~ by the numbers ~ 'simply creating a numerical perspective of pitch and theory ... '
'examining each of our 'pitch positions over a two octave span ... ' 
In a nutshell: Thinking the pitch letter names of the diatonic and chromatic scales 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 :) 
The tricky part is that each of our essential components have a bit of a different counting system but the good news is that once a letter name is chosen to be '1'. It stays one. For example, in the key of 'A' is always '1' :) Scales are thought of as 123 not A B C, arpeggios are 135 not A C E, triads are also 135, rhythms are 1234 2234 3234 4234 etc. Then there's the ratios for our intervals; the 2:1 octave basis of all, 3:2 of the perfect fifth to get the wheel to create new pitches a turnin. 'The '440' frequency pitch of today's tuning note, 'A' 440, and its detune to 432 and beyond even, making new musics. 

So not quite on and on depending (unless you be a jazz leaning artist) but for those so curious for sure, that any of these last ideas can probably become a thesis in academia is cool to know. The knowledge base is deep all is related to one another, forming the loops within our Americana musics. 

Jazz leaning artists. Just to note that this numbers approach can get applied to the shedding method too, ensuring that all of the reasources are fairly available over the first 12 frets or so. Scale shapes can be numbered into a loop of 5, there's working with a metronome (really for everybody) there's numbers for the chord voicings; 1 5 b7 3 5 8 barre chord, interval studies; major scale in 3rd's, chord progressions so now, on and on might be true, at least for the forseeable :) 
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 :) 

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

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 
Scale numbers. A supereasy way i 
Arpeggio numbers. A supereasy way i 
Triads / color tone numbers. A supereasy way i 
Progressions and cycle numbers. A supereasy way i 
Intervals numbers. A supereasy way i 
Science math. A supereasy way i 
Time numbers. A supereasy way i 
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. 

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

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 ... 

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. 

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. 

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. 

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. 

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. 

1 

transition into the 2nd octave / the melodic and harmonic color tones 

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. 

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. 

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. 

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. 

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. 

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. 

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. 

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. 

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. 

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. 

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 

transition into the 2nd octave / harmonic color tones 

"I have to be my own teacher, curious to know the reason for things." 
Footnotes: 
(1) Isacoff, Stuart. Temperament ... The Idea That Solved Music's Greatest Riddle, p. 4042. 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 
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D 
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E 
F 
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G 
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A 
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B 
C 
non diatonic pitches 
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C#/Db 
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Eb 
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Gb 
Ab 
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Bb 
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. 