~ loops of pitches ~

~ tritone through the octave ~

'discovering the perfect closure of each of the intervals and what they create ... '

.

... just picking up here where we left off on page one of this discussion titled loops of pitches.

Loops / the perfect fifth / Five. So named perfect simply by nature of its aural clarity, the sounding of the perfect fifth has often been the herald of great events in our histories for as far back as we can go in our written and collective memories.

As this interval is nearest to our octave in purity of sound, it'll come as no wonder as we proceed through these studies, just how heavily we lean on this pitch. For the perfect fifth interval is the key catalyst for so many of the essential events within our AmerEuro musical styles and sounds.

Reach for the stars. A most familiar melodies built on the perfect 5th interval encourages us to reach out to the heavens above. It also could very well be one of the first melodies we ever learned growing up. I often segue into this one when working if the little peeps come to say hi. So often to their great surprise and wonder that they recognize the tune and can sing along with my playing. Sing this first measure of the perfect fifth interval pitches that represent the penultimate consonance of our musical intervals, from antiquity to our modern day equal temper tuning. Example 1.

The cycle of fifths. A familiar melody to sound out? Those so inclined and fortified, consider running the last four bars through each of our 12 major key centers. Using the opening perfect fifth interval of the melody just above, we can move successively by perfect fifth's and create our cycle of 5th's. This visual arrangement of the 12 pitches of our musical system is one we'll see and use many times to organize our studies. Examine the graphic and the music. Example 1a.

.
C
G
D
A
E
B
Gb
Db
Ab
Eb
Bb
F
C

A six and change octave span. As we locate our cycle of fifths pitches on the grand staff, the pairing of our treble and bass notation clefs together, we encompass the core six and change pitch range basis which we build into the seven octave span featured in the '88' keys of the piano keyboard. For guitar this translates to a very, very solid E to E for most acoustics, and well beyond to a full fourth octave closure with access and a bend.

Loops / perfect 5th / minor / Scarborough Fair. If all of our musical resources somehow seem even yet more poignant in the minor tonality, the perfect fifth still remains the true traffic cop of directing our musical journeys. The power of the perfect 5th is epic in the minor key. Example 1b.

Remember this melody? Note the perfect fifth leap in pitch into the second bar? As perfect a melodic cell as any ever written? That's the theorist in me talking. Scarborough Fair was a big pop hit for Simon and Garfunkel back in the 60's, maybe time for another rendition ...? Oh, cool with the 3/4 time?

Loops / past halfway / inverting intervals. Now that we're past the halfway point in examining our intervals within an octave span, (remember that the tritone divides the octave perfectly in half), we can add an interesting property to our intervals. In musical terms we say that each of our intervals can be inverted.

By basically flipping them upside down, i.e., inverting, we of course can find the same letter named pitch by moving in the opposite direction from our chosen starting point. We can measure the distances by simply counting the lines and spaces on the staff or even using our fingers and toes to help count the pitches.

Up a perfect 5th = down a perfect 4th. For example, we can move from middle C up to G, which is a perfect fifth, or C down to G which creates the interval span of a perfect fourth. Example 1c.

Why we invert intervals. Inverting intervals helps us in a number of ways. It provides variety, helps in transposing from key to key, in shaping lines to fit registration for melodies, chords and different instruments as well as in generating new chord voicings.

In addition there is the theory side of inverting intervals and that knowledge of the process might just shake something loose for you in your own creations. For we just never know where the next coolness is going to come from.

Interval studies. Motivated players often include various intervals studies into their core training to simply help get the resources they need completely under their fingers. Of course like many aspects of our musical development aside from theory knowledge, these are longer term shedding exercises that develop by necessity and morph on their own as our own sound emerges.

I'd imagine that anyone who wanted to tear it up with their single line playing would explore these ideas at some point. Folk artists might use these interval study ideas in training their voice. Especially in working on their vocal harmonizing chops. In this next idea, we use the interval of the perfect fifth and diatonically filter it through the pitches of the Ionian mode / major scale. Example 1d.

Essential challenges. The above exercise is not easy to play. If it is easy for Ya, speed up the tempo. For those so inclined, the interval studies become a sort of second tier depth in the preparation for the improvisatory nature of the American musical styles. For jazz players they are probably really a must nowadays. If for no other reason than to thoroughly learn the instrument, its pitches and localized key centers as well as developing the chops to play the wider interval melodies of today's modernista.

