~ 15 ~ Fifteen ~

'ascending our tonic One for two full octaves to perfect closure ...'

the core of the theory the most popular spot for natural 11in voice and guitar examples also on every page

 

 

In a nutshell. Two full octaves and perfect close. In theory, a perfect nut in a perfect shell.

So why 15? Reaching the number fifteen in this section of this theory primer we have ascended to a point two full octaves above our starting pitch. I've never seen this number in any chord symbol anywhere in the American songbook. That anything theory wise Fifteen would be the same as One and Eight.

And again of course, no real surprise here. So again up an octave and leave it out? Pretty much; Ten, Twelve, Fourteen and Fifteen, all share a this obscurity. Examine the pitches and their corresponding numbers of two full octaves thinking C major. Example 1.

scale degrees
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
two octave C major scale
C
D
E
F
G
A
B
C
D
E
F
G
A
B
C
arpeggio degrees
1
3
5
7
9
11
13
15
13
11
9
7
5
3
1
two octave C major scale
C
E
G
B
D
F
A
C
A
F
D
B
G
E
C

Again the perfect closure. And again the rote learning method of repetition. Wonderful think about rote learning something is that we'll generally only have to do the work one time and we'll have it forever :)

Symmetrical Dorian loop is perfect. Another way we can get clear up two full octaves to 15 and perfect closure is by creating an interval loop with minor 3rd / major 3rd / minor 3rd / major 3rd till our loop closes back upon its starting point. Examine the pitches as this symmetrical interval sequence creates Dorian minor. Thinking D Dorian minor. Example 2.

scale degrees
1
.
3
.
5
.
7
8
9
.
11
.
13
.
15
minor / major 3rd's
D
.
F
.
A
.
C
.
E
.
G
.
B
.
D

Any Dorian grouping in minor and major 3rds? Will any Dorian grouping filtered thus arrive with perfect closure up the two octaves? Could very well be. Is there a yang to this yin or vice versa? A perfect symmetrical loop of alternating major and minor 3rd's that creates and sounds a more major grouping? There is. Any guesses as to it's tonal character and theory labeling?

wiki ~ Yin / Yang

What Charlie Parker heard? Rumor has it, I mean I know I read this somewhere, probably Bird Lives, that Mr. Parker, while working over the changes to "Cherokee" warming up before a gig, discovered by himself the upper most reaches of our diatonic arpeggio. Perhaps in simple form something like this. Example 3.

wiki ~ "Cherokee"

Arpeggiating the Two chord. So Bird got his arms completely around the diatonic resource by arpeggiating the Two chord? Yep. That is, the diatonic resource of his day of course. For Mr. Parker as an up and coming player knew Coleman Hawkins, who pioneered this arpeggiated style idea for creating improvised melodic line over every chord change the song. .

Within a few years, this new approach became a game changer for American jazz. Mr. Hawkins' solo on the standard tune "Body and Soul" set cats on a new pathway that Bird not only couldn't resist, but followed into the land of legends, show biz stardom and beyond.

wiki ~ "Body And Soul"

Isn't this last musical idea a bit vanilla for the likes of Hawk and Bird let alone any jazz artist? Sure is. Just that this plain old giant vanilla arpeggio covered all the diatonic pitches and maybe just sounded more as if it wanted to resolve. In doing so it initiates a stronger sense of forward motion and its attendent tonal gravity; the idea of going towards something, somewhere in the future using usical sounds. Doesn't even the ii-7 arpeggio do this? Yep but not like the full running of the chord.

Mr. Parker not only extended ii-7 to include Nine, Eleven and Thirteen, their half step alterations and blue notes hues as did Mr. Hawkins, Mr Charlie projected all of this on nearly every chord of every tune at twice or beyond the usual tempo for his times and hardly if ever missed a beat.

V7 color tones and the blue notes. Now take all this diatonic Two chord arpeggio resource and swap out or pepper in or after it any of the possible combinations of V7 color tones and their blue notes. For around these times, in the 1940's, the sleeker Two / Five cadential motion truly becomes the chord cycle that can easily move around chord and key wise at the accelerated tempos of bebop.

Then as musicians ourselves we can begin to approximate Parker's contributions. In learning to perform his music, the bebop of the 40's, we each realize the strength of the player necessary to create the lines of bebop. And off to the shed we go.

So is bop the top? For many reading here it sure is. For the performance of the music demands top chops at blistering tempos. It swings in a new way for advancing players, and sets the tools in place to advance to the more polytonal cycles than diatonic chromatic. Chances are bop players can technically and professionally handle any improvisational gig.

So scour around to find then flip open the Charlie Parker Omibook to any page and discover his fully chromatic yet exclusive (?) diatonic approach to soloing over the changes. Did Parker explore every nook and cranny of the diatonic pie? The idea of anything from anywhere within an essentially 12 pitch diatonic realm?

What John Coltrane heard? So in working through the theory in the above manner we can project the Hawkin's / Parker idea through the b9 theory filter as exhausted by John Coltrane in the decades which followed. Ex. 4.

This last idea was created by arpeggiating just the Two chord associated with the four, Two / Five cadential motions associated with the V7b9 / fully diminished 7th chord. Sounded from most out to most in, we simply gravitate to our tonic center via the minor 3rd interval of the fully diminished 7th color.

Of course Coltrane added in V7 to each of these to include; color tones both altered and diatonic, cliche sorts of character sounding blue notes and licks (so as to distinguish the notes from simple chordal altered color tones), and super charged the velocity of the notes and musical lines beyond anything anyone imagined was even possible :) The results come to us today known as 'sheets of sound' and historically center around 1957.

Review and forward. Seems as if we found a few things in 15 anyway. Not much theory really except using the closure as the top of the diatonic arpeggio utilized to extend the tonal range of our Americana sounds. Next up, the perfect symmetry to arrive at #15 and how this new loop of pitches opens new doors for exploration.

"Knowledge is the most precious treasure of all things because it can never be given away, stolen or consumed."

Sanskrit proverb
1
#1
b2
2
b3
3
4
#4
b5
5
#5
b6
6
b7
7
8
b9
9
#9
-10
10
11
#11
12
b13
13
b14
14
15
#15
Footnotes:

(1) Isacoff, Stuart. Temperament ... The Idea That Solved Music's Greatest Riddle, p. 40-42. USA Alfred A. Knopf, New York. 2001

(1)Duffin, Ross W. How Equal Temperament Ruined Harmony, p.32. USA W.W.Norton and Company, NY, New York. 2007.
(2)Aebersold, Jamey and Slone, Ken. The Charlie Parker Omnibook. New York: Atlantic Music Corp., 1978.

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