~ groups of pitches ~

'a pitch by pitch discovering of the groups of pitches from which we create our melodic ideas ... '

~

In a nutshell, 'groups of pitches.' Just a fancy way to say 'a scale?' Yea pretty much. The only caveate being that if we think of and practice scales as scales our melodic ideas when making music just might end up sounding like scales, so surely an artistic concern here. So we flip the bit to think that scales are super selected 'groups of pitches.' Set in stone groups of pitches that we create our melodic ideas from. So, same critters, same spots and stripes and same notes yet a different take on this whole pitch / theory tamale.

whole tamale

Americana pitches. In creating the necessary pitches to make the various Americana musics, we really need two sets of pitches; one set of very finely tuned pitches to make the chords. And one not so fine tuned set to make the blue note hues in the melodies. And while we can measure and label these blue notes in regular terms, we can also alter them past their regular limits and in doing so, create the blue's rub; that purely original Americana magic that sounds out loud and clear when we purpose rub together these uniquely tuned sets of pitches.

fine tuned pitches
blue note tuning
blues hue

In a nutshell. So in the following discussions we extract our core melodic loops from the 12 pitch chromatic scale. To form up the basic groups of pitches, the various scales and modes, from which we create our melodies.These will then become the arpeggios, whose pitches we then stack up and sound together making the chords.

Three main elements + time. We theorists form our pitches into the scales, arpeggios and chords that we motorize through time to make our music. This work's core discussion of the Americana scales follows below. Click off for the arpeggios, chords and time discussions.

time

An additive evolution of melody. Woven throughout the discussions in this work is a theoretical and philosophical basis of simple numerics. That any given topic or component can be initially defined stylistically by its number of pitches. Further, that by adding or removing pitches from our creative palette, we can sense and trend an evolution of musical style. With grouping pitches for creating melody, our endpoints are five and twelve, corresponding to children's and folk melodies (5) and on through blues, rock, country and pop to the melodies of jazz (12).

Number of and location of the half steps. Locating where the half steps live in any group of pitches just might be the easiest way to capture each mode's unique character. And does the number of half steps in a group help shape and tell of its tonal gravity? The various degrees of pull between each of the pitches? Pull like swing ? Kinda, read on and we'll see :)

Advanced theorist. For the advanced theorist reading here, there's really just one idea for the general topic of this page, groups of pitches. Simply that our 'groups of pitches' today are the perfectly closed loops of pitches from which we create our ideas; melody, harmony etc. Subbing for the term 'scale' to a certain extent, a 'group' includes the multifaceted diatonic properties that each pitch in a 'scale' brings to the conversation.

Many solid properties including; modes, shades of major / minor, arpeggios, colortones, 'parent scales' for phrases, intervals, sequences, soloing through and or over the changes revolve around this 'group' idea. Our chosen group creates what is diatonic, thus establishing the boundaries of a select group of pitches. Surely a stabilizing perspective for venturing on.

History ~ theory overview. We modernés of today know of the ancient music potentials by way of the cave bear flute. What we do not know of course is what melodies got played. Oh well, can't know everything. We can know our Americana roots, the pitches used and the general idea of the music being created. And once we get to post 'Edison' days, we're really kind of good to go in knowing of the music through recordings.

Overview: Having created an overview of our 12 pitch musical resource in the silent architecture of music and then examined the interval loops, then added the Yin / Yang balance of major and minor, all with a dash of historical spice, mathematics and whatever else came to mind, we can begin to perhaps more logically comb out the more defined groups of pitches from which we create the American sounds we love. So as with our loops study, where we started with our smallest intervals, we'll create and sequence our melodic groups here by starting small and evolving pitch by pitch.

Of course it is no coincidence that our smallest grouping of musical pitches may also live at the historical core of all our music. And while there are of course other possible loops, using additional intervals in the mix, it turns out that in our everyday musical lives that just one interval grouping or formula has created the bulk of our melodic material. This of course is the seven pitch diatonic major scale / Ionian mode / natural minor / Aeolian mode partnership. For me the Yin/Yang balance of our local musical universal.

Tuning magic. And while the melodic importance of the major scale grouping in our AmerEuro music can never be overstated, we should add into the mix that how we modernists tune these pitches today is what truly creates our entire pitch resource. For in today's modern system, all of our scales, modes, arpeggios and chords are equally project-able from each pitch thanks to equal temper tuning. Even rhythms? Of course, rhythms too. Everything from any pitch. Crazy I know and all of it based on the nearly 2500 year old Pythagorean cycle of pitches and its eventual equal temper tuning firmly established in the 18th century.

So if we get all of our melody and all of our chords from these ancient groups, no wonder they are still around eh? What about the blues? I knew you'd ask that. As we'll soon see, the blue notes / melodies are theoretically core pitches too. That we find the blue colors woven into nearly every nook and cranny of our myriad of different American styles and sounds makes them all the more difficult to theorize about. We'll theoretically find them in the following discussion sandwiched in between the organic evolution of our five note group into a six for the blues before adding one more for our grouping of seven. Sort of a missing link? Maybe. Do read on and discover their theory and then just decide for yourself.

~ five pitches and a place to start ~

Groups: A five note grouping of pitches. At the historical and theoretical core of the Americana melodic sounds we find the five pitch grouping commonly referred to as the pentatonic scale. Found by musicologists in many indigenous cultures, our own Native Americans own this group of pitches. Turns out that all improvising musicians love these pentatonic groupings in that there are really no 'bad' pitches in the bunch when used for improv over appropriate changes.

Initially two basic varieties of this grouping of five; major and minor, can you hear the difference between the two? Major and minor? This first idea is in the major tonality. Remember this ditty from way back when? Thinking from the root pitch C. Example 1.

"Shortnin' Bread." "Mama's little baby loves shortnin' shortnin' ..." Know this melody? The carefree, whimsical nature of this melody embodies one of the essential emotional character qualities of the major pentatonic group of pitches. When we hear melodies that create this sense of jaunty-ness and joy, good chance they too are pentatonic lines.

pentatonic melodies

With its handful of pitches and joyous nature it is no surprise that we find this color creating musical tones for children, world music, rock, reggae and the pop styles. Why even those garden wind chimes bless us with their melodic strains, as freely wrought as the breeze that stirs them to life.

Historically an essential grouping of pitches, we'll find pentatonic melodies in the early music cultures of China, Africa, our own Native American Indian cultures and that of the Celts and Scots of the British Isles. So it's pitches surely have been with us for a very long time.

Extracting the pitches. Thinking of the "Shortnin" melody just above, now that we have a wee bit of the art, let's become the scientist and figure out what pitches and intervals the composer used, look for patterns and generate new avenues to explore based on the theory.