For at the historical core of the American sound is the timeless human conversation of call and response. Spiced up with the theme and variations idea and improvising over and or and through the harmony, the interval studies are a sort of calisthenics that strengthen up our vocabulary and spontaneous abilities in the prep-aration to negotiate composing music in real time.

Root / fifth melodies. The idea of combining the perfect fifth with melody notes is not all too common but it is in the literature and can be a very powerful sound. Blues rocker Duane Allman does this a bit as does jazz man George Benson, who sometimes adds a fifth between his octaves to turn up the heat a wee bit more. Example 1e.

Root / fifth chords. As the overdrive and sustain gear evolved in the 80's and forward, the number of pitches in the power chords were reduced to ease up on the amount of pitch processing, creating cleaner distortions. Root and 5th is the staple for all kinds of coolness. Example 1e.

guitar gear
jacmuse
link to overdrive sound looper created file / pitches go across and up and down

Perhaps needless to say, these two note chords run through a pedal or two and stack can create a real roar. Their sleekness encourages quickness, both up and down and across the strings directions.

Loops / the minor 6th. The minor sixth interval loop closes upon itself in three quick leaps. As an integral part of the minor tonality, the minor sixth provides a poignant and somber touch to minor tonal environment. A crucial component of the minor Four chord, this interval also creates a nice suspension, typically resolving by moving downward to the 5th of our tonic key, so b6 to 5.

Here are the three leaps to span the octave. Do note the enharmonic spelling between the pitches of the second and third measures below. That Fb and E natural are termed enharmonic equivalents. Example 2.

One powerful interval. The emotional character of the following melodic idea is in a large part based on the interval of the minor 6th. Even without the harmony or bass line for support, the artistic and emotional intent of the line kinda just jumps right out. One of my own melodies from wayback, normally in more of a samba 2 feel, I wrote it for a dear friend Sky, who was having a blue kind of day. Here presented with a bit more poignancy as in a ballad. Example 2a.

The minor 6th / the leading tone and natural 9. Theoretically this last line combines some interesting elements. As our entire minor tonality is comprised of a rather wide variation of pitch combinations; the natural, harmonic and the melodic minor groups of pitches, its crucial core remains centered between our root pitch and the minor 3rd above. Everything else is pretty much negotiable, like most things in the American fabric of sounds. So in the above melodic line, by including the minor 6th, leading tone and natural nine together our overall parent scale for this section of the song becomes the harmonic minor grouping of pitches.

In the bridge. In this next melody idea the minor 6th interval opens up the bridge section of the composition. As the 'A' section pitches stay within a fifth, the sounding of this minor 6th is quite effective. Ex. 2a.

This last melody is based on just a 'wisp' of a motif that I learned from a friend here in Alaska years ago now. She grew up on the Yukon River and her grandmother used to sing the song to her as a child.

Loops / the magical number ( # ) 9. So an interval leap up a minor 6th / down a major 3rd involves the same letter name pitches. I'm not sure why this happens but something mathematically occurs with intervals and their inverse. Each of our intervals within the octave span, when identified by number, when added to their proper inverse combines to equal nine. Examine the following chart. Example 2c.

interval motion up
interval motion down
9
minor 2nd
major 7th
2 + 7 = 9
major 2nd
minor 7th
2 + 7 = 9
minor 3rd
major 6th
3 + 6 = 9
major 3rd
minor 6th
3 + 6 = 9
perfect 4th
perfect 5th
4 + 5 = 9
augmented 4th
diminished 5th
4 + 5 = 9
perfect 5th
perfect 4th
5 + 4 = 9
augmented 5th
diminished 4th
5 + 4 = 9
minor 6th
major 3rd
6 + 3 = 9
major 6th
minor 3rd
6 + 3 = 9
minor 7th
major 2nd
7 + 2 = 9
major 7th
minor 2nd
7 + 2 = 9

Crazy huh? We only mention it here in so much as it is a cool discovery for sure, or was when when I found it 30 some odd years ago. Imagine that. Also that as a self check when calculating music and math numbers, thanks to the perfect closure of equal temper tuning and our basic system of theory and organization, we'll find this kind of perfect closure of numerical magic happening in lots of cool ways. This is just one of many. Here is the musical sound of the above chart. Example 2d.

Loops / the major 6th. A joyous leap like no other in the American sounds, the major sixth holds a cherished position of our intervals. Jumping into the wayback machine, this next melody goes way back indeed into the American book of popular song. Its jaunty air is in good measure created by the major 6th interval, a core pitch within the major pentatonic color. example 3.

