absolutely limitless and in experienced hands, flawless as well. Examine the pitches and sound and do note the circle symbol designating diminished in its chord symbol. Example 7j.

Perfect symmetry. The perfectly symmetry of the diminished structure initially gives us guitarists two core theory principles or techniques. First, is as above, so here below. Now each of the four pitches enjoy the leading tone magic, functioning as a leading tone to four major keys as in the following idea and four minor keys. Example 7k.

diminished arpeggio pitches
Ab
B
D
F
resolves up to
A maj
C maj
Eb maj
Gb maj
diminished arpeggio pitches
Ab
B
D
F
resolves up to
A min
C min
Eb min
Gb min

Hear how strong the diminished sits in the minor tonality? That's the balance to the brightness of the major key. The Yin and Yang of all great art. Sense the softening of the resolving chords as we add the 7th and 9th colortones? It's almost as if the emotion / music style evolves right before our eyes. So really no surprise that our organic, diatonic source for the diminished color is from the harmonic minor group. Vanilla natural minor but with a leading tone.

Leaps of minor thirds. So, secondly from above, that the diminished minor 3rd symmetry allows for all of our diminished chord shapes to be moved up or down every three frets, in minor thirds, and still retain the same core pitches, they just trade voices or places in the chord. Example 7l.

leaping in minor 3rds
.
up min 3rd
up a -3rd
up a min 3rd
soprano / diminished 7th
F
Ab
B
D
alto / diminished 5th
D
F
Ab
B
tenor / minor 3rd
B
D
F
Ab
bass / root
Ab
B
D
F

Three core diminished shapes. This last idea uses our three core diminished chord shapes or voicings. These three are the starting points for evolving the artistic nuance described just above. By simply having one solid shape for each of the bass strings, we can cover the entire range of the neck rather quickly when needed. Here are the three shapes. Example 7m.

So where in the music? These diminished chords are big Jazz chord voicings, we'll see them all the time either written in or added as a substitute chord. From there we'll see and use the diminished colors less and less. Again the tritone interval is in Metal for sure. Once in a while in Pop and Rock. In the Blues, in more modern times it's not so apparent. In old time Blues we hear oftentimes as a common tone tonic chord. In Jazz blues as the substitute sharp Four / #4 dim 7 chord.

Another double tritone / V7b5 chords. There is another 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 diminished 5th, opening up the "whole tone" universe. Examine the pitches and their sound. Example 8.

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

So where in the music? Bossa Nova Cats dig this chord V7a lot. The last example is similar to Jobim's "Desafinado." It appears most often as an altered Two chord or as a colortone for Six. Jazz players of course find all sorts of places for this color. It is a common last chord in arrangements for a splash of dissonance. In more modern playing, Cats will 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 loved this color.

wiki ~ Bossa Nova / Jobim
wiki ~ Bill Evans piano

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 but moving the #4 / b5 up one octave in the arpeggio. Examine the pitches. Example 8a.

arpeggio degrees
1
3
5
7
9
#11
13
15
G 9 #11 pitches
G
B
D
F
A
C#
.
.

Colortone numbers. While the pitches / letter names remain the same, the numbers change based on where they live in the arpeggio. The reason our #4 / b5 is now # 11 is simply that it is an octave above the root pitch and when assuming such a lofty position in the arpeggio, there usually some combination of 7th and 9th below it to help support it. Example 8b.

Modern Latin vamp. This last idea is very common these days among Jazz players looking for extended solo sections with an almost static or non changing harmony. The voicing above, a true Dr. Miller Hollywood chord, easy phases back and fourth 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 most commonly arranged as a chord, which also like the diminished shapes, can be moved as a constant structure by whole step, major third 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 8c.

arpeggio degrees
1
3
5
7
.
.
G 7b5 pitches
G
B
Db
F
.
.
G whole tone scale
G
A
B
Db
Eb
F
V7b5 chord pitches
GBDbF
AC#EbG
BD#FA
DbFGB
EbGADb
FABEb
V7b5 roots
G7b5
A7b5
B7b5
Db7b5
Eb7b5
F7b5
resolution keys
C / A-
D / B-
B7b5
Db7b5
Eb7b5
F7b5

To the minor key center. The b5 dominant color into the minor tonality can get pretty tangled up as the b5 is a half step above our tonic / root pitch. Note in the next idea that we briefly move up to the 9th 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 8d.

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 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 8f.

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 8g.

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

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 9a.

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 :) Do print and tack these two up for reference.

So where is 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 neighborhood. So in thinking of the American sounds, in a word, everywhere. Well, probably not in Children's songs of course, unless they're 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 Rock styles of course needs the tritone pitch / interval.

The Metalists love the tritone interval. It's all over their music and used to 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" from West Side Story, 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 loses its demonic edge and becomes a key step in the stairway to the musical stars and beyond.

wiki ~ "Maria" West Side Story

Where in history. Well history has not been overly kind to our tritone. Known at one point as the "Diablo de Musica", the big tritone players probably have had a bit of a rough go of it. Of course even early on, when encapsulated within within the V7 chord, the tritone has always been cool. Once the Blues took hold, the tritone found a home of its own and even as a melody note, has been a cherished member of the family.

When the Jazz harmony started to evolve in the later 30's toward Bebop with Cat's like guitarist Charlie Christian working the magic, the diminished chord color and its organic "double tritone" opened up a new way to look at things. As Cats got hipper, V7b9 created a new way "out" in Jazz speak. Within twenty five years or so of Mr. Christian and his bandmate's work, John Coltrane wrote and released his masterwork "Giant Steps." A composition which even today sits as the crown jewel atop the theory / shedding challenges that Mr. Christian helped initiate and Mr. Coltrane developed and conquered.

Review. Perhaps needless to say the tritone has come quite a ways since its days as "the diablo of music." A core component in American Blues, which of course is at the root of all things American music, the tritone and its related activities plays an essential role in anything Blues and beyond. And while we'll find the dominant chord's inner tritone sounds in Folk music, any other use of its sound is simply not a part of the tradition.

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 key 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 their palette of techniques to continue their search for the myriad of nuanced ways to create the tension and release of their art.

"Even if your on the right track, you'll get run over if you just sit there."

wiki ~ Will Rogers

References. References for this page's information comes from school, books and the bandstand and made way easier by the folks along the way.

References academia Alaska. And when you need university level answers to your questions and musings, and especially if you are considering a career in music and looking to continue your formal studies, begin to e-reach out to the Alaska University Music Campus communities and begin a dialogue with some of Alaska's own and finest resident maestros !