We can do this by simply extracting the five different pitches of our melody from the twelve pitches of the chromatic scale. We then examine the distance between the pitches, termed intervals, to create our pentatonic scale formula. Example 1a.

chromatic scale
C
C#
D
D#
E
F
F#
G
G#
A
A#
B
C
pentatonic scale
C
.
D
.
E
.
.
G
.
A
.
.
C
intervals
whole step
whole step
minor third
whole step
minor third
C to D
major 2nd
.
C to E
major 3rd
.
C to G
perfect fifth
.
C to A
major sixth
.
C to C
perfect octave
formula
whole step
whole step
minor third
whole step
minor third

Examine the intervals. Thinking from our root pitch 'C', the major 2nd, 3rd and 6th intervals combine to create the overall coloring of the major emotional environment. Easy enough huh? Also, in measuring the intervals between the pitches, we find two minor third intervals within the octave span. Hmm, what might that imply? And note also that there are no half steps in the formula yet, the base interval of our chromatic scale.

Major pentatonic melodies. So what style of music can we create with these five core pitches? What triads or chords if any? The melodies would be along the lines of "Shortnin' above, so mostly jaunty songs for kids to sing along with easily. Surely some folk and gospel tunes.

pentatonic melodies
Amazing Grace
Swing Low Sweet Chariot

Want chords with these pitches? Working with five pitches we get two triads; one major one minor. And these are the relative major and minor triads? Yes they are. The core of it all? Yep pretty much, at least through the styles up to when the blues comes along. Chords happen real nice with the seven pitch diatonic scale. We'll get there soon enough adding one pitch at a time.

triads
relatives
diatonic scale
chords

A Yin for every Yang Within the intervals in the major pentatonic scale scale formula we of course quickly discover the seeds of the minor tonality. The minor third interval from A to C is the key. Here are the pitches, this time using the 'flat' accidentals in making up the chromatic group, of C major pentatonic group of pitches morphing into its relative minor, the A minor pentatonic group. Example 2.

chromatic scale
A
Bb
B
C
Db
D
Eb
E
F
Gb
G
Ab
A
pentatonic scale
A
.
.
C
.
D
.
E
.
.
G
.
A
intervals
minor third
whole step
whole step
minor third
whole step
A to C
minor 3rd
.
A to D
perfect 4th
.
A to E
perfect fifth
.
A to G
minor seventh
.
A to A
perfect octave
formula
minor third
whole step
whole step
minor third
whole step

Examine the intervals. The first leap of the minor third from our root pitch 'A' up to the minor 3rd 'C' gives away the tonality. Any group, arpeggio or chord that uses this root / minor third interval is minor. Conversely, root / major 3rd is always major n'est-ce pas? So we can see the exact same pitches creating our two distinct tonalities. While we lose the 6th from the major group, we do gain a 7th, which here is a whole step below or octave root. This is the essential minor or blue 7th of the musics we call the blues.

A place to start. For many of us a guitar players, the minor pentatonic grouping of pitches is where we started our journey into the world of creating the sounds of American music. This next idea is the somewhat ancient European melody that becomes in 1800's America the newer "House Of The Rising Sun." Way later it becomes a #1 pop hit for The Animals in the 1960. Find these pitches and express some built right-in core essential coolness. Example 2a.

Classic line yes? Maybe play it real simple at first. Sing along with your guitar notes. Combine the two and strengthen up knowing exactly where to find the pitch you're hearing, then lean hard on these pitches with practiced confidence. Jazz it up by adding your own voice inflections on the pitches. Then find these inflections on the strings. Really a very simply process, in theory to just 'sing the line play the line.'

These melody notes of the minor pentatonic are the essential basis of much blues music and the blues scale, whose theory follows just below. Strengthen up to be able to count it off and weave and string these five pitches through a few choruses of 12 bar blues and a true cornerstone is laid. One that shapes the foundations of so much good music over our entire recorded history.

audio / vid of the process /

Original forms of music. One aspect of creating this type of minor pentatonic / Native American melody to remembered is that a large number of voices usually sang the same line together, in unison. And while they probably strove to be in tune (?) or not as the case maybe, recordings and 'ear witness' accounts tell a different story. That the 'in and out' of tune quality of multiple voices might be the missing spice to get the full flavor and emotional impact of the melody and the story that it supports and tells.

unison
out of tune

As guitarists, we might try varying types of vibrato and phrasing to dig deeper into these pitches. Do consider researching to check out original Native American performances, whereby everyone is singing the same melody. This multiple voice / pitch quality is probably also found in the early American gospel / early blues singing. That the 'out of tune' quality of intonation, created by many voices raised together in song, just very well might be an integral component of how we recreate the spiritual allure and magic of this historic music today.

vibrato
intonation

7 + 5 = 12 ~ another grouping of five pitches. Already hip to the pentatonic major and minors? Have the scale shape included above in hand? In a couple of different keys up and down the neck? Cool. So then chances are good you understand the math equation too. The seven pitches of the diatonic scale plus five other pitches brings us to a total of 12 different pitches. These make up the chromatic scale. Know what the other five pitches are and their relationship to the diatonic seven?

~ six pitches ~ super theory game changer ~

5 + 1 = 6. Our next evolution in creating our groups of pitches evolves by adding one additional pitch to the five notes of the minor pentatonic color. Turns out that the pitch we need is the one that lives at the midpoint of our perfect octave span. Examine the pitches. Example 3.

chromatic scale
A
Bb
B
C
Db
D
E
E
F
Gb
G
Ab
A
octave midpoint
A
.
.
.
.
.
Eb
.
.
.
.
.
A
A to Eb
augmented 4th / 5th
tritone
A to A
perfect octave span
blues scale pitches
A
.
.
C
.
D
Eb
E
.
.
G
.
A

Minor pentatonic five + one tritone = blues scale. By adding in this octave mid point pitch, also named an augmented 4th or diminished 5th or simply the tritone, the all important core blues scale or grouping of pitches emerges. As the term itself implies, the tritone interval encompasses 'three tones,' or three whole steps. So six frets on one string? Yep, six frets.

Purely chromatic. With this tritone insertion we also gain a bit of purely chromatic color and its two half steps into what was a half step free zone in the minor pentatonic group. Work these pitches over an A minor or A7 chord vamp or a 12 bar blues track and search for the coolness within.

If there was ever a historical home for the American sounds, surely this grouping of pitches would live there. We can easily research and find documentation of these default American blues colors in Ragtime (1890's), early jass (1900's), the blues (1910), Louis Armstrong's jazz (1920's onward), swing jazz (1930's), bebop (1940's) rock n' roll (1950's), blues / acid rock (1960's), electric blues and rock (1970's), disco (1980's ... well maybe not disco) but surely in James Brown's 1980's funk, Stevie Ray Vaughn blues (1990's) and even today in the _________ style (s) of this new millennia. And surely this essential color existed prior to our known written records. How far back is everyone's guess. Is there any real blues-less America musical era?

Adding the tritone. This next idea simply bluesifies the minor pentatonic idea included just above. We blusify by slipping in the tritone into the line. Example 3a.

So very common. This tritone additive is very, very common in any of the blues infused rock and beyond American musical styles. Metalists might surely recognize this rip off from what today has become a metal anthem originally done by British rockers back in '72.' Simply a timeless minor pentatonic idea with a dash of the tritone spice.