Remember this line? "Shortnin' Bread" is the kind of melody that can go right to the core of American swing. I firmly believe that similar melodies, being part of the public school music/band curriculums since the 1900's, are surely the melodies that so many of our heroes played as kids in school. Further, that from these core lines the magic of our rhythmic swing in all of the styles of American music has evolved.

I've added in the major pentatonic scale shape for folks new to guitar. This one shape can yield a lot of good melodic jamming. Start by getting it under your fingers and finding "Shortnin' Bread." Do work at the rhythm, capturing the joyfullness in the line as generated from the major pentatonic color.

Again the idea that this melody can be equally projected from each of the 12 pitches of the chromatic scale. So for those so inclined, do shed this melody by ear through all 12 major keys and then maybe look to quote it in your next solo :)

Loops / major 6th / home of the relative minor. We can also find or locate the relative minor scale from the major sixth degree of the major pentatonic and major diatonic scales. There's just a natural warmth, balance and power to how the major 6th sits in the major tonality that tells us there surely must be more to explore from that point into a new dimension. And sure enough we find the yin-yang portal pitch :)

portal

So while the intervals / scale formulas in creating the two groups must shift, their letter name pitches as shown in the following chart, remains just the same. Ah, the ancient looping modal magic of it all :) Examine the following chart of letter name pitches pairing up our relative major / minor groups of pitches.

scale degrees
root / 1
2
3
4
5
6
7
8
C major scale
C
D
E
F
G
A
B
C
A minor scale
A
B
C
D
E
F
G
A

In composition. This pairing is all too common in composing music. Its probably the easiest way to go as the same pitches will create the essential two part, major minor emotional environments. There are classic songs in each of our styles that pair these two colors. 'Summertime' probably tops the American list. Into the wayback yet again to discover the song "Greensleeves", a hybrid pairing of relative key centers.

Loops / major 6th chords. This interval also lends itself well to coloring both our major and minor triads. We often find the major 6th chord in the 'jump' blues and jazz styles. With an added 9th, thus heading towards quartile harmony, we also achieve a nice, bright and tight colorful chunk of harmony which can feature the tonic pitch in the lead. This tonic 6/9 chord shape often being essential for the chord melody players. Example 3b.

These relatively easy (?) chord shapes come in handy when we want to get a bit of 'jump' in the music. The 6 / 9 coloring is a bit broader sounding in this register and the root pitch is optional, especially if you're working with a bassist, keys etc. The 6/9 is additionally handy in its ability to move latterly up and down the neck, what is often termed planing or parallel motion, potentially adding rhythmic drive as our artistic motors determine.

Loops / minor 6th chords. There's a solid pitch motion to jump start this part of the discussion. Its often called a 'passing 7' idea that gets us by half steps from the tonic down to Six. So chromatic? Yep, 1/2 step ='s chromatic. This lick is fairly common in many songs in many styles. If the band plays a couple of songs in minor, chances are you'll get to this too. Blues pianist and composer Leon Russell's lovely pop ballad 'This Masquerade' is a top 40 Grammy winning gem, featuring the 'passing 7th' line in the front four measures of the eight bar A sections. A passing 7th in A minor. Example 3c.

wiki ~ Leon Russell

Nice sound yes? Have heard it before? Cool. No? Oh then yet another first :) There's probably three solid ways to sound this out, one each from three different groups of strings. And these three are root pitched based. Then depending on the musical setting where we fit this in, these and other options become available.

The evolutions of a minor 6th chord. This last voicing is a pretty neat one. Of course it's an A-6 chord but its pitches also create a second inversion dominant D9 and a first inversion, half diminished F#-7b5 chord. All of which are diatonic to G major. Does this mean we can sub out for the these chords with one another? Yes, pretty much depending on the setting, the instruments involved and direction of the music. We 'sub out' to create variety in improvisation, to find a better 'fit' for a piece in a puzzle in supporting a melody.

A tricky spot in the theory. In most cases, if a cat see's A-6 written, chances are they'll sound the 6th as an F# in the chord. This shades things towards the Dorian color. For the natural minor 6th from A is F natural. This creates a half step interval between the 5th and 6th, a sound usually avoided and a fingering for guitar that can create proximity challenges in chord voicings. Examine the pitches and sounds. Example 3e.

pitches
root
-3
5
- 6
root
-3
5
maj 6
A - 6
A
C
E
F
A
C
E
F#

So just what is this in terms of the theory? Surely the F# is a lean towards G major. It's also a lean towards A melodic minor. If we voice the chords as in the above manner we place the 5th E above the 6th, either F or F#. These are both fairly common chord shapes. So even in the above passing 7th idea, we first use the major 6th for the lick and then use the minor 6th for the root of a flat Six chord which proceeds Five by half step. Half step equals chromatic yes?

