~ diminished triads ~

~ -7b5 / half diminished 7th ~

~ °7 / full7 diminished 7th ~

'simply making minor more minor ...'

essential diminished shapes

'the portal color into the whole Americana harmony tamale ...'

.

In a nutshell. Simply stated we get just the one diminished triad from our diatonic theories. Built on Seven of the relative major / minor group, to this three note diminished triad we commonly add a 7th. Here we get two choices; the diatonic minor 7th or a diminished 7th, which is simply a minor 7th further reduced by half step. A diminished triad plus a minor 7th creates the 'minor 7th b5', also labeled as 'half diminished.' A diminished triad plus a diminished 7th we label as the fully diminished 7th color. Examine the common chord symbols for these diminished colors.

So a circle on the chord symbol means full diminished, which with a line through it, becomes half diminished. Easy :)

Pre-nutshell ~ quick review. As the basis of much of what follows is contingent on understanding the idea and concept of 'diatonic' to a chosen key center, here's a quick review. Already solid with the concept of diatonic? Easy read coming up no worries. Not hip? Easy fix right here.

12 key centers

'Diatonic' simply groups seven of our 12 pitches into a key center based on a set interval pattern. These seven pitches are then termed diatonic to that key center. The remaining five pitches are not. We theorists term these five as non-diatonic, 'outside', even as a 'blue note' if style appropriate. Here noted as sharps as would be found in an ascending melodic direction. Examine the seven diatonic pitch letter names of C major and five non-diatonic pitches remaining. Example 1.

7 + 5 =12
interval formulas
outside
blue notes
enharmonic equivelents
scale degree
root (1)
2
3
4
5
6
7
8
interval formula
.
whole step
whole step
half step
whole step
whole step
whole step
half step
7 diatonic scale pitches
C
D
E
F
G
A
B
C
5 diatonic scale pitches
.
C#
D#
F#
G#
A#
.
.

All cool? Right on. No? Take a minute then and rote learn this chart. As these pitches and key center get the majority of the ride time within Essentials. If need be click around a bit on the links to explore and sure up your understanding of 'through the tones' diatonic.

That this page's topic and discussion just might be the most complex of 'em all here in Essentials for the emerging theorist best to have these pitches firmly in hand. Generally, once the theory of it is in place, rote memorization and learning will always win the day for those so impassioned for knowledge.

In a nutshell. While the diminished color's intervals, core triad, two types of seventh chords, symmetrical scales and arpeggios are an integral part of Americana, with one essential exception they for the most part fall outside the core 'diatonic 3 and 3' harmony building blocks that constructs the majority of our musics over the wide span of Americana styles. For in the day to day making of our musics, styles on the folk end of our musical spectrum rarely if ever get near the diminished colors. Yet going the other way? Towards the jazz end of our spectrum? Then there's simply no end to the mixing potentials of the diminished color on our palettes.

intervals
triads
symmetrical scales
diatonic 3 and 3
musical spectrum of colors
palette

While in theory we can diatonically generate the three note diminished triad from many different associated parent scales; relative major / natural minor and all their diatonic modes, melodic and harmonic minor and the purely symmetrical whole tone / half tone group, this all changes rather dramatically when we look to add a 7th to the triad. And as with chords generally, when we add a 7th to the triad, the new 7th chord opens new and often big theory vistas to explore. The idea of chord type for one. Dominant 7th substitutions for another. With the diminished colors, we get two varieties; the half and fully diminished seventh chords, each with their own unique properties that shapes how we use and where we find them in our Americana spectrum of styles.

diatonically generate
parent scales
relative major / minor
diatonic modes
melodic minor
harmonic minor
symmetrical scales
adding the 7th
chord type
dominant 7th
Americana spectrum

So once we diatonically generate the diminished triad from the major scale and find its most common spot in the music, we then add the 7th and create the distinction between half and fully diminished. What then follows is a fork in the road for each reader to choose and then explore as they choose; the half or fully diminished 7th arpeggio / chord. This is a fairly deep level of the theory depending on what you bring to the process today.

add the 7th
levels of theory

For once past this fork it's nearly all fully diminished seventh chord theory on this page; and there's a ton of it, with a couple of tons of associated links to explore. For the fully diminished 7th color is our consummate catalyst and portal to points beyond the diatonic center of most local universes. Yet truly no worries with either choice, for these 'e books' make it easy easy to go explore the beyonds and come right on back with just a couple of clicks :)

the diatonic center
'e' books

Diminished triad / a diatonic source. The diatonic source of our diminished triad comes from the pitches of our natural, relative major / minor scale. We locate the root pitch of this triad from the 7th scale degree. In the diminishing process we just make our regular old minor triad a bit more minor, we simply 'diminish' one of the intervals in the minor to create a diminished triad. Examine the building blocks of thirds as we evolve a minor triad into diminished one. Example 1.

four triads / building blocks
thirds
tertian harmony

Evolving the minor triad into diminished. Example 1a.

So we simply diminish the upper major 3rd of the minor triad by half step to create the diminished triad; two stacked minor 3rd intervals above our chosen root pitch. Next we can locate these two intervals as we evolve our parent scale C major into its arpeggio form and spell out the pitches. Example 1b.

parent scale
scale degree
root (1)
2
3
4
5
6
7
8
scale pitches
C
D
E
F
G
A
B
C
arpeggio degree
root (1)
3
5
7
9
11
13
15
arpeggio pitches
C
E
G
B
D
F
A
C
arpeggio intervals
.
maj 3
min 3
maj 3
min 3
min 3
maj 3
min 3

The diminished triad in V7. In the just above chart helps to focus our attention as to just where our two consecutive minor 3rds appear in the diatonic arpeggio to create the diminished triad. Finding B natural in our scale we see it is located on the 7th scale degree, Seven, thus it is the leading tone in C major. We simply spell our triad pitches from there. Example 1c.

Clearly we might hear and see this diminshed triad as part of the vanilla G7 chord; a super essential to all of our styles of Americana musics, thus a consistent style exception to the general absence of the diminished triad colors on the folk end of our Americana style spectrum.