A big tritone vamp. Getting momentarily away from things a bit but in this next idea, we give the tritone color a bit more of the spotlight. Here is a very simple yet potentially essential vamp based the interval of a tritone. Something we might hear as a head arrangement, a vamp behind a soloist or an entrance of a intriguing type yet perhaps comical character in theatrical spoofs. Count Basie and the Kansas City sounds of the late 30's and forward grooved hard on this sort of energy. Ex. 3b.

A key theory element. Do you remember the interval formula for the pentatonic scale? And if there were any half step intervals in the formula? Well, there are none and the addition of the one pitch tritone here adds the half step interval to our blues group. Actually two, as we now have chromatically filled in the whole step interval span between the 4th and 5th scale degrees. Hold onto this half step key as we're going to need it momentarily.

Back to the Blues. The blue notes go way deep of course in the American sounds and as such we can use these roots to great advantage in our music. One absolutely cool thing about the blues scale (notes) in nearly any situation is that they can be used as an 'anchor' to ground even the zaniest improvisations. That no matter how far out we go, a honking blue note can and will bring us quickly home. (That is if everyone in the band hears it :)

With roots so deep in our music, the blue notes also gives the listeners of your music, from all walks of life, something familiar to identify with and dig their ears into. And chances are that a hint of the blue color outside its traditional setting will so often bring a smile to those ears it finds to grace.

~ six pitches ~ super theory game changer ~

5 + 1 = 6. As there has got to be a balance for all, our six note minor blues has a six note major version with the addition of the one pitch. In this group the diatonic fourth scale degree is added to the five pitches of the major pentatonic grouping. I call this grouping the 'Americana + 1' scale, as it's more hybrid than set in stone ancient theory etc. Examine its letter name pitches and scale degrees as extracted from the 12 tones of the chromatic scale. Thinking in C major, example 4.

chromatic scale
C
C#
D
D#
E
F
F#
G
G#
A
A#
B
C
pentatonic scale
C
.
D
.
E
.
.
G
.
A
.
.
C

major scale

C
.
D
.
E
F
.
G
.
A
.
.
C

scale degree

1
.
2
.
3
4
.
5
.
6
.
.
8

A pure Americana melody. With the inclusion of Four into the grouping, melodic and harmonic motion to Four becomes a truly official, exciting and uplifting theory destination. For we add the pitch and its major triad built on Four to our palettes. We hear this theory in action in the classic "Oh Susanna." Here presented in C, in 2/4, in an AAB form. Example 4a.

So the major pentatonic group plus a diatonic Four. Now we've the pitches to Four with authority as some have quipped. Next? We add one to make seven.

~ 7 pitches ~ beyond a super super theory game changer ~

5 + 2 = 7. Well, for every Yin there's a Yang so there must be a way to add a tritone color into the major pentatonic color. And of course there is. Same concept, new additive process, super nova complete game changer yet a totally organic evolution of our resource. (Please to remember that we're music theorists here and it really doesn't take a whole lot to elevate our game to the super nova level :)

One pitch two pitch. Turns out to create super nova level theory evolution we need to double up our tritone color. Two pitches then? Yep. So while the 'one pitch tritone octave split' made the blues we go super nova level with a 'two pitch tritone.' Now the tritone interval we are adding becomes the span between the two new notes? Right on and read on brothers and sisters ... :)

And from somewhere out of the chromatic ... In examining the remaining pitches of the chromatic scale, once the major pentatonic group is extracted, there's only one combination of the remaining pitches that solves this two pitch tritone interval requirement, these will become the 4th and 7th scale degrees of the major scale. Examine the letter names. Example 4.

chromatic scale
C
C#
D
D#
E
F
F#
G
G#
A
A#
B
C
pentatonic scale
C
.
D
.
E
.
.
G
.
A
.
.
C

major scale

C
.
D
.
E
F
.
G
.
A
.
B
C

scale degree

1
.
2
.
3
4
.
5
.
6
.
7
8

So to evolve our five note major pentatonic color by addition of the tritone color, we'll add two new pitches whose interval span is a tritone interval. Two notes, three whole steps apart, that when sounded together create musical tritone tension. The additive results create a group of seven pitches whose capabilities, now both melodic and also harmonic, have all been rather just stunning. Compare the two major groups. Ex. 4a.

Stunning? Well yes. How so? By adding the two pitch tritone, designated by the x's in the scale grid above the notation, we've added in two half steps into our grouping and now create the major scale or Ionian mode grouping of pitches. These two groups have the exact same of everything, just different labels based on their histories. Most of the theory discussions in this work create the view from the major scale, Ionian perspective of things.

The Ionian major scale is the primary melodic resource for creating our AmerEuro collection of songs. By far and away. When the pitches are equal temper tuned, this seven note group provides the pitch resource to create all of the arpeggios and chords of functional harmony that so lovingly support and create all of our melodies and as we'll soon see, a whole lot more modally created resource to potentially shape our art.

The minor within. Just as with our pentatonic major and minor groups, our seven pitch scale has the same pairing of tonalities. In chart form, evolving the minor penta five into natural minor seven from the chromatic grouping starting on A. Example 4b.

chromatic scale
A
B
B
C
Db
D
Eb
E
F
Gb
G
Ab
A
pentatonic scale
A
.
.
C
.
D
.
E
.
.
G
.
A

minor scale

A
.
B
C
.
D
.
E
F
.
G
.
A

scale degree

1
.
2
-3
.
4
.
5
-6
.
-7
.
8

Our minor keyed balance is termed the natural minor, Aeolian or relative minor depending on where we find the loop. Relative to what? Well ... major of course. Exact same pitches just a modally created, different whole step / half step interval formula. The theory knowledge in this one paragraph alone is worth the price of admission here as a full understanding of this essential pairing can become and very often does become the basis of all one's thinking.

Major = relative minor = Ionian = Aeolian. So do all of these groups have the same pitches? Indeed they do. Is there a way to theoretically take advantage of all this 'pitch sameness' in the music we create? Indeed there is. We can start the sorting process of these four 'unique groupings with the same pitches' by simply comparing the pitches of the groups and their relation to the 12 pitches of the chromatic scale. Example 4.

chromatic scale
C
C#
D
D#
E
F
F#
G
G#
A
A#
B
C
major
C
.
D
.
E
.
.
G
.
A
.
.
C

relative minor

A
.
B
C
.
D
.
E
F
.
G
.
A

Ionian mode

C
.
D
.
E
F
.
G
.
A
.
B
C

Aeolian mode

A
.
B
C
.
D
.
E
F
.
G
.
A

Four uniquely labeled groups of pitches all with the exact same letter names. Crazy huh? Well it is what it is. So each of these four groups have the exact same pitches? Indeed they do. Are there any other ways we name this particular loop of pitches by using different starting points? Yes there is, for this is one theoretical way into understanding the now ancient modes. We simply create loops within a loop, each unique by the location of these two half steps. Oh, is this where the breakdown of our common scales into two 'tetra chords' can come into the discussion? It surely is.