1/2 step = chromatic

So again we see the chromatic motion tastefully handled, here with the half step lead in with the dominant type harmonies in the second half of the phrase. All of this is not uncommon when exploring the minor tonality, just your basic 'pushing past the boundaries' of what is diatonically available to create the sounds we need to express the 'art in our hearts.'

A bit more major 6th loop theory. So if we invert the major 6th to the minor 3rd and we know that the minor 3rd closes its loop in four leaps, then surely our major 6th interval should do the same yes? Examine the music. Example 3a.

Yep, four leaps. These closed cycles of pitches can create formats for composition, a framework that we composers can use as an architecture for songs. And while they potentially become too predictable based on their perfect closure, we can artistically alter things in unpredictable ways to suit our muse, as we puzzle our ideas together, shaping their emotional dynamic with tonal gravity and its balance, aural predictability.

Loops / the minor 7th. Melodically, the minor seventh interval or blue seventh historically plays a rather crucial role in creating the American sounds. Perhaps more commonly known as 'flat seven', its proximity to the tonic creates an essential suspension for infusing a blues color into the music. Minor 7 is also a part of the Mixolydian formula, that essential grouping for bringing forth mucho mucho Americana.

Harmonically, the minor 7th interval is one half of the two note, tritone catalyst (a combined major 3rd and minor 7th above the root ) of the dominant seventh chord. This pairing creates the dominant V7 chord type, which provides the aural tension to direct the flow and direction of the music.

We often create cool and danceable vamp ideas with the blue 7th, most often from tonic to b7. We find these vamps in many of the American styles of music and dance. And of course, the minor 7th is a must have in creating the natural minor tonal environment and associated modes. So like its inverse the major 2nd whole step, it'll probably take 6 leaps to close the loop. Here is the music. Example 4.

Six leaps it is ... I love this theory! This b7 is a big pitch on the bluesman's palette. This next idea is a 'Doors' inspired chant, whereby we're simply encapsulating the tonic with the blue notes b3 and b7. Generally an easy lick that gets good mileage. Example 4a.

Shake these pitches and give them some wobble, to bluesify as they say. The major 3rd C# in the chord and the blue 3rd C natural in the line making for some of the blues rub spice of the Americana sounds.

Loops / the major 7th / leading tone / Seven. Like its inverse the minor 2nd or half step interval, the major 7th interval will need 12 occurrences to close back upon its starting point. This next idea, based on the octave transposition technique, creates an interesting descending chromatically enhanced noire character of line, a mood which somehow vanishes with the sounding of the major seventh chord to close the idea. Example 7.

Leading tone. As its name implies, the interval of the major 7th above our root also becomes the strongest of our pitches in terms of our tonal gravity. Proximity to the tonic surely plays a role, as does the half step interval. So named by its ability to lend an urgent and poignant direction to the music, artists use this pitch to shape the tension / release dynamic within their work. Located a half step below the tonic, its natural inclination is to resolve upwards by half step.

Jazz and pop players also include this pitch in their harmonies, creating a lovely softened yet still passionate tonic color for supporting their melodies. This next idea is more of an interval study than a melody but it does eventually get after the resolving qualities of the leading tone. In C major, our penultimate pitch is our leading tone, B natural. Example 7a.

Sense the direction? Sense the direction in the line and its impending resolution? Cool. That's what the leading tone is all about. Of course the repetitive motion of the interval idea lends to the predictable outcome, but the leading tone seals the deal. It is this aural sense of predictability in the music that begins to shape our understanding of the theory and how we will use it to fashion our own work with the American sounds we dig.

While this may sound like a big ol' can of worms and it potentially is, the basic idea is that regardless of musical style, we as artists must handle the tension and release of the music we create. Whether instrumental or voice and storytelling, all good art often contains some element and degree of tension and release. And while there are a zillion ways to create this tension and release, to create expectations and surprises in the music, theorywise with pitches in tonic centered music, the leading tone is a king creator of tension.

A new direction. Being the child of the 60's that I am, I grew up with the minor 7th being the predominant 7th color in my blues based, rock and country music. Of course back then anything with a major 7th was more towards a pop styling which we often called 'bubble gum music' for some reason or another.