Americana style spectrum

In this next idea we find a couple of movable G7 voicings to resolve C major. Example 1d.

chord voicings

As we move up the neck and reshape the chords, we can evolve through the styles by also adding on the color tones as additional pitches above the triads. From this three note, triad basis, we begin the next phase of this discussion by adding the 7th, the color tone that evolves our three note diatonic triads into four note 7th chords, and in doing so opening up a vast new universe of harmonic colors and possibilites.

adding the 7th
color tones
harmonic universe
anything from anywhere

Half or fully diminished 7th chord. For many emerging theorists, the distinction between these two colors often creates a bit of a connundrum. Actually, this distinction is often at the top of the 'confusing' list for many of us. There's basically just the two; half or fully diminished 7th chords. And as their name implies, one is simply a bit more diminished than the other; 'half' versus 'full.'

emerging theorists
intervals

Sharing the same triad. So these two critters share the same diatonic, diminished triad as generated just above. It is in adding the 7th above the triad that allows their individual magics to unfold. It goes like this. Generating our 7th from the major scale grouping to add to our diminished triad creates the diatonic half diminished. We then need to diminish this 7th by half step, to create a 'fully diminished 7th chord.' Our fully diminished 7th pitch, being non diatonic to our starting key center, creates the needed extra wiggle for the diminished color's inherent magic.

adding the 7th
groups of pitches
diatonic / non diatonic

So we diminish a component in music theory simply by reducing in size the pitch intervals in scales, arpeggios and chords as measured from our chosen root pitch. With diminished, a 'half becomes a full' simply by reducing chord's 7th just a bit wee more. Examine and compare their sounds using the key center C, and building off of Seven. Example 2.

Subtle yes but profound in their implications, just the one pitch, the 7th, gets us a wee bit more diminished, its interval as measured from the root further reduced by half step. The organic basis of their theory difference is that the half diminished color has a major third in its construction, as such it is diatonically available from within our natural scale; the relative major and minor group of pitches, i.e., the major scale. Thus it has its own mode; Locrian on Seven.

Thus deeply organic and imbedded within our ancient core pitches, half diminished can thus seemlessly bolt right up into all of our Americana genres and its vast vast library of Americana compositions within. Examine its chordal intervals. Example 2a.

major scale
C
D
E
F
G
A
B
C
arpeggio pitches
C
E
G
B
D
F
A
C
arpeggio intervals
.
.
.
.
minor 3
minor 3
major 3
.

Common chord voicings. For each of these colors there's a couple of core chord shapes to be familiar with. We organize and name them simply by their root pitch on each of the botton strings three on our guitars. Here are three common voicings for both the half and the fully diminished 7th chords. Example 2b.

chord voicings
root position

Inversions for half and fully diminished 7th. A next step with exploring these chord voicings is to find or create chord shapes that use each successive pitch of their arpeggio as their lowest pitch. Termed a chord 'inversion', 1st, 2nd and 3rd, in doing this we create variety as well as new pathways for voice leading; how each of the 'voice' (notes) in a chord move as we progress from one chord to another in our songs.

chord voicings
root position

As we'll see in just a bit, the fully diminished 7th color is constructed as a symmetrical shape of the minor 3rd interval, so thanks to the nature of our stringed instruments, the exact same diminished 7th chord shape 'perfectly inverts' its four pitches every three frets while moving up or down the fingerboard. So while the half diminished is very close in pitches, the shape of the voicings change as we move through the inversions up or down the fingerboard. Here are the basic four shapes of the upper four strings. Example 2c.

symmetrical

Cool? Simply moving one shape up the neck and rearranging the pitches as we go. Mostly a jazz guitar thing? Yep, though knowing this process is helpful when in the hunt for passing chords or the one exact chord in that certain spot to solve a compositional puzzle Here's the basics for half diminished for the 6th and 5th strings. Use the tab to find the shapes. Oh, are there arpeggio shapes for half and fully diminished too? Of course, we have it all here :) Example 2d.

Parent scale / half diminished. In this next idea we use the diatonic parent scale for half diminished and simply create a melodic idea over the the half diminished chord and resolve to a tonic major chord. Thinking Locrian mode of C major, we're simply running the pitches of the C major scale from B to B or so :) Example 2b.

Fits like a glove. Easy to hear how the diatonic Locrian bolts right up to the half diminished 7th chord. Creating a sequence with the pitches helps of course. For sequences just seem to create their own direction and impending resolution.

Non-diatonic. The fully diminished 7th color is simply not completely diatonic to our major scale group. Is this a problem? Of course not, it's just that as theorists we want to know the source of our musical colors. And as the major scale is the center of most of our local musical Americana universe, we simply want to be as clear on this distinction as we can. Examine the pitches. Ex. 2b.

major scale
C
D
E
F
G
A
B
C
arpeggio pitches
C
E
G
B
D
F
Ab
C
arpeggio intervals
.
.
.
.
minor 3
minor 3
minor 3
.

The pitch Ab is our non-diatonic tone in relation to our major scale. While we loose our diatonic status here in relation to half diminished, we now gain a symmetrical and consecutive grouping of three minor 3rd intervals. This simple tweak in pitches plays giant in our theory evolutions. For while we loose diatonic status we gain a portal into the whole process of Americana chord substitution, which can be theorized and projected with this interval symmetry.

Also, this minor third symmetry is one of a handful of our main uniform structures examined in Essentials. Each can play a intergral part in our own creative process, as the symmetry of intervals can create a more decidedly 'modern' sound beyond the traditional diatonic realm's alighnments of various now age old diatonic balances. Might symmetrical structures in composing aural music be thought of as a 'cubist' compositional approach in visual painting? Sure why not :)

modern guitar
composing your own music
wiki ~ cubism

Half diminished arpeggio exercise. This next idea is found as part of the bridge of a popular jazz song.

we use the diatonic parent scale for half diminished and simply create a melodic idea over the the half diminished chord and resolve to a tonic major chord. Thinking Locrian mode of C major, we're simply running the pitches of the C major scale from B to B or so :) Example 2b.