Gains in a major key with these seven pitches. There's initially three super key theory things now possible with this seven note grouping of pitches. First, we add two half step intervals into our mix which become the fourth and seventh scale degrees. The second key is a fully functioning system of modes. And third, now fully empowered with our seven pitch scale, we're ready to create the diatonic arpeggios and chords.

A half step into Four. We use the first of our two new pitches to create the fourth scale degree. We commonly call this Four, as in motion to Four, when talking chords. This forms the first of our two tetra chords in C major. Here we focus on the half step from E to F. Example 4b.

first tetra chord
C
D
E
F

Here the stepwise direction and intent of 'arriving' at Four? Known in theory as the subdominant, the role the it plays in our music over a wide spectrum of styles is rather vast. Towards the top of this list is this pitch's / chord's position to create a second 'resting place' within our chosen key center. Four is also very often the 'go to' pitch and chord for adding a Gospel spice to the music. (Note Roman numerals to designate chords by their numerical scale degree.)

A half step into One. The second half of our two pitch tritone becomes the leading tone or 'super tonic' of any major key. Often as the penultimate pitch in melodic lines, the resolution or seeking to rest happens as Seven gets pulled up to One by the sheer tonal gravity between the pitches. Here we focus on the natural half step between the pitches B to C. Example 4c.

super tonic
second tetra chord
G
A
B
C

What we gain from the leading tone is the sense of impending resolution and release of aural tension. We often encapsulate this leading tone with its tritone partner in our vanilla dominant seventh chords as shown in the last example. This Five chord is not only the key to directing our local harmonic traffic universe but the catalyst to all points beyond ... at least in a theory sense.

Interesting in that in the addition of our two new pitches, one provides respite (Four) and one provides momentum (Seven). So perhaps needless to say that the addition of both of these pitches to the pentatonic color are crucial to all of the AmerEuro musical sounds we love.

With 7 pitches we gain the arpeggios and chords. Another super colossal advantage to the seven note groups is their ability to create chords. With the seven pitches, we can now build a triad (and way beyond) on each of the seven scale degrees within the groups. Are all these chords the same? Well, yes and no. Obviously the major scale and Ionian mode pitches are exactly the same so their chords are identical. Similar with the natural minor and Aeolian modes? Yep. And if all of these groups have the same pitches then their chords are identical? Well in theory yes.

The no part of this 'sameness' involves the mood of the music we are creating, and that mood is based in its key center. And while the pitches, thus chords are the same, which pitch is the center (tonal) becomes the key to opening that particular universe. For from that one pitch we will measure our interval distances to its brethren pitches, these 'intervals between' determine the moods and character of the sounds we shape to tell our tales.

The following chart spells out the major scale and evolves its pitches into its arpeggio, which is then segmented into the seven diatonic triad. Thinking C major, the chart becomes thus. Example 5.

scale numerical degrees
1
2
3
4
5
6
7
8
C major scale pitches
C
D
E
F
G
A
B
C
Arpeggio numerical degrees
1
3
5
7
9
11
13
15
C major arpeggio pitches
C
E
G
B
D
F
A
C
chord quality
I
ii
iii
IV
V
vi
vii
VIII
triads
CEG
DFA
EGB
FAC
GBD
ACE
BDF
CEG

This last chart is in itself worthy of the price of admission into the Essentials world. All depending of course, but the ability to rote learn to spell any chord that comes along accurately and eventually in a split second is super giant leap for the emerging theorist.

The half steps emerge. This next chart of pitches is all about locating the two minor 3rd intervals of the five pitch pentatonic group and how each is divided into its component pieces; a whole step now designated by the number one, (1) and the fraction one half, (1/2) for the half step interval. We'll use these symbols in describing all of our various scale formulas from here on out. Example 5b.

chromatic scale
C
C#
D
D#
E
F
F#
G
G#
A
A#
B
C
pentatonic scale degrees
1
.
2
.
3
.
.
5
.
6
.
.
8
pentatonic scale pitches
C
.
D
.
E
.
.
G
.
A
.
.
C
pentatonic scale intervals
1
1
minor 3rd
1
minor 3rd
major scale degrees
1
.
2
.
3
4
.
5
.
6
.
7
8
major scale pitches
C
.
D
.
E
F
.
G
.
A
.
B
F
major scale intervals
1
1
1 / 2
1
1
1
1 / 2

Minor 3rd holds the half steps. From the chart above we can see that the two minor third intervals within the pentatonic group formula are broken up into a whole step and half step. Our first half step is between Three and Four. It is this half step motion, along with Four being the same tonic chord type as One, that help to create the sense of 'restfulness' of the subdominant's position within a major scale key center.

In this next idea we get a wee bit ahead of ourselves and jazz things up a bit by simply adding the 7th to each of our triads / chords in the following progression. This idea simply moves stepwise from our tonic One to Two to Three and then by half step to Four. Example 5c.

New sounds here, maybe a new voicing or two for you? The major 7th chord does seem to be making a bit of a comeback in pop music these days. As we'll see in the following discussions, it is where these half steps reside in each of our various groupings of pitches formulas that plays the key role in determining their aural color.

The leading tone. The second minor third interval of the major pentatonic group lives between Six and Eight. This time we flip the split into first a whole step from 6 to 7, then the half step 7 to 8. This last 'half step lead in' creates the leading tone built on the 7th scale degree. This is the second pitch of our two pitch 'tritone within', creating the essential diatonic aural tension of the major scale. Here's two ways of resolving the F / B tritone tension by contrary motion of its pitches to their tonic resting points (4 and 7 to 1 and 3). Example 5d.

no sound

Encapsulate the tritone within V7. Perhaps the most common of places we'll find this tritone tension is within a vanilla V7 chord. For from children's songs to folk, to the blues and into rock, pop, country and jazz, the tritone within V7, properly adorned, is never really out of place. In this next idea we use the open chord form of V7 resolving to its diatonic One chord, here voiced as a 'solid C' with the G bass held over as a common tone creating a second inversion tonic chord. For clarity, the tritone within and its resolution are bared. Example 5e.

A common jazz way. In this next idea we take the same two pitch tritone and jazz it up with the color tones, creating more of a jazz styling for the essential Five / One cadential motion. Example 5f.

This last idea uses common jazz chord shapes to create the cadential motion. We would often find a Two chord before Five, creating the Two / Five 'cell' that opens up harmonic new ground for the evolving guitarist.

The art of ... In using our tritone bearing dominant V7 chord, we can legitimately cruise to any of our 24 key centers, 12 major and 12 minor. While the raw dissonance of the tritone is often too overpowering of a color in some musical styles, used artistically it can, and surely has over the last 500 years or so, been a crucial artistic catalyst whose resolving properties have enabled the musical artist to evolve the harmony, thus expanding the basis of melody, both written and improvised.

