~ by the numbers ~

'simply creating a numerical perspective of pitch and theory ... '

the theory of 'atfaw'
a shedding perspective
a syllabus of musical colors
mostly a jazz thing
a modern guitarist
soloing over one chord

'examining each of our 'pitch positions over a two octave span ... '

.

In a nutshell: Thinking the pitch letter names are already known to the reader, a supereasy way into our music theory is to simply begin the process of matching pitch letter names with a corresponding number. 'C' is now also #1 etc. That's the easy part :)

equal tempered pitches

fret spacing

Americana musics

The tricky part to this easy way is that each of our essential components; time, scales, arpeggios, triads and colortones, various progressions and cycles, the intervals and the way deeper science math of ratios and frequencies, each have a unique counting system. Of course they're all related to one another, forming a loop of ideas that bases all our Americana musics.

equal tempered pitches

fret spacing

Americana musics

Why do? Numerical theory allows us to project any idea onto any pitches of any music, into any key scheme in any style of the past, present and forward. So, anything from anywhere? Yes but we have to flip around the AFA telescope view to get the right focus here. For here are view is all a numerical center :)

AFA

equal tempered pitches

fret spacing

Americana musics

Eggs in a dozen? 12. So the trick to the whole tamale turns out to be

AFA

equal tempered pitches

fret spacing

Americana musics

One through #15. This goofy looking chart stage left is the numerical linking to the original intent of this 'by the numbers' discussion. Based on an idea sparked to life during a lesson I took with longtime Alaska jazz guitar ally Mark Manners, in its writing each of our numerical positions within a two octave chromatic scale are examined. The half dozen or so letter / number swaps listed above became the narrative basis for discussion.

Time numbers. A supereasy way i

time

equal tempered pitches

Scale numbers. A supereasy way i

time

equal tempered pitches

Arpeggio numbers. A supereasy way i

time

equal tempered pitches

Triads / color tone numbers. A supereasy way i

time

equal tempered pitches

Progressions and cycle numbers. A supereasy way i

time

equal tempered pitches

Intervals numbers. A supereasy way i

time

equal tempered pitches

Science math. A supereasy way i

time

equal tempered pitches

Time numbers. A supereasy way i

time

equal tempered pitches

The accomplished groovinator. Then chances are you know why rock power chords are so powefull. of power chords

to set the whole thing in motion and keep it there. Cool. You probably tune your gitfiddle to concert tuning; EADGBE and have some licks under you fingers. Now would be the perfect time to retune your ax and find some riffs in open G. Takes about 2 seconds and if nothing else becomes a great way to work out gallops with the strum hand.

evo power chords / gear
gallops
Footnotes:
(1) Isacoff, Stuart. Temperament ... The Idea That Solved Music's Greatest Riddle, p. 40-42. USA Alfred A. Knopf, New York. 2001
(2)Aebersold, Jamey and Slone, Ken. The Charlie Parker Omnibook. New York: Atlantic Music Corp., 1978.
(3) Ottman, Robert. Elementary Harmony, Second Edition. New Jersey: Prentice-Hall, 1970
4) Ottman, Robert. Elementary Harmony, Second Edition. New Jersey: Prentice-Hall, 1970

'It don't mean a thing if it ain't got that swing ...'

Duke Ellington

~ by the numbers ~

' ... simply creating a numerical perspective of pitch and theory ...'

fiene infused stereo guitar lesson I was taking a few years back I realized that I had a

If Ab is the b9 of G7 waht is it around the cycle of 5'ths

Ab is b5 of D7

maj7th of A etc

Five color tones ? Db, Eb, Gb, Ab, Bb ...