Charlie Christian
"Air Mail Special"
 

Fits like a glove. Easy to hear how the diatonic Locrian bolts right up to the half diminished 7th chord. Creating a sequence with the pitches helps of course. For sequences just seem to create their own direction and impending resolution.

Diatonic source / fully diminished 7th arpeggio. We can diatonically locate the fully diminished 7th arpeggio and thanks to equal temper tuning its chord, from the harmonic minor grouping of pitches. Generally off the radar for most composers and players until we near the jazzier end of our style spectrum, the harmonic minor flavor goes way back in our music histories and is perhaps most commonly sounded in our Klezmer musics of past and today. Let's quickly source this arpeggio from harmonic minor group before moving on. Examine the letter name pitches building from a C root pitch. Example 2c.

music histories
wiki ~ Klezmer music
harmonic minor scale
C
D
Eb
F
G
Ab
B
C
harmonic minor arpeggio
C
Eb
G
B
D
F
Ab
C
dim 7th arpeggio pitches
.
.
.
B
D
F
Ab
.

Cool? Just stacking of minor 3rds really, (B, D, F, Ab) but always good theory to know our diatonic source of each color.

minor 3rds
diatonic source

Parent scale / fully diminished 7th. As done with the half diminished color above, our diatonic source for our fully diminished 7th arpeggio, harmonic minor, becomes one of our parent scale choices for creating melodic ideas over the fully diminished 7th colors. Mostly the same idea as above with the pitches adjusted to create our parent scale harmonic minor resolving to C minor. Example. 2d.

Well, maybe not so glovelike. Needless to say we're getting further and further away from our most common compositional center of the relative major and minor. In doing so, and sounded here through a digital mix, the pitches become increasingly difficult to manage and to create meaningful melody lines with. Just theory here; an organic, diatonic parent scale choice for the diminished color. And thankfully, leaving the real art to each artist to create.

diatonic center
relative major / minor

Loops / symmetrical scale / fully diminished 7th. A second parent scale for the fully diminished 7th color comes to us through the perfect symmetry of the color's construction. For in stacking just minor 3rds, we get some additional magics to work with. Here we simply divide each minor 3rd into whole step and half step, creating the most common of our 'diminished scales.' Example 2e.

Arpeggio, scale and chord. All quite diminished. So depending on the art in your heart, this color might be off to one side, here now front and center to get familiar with and locate on our palettes.

scale / arpeggio /chord
impending resolution
palette

Quick review. So depending on how you art flows, both of these two diminished colors can become equal partners in working the relative major / minor basis of most all of our Americana musics. For with songs fromthe 'diatonic 3 and 3' basis, the diminished colors often become a portal between the mixing of major and minor of well crafted compositions all within one key center. Here's a common idea or two for these two colors in our diatonic '3 and 3.' Example 2f.

What follows. So what follows here is simply a look at the most common ways we'll find and use these two puzzle pieces in our work. While half diminished is diatonic from Seven of the major scale and thus enjoys a wide organic basis all throughout our Americana musics, the fully diminished has a harmonic minor group basis. Thus, similar to the blues rub, the mixing together of pitches of different parent scales creates a powerful energy potential to add into the relative major / minor diatonic realm.

blues rub

This is quite apparent in the diminished color's ability to energize the sense of aural motion between the diatonic degrees as passing diminished 7th chords, as in measures three and four just above. This same passing chord also becomes a theory basis of dominant chord substitution and the evolutionary process of our harmony. For the fully diminished 7th lives right within V7b9, perhaps our most senior ranking tritone bearing Americana harmonic traffic cop, who with authority directs our harmonic directions with the b9 colortones. From this basis all manner of chord substitution may evolve.

V7b9
b9
chord subsitution

Another half of the diminished nutshell. So are there ways to make our music sound more exciting? Or even to accelerate the sense of the forward motion of the musical process of pitches and rhythms moving through time? Can we splice in elements that consistently create a hightened sense of energy, motion and excitement in our musics? Can these elements also ramp up the challenge for the fully engaged artist?

forward motion
fully engaged artist

Of course there are and in theory these often include; the brighter (faster) tempos of course, big quarter note downbeat swing for sure. The triplet rhythm figure in numerous ways can surely lift and light the music right up. And there's my fave, the gallop never fails :) Might we turn the beat around to swing a bit harder and drive the energy onward and upward ? Absolutely.

brighter tempos

big 4 swing

triplet
the gallop
turn the beat around

Why, there's even riffing on just one note for a spell, giving the band behind us a chance to let 'er go. An old time trick that works like a charm. So all of these 'treatments' work just fine to get things cookin' a wee bit more and over the top. To this list we now add the fully diminished colors, 'outside' of the mostly diatonic realm associated with the above techniques. Termed here the 'great accelerator', splicing in the diminished color between the diatonic scale degrees consistently ramps up the sense of forward motion in our musics. For those improvisors 'blowing through the changes', add another challenge to your shedding while creating portals for new discoveries within the diatonic as well as beyond.

'a one note samba ... '
an 'outside color ...'
the great accelerator
polytonality
#15
soloing through the changes

Diminished between the diatonic pitches. That our diatonic scale is created by five whole steps and two half steps, we've the opportunity to slip in a diminished color into each of these whole steps. Some will accelerate the sense of forward motion, while others create a sense of sort of a temporary pause or hold. Here listed as links, explore each in turn to get a sense of their placement within the diatonic group.