Composers often use these half steps as the lead tone to create the artistic sense of direction, what I term in this work as tonal gravity and aural predictability, basically creating the sensation of tension and its release in our music. The idea of controlling this powerful dynamic, especially in improvising musicians, is termed here the strength of the player. The idea of the traffic cop mentioned above is all about the tritone color that lives within a dominant 7th chord, which creates and directs the tension to energize the sense of moving towards a resolution or not as the case may be.

The blues. Of course this tritone dominant chord tension lives at the core of the American blues musical style. The One or tonic chord in a blues tune is most times a dominant type chord (root, major 3rd, perfect 5th and minor 7th), unless the tune is in a minor key. Thus, the encapsulating tritone tension between 3 and 7 is one half of the 'blues rub.'

The other half of the 'rub' is created by the melody pitches we so often play over the dominant blues chord changes. The blue notes are usually the minor pentatonic color with or without a one pitch tritone (see this evolution just above). Minor pentatonic means a minor 3rd, which in our American blues, gets rubbed all the time up against the major 3rd of V7. The blues rub. Are there other 'rub' spots? Yep, but none like this one.

This is the combo that can make our hair stand up? Yep, it surely can. Bring tears of joy to grown man's eyes? Indeed. Theorywise, we love a perfect diatonic world of a melody / chord pitch relationship, but as those in the know often know, 'it ain't necessarily so' and this is my friends is especially so in the blues.

The half step truth in black and white. Of course on our geetars these two essential naturally occurring half step intervals, B to C and E to F, are found in a couple of spots on the fingerboard. But for us, any half step interval is simply one fret away yes? Perhaps then it is also beneficial to see these theoretically locked in letter name half steps on the piano keyboard, as they locate the correct half steps in the keys of C major, A natural minor and their modes in between.

Adjacent white keys with no black key in between? B to C and E to F, simply the natural half steps that are permanently built right into their location of our conventional pianos. These two make for C major / A minor. There's half steps all over this critter, any two adjacent keys. Do examine the keys the next time your near a piano as these are set in stone so to speak, thus the same on any piano, providing a solid 1000 year foundation for our theoretical musings. Example 5g.

 

It must be. Of course it is. If there is an A minor pentatonic scale made with the same pitches as the C major pentatonic scale, then surely is there an A natural minor scale that shares the same pitches as the C major scale? Absolutely. Locate the pitches on the keyboard illustration above. Here are the pitches in mp3 action. Example 5h.

Same pitches / different intervals. As we can see from the chord diagram above the notation that we're using the same pitches to get both the major and minor environments. So as discussed above, it is the intervals between the pitches which create the two tonalities which we conveyed in just four bars. Pretty handy for sure and a simple beginning for a sky's the limit perspective of our creative potential.

Same pitches create other groupings? Absolutely. So if we can work these same pitches from C to C and create the C major scale and A to A for the A natural minor scale, why not create a looping group from each of the pitches? Well, we absolutely can and depending on musical styles, we so often do just that. What shakes loose from this different grouping approach of the same pitches we today term the modes.

These groups go way back in history, having origins in ancient Greece. As we move forward in history, we can hear modal sounds in various cultural and ethnic stylings. In today's cornucopia of musical sounds it is not uncommon to associate the Mixolydian grouping with Celtic music or the Phrygian color with the flamenco sounds of the Iberian peninsula.

flamenco strumming

Most of today's modal system comes to us from this cat Glareanus, who nearly finalized our modern system of modes by adding in Ionian and Aeolian, the most popular 'tavern' modes of his day i.e., 1550's. The next evolutionary theory step will be to equal temper tune the pitches and build all this into a piano forte, so named by its soft and loud key touch capability, creating the 'anything from anywhere' abilities we've enjoyed for the last 300 years or so. Thusly tuned, melodies, arpeggios and chords equally in tune from any of the 12 pitches of the chromatic scale. Since the 1500's or so, the 'rule of 18' spaced the frets to equal temper pitches for cats such as Vincenzo Galilei, master lutenist and composer whose written work survives, is Galileo's the astronomers pop.

~ three in one minor groups ~

Advancing the minor tonal environment. By defining our groups of pitches spectrum with the relative major and minor groups as bookends, we could view the groups in the middle, the modes discussed above and groupings which follow here, as colors that lean towards one end or the other, providing a progression of gradually differing hues of color towards each endpoint. The following melodic groups in one sense are borrowing musical aspects to lean towards the major color end of the spectrum and to spice up and strengthen our natural minor grouping of pitches.

Evolving the natural minor Aeolian group. We initially have two historically common alterations of pitch and interval that we apply to the pitches of our natural minor scale. We can facilitate this evolution process by using our half scales, the tetrachord, which in the modern sense of today is any group of four pitches. In creating these next two groups, we'll simply alter the upper tetrachord of the natural minor scale. Examine the pitches of the natural minor scale's two tetrachords from our root pitch A. Example 15.

number problems

Two tetrachords. Nothing fancy here, we simply divide our eight pitches (with octave closure), into two equal parts. In the following two groups, our lower tetrachord remains the same, providing the stability and essence of the minor tonality. We'll jazz up the upper tetrachord to open up our pitch options for melody and to create stronger, more directionally defined cadential motions.

Harmonic minor / altering one pitch. In our first evolution from natural minor, we raise the 7th up by half step to the leading tone position, in the same sense as with the major scale group. This arrangement, termed the harmonic minor scale, is a rare bird indeed. A one of a kind really as there are three half steps in one grouping within an octave span. Here are their respective pitches. Example 15.

wiki ~ "Sunrise, Sunset"
scale degrees
1
2
3
4
5
6
7
8
natural minor
A
B
C
D
E
F
G
A
1/2 steps
.
1/2
.
1/2
1/2
harmonic minor
A
B
C
D
E
F
G#
A

What we gain with harmonic minor. Three half steps in the one group creates some interesting options in creating melodies. Even right out of the box the group sounds fairly ancient, especially when used over a minor triad. Click the pic to hear some muse.

In the harmony? A real influence is specifically with the Five chord. For with the addition of the leading tone we gain the two pitch tritone interval between the 4th and 7th scaled degrees. This translates into V7 and thus, all of the possibilities of the dominant chord type harmony. Examine the cadential motions in the following lines. Cool with the numbers? Upper and lower case Roman numerals? Five / One in A minor. Ex. 15a

dominant chord type

The V7 is thought to be a more 'perfect' sounding resolution, thanks to the leading tone / half step to our tonic pitch A. All debatable really. Any rootsy vibe organically wants to go with all minor chords. V7 on the last hold perhaps? Yet, there's now some blues hue in the V7 chord; it's two pitch tritone within has the DNA.

perfect

Solid American roots. A nice example of the leading tone in a clear minor melody is "Go Down Moses", the 19th century gospel standard. Here in A minor and starting out with a nice leap of a minor 6th, the line clearly sounds the leading tone / half step resolution at its close. Example 15b.