My favorite guitarists in those early days were mainly Duane Allman, Jerry Garcia, Eric Clapton, Carlos Santana and Robbie Krieger. As both writers and players, these cats lean heavily on the blue 7th, the leading tone / major 7th interval just isn't as core to their music. It was the blue 7th. So what's your point here Jacmuse?

The point. Well, simply that musical colors are evolving in our modern times. Not so sure about the when and where of this but it surely is in what might be called the rock music of today. Not all mind you, blues based cats still hang with the b7, but a lot of the rock of the 'double aughts' and forward uses more of the leading tone coloring. The result just might be a softening of the blues influence in the music as we move forward.

Is this a new current in the American sounds? The one song that comes right to mind here is the wonderful Lady Antebellum gem "Need You Now." There's a slide solo in the middle and at the end that finds the leading tone a couple of times. No blue 7th to be found. While the blue's roots obviously go way deep in the American heritage, are we finally lifting the historical burden associated with the blues? So let the art be art and surely it will go where it wants and needs to go to express the happenings of the times in which we live.

Octave / our one leap wonder. A one octave leap is all it takes to gain the perfect theoretical closure we seek. With its 2:1 ratio and an aural purity unmatched by any of our other intervals, the octave pitches become two focus points, between which we locate all of our other pitches. Remember this old time melody? Example 8.

What a line! The octave leap that starts this pentatonic sporting ditty is potentially unmistakable to musical ears and gets things off to a rousing start. Other classic melodies that initiate with an octave leap? Harold Arlen's "Over The Rainbow" and Mel Torme's "Christmas Song" are two beautifully crafted American classics whose melodies initiate with the an octave leap. Of course, we can find this interval in the middle of the line also. The age old classic "House Of The Rising Sun" is one such melody with a descending octave interval to start its second phrase.

Whomping on the tonic. Changing gears a bit here, blues cats do this often enough to mention it here while talking octaves and come to think of it, many blues licks simply end up with the upper octave pitch to complete the idea.

whomping the tonic video

Here are four, one measure blues ideas that do just that. And that whomping on the tonic thing? Oh, just a reminder that when all else fails ... we can whomp that tonic pitch / octaves, in the blues and beyond, and drive it all right into the barn. Example 8a.

Find any coolness? I think the second idea is my tops. These ideas are all from the one core, movable scale shape. Got one to share? There's a few more included at the other end of the click to the right.

Blues mojo. I'm not exactly sure if this is the right way to use this term but we'll see. In every blues player's development, there comes a point where they discover and can create a phrase unaccompanied, often four bars, that absolutely locks into the blues groove of their locally created universe. Any time, any key and any weather etc., they can play 'their' lick and set the blues mood a happening.

Once they have it then we'd might say they have a bit of the blues mojo. So often this mojo lick is also bookended by the octave pitches. Thus the case in the following line titled "Truth Is ... Ya Just Don't Love Me No More" by Jacmuse. Example 8b.

"The Truth Is ... "

Three's a charm. This above blues mojo four bar phrase is also a core idea that can be repeated three times and create a blues tune. Simple as that? Yep, simple as that. We also call this lick the hook, that essential bit of spark and magic that brings our true life experiences to a musical life. Just match up the words of the title with the pitches and a song is born.

Octave doubling. Another fairly common sound with octaves is to play the melody, written or improvised, with an octave doubling technique. Jazz guitar legend Wes Montgomery was the king of this sound in his day. Mr. Montgomery's clear sense of swing found new heights with his octave melodies and improvisations. They are a real trip to play, very powerful yet can be poignant and soulfully all blues.

Southern rock pioneer Duane Allman also used this approach, adding yet another way to approach the pitches. Nowadays, most jazz players find a way to work in this very cool sound somewhere in their music. Here is the first phrase of "Scarborough Fair" in octaves. Example 8b.

Octave purity. Interesting that with the purity of the octave intervals, and of course being perfectly in tune (thanks to this computer software), we really can't hear the strength of the octaves in the above .mp3 file. I guess you'll just have to take my word for it, hear the jacmuse version and give them a try yourself. And as time permits do find some Wes Montgomery and hear him work his magic. We can also add octave doubling to our scale and interval study workouts.

jacmuse octaves

Beyond the octave. Moving past the octave and into a second octave span we simply start back at the beginning, with a half step interval. Our numerical labels increase by 7, the number of relative major / minor scale degrees within a one octave span. And while we do hear these wider intervals in improvised melodies, they are rather rare in our American songbook. So maybe we should write a few new ones eh?