# 1 dim 7
#2 dim 7
#4 dim 7
#5 dim 7
b7 dim 7
cadential motions

In truth, using the diminished color to create this sense of renewed energy and accelerated motion is hands down a jazz style thing. For while there's a few spots in complimentary genres, mostly the blues, using the diminished colors to accelerate the sense of motion is a jazz thing. Yet knowledge of a color, its structural theory and what it can do, is truly the crux of how in theory and philosophy a 'modern guitarist' is celebrated in this work.

jazz / atfaw
#4 in the blues
a modern guitarist

Theory empowered to find that perfect note, chord, rhythm whatever to 'solve the puzzle' can help elevate a song to 'gem' status. And gems are often top 10's yes? Self penned "Hey Jay Bell", among Alaska's favorite sound men for the last couple of decades, is a pure stompin' cloggin' pencil dancin' bluegrass cooker' of a pure country tale (yes with a bear too :) that gets all jazzed up simply with a #i dim 7 chord motion going to Two in the opening bars of the 'A' section. Can we find a fully diminished 7th chord to fit on a mando ... :) Surely. I've know heard them on banjos for sure. So yet more shedding for those so inclined to play 'through the changes' and knowledge is power yes? Si Amigo, and back to the shed we go to open up a new can of theory.

the puzzle
gem status
the top 10
"Hey Jay Bell"
jazzed up
mandolin monsters
banjo monsters
shedding
solo through the changes
a can of theory

Darkness before dawn. If 'in theory', we can assign actual endpoints to our diatonic spectrum of musical colors, placing the diminished group of pitches on the end that creates the 'darkest before the dawn' emotional moods of our music would probably not raise a eyebrow of even the staunchest of our didactics.

'... before the dawn'
s pectrum of aural colors
emotional environments
didactic

As a chord, the fully diminished 7th simply bristles with aural tension that has little of the organic or diatonic sense of resolution or at peace when sounded on its own. For there is no pitch in this chord that does not contribute to this sense of bristle, yet each of its pitches can equally become a leading tone to point us back to the tonality of a key center. That the diminished colors contain this dual quality of moodiest of tensions that also create pathways to the joyest of resolving light is the basis of the theory discussions which follow.

tonality
leading tone
key center

Defining 'diminished.' As the word's standard meaning implies, when we 'diminish' something, we're simply reducing its stature. In our music theory same thing, we are simply reducing the stature or diminishing the size, of a musical interval. There's a bit of an evolution here as we diminish an interval, depending on our starting point. And while there's a theorist's way to fully account for every knook and cranny, shape and size of all of our intervals, in our discussion here we've initially just a select few interval labels that we must rote learn. For we're simply looking to internalize and label the aural and theory properties of the diminished 7th color's basic components; a scale, an arpeggio, a triad and a 7th chord. Examine the following idea from C. Example 3.

rote learn

Familiar sounds? Cool. No? Check it out in context in this next idea. Extracting from the 1967 radio pop hit "Spooky" by the Classics IV. Example 3a.

wiki ~ Classics IV

Sorry about the notation playback, get the right rhythms right off the recording, the chord voicings should be cool, their pitches are just the top three notes of the chords, partial chords with no root pitch, leaving a big space for the bass player to lay the groove in. Younger players coming up should probably learn this standard pop tune. Easy tune, cool pocket, easy bass line, everyone knows it in the room so it usually fills the dance floor. Also, there's been some remakes with super smokin' way creative modern guitar solos over the two chord vamp.

two chord vamp

Fully diminished 7th chord intervals. The core interval used to construct the fully diminished 7th colors is exclusively the minor 3rd interval. As we stack these one atop another the diminished colors evolve. The first minor 3rd above a root pitch gives us the essential minor / blue 3rd. The second stacked minor 3rd creates a diminished 5th which completes the diminished triad. The next minor 3rd atop creates a diminished 7th interval as measured from our root pitch and completes the fully diminished 7th chord. Example 4.

minor 3rd
blue third
diminished 5th
diminished 7th

So we're starting to get at that 'bristling sound' yes? So one minor 3rd interval is a blue note. Two minor 3rd intervals stacked is a diminished 5th interval and three creates the diminished 7th interval. Add them all up into a fully diminished 7th chord. And two minor 3rd's stacked becomes a diminished 5th, which is also known as the tritone? The 'musica diablo?' The juice within V7? Super dominant chord catalyst to all points beyond? That unmistakeable blue honk and ultimate deep blues rub? Yep, that's the tritone. Quite a lot from one pitch :)

wiki ~ musica diablo
tritone within
resolving qualities

Diminished 5th / 'three tone' interval. Another way to find our diminished 5th is by just whole steps up from our root pitch. In doing so we'll need 'three whole tones.' As in a tritone? Exactly, 'tri' = three and 'a tone' + a whole step. Example 3.

Recognize the sound? Pretty character and unique. And cool with the different interval pitch spellings between bars 3 and 4 above? The F# = Gb ? That these two notes are said to be enharmonic equivalents? And how about the lick in the last bar? The tritone interval centers the Euro emergency siren, telling us needed help is coming.

enharmonic

Tritone a la J.S. Bach. This next idea is a classic tritone sort of 'question.' Lifted from the original keyboard monster himself JS Bach of the Baroque era, clearly we can hear the creation of a tritone's nature to create a sense of musical question ... a sort of curiosity ... 'listen up' for there's some serious and important coolness to follow :) Example 3a.

J S Bach
Baroque
monster

As aurally clear as clear ever gets yes? This tritone sound is the basis of diminished color. Rote learn it here if need be and you'll have it forever.

WTC

J.S. Bach. Those of us impassioned about the theory of our Americana harmony should look into this cat. For there's a couple of tons of musical invention that exhausts our equal tempered resource with an aural clarity that simply stuns again and again all throughout his musics. If there's one artist of the European contribution to our Americana musics that covered the theoretical whole tamale in his vast output of creative musical art, JS is this cat.

wiki ~ J.S. Bach
the Euro contribution
author's opinions

Fully diminished 7th / 'double' tritone. In the fully diminished 7th chord, we'll end up with two pairs of tritones, a 'double tritone' if you will. This pairing within a single chord voicing is what creates the diminished chord's one-of-a-kind aural 'bristle.' It also energizes its potential for its multiple resolving qualities. Building a fully diminished 7th chord from the root pitch C. Ex. 4.

tritone
#4 / b5
tritone within
resolving qualities

So fully diminished 7th has two pairs of tritones. Well it turns out that this four note chord sits right atop the dominant pitch of any key center and provides some wonderful opportunities for artistic, musical, technical and spiritual advancement. Jazz artists in the house?