Know this melody yet? I first learned it in elementary school, imagine that. Learn it here if need be.

full song

Diminished 7th arpeggio ~ diatonic source. Taking full advantage of the major seventh leading tone of the harmonic minor grouping, we discover the only organic, non symmetrical source (soon to follow just below in this discussion) of fully diminished seventh arpeggio and chord. Example 15c.

scale degrees
1
2
3
4
5
6
7
8
natural minor
A
B
C
D
E
F
G
A
harmonic minor
A
B
C
D
E
F
G#
A

For while we've had the three note diminished triad since our evolution to the seven pitch major / minor group, in diatonically adding the seventh we create the fully diminished seventh chord, which in theory and practice becomes a core catalyst to the historical evolution of our American harmony. Examine the distillation of these pitches from A harmonic minor. Example 15c.

fix

Augmented triad ~ diatonic source.

just below in this discussion).

scale degrees
1
2
3
4
5
6
7
8
natural minor
A
B
C
D
E
F
G
A
harmonic minor
A
B
C
D
E
F
G#
A

For. Example 15d.

 

An exotic 'minor within a minor' group. We can also dig into the harmonic group and create an important mode within a mode that becomes one of the core group of pitches used in creating the popular Klezmer style of music. Known for its twisty half steps and toe tapping tempos, Klezmer lines often rely on the cluster of pitches in its lower tetrachord to create its character sound.

We create this group from within the harmonic minor by thinking from a fourth below the root to a fifth above. Fourth below to fifth above. Examine the pitches and a melody. Example 16.

scale degrees
1
2
3
4
5
6
7
8
natural minor
A
B
C
D
E
F
G
A
harmonic minor
A
B
C
D
E
F
G#
A
Klezmer pitches
E
F
G#
A
B
C
D
E

Interesting sound yes? The half steps between tonic and Two, as in Phrygian and Locrian, and then again between Three and Four, as in the major scale, creating the core uniqueness of this grouping. For it surely is a one of a kind.

A second evolution of natural minor. In our next evolution of the natural minor group, we'll again alter another pitch of the upper tetrachord. Needing our tonic and 5th scale degrees intact to maintain our tonal center, and that the 7th has already been altered, we are left with the 6th scale degree, which we now also raise by half step to create our melodic minor grouping of pitches. Compare the three groups. Example 17.

scale degrees
1
2
3
4
5
6
7
8
natural minor
A
B
C
D
E
F
G
A
harmonic minor
A
B
C
D
E
F
G#
A
melodic minor
A
B
C
D
E
F#
G#
A

Almost ... but not quite. From the pitches above, those in the know will see we've only a one pitch difference now between the groups of A melodic minor and the diatonic A major group of pitches. Examine their letter named pitches. Example 17a.

scale degrees
1
2
3
4
5
6
7
8
natural minor
A
B
C
D
E
F
G
A
harmonic minor
A
B
C
D
E
F
G#
A
melodic minor
A
B
C
D
E
F#
G#
A
A major pitches
A
B
C#
D
E
F#
G#
A

A 'tidal' motion. The gradual addition of pitches to the minor groups in a sense is a motion back towards the major scale. Compare the sounds of the letter name pitches from the chart just above. Example 17b.

A classical approach. While not something at all common in the American musical sounds, there is a pure theory of the classical cats that stipulates that in using the melodic minor grouping, we use different pitches depending on the direction of the melodic line. Ascending we want the major 6th and 7th, descending is natural minor. Example 17c.

HBDM p.262

Greensleeves. Might melodic minor be the best of both major and minor worlds combined into one grouping of pitches? This surely seems to be the case for the well crafted 16th century melody "Greensleeves." So again into the wayback we go this time to find a melody line that uses aspects of each of our three minor group variations discussed just above plus a hint of major into one gorgeous tune. Know this melody? Perhaps begin to learn it now if needed. Thinking in A minor. Ex. 17b.

60's guitar master Wes Montgomery had a nice hit with "Greensleeves." Sounded in octaves, the line swings just fine 400 years or so later in a modern jazz setting.

Wes Montgomery
'in octaves'

An important jazz color. The melodic minor group can be a key color player for the evolving jazz artist. Many modern leaning players might also call these pitches Lydian b7, simply a Lydian mode with a dominant blue 7th, which is a key mode found within this melodic minor grouping. Long story short for this discussion here, is that in jazz we often substitute one element for another. This is primarily done with chords of the songs we play. Once the chords are subbed out, our melodic improvisations have these 'subbed' out changes creating new pathways to explore.

Soloing over and through a song's written changes and then finding additional substitution chords to spice things up and evolve the music, all have been a traditional part of the Americanblues and jazz art form since its inception back in the 1880's or so. Probably stemming all the way back to the age old format of theme and variations, the harmony, sounded by single line notes through arpeggios, continues to the rule the day and is the basis of our evolutions over generations.

single note lines
arpeggios rule the day

So if you venture far enough on the jazz path you should eventually bump into the V7b9 chord. Its arpeggio pitches from the 3rd through to b9 builds the fully diminished chord. We'll base many of our chord substitution choices initially on V7, then into the fully diminished chord's properties found in V7b9.

So what many players do is use the melodic minor grouping as they might use the diminished scale, to create lines over similar harmonic structures, tensions and motions. As we'll see just below, the symmetrical diminished color is a very bold and recognizable character. Which down the road, might gradually wear thinner on the ears and art for the advancing artist.

Melodic minor, with its closeness to the major scale interval formula and sound, becomes what I often term a 'softened' substitution choice of the diminished sounds, that when carefully applied can retain much of the diminished colors cool essential colortone tensions without invoking its symmetrical rigidness of character and sound. Thus, melodic minor is just more of a naturally melodic sounding group for substitution that hones closer to the select groups of a particular chords colortones. Here back in the key of C major, in this next idea we grab a snip of the C melodic minor color over V7+5 and resolve to C major. Example 17d.

no sound

Cool with the above motion? While we're not really in Kansas anymore, we can begin to see how the theory generates ways to get out there a bit and back home.

Beyond groups of seven pitches. Numerically getting past this seven pitch group finds us very near the edge of our Americana tonal limits. While there's a couple of interesting ways to go theorywise beyond this point, the music generally created and the ways it is crafted are not something we would ever really hear on the radio, thus beyond our immediate discussions here.

Way beyond. That said, two modern theory methods for 'interesting compositional techniques' that move beyond using our core seven pitches are often termed '12 tone' and 'serialism.' And while jazz cats will find and use all 12 pitches on a fairly regular basis, the compositional properties of 12 tone and serialism is just a whole different way to get there. For in this approach to the pitches we lose our sense of the diatonic and its related tonal center and tonality; the loyalty to a tonic pitch, which essentially bases all our Americana musics.

~ symmetrical groups of pitches ~

Symmetrical groups of pitches. In our symmetrical groupings; the chromatic, whole tone and diminished groups, we create our scales based on symmetrical patterns of the two core scale building blocks; the half step and whole step. Not generally used as the parent scale in composing, an awareness of each of these three core symmetrical groups is helpful in completing our melodic palettes.