 

And while melodically these wider intervals are somewhat rare, we surely do find these spans in the harmony. We guitarists refer to the arrangement of the pitches in our chords as its 'voicing.' Lots of variables in how chords are voiced with concerns ranging from styles, sound quality and what's possible.

The terms color tones, upper extensions and tensions being three common ways to describe these pitches whose interval above the root pitch exceeds the octave span. So while piano players can close 'voice' their pitches, we guitarists must often rely on the interval pitches into a second octave.

Octave + intervals. Here is the music showing our upper pitches into our second octave above the root C. To avoid confusion and to stick with what we see in common practice, I've included numerical names for just those intervals we use everyday. These numerical designations are above their corresponding notation.

In common practice, the intervals unnamed in the following graphic do not get any special numerical designation as they simply retain their lower octave labeling. Look to the written chart which follows the written music for an explanation of each of the intervals and additional links for discovery. Example 8c.

Intervals beyond the octave.
b9
a rather common jazz dominant chord color
9
commonly used in all three chord types and the bossa, pop, blues and jazz stylings, a very handy color to deepen the passion of the moment, the dominant 9th chord is THE core funk chord of the 80's or so, also a strong basis for adding additional colors or altering the 9 to b9 or #9
#9
exclusively a dominant chord color tone, very common in blues and jazz
minor 10th
simply our minor 3rd moved up one octave, a wider interval oftentimes used in the left hand of piano voicings
major 10th
simply a major 3rd up an octave, important in chord voicings especially in the left hand of piano bigger chords on guitar, also used like an octave doubling but with the major 3rd coloring
11th
essentially a perfect 4th up an octave but a common designation is suspended chord harmony, especially on Two and Five chord types
#11
essentially a flatted 5th up an octave, designated as #11 if there is a normal 5th in the chord also, generally implies a whole tone quality
p 12th
simply a perfect 5th with no special designation up an octave
b13
essentially an augmented 5th in blues and pop chords but often seen as b13 in jazz chords if the voicing also has a p.5th below
13th
simply a major 6th up an octave, a rather cool dominant chord in blues and jazz with easy chord shapes to create the coolness
b14 / b7
simply a minor or blue 7th with no special designation up an octave
14 / maj 7th
simply a major 7th with no special designation up an octave
15
our tonic up 2 octaves with no special designation up an octave
#15
comprised of two octaves and a minor 2nd, very uncommon and a real trainwrecker overall, but it is the correct sounding pitch of a purely built ascending major 3rd / minor 3rd arpeggio and can be hauntingly beautiful one of a kind when appropriately placed, the basis of a newer more modern system of composition and improvisation

That's all for this second chapter folks. Feel like you've got your arms and intellectual confidence completely around this concept of our perfectly closed loops of pitches? Find any ways to get outside or break the loop? If so surely let everyone know. It is fairly simple but potentially crucial to obtaining a complete view of our music theory system. Pour moi it illuminates the entire resource.

Though I still do not clearly know and thoroughly understand all of the nooks and crannies and surely never will, as I discover new elements, knowledge of this perfect closure gives me a solid structure to logically place them into my creative and reasoning process. I sincerely hope that understanding this idea of a 'perfect theoretical closure' is helpful to you.

Larger loops? And what happens when we combine two or more different intervals in creating our loops? And for those advanced readers just too curious, is there an even larger symmetrical loop of the twelve pitches than the one octave chromatic scale and its intervals? Is this a basis for compositional schemes? Hmm ... ?

One such possibility included here is based on our two thirds; alternating major and minor and vice versa, and as such probably more theoretically aligned with arpeggios and chords than scales. In future times, as we evolve away from our tritone based system of tension and release, perhaps this new system will provide the basis and vocabulary for a new approach for composition and improvisation for the modern guitarist.

So what's next? Well, now that we know that any way we slice and dice our pitches that our loop will hold, we need to place them into the musical environments or settings we commonly create. As articulated throughout, understanding the idea of a 'yin for every yang' becomes our next theoretical challenge.

For 99 and 44 / 100 % of the American music is written with an overall major or minor color scheme and the weaving of the two together. And while variations are endless, we composers are also often tasked with energizing new ways to capture, express and transform the ancient magic of our musical heritage and tradition into new settings for the modern world we live in.

"Music is the mediator between the spiritual and sensual life."

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.