Fully diminished double tritone / V7b9 chords. Theorywise we begin a next level of our diminished harmony evolutions for in one swift, bold move we can double the leading tone possibilities discussed with the tritone bearing V7 chord simply by adding the flat Nine pitch. Here thinking in the key center of C major, examine the pitches of its dominant chord G7b9 and its two pairs of tritone pitches. Example 5.

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
.
.
.

Two pairs of tritones in one chord. And it sits right atop the dominant pitch of any key center and provides some wonderful opportunities for artistic, musical, technical and spiritual advancement. Jazz artists in the house?

Notice that one pair of tritones are the 3rd and 7th of the chord? Might these be flipped upside down to create the the 3rd and 7th of a chord with a different root pitch? And if so, can the 'D' and 'Ab' tritone be the 3rd and 7th of a differently rooted chord? And flipped also? In mathematics, if A and B are equal, and B and C are equal, is C then equal to A? :)

Where in the music. The V7b9 is mainly a jazz color. On ocassion we hear it in the blues and pop music. And within this library, b9 is probably more often used in a minor key, as the b9 pitch is diatonic to the natural minor grouping of pitches, thus its effect can be said to be muted or softened in contrast to a major key. Examine the pitches of C natural minor / G7b9. Example 5a.

softened musical colors
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 and the borrowing of any pitch any time when necessary to express the art of the heart.

So we borrow pitches all the time in creating the American sounds? Yep. For instance, anytime there's a blue hue in a non blues based tune, chances are it's non-diatonic and borrowed. The idea of diatonic exclusivity simply provides an essential perspective for we theorists who like to know the organic source of all things. Thus empowered, our potential source for new ideas nicely expands as even hearing a wisp of music from any source, that we can theoretically identify and perhaps better recall or write down, might become another spark for new art and expression from our heart.

blue's hue
reading music
writing music
composing

Deserted island flat nine shape. If I had to be on a deserted 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 it is 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, jazz or blues etc. Example 5b.

wiki ~ Ted Greene
G 7b9
w/ four fingers

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. Unsual? No. Happens all the time in lots of our guitar chord voicings when we expand our pitches on past our triads and into the color tones. Remember, it is the 3rd and 7th that determine chord quality thus a 'chunks' function.

voicings
color tones
chord function

The root pitch basses the chord so the 5th can be ommitted when needed. Bass player on the gig? Well then maybe the root pitch is not quite so necessary, leaving a spot for the 5th to be included? Just might be the case :) Do examine the four pitches included in the V7b9 shape just above. In C major, thinking from the dominant, Five. Example 5c.

bass players
dominant
Five
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, no 5th in the voicing. When we do add a perfect 5th interval into this V7b9 chord's pitches, and that's next, the theory and consequently all of its artistic potential in all things dominant, i.e., V, V7, V7b9 / #9 / b5 / #11 / 13 / b13 / sus 4 / and all of their mix and match combinations, substitutions and manifestations, all can advance dramatically via the symmetrical nature of the diminished 7th color.

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

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
.
.
.

Quick review / easy do. Now with the addition of the 5th we create a symmetrical arpeggio within our G7b9 chord whose 3rd, 5th, 7th and b9 pitches are all a minor third apart. Back to where we started? Yep,a fully diminished 7th arpeggio. Symmetrical; only one build interval, all intervals are the same, thus symmetrical :) Four pitches by minor third interval we term a fully diminished 7th chord. Examine the pitches and their evolution into chord shapes. Example 5e.

G7b9 pitches
G
B
D
F
Ab
minor 3rds
.
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 jettising the root pitch G, and we can often leave that to the bass player, the perfectly symmetrical diminished color is capable of many lovely hues of nuance and shading by filtering its organic properties through our various musical filters. Filters such as; softening back into V7, pairing with Two chords, ascending or descending motions by whole step / half step / minor 3rd, sequencing, revoice the tritones with appropriate key wise color tones etc.

Examine the pitches and sound of the V7b9 in action with an eventual resolution to a tonic major chord. Do note the simple circle symbol designating a diminished triad. Example 5f.

Run out of frets? This last idea is a fairly common diminished chord run for guitar. Simply moving the one shape up in minor thirds. Which incidently can go equally up or down yes? And a minor 3rd is equal to a whole step + a half step so we've some options from within also.

ascending
descending

Multiple leading tones. Way back in this discussion we determined that an organic source of the diminished triad is from the major scale and that we build the diminished triad on its 7th scale degree. Seven of course being the leading tone to resolution and a resting point in the music. And since the diminished color is perfectly symmetrical, might each of its pitches be leading tones, the 7th scale degree, to their appropriate key centers?

parallel minor
key centers

This is indeed the theory 'case' with fully diminished 7th. Examine these possibilities in the following idea; four approriate major keys followed by their four parallel minor keys. Major keys first. Example 5g.

parallel minor
diminished 7th arpeggio pitches as leading tones
Ab (G#)
B
D
F
resolves up to
A maj
C maj
Eb maj
Gb maj
diminished 7th arpeggio pitches as leading tones
Ab (G#)
B
D
F
resolves up to
A min
C min
Eb min
Gb min

Hear how seemlessly the diminished resolves in the minor tonality? Also, 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 fully diminished 7th color is from the harmonic minor group; simply a vanilla natural minor grouping with an added leading tone.

colortones
evolution of musical style

Relative and parallel keys. So aren't those key centers in the last idea also the relative minor of one another? That A minor and C major, Eb minor and G major, parallel key A major to Gb (F#) minor etc., are all these centers relatable to one another through these diminished theory permutations?

relative key centers
permutations

They sure are. So these '4 way' resolutions can work beautifully with one another. In composing music, writers are oftentimes using a 'pivot' chord to get them from one key center to another. The fully diminished 7th chord, with its symmetry inherent tensions, is often just such a chord. So along this line of thought, in this next idea we use the same shape and stay in one spot, simply change the root pitch of each chord and resolve to the four, relative minor key centers. Example 5h.

relative key centers
permutations
pivot chord
diminished arpeggio pitches as leading tones
Ab (G#)
B
D
F
resolves up to
A min
C min
Eb min
Gb min

Resolves like butter! Sorry :) Regardless, this is what the theory can do for us. Create new ways to understand the relationships between the pitches, key centers and such in composing our music, finding chord substitutions, discovering new ways to cover old ground. Tis' all good.