While rarely if ever in children's songs or even folk music and its near brethren; in pop, blues and jazz these three colors often create a bit of color for the perfect line or a single chord to complete our musical puzzles. Survey the Stevie Wonder or Beatles song book and you'll discover bits of these three colors deftly woven into many of pop music's most well recognized, crafted, and loved songs of the last couple of generations.

Parallel motion / constant structure. A rather neat feature of really anything 'symmetrically structured' is its ability to smoothly move up and down the neck by its core interval, while retaining its 'theoretical' basis and key center relationships. Adding this theory with the built in, linear layout of fretted stringed instruments, there's some real coolness just waiting to be explored.

parallel motion
constant structure
key center

Symmetrical scale; half steps only. Those that worked through the first two chapters of this section are already well acquainted with the chromatic scale. Constructed exclusively by the half step interval, we rarely see any more that bits of this color within compositions. What we so often do as guitarists is to use chromatic passages or a half step (chromatic) lead in to an important note or chord in the music we're playing. Blues and jazz cats do this an awful lot. With good timing and rhythm, using the half step lead in with a chunk of harmony is one power-ful component in getting things to swing. Examine the pitches. Example 18.

chromatic scale formula
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
letter pitches
C
C#/Db
D
D#/Eb
E
F
F#/Gb
G
G#/Ab
A
A#/Bb
B
C

Ain't that a beauty. Well that's all of our pitches folks, well, one octave's worth anyway, our theory granddaddy of em' all, enharmonic equivalents included at no extra charge :) We can not only extract all of our musical elements from this group but we can create all of our musical elements from each of the 12 pitches. Is this the 'anything from anywhere' idea? Yep. Here is the sound, do sing along to check your vocal intonation. Ex. 18a.

anything from anywhere

How are your pitches as you sing along? It might take a couple of tries but it'll surely happen. Down the road do strive to sing this group from just a starting pitch. No better way to dial in our stereo radar than strengthening to deliver an accurate accapella vocal rendition of the chromatic scale pitches.

Chromatic scale melodies. Notable written melodies created with the chromatic scale are rather rare in our American literature. From 1880's Europe we get the clearly chromatic constructed melody line titled "Entrance Of The Gladiators." Example 18b.

Remember this line? A fairly easy line to quote due to its chromatic nature yes? Pretty much start on any pitch and just move lower while adding in the rhythm.

Chromatic motion. As the name implies, our symmetrical motion will be by half step. So depending on all things considered, up or down the fingerboard and any pitch, lick, ditty, arpeggio, chord or doohickey can be 'chromatically enhanced.' This chromatic idea finds the melodic 'Coltrane's motiv' ascending by four half steps which evolves into a C major bar chord, which continues our ascent before finally resolving in the key of center Eb major. Example 18c.

Did we just span eight major keys in four bars? A to Eb is a tritone yes? Six half or three whole steps? Yep. Sense what moving one melody lick or chord shape by half step might do for us? There's bits of this chromatic motion all over the American sounds.

Tops on this list is probably the half step lead in, that quick slip of the fingers to enhance where we land, that we can use somewhere somehow nearly in every style. Probably essential in blues and jazz, this half step lead in might be the 'easiest trick in the book.' Also for those 'chromatically' inclined, there's of course a safety helmet available for adventurous jammings.

~ the symmetrical diminished color ~

Symmetrical scale: whole step / half step. This pairing of steps combine to create the minor third interval, which we can divide two ways. Commonly known as a diminished or whole tone / half tone scale, its exclusive reliance on the minor 3rd interval places this way to the edge of our minor hued colors.

Diminished scale formula. Looking to the following chart of letter name pitches we see the reoccurring interval pattern whole step (1) then half step (1/2) creating the minor 3rd cell. Repeated four times, the formula closes the loop back to its starting pitch. This repeating pattern is the symmetrical basis of the group. Examine the pitch letter names from C. Example 19a.

scale degrees
1
2
3
4
b5
b6
6
7
8
diminished scale formula
1
1 / 2
1
1 / 2
1
1 / 2
1
1 / 2
letter pitches
C
D
Eb
F
Gb
Ab
A
B
C

And a scale shape. This whole step / half step configuration grouping works fine for creating diminished color melodies over anything diminished. In the brighter tempos of some jazz music, it is oftentimes initially beneficial to have a movable scale shape that naturally lives right under our fingers.

Interesting perhaps is that the symmetrical theoretical qualities of the diminished group also provides a symmetrical fingering shape, even with the guitar's traditional, unsymmetrical perfect 4th / major 3rd sequence of it's 'concert' tuning scheme. Dig the symmetrical diminished scale shape. Example 19b.

Find the symmetry in the scale shape? It surely follows the four finger / four fret potential for our fretboard hand and is potentially blaze-o-matic.

 

Symmetrical scale: half step / whole step. In this pairing of steps we flip the above symmetry to create our second division of the minor 3rd interval. Examine the pitches. Example 19c.

scale degrees
1
b2
b3
4
b5
b6
6
7
8
whole step / half step
1/ 2
1
1 / 2
1
1/ 2
1
1 / 2
1
letter name pitches
C
Db
Eb
E
Gb
G
A
Bb
C

The half / whole symmetry highlights colotones associated with C7, a Five chord type. Using the scale shape just included above, here is a 2 / 5 / 1 lick featuring the diminished scale shape and its pitches in 5th position, as we create a cadential motion with a full run of the diminished color while resolving towards F major. Example 19d.

Compare the two. These two divisions of the minor 3rd interval create two groups of pitches. Examine the letter name pitches. Example 19e.

whole / half step pitches
C
D
Eb
F
Gb
Ab
A
B
C
half / whole step pitches
C
Db
Eb
E
Gb
G
A
Bb
C

Shared pitches. From the above chart we can see the shared pitches between these two symmetrical groups. Highlighted in blue, these pitches spell our fully diminished 7th arpeggio and chord from the root pitch 'C.'

So what about the other pitches in the above chart? Somewhat hidden away are the two other fully diminished 7th arpeggios. And when all combined, the potential and eventual realization that we've really just three different diminished groupings to work with.

Three's a charm. In this next chart we simply extract the three possible combinations that create our fully diminished 7th arpeggios, which we could stack and sound together to create the fully diminished 7th chords. Note that our pitch 'A' natural is enharmonically entered as 'Bbb', the proper fully diminished 7th interval pitch or letter name from the root pitch 'C.' Example 19f.

fully diminished 7th chord
C diminished 7th arpeggio
C
Eb
Gb
Bbb (A)
Db diminished 7th arpeggio
Db
E
G
Bb
D diminished 7th arpeggio
D
F
Ab
B

Numerically we can add all these pitches up and be right back to our ' # of eggs in a dozen', #'s on a clock, pitches of the chromatic scale, i.e., 12. Imagine that, yet again that perfect closure of the pitches :)

Further, that due to the perfect symmetry of interval construction, that in each four note group, that any of their pitches can equally be the root pitch is another feature of what symmetrical interval construction offers. And while these arpeggios could be viewed and are chord inversions, they also function as root position chords within a storyline. So best of both. Examine the pitches and chords within a 'C' diminished 7th chord rearranged to create the four possibilities. Example 19g.

