loops of pitches

Is it possible that all of the musical resources we use to create the American sounds are created from a closed looping of pitches? That there is complete and perfect closure to the theory of equal temperament? The ideas on this page simply try to create this closure in regards to the melodic musical resources most commonly used to create the various styles of American music.

Is the chromatic scale the perfect loop? In theory, approximately 95% of the pitches we use to create all of the melodies styles of American music can be derived from the chromatic scale, 100% of the chords. Selected groupings that we can "extract" from the chromatic scale create closed loops, scales, the modes etc. If ever there was a "theory grandparent" of them all, it's probably the chromatic scale. Here the sound of this loop of pitches spanning two octaves. Example 1.

Cool huh? So what is meant by a "closed loop of pitches?" Simply that in theory, all of the melodic and harmonic colors we use to create the American sounds are closed sets of pitches, as shown above with the chromatic sale. That all the musical colors will close back upon their starting points if we extend them far enough using their intervalic formula.

Chromatic scale theory. The theory of this scale is rather simple, it's intervalic formula is created exclusively from the half step. Here is a chart spelling out the pitches of the chromatic color. Note the "closure" as the group starts and ends on the pitch C. Example 1a.

If we were to extend past C above using the 1 / 2 step motion would we simply repeat the cycle? Absolutely, positively 100% no doubt. Do all of our resources "loop" like this? Totally. Cool with this?

Are there purely chromatic melodies? Of course, we have everything here. Example 1b.

Are these all of the pitches? Well, yes and no, see any of the sharp ( # ) accidentals in the above chart? How can we can include the sharps in the chromatic scale? Perhaps by respelling the pitches with flats ( b ) to what theorists term their enharmonic equivalents? Example 1c.

Easy enough eh? Here is the sound of the above chart of chromatic pitches. Example 1d.

Now is this all the pitches? Well, again, yes and no. Yes in that we've covered the pitches as as found on say a tuned piano, but what about the "really blue notes?" ( Are these pitches the other 5% from the 95% mentioned above? Yep. ) The one's that seem to hang "between" the pitches ( keys ) of a piano? By adding these pitches, along with the various honks, squeals and other assorted blues sounds, we create the entire pitch resource used to create the various styles of American music.

The crux of the theory here is that all of the "tuned" scales and chords we have at our creative pleasure can be extracted from the chromatic scale. We can see from the above charts the looping quality of the pitches ( C to C ) created by fulfilling the pattern of the interval structure. Do all of the various scale configurations loop the same way? Yep. Do the major and minor arpeggios / chords also follow a structured looping that also encompasses all of the pitches of the chromatic scale? Yep. So does this imply that the resource is in one sense finite? Yes it does. Is that important? Well, thinking along these lines allows us theorists to discover the various loops that exist within the equal tempered system, and as we struggle with understanding the theory, knowing that the loop under scrutiny should "theoretically close" on itself helps dramatically during the process of learning. And when things do "prove out" theoretically, our discoveries can be very exciting. Cool with this?

So, all of the groups of pitches we have will loop / close huh? Yep. Do they have to? In theory yes, in composition no. Let's extract the more common melodic colors from within the chromatic grouping of pitches and build them from the root C. Example 2.

Here is the sound of the pentatonic major scale from the above chart. Example 2a.

Isn't there a relative minor to this major group? Yep.

Here is the sound of the above group of pitches. Example 2b.

Here is the sound of the above group of pitches. Major scale = Ionian mode yes? Example 2c.

Here is the sound of the above group of pitches. Example 2d.

Here is the sound of the above group of pitches. Example 2e.

Here is the sound of the above group of pitches. Example 2f.

Here is the sound of the above group of pitches. Example 2g.

Here is the sound of the above group of pitches. Example 2h.

Here is the sound of the above group of pitches. Example 2i.

Here is the sound of the above group of pitches. Example 2j.

Here is the sound of the above group of pitches. Example 2k.

Here is the sound of the above group of pitches. Example 2l.

Here is the sound of the above group of pitches. Example 2m.

Here is the sound of the above group of pitches. Example 2n.

Here is the sound of the above group of pitches. Example 2o.

Here is the sound of the above group of pitches. Example 2p.

Here is the sound of the above group of pitches. Example 2q.

Cool with this concept of the looping of the pitches? That different interval formulas create the various melodic groups or loops that we use all the time to create our music? That from within the chromatic scale, all loops are possible, scales, chords and keys? And that any of these loops can be created from any of the 12 pitches of the chromatic scale? And even though all of these loops are possible, the system is still said to be finite in it's resources? Wow, too cool huh? Do the pitches loop in the chords too?

Where to next?

review new ideas

Other artistic ideas in this section? How about artistic techniques?

One person cannot hold another down in the ditch without remaining down in the ditch with them. Booker T. Washington