Quick review ~ one chord four names. So if we follow the rule that 'if we think from the root we'll never get lost' then chances are we won't. Yet, the diminished 7th colors have a bit more trickery in their naming. Why? Well in theory, the perfect symmetry of their interval construction creates just three unique loops of four pitches that cover all of our 12 possible root pitches. These can become a shorthand way for labeling as the diminished theory evolves into chord substitution and their resolutions. for often times if the theory is 'close enough', artists come along and make these sorts of resolutions work just fine. Examine the pitches of our three fully diminished 7th chords. The three perfectly closed loops of pitches. Example 5i.

emerging theorists
loops of pitches
diminished 7th arpeggio
.
up min 3rd
up a -3rd
up a min 3rd
up a min 3rd to perfect closure
C
C
Eb
Gb
A
C
Db
Db
Fb (E)
G
Bb
Db
D
D
F
Ab
B
D
Eb
Eb
Gb
A
C
Eb

So by the time we get to Eb, we're back to the same pitches as with the C diminished 7th arpeggio. While there's a few ways to look at this, thinking from the root of whatever we have in front of us is a sure way to keep it all straight. Cats probably end up applying their own way of understanding this theory based on how they first learned it. Here it is presented as a sort of 'just so ya know' quick review to help keep things straight.

Melodic resolutions. Melodically, advancing jazz leaning guitar players might run each of the five diatonic melody shapes through this theory; one shape / one position, four parallel key centers of diatonic major, parallel and relative minor, using their common diminished scale group or chord voicing. Here's the scale shape, sound and a suggested fingering for the fully diminished 7th color in 5th position. Example 5j.

advancing players
five diatonic scale shapes
four fingers / four frets
pitches
fingering

So the idea is that with these 'groups of pitches', we simply try create a melodic idea from one group and move to the next. So in this case some diminished tension followed by its release into an idea from the major scale group of pitches. Here in 5th position thinking C7b9 into F major. Example 5k.

The shedding here is to simply run a similar diminished color idea into the four key centers related to F major so; F, Ab, B and D, and stay roughly in a localized position, so for this exercise, around the 5th fret or so. Jazz players dig this 'local' as oftentimes the tempos are brighter and they play through the changes in songs that often modulate, meaning changing from one key center into another. Resolutions to multiple key centers in localized positions is one goal. Eventually this probably becomes more chromatic .

localized position
play through the changes
modulation

V7b9 resolutions. So the basic idea is that we've three fully diminished 7th that are interchangeable to sit atop of the 12 V7b9 chords that resolve to each of the relative major, minor and parallel key centers. A ton of shedding for those so inclined, there's the basic five positions for finding the various chords also. In this next chart we simply group resolutions for each of the three diminished 7th scales. Example 5l.

advancing players
five diatonic scale shapes
four fingers / four frets
diminished 7th within V7b9
root of key center resolutions
C dim / Ab7b9, B7b9, D7b9, F7b9
Db, E, G, Bb
Db (A#) dim / A7b9, C7b9, Eb7b9, F#7b9
D, F, Ab, B
D dim / Bb7b9, Db7b9, E7b9, G7b9
Db, E, G, Bb
Eb dim (C) ... and back to where we started
~

Keeping track of the enharmonic equivalents of this theory mayhem is well, your responsibility. For truth be told, most of the songs we play live on the top half of the 'C' centered cycle of 5th's. Decide what you need and do the shedding in a way so it sticks and is usable. Those that will venture down to the end of the evolution of our Americana harmony path; where all of the chords become some sort of V7 chord type and the melodic lines lean towards the 'chromatic buzz', will in shedding the above resolutions have laid the goundwork, both intellectual and chops' wise on their ax, to conquer the whole of the Americana tamale through the organic evolutions of the theory as encapsulated by Coltrane.

enharmonic equivalents
evolution of harmony
chromatic buzz
whole Americana tamale

Leaps of minor thirds. So, our diminished minor 3rd symmetry allows for all of our diminished chord shapes to be 'theory' 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. Examine the letter name pitches and sounds of the Ab, B, D and F fully diminished 7th chords. Example 6.

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 three lower bass strings, we can cover the entire range of the neck rather quickly when needed. Here are the three movable shapes. These are the same three shapes from earlier in this discussion. Example 6a.

OK with these shapes? See the similarity between the first and third voicings just above? Our bass note has simply been moved to the top string while retaining the middle voices. Play through the following chords that use these three shapes in order as a #1dim 7 between One and Two. Example 6b.

Triangle is major as in G major 7? Yep. Feel a bit of the acceleration in the motion between One and Two with the diminished in between? It's in there somewhere :)

Fully diminished 7th / where in the music? So diminished chords are mostly found in the jazz styles, we'll see them all the time either written in or added as a substitute chord. Common spots; as a passing diminished chord between diatonic pitches built on #i, #ii and #iv. Replacing the diatonic half diminished on vii. Delaying the resolution to a tonic One chord by using a fully diminished 7th chord with the same root pitch. And as part of the b9 in V7b9? Very common in indeed.

substitutions
old time blues
common tone tonic
sharp Four
V7b9

Further, again the tritone interval is in the metal musical style 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 oftentimes here it as a common tone tonic chord. In jazzed up blues songs, the fully diminished 7th chord slipped in as a sharp Four chord in bar six of a regular 12 bar blues which follows right here.

metal / style
old time blues
common tone tonic
jazzed up
sharp Four
12 bar blues

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 sort of just begs to go to the #iv dim 7 chord. Really? Every time? No, but often enough 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's the basic changes, thinking C blues. Example 7.

penultimate
12 bar blues

forward motion

changes
blues chord substitutions

Taking it out. This next idea for locating a fully diminished 7th chord on 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 the descending bass line and progression as we take it out. Thinking F major. Example 7.

arrangements
common tone

take it out

Nice series of chords to play a single line through yes?

improv / through the changes

Wheel of tritones / cycle of fifths. Since the tritone interval plays a nice role in the diminished colors, let's chart out the intervals a bit via the cycle of fifth's. For it turns out that 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 8.

cycle of 5th's
keyclocks
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 8a.