C diminished 7th arpeggio
C
Eb
Gb
A
Eb diminished 7th arpeggio
Eb
Gb
A
C
Gb diminished 7th arpeggio
Gb
A
C
Eb
A diminished 7th arpeggio
A
C
Eb
Gb

Cool huh? Read left to right or up or down, same results. Same theory for our other two arpeggios from the roots Db and D? Yes absolutely. Examine the pitches, 19h.

Db diminished 7th arpeggio
Db
E
G
Bb
E diminished 7th arpeggio
E
G
Bb
Db
G diminished 7th arpeggio
G
Bb
Db
E
Bb diminished 7th arpeggio
Bb
Db
E
G
D diminished 7th arpeggio
D
F
Ab
B
F diminished 7th arpeggio
F
Ab
B
D
Ab diminished 7th arpeggio
Ab
B
D
F
B diminished 7th arpeggio
B
D
F
Ab

Well probably no surprise we went a bit beyond and were heading yet again for the whole tamale. That's the coolness of our theory; its own perfect closure of loop creates and endless number of ways to slice and dice the pitches and still end up with whole tamale. Click the link for full on, dedicated diminished studies discussions.

~ the symmetrical whole tone color ~

Symmetrical scale: whole step / whole step. Our last popular symmetrical scale has only six pitches before closing. So while it is a bit out of place numerically, as we'll soon hear its not your run of the mill six note scale.

We create the whole tone symmetrical grouping of pitches by exclusively employing the whole step interval. Often termed a whole tone scale, we generally associate this melodic group with any of the triads with an altered 5th (b5 / #5). Its character of sound is quite distinct and somewhat hard to tame at times, so just not a common a color overall in our Americana songbook.

When we do hear it in well crafted songs, the whole tone color will often create the perfect set-up chord for what is to come. Heard a bit in pop, blues and jazz, whole tone is cool in both the natural major and minor tonal centers. Examine the pitches from the root pitch C. Example 20.

scale degrees
1
2
3
#4
#5
b7
8
whole step formula
.
1
1
1
1
1
1
whole tone pitches
C
D
E
F#/Gb
G#/Ab
Bb
C

Simple but rather potent. While our interval configuration is quite elementary, its resulting sound and color are anything but. Here are the pitches and a common scale shape for sounding them. Example 20a.

 

In practice. While often handled carefully by composers, improvising composers often come to love the poignancy of the whole tone color in some key spots in the music. Here is one idea for the whole tone being used over V7+5 in the key of F minor. Example 20b.

Whole tone chords. With the harmony, the whole tone color is probably more common in the minor keys as the augmented 5th of V7 also being a common tone minor 3rd of the tonic chord key. It also teams up well with the b9, natural 9 and sharp 9, common dominant chord colors in blues and jazz. In a major key, a most common spot is between One moving to Four. Example 20c.

Cool? The pure theory gets a bit in the way with the enharmonic spelling of the pitches between the chords but surely the 'D#' of one equals the 'Eb' of the other in minor. The motion for augmented 5th in last two bars is chromatic and kind a right out of the pop song "Because" by the Dave Clark Five, which got to #3 on the charts back in '65.' Great wedding tune, nice payday.

Other groupings of pitches? There is a major scale / flat 6 group and its minor Four triad to consider. There's a hybrid blues and the Bebop scale. Lydian flat 7 is a mode of melodic minor and is popular in some circles. If or when our tuning evolves to include quarter tones new groupings will emerge. There's the 'make-your-ownian' mode with any number and intervals of 12 tones.

We might look to the Near East to explore a music whose pitch theory still predates our own modern temperament with its sophisticated harmony of today, whose rhythms are also in set historical groupings, rhythmic modes along side its ragas. There's the global 'folk' community of local music of a thousand cultures to explore. The internet or 'cable' music is packed with variety ... suffice to say that there's always lots to explore for those so inclined.

That's all for this third chapter folks. OK with the idea of groups of pitches? And how they can be extracted from the chromatic scale? In terms of creating the written and improvised American melodies, we surely rely mostly on our two main groupings, the blues and diatonic major / relative minor. Modal and slight pitch variations of these groups plus our symmetrical scales round out a common pitch resource we've now used for a couple of thousand years, if not more.

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Now that we have established this idea of groups of pitches, we'll use this concept in a couple of ways throughout this text; when discovering additional groupings, examining improvisation and creating lines over chord changes and discussing the idea of parent scales, which in reality are simply our 'groups of pitches to create melodic ideas from.'

The idea of groups of pitches will also play a role in our more complex musical techniques such as sequencing, parallel motion, plane-ing and constant structure ideas, all of which also involve pitches and intervals. We'll also use the concept of groups of pitches in more general terms when the idea of a set group of pitches, which forms a perfectly closed and balanced loop, is simply the best way to describe the relationship between the theory and the art we create with it.

So what's next? Now that we have begun to define the exact sets of intervals / pitches we use in crafting Americana musics, we can further understand their role in the music we create. Our next theory step will be to transform our scale groups into their arpeggios. This becomes the intermediate point between scales and chords, our two main compositional components that energize our musical stories.

"If I have seen further it is only by standing on the shoulders of giants."

Sir Isaac Newton
Footnotes:
Appel, Willie and Ralph T. Daniel. The Harvard Brief Dictionary Of Music, p. 221. New York: Pocket Books, a Simon and Schuster Division of Gulf and Western, 1960.
Appel, Willie and Ralph T. Daniel. The Harvard Brief Dictionary Of Music, p. 221. New York: Pocket Books, a Simon and Schuster Division of Gulf and Western, 1960.

(1) Ottman, Robert. Elementary Harmony, First Edition, p. 4. New Jersey: Prentice-Hall, 1970.

(2) Isacoff, Stuart. Temperament ... The Idea That Solved Music's Greatest Riddle. U.S.A. Alfred A. Knopf, New York. 2001. The theme of this wonderful book explores the historical struggle to conquer the process and implementation of equal temper tuning within European society. For those that need to get to the historical core of the evolution of our tuning, "Temperament" weaves a fun, fascinating and researched historical perspective.

(1) Appel, Willie and Ralph T. Daniel. The Harvard Brief Dictionary Of Music, p. 221. New York: Pocket Books, a Simon and Schuster Division of Gulf and Western, 1960.

Aebersold, James and Slone, Ken. Charlie Parker Omnibook. New York: Atlantic Music Corp., 1978. I know this is a troubling stand to take but I felt I had to and as jazz player, I based it on Charlie Parker's compositions in the Omnibook. Find a copy, count the number of tunes, then compare the number of major key to minor key songs. Any real book of popular American song, by a mix of composers, will follow along similar lines in this regard.