C G7 D7 A7 E7 B7 F7 C7 loop

C# / A7

D# / B7

F# / D7

G# / E7

Bb / C7

 

her keen sense of the numerical representation of the pitches. As my mentor sorted out the theory I was struck by this incredible sense of a puzzle, with just so many pieces or maybe not ...

tuning
intervals
octave
half steps

In a nutshell. In a caffiene infused stereo guitar lesson I was taking a few years back I realized that I had a rather keen sense of the numerical representation of the pitches. As my mentor sorted out the theory I was struck by this incredible sense of a puzzle, with just so many pieces or maybe not ...

tuning
intervals
octave
half steps

In writing this section I learned that even by understanding the numerical theory of the music, integrity to musical style becomes the defining point of the numbers. And with 100 years or so of American music history, surely now we have a solid handful of generations that each in their own way described the style of their day in the music they learned and passed on. The songs they wrote capturing their era in time.

tuning
intervals
octave
half steps

So on one hand we're numerically limited ... ? Just the twelve unique pitches whose sequencing can always perfectly close back upon its origins? Ideally knowing of this numerical limitation helps us understand and create a fairly complete picture of the resource.

tuning
intervals
octave
half steps

And on the other hand we have a love of music and to be creative. Through the writings of Miles Davis I now personnally understand that by playing music over a period of decades, our creativity infuses all of our life with music's natural energies to build community. That there's a potential 'oozing of the creative' into our music that is readily absorbed through physical rhythms and sound, often energizing the creative in the hearts and minds it touches.

tuning
intervals
octave
half steps

I'm always thinking about creating. My future starts when I wake up every morning ... every day I find something creative to do with my life.

Miles Davis

Explore. So in these 'by the numbers' discussions we get to put each of our numbers on the map one by one, and in doing so create a broad view of the resource with all things in one mixing bowl. Organized chromatically, by half steps we ascend two full octaves and a wee schosh. So just go on and 'pick a number, any number and off you go. Or read on below the links for additional ideas and applications of theory by numbers.

chromatic
loops of pitches
octave
half steps
1
#1
b2
2
b3
3
4
#4
b5
5
#5
b6
6
b7
7
transition into the 2nd octave / the melodic and harmonic color tones
8
b9
9
#9
-10
10
11
#11
12
b13
13
b14
14
15
#15

Ideas for linking to other sections. Additionally, these 'by the numbers' discussions take on a couple of unique rolls of our music and it's theories. For instance we use the numbers of math to understand; our ways of tuning, to measure the interval distance between pitches, to label our scale, arpeggio and chord degrees. We number our chord progressions and as a way to organize a discussion about what common theory elements we find on each position within a two ocyave chromatic scale.

tuning
intervals
octave
half steps

Exploring each one in turn, we're looking for each interval's essential aspects and prominent stylistic contributions. And while a lot of what is included is probably now cliche, taken all together we ultimately create a library of ideas that have helped define the American sound of the last 100 years or so.

intervals
cliche

What we gain. Hopefully a couple of things. First, an overview of what's commonly available within a key center while thinking musical style. This can help us find that new thing to energize our own development. We also get to add another piece to the 'number of pitches / musical style' continuum puzzle which centers this entire work, to empower us with the theory to modernize our own playing over the course of our careers.

key center
number of pitches / musical style
evolution of the artist

Anything from anywhere. The ultimate ability to improvise 'anything from anywhere' in brighter tempos often flows from this line of numerical thinking. That any pitch, scale, arpeggio or chord can be represented numerically in relation to its placement in the music, helps us to project any and all of our theory and artistic ideas from any of our 12 pitches of the chromatic scale.

improvisation
anything from anywhere
scale / arpeggio / chord
12 pitches

Key center and proximity to the tonic. In the following linked discussions, we'll be examining each of the numerical positions available from our chromatic scale in relation to our chosen tonic pitch C, in the key of C major. Thinking of the pitch C as the center of our local musical universe, thus the number One (#1), each step by half step brings new ideas in regards to tonal gravity and it's cousin, aural predictability. Which when paired up together brew up the juice of well crafted art.

tonic
tonal gravity
aural predictability

Transition to our second octave / color tones. As we numerically move from eight (8) to flat nine (b9), we cross into a second octave. And while the pitch letter names of course remain the same, our intervals evolve from simple to compound. This new designation of compound intervals reminds us to include an octave in our interval measurements.

color tones
intervals

The discussions of our simple intervals, found within the first octave span, are for the most part concerned with melody characteristics. And while the triad / chord degrees are discussed, our resouces within the octave mainly include, our diatonic scales and modes, their interval studies and triadic and 7th chord arpeggios. Of course the five essential blue notes live in this forst octave also and are explored in proper turn.