WOW ! Now the compass points show us four key centers, each of which is the major / relative minor tonic of each other. This visualization of the major / minor key centers / tritone from within the cycle of fifth's is new for me. I just discovered this :) Do print and tack these two up for reference if so empowered.

major / minor

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 interval in the neighborhood. So in thinking of the Americana sounds, in a word, everywhere. Well, probably not in children's songs of course, unless they're spooky Holloween tunes. In folk, never ( did I just say never that ... ) 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.

musical styles

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" 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 often sad and demonic edge and becomes a key step in the stairway to the bright musical stars and beyond.

wiki ~ Maria ~ West Side Story

Tritone / 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 in those days probably 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 whole of our Americana family.

Diablo de Musica
encapsulate
blue notes

When the jazz harmony started to evolve in the later 30's toward bebop with cats 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 things 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 song "Giant Steps", a composition which even today sits as the crown jewel atop the theory / shedding challenges that Mr. Christian helped initiate and that Mr. Coltrane developed and conquered.

bebop
Charlie Christian
diminished chord
V7b9
John Coltrane
theory / shedding

Softening the diminished color / part one. In this penultimate entry for our various diminished colors, there's a way to 'soften up' the bristlyness that the diminished intervals bring. Turns out that with the fully symmetrical minor 3rd's of the diminished 7th chord, we can lower any one of the four pitches and evolve a vanilla V7 chord. So four pitches in the diminished 7th chord become the root pitches of four different dominant 7th chords. Examine the pitches. Example 9.

softening colors
vanilla
diminished 7th / minor 3rd's
Ab
B
D
F
chord
root
3rd
5th
7th
G 7
G
B
D
F
Bb 7
Bb
D
F
Ab
Db 7
D
F
Ab
B (Cb)
E 7
E
Ab (G#)
B
D

Wow, now that's interesting for those so inclined. What do these become? These four chords become the basis of V7, dominant chord substitutions. In C major, G7 is Five, The Bb7 is bVII and a blues / Mixolydian flavor and often the basis for various two chord vamps. The Db7 is the essential tritone substitute chord, a staple for many jazz players. While the E7 is usually a Five chord to C major's relative, A minor. So a bit of a surprise when used in cadential motions towards C major. Explore the links forward as your curiosity demands.

chord substitutions
Mixolydian
tritone sub

Softening the diminished color / part two. In this last entry for our various diminished colors, there's another way to 'soften up' the bristlyness that the diminished intervals bring. Turns out that with the fully symmetrical minor 3rd's of the diminished 7th chord, we can raise any one of the four pitches and evolve a half diminished 7th chord that is the ditonic Two chord of each of the vanilla V7 chords from the last idea. So four pitches in the diminished 7th chord become the root pitches of four different half diminished 7th chords. Examine the pitches. Example 9.

softening colors
vanilla
diminished 7th / minor 3rd's
Ab
B
D
F
chord
root
3rd
5th
7th
B -7b5 / E7
A
B
D
F
D -7b5 / G7
C
D
F
Ab
F -7b5 / Bb7
D#(Eb)
F
Ab
B (Cb)
Ab -7b5 / Db
F#(Gb)
Ab
B (Cb)
D (Ebb)

So as with four V7 chords, we can now pair up each one up with its Two chord. What do it mean? Well mostly about chord substitution and finding new ways to get to usual places. We can also trace things back towards their diatonic basis opening up additional modal possibilities. Lastly, we've similar ideas for the melodic minor grouping of pitches, using the diminished principles of symmetrical resolutions but with a softer hue. And the melodic minor group does = Lydian flat 7 yes ?

chord substitutions
Mixolydian
tritone sub
Lydian b7
C melodic minor
C
D
Eb
F
G
A
B
C
F Lydian b7
F
G
A
B
C
D
Eb
F

Tritone review. Perhaps needless to say the tritone has come quite a ways since its days as "the diablo of music." A core component in Americaan 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 V7 sounds in folk music, most any other use of its sound is simply not a part of the original folk tradition.

musical styles
three chords and the truth

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 penatonic core. While the two pitch tritone evolves the major pentatonic grouping of pitches into the diatonic major / relative minor scales.

one note tritone
two note tritone

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, thus continuing their search for the myriad of nuanced ways to create the tension and its release of their art.

tension and release

Diminished colors / Americana harmony evolutions. A central thread through this Essentials text is the idea of an evolution of Americana harmony that runs through our spectrum of musical styles. The idea hear is that by understanding how our harmony is sourced and used to create music within a style or genre, we can see it's numerical evolutions as we move from the mostly three chord folk styles and blues styles into the 'diatonic 3 and 3' of rock, pop and country to arrive at the often 'chock full of changes' jazz aproach to Americana harmony. With such a basis, we can become more of a 'modern guitarist' in our own work, in that we've a wider spectrum of understanding the harmony of our styles that might be an influence our own creations.

The diminished colors play a pivotal role in a couple of ways. For one; the V7b9 chord's ability to slide by minor 3rd's creates a new improvisational challenge in jazz in the mid to later 50's. Coltrane's composition "Moment's Notice" evolves the more diatonic leaning Three / Six / Two Five motion to become a 'double Two / Five' whose root pitches are a half step apart. This can necissitate that the improvised idea being created would need to modulate by half step 'mid stream' to stay inside the changes as written. So we not only need to come up with an idea, we need to transpose it up a half step as the measures move along. Ramping up the challenge is part of the 'mother of necissity' of this evolution of Americana harmony

The down a minor 3rd then up a perfect 4th motion that this creates later comes along again in Coltrane's "Giant Steps." Now the minor 3rd is ascending followed by a perfect 4th to resolve to key centers that create an augmented triad. Those that have worked over this piece know of the ascending intellectual challenge that it creates from the mostly Two / Five modulatory level that preceeds it. So a gradually advancing degree of challenge for the modern, improvising artist.