simple intervals
diatonic
blue notes

Our compound intervals, beyond this first octave, will now lean our discussions more towards the harmony. We still have some melodic aspects; our wide interval studies and of course the extended arpeggios, but in this second octave we discover our chordal colortones.

compound intervals
harmony
wide interval studies
chordal colortones

These colortones are simply the chordal extensions we find when adding additional pitches to the more triadic harmony of the folk and rock stylings, moving towards a more pop and surely a jazz sounding direction. And as our American jazz is historically based in the blues core, we'll commonly find these same upper colortones spicing up the popular blues harmonies we often hear today.

musical styles
triads
blues harmonies

Lastly, enharmonic equivalents. Those in the know of course know about these critters. No other aspect of pitch discussions can goof up our theory discussions as much as 'one pitch with two names.' The why and how of our numerical system is all about a sort of triangulation of the theory. For when one numerical version of a pitch is used a cool way in one style, and then takes on a new role with a different numerical identity in another ... as theorists we can strive to be more consistent by using the numbers.

enharmonic equivalents
triangulate the theory
theory / art
shake loose

Pick and click. So potentially a couple of rather key potentials provided by learning to create a numerical perspective of the resource. Just pick and click and off ya go ... pick and click and off ya go ... :)

1
#1
b2
2
b3
3
4
#4
b5
5
#5
b6
6
b7
7
transition into the 2nd octave / harmonic color tones
8
b9
9
#9
-10
10
11
#11
12
b13
13
b14
14
15
#15
"I have to be my own teacher, curious to know the reason for things."
Laurindo Almeida
Footnotes:

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

(2)Aebersold, Jamey and Slone, Ken. The Charlie Parker Omnibook. New York: Atlantic Music Corp., 1978.

#'s

1
#1/b2
2
#2/b3
3
4
#4/b5
5
#5/b6
6
b7
7
8

diatonic pitches

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

non- diatonic pitches

.
C#/Db
.
Eb
.
.
Gb
Ab
.
Bb
.
.

C up to C# augmented unison 1 .5 sharp one
C up to Db minor second 1 .5 flat two
C up to D major second 2 1 two
C up to D# augmented 2nd 3 1.5 sharp two
C up to Eb minor third 3 1.5 flat 3 / blue 3rd
C up to E major third 4 2 major third
C up to F perfect fourth 5 2.5 fourth
C up to F# augmented 4th 6 3 sharp four / tritone / blue 4th
C up to Gb diminished fifth 6 3 flat five / tritone / blue 5th
C up to G perfect fifth 7 3.5 fifth / dominant
C up to G# augmented fifth 8 4 sharp five
C up to Ab minor sixth 8 4 flat six
C up to A major sixth 9 4.5 six
C up to A# augmented sixth 10 5 sharp six
C up to Bb minor seventh 10 5 flat seven / blue 7th / dominant 7th
C up to B major seventh 11 5.5 major seventh leading tone
C up octave to C octave 12 6 octave
C up octave to C# augmented octave 13 6.5 sharp octave?
C up octave to Db minor ninth 13 6.5 flat nine
C up octave to D major ninth 14 7 ninth
C up octave to D# augmented ninth 15 7.5 sharp nine
C up octave to Eb minor tenth 15 7.5 minor tenth
C up octave to E major tenth 16 8 tenth
C up octave to F perfect eleventh 17 8.5 eleventh
C up octave to F# augmented eleventh 18 9 sharp eleven
C up octave to Gb diminished twelfth 18 9 diminished twelfth
C up octave to G perfect twelfth 19 9.5 twelfth
C up octave to G# augmented twelfth 20 10 sharp twelve
C up octave to Ab minor thirteenth 20 10 flat thirteen
C up octave to A major thirteenth 21 10.5 thirteenth
C up octave to A# augmented thirteenth 22 11 sharp thirteen
C up octave to Bb minor fourteenth 22 11 flat seven
C up octave to B major fourteenth 23 11.5 leading tone
C up 2 octaves to C major fifteenth 24 12 octave
C up 2 octaves + 1/2 step to C# augmented fifteenth 25 12.5 sharp fifteen