A second aspect of "Giant Steps" is the simple dominant to tonic resolutions of the first half of the song. This preceeds the later evolutions of later generations of players that in today's jazz art, find a V7 type chord preceeding each of the written chords of a song. And then further along, where all of the chords used in the improv sections are dominant chord type, often altered with various colortones into a tightly woven fabric of varying degrees of stability. The artist then 'negotiates' this 'uncertianty' as the music moves along, coming to resting points with the ebb and flow of the groups dynamics and crescendos.

evolution of harmony
diatonic 3 and 3
numerical evolutions
emotional environments
diatonic 3 and 3
dynanics
crescendo

Review ~ diminished colors ~ '... half or fully diminished ... that is the question. Thanks Shakespeare for all your quips including this one from "Hamlet." For it phrases our theory studies in such a way by creating a neumonic device, a memory note that helps us to rote learn and remember. In this case, 'to be or not to be' is our 'half or full diminished' qustion. As their sound is nearly identical, no wonder they oftentimes create a bit of theory confusion. And while the difference is slight, the theoretical ramifications can be giant. As part of the review of this page, here's a chart outlining their basic diatonic theory, pitches and construction.

wiki ~ Shakespeare
wiki ~ 'to be or not to be ...'

~ half diminished ~

~ full diminished ~

C major
parallel key centers
C harmonic minor
.
1
1/2
1
1
1/2
1
1
C
D
E
F
G
A
B
C
.
.
.
1
b3
b5
b7
.
C
E
G
B
D
F
A
C
 
.
1
1/2
1
1
1/2
1
1
C
D
Eb
F
G
Ab
B
C
.
.
.
1
b3
b5
bb7
.
C
E
G
B
D
F
Ab
C

half diminished

 

fully diminished

Half diminished is a diatonic chord built from the major scale. Built on Seven, it plays a portal role between major and minor within a center. In construction the triad is diminished; a minor triad with a diminished 5th. Its b7 is simply a minor 7th.

major scale

harmonic minor

Fully diminished is diatonic to the harmonic minor group. Its triad is diminished; minor 3rd under a diminished 5th. Its 7th is also diminished; from a minor 7th reduced by half step to diminished, noted by the 'bb7' in the chart above.

B D F to A / major 3rd
 
B D F to Ab / minor 3rd

Diminished scale melodies. Notable written melodies created with the diminished scale are rather rare in our American literature. The eight bar bridge of the jazz standard "Air Mail Special" by guitarist Charlie Christian is the only real symmetrically diminished melody I can think of. It is created by a fully diminished 7th arpeggio that moves down by half steps and closes on V7.

Further diminished evolutions. In continuation from the discussion just a bit above, that in some music circles today that a diminished color potential helps evolve two modern valences of harmonic motions for improvisation and composition. The first is where each chord in the progression is preceded by a V7 type chord. Second is where every chord within a progression becomes a dominant chord type, often featuring altered colortones.

In the rapid tempos of jazz, this type of continuous dominant chord substitution gives rise to what I term the 'chromatic buzz.' This simply describes the effect of how aggressive dominant chord substitution creates a seamless and chromatic leaning overall sound of the contributing voices of a group. Speculating here but this approach may recreate today what was once termed 'sheets of sound', a high velocity arpeggiated approach pioneered by John Coltrane in the late 50's.

wiki ~ sheets of sound

Harmonically, 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 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 adding notes one by one. For example; V7 to V9, ii-7 to ii-9 ect., 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.

adding color tones

Using the theory to evolve. As in the ' 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 philosphy and core basis of this text emerges.

The basis. As this "Essentials" work is in the end simply a music theory text and primer for jazz guitar, once the basic elements and a certain understanding are in place, the theory and its impact on the music rapidly evolves thanks in great measure to the music of John Coltrane.

Sensing that Mr. Coltrane searched just like the rest of us, we can examine his compositions and clearly see his evolving sense of tonality. That his evolution includes a gradually increasing degree of challenge should come as no surprise. These theory evolutions, based on his original composing, form the intellectual basis of this work. (The Beethoven string quartets have a similar career trajectory and evolution of tonality.)

Understanding of these theories is first initiated by the tritone sub theory and then the idea of giving various pitches within a V7b9 chord leading tone capacity. Thus we've found the bridge for the inclusion of more of our 12 pitches in a diatonic centered environment, as the altered non-diatonic chords add new pitches to the mix.

Two American titan kings blaze the trail. In my own humble opinion, Mr. Coltrane's 'thing' was about chords, the harmony. And while his predecessor Charlie Parker modernized our music by exhausting the diatonic possibilities both melodically and harmonically, Mr. Coltrane advanced and modernized the music through chord substitution beyond the traditional diatonic realms he inherited. We can understand these advances as Mr. Coltrane created greater improvisational challenges for himself, by simply manipulating what the theory 'allows' into art. We do this by simply examining his works in the historical recording order that he gave them to us.

wiki ~ Charlie Parker

For even in his most advanced pieces up to and including "Giant Steps", it is the chord changes that challenge the performer. While Mr. Coltrane's written melodies retain a sense of gospel and American lyricism, it's when his improvisations begin over the new more complex harmonies he conjured that our jaws tend to drop. For so many and even some jazz players, it is simply beyond artistic comprehension. For us theorists, thanks to Mr. Coltrane's clarity of vision and the perfect closure of our theory system, understanding his evolution of the theory is a walk in the park. Of course those in the know probably know that confidently perfoming "Giant Steps" in a jazz tradition is our goal here, which is generally not a walk in the park for the unaquainted improvising musician :)

wiki ~ Giant Steps
'Invest yourself in everything you do. There's fun in being serious.'
John Coltrane
Footnotes:

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

Bach, Johann Sebastion. The Well Tempered Clavier Volume One, prelude #8 in Eb minor, measures 21-25, BWV 853.

wiki ~ J.S. Bach
wiki ~ Well Tempered Clavier
wiki ~ BWV