melodic permutation / sequence

Composing ( creating ) music is sometimes said to be "10% inspiration combined with 90% perspiration." The ideas and discussions of melodic permutation which follow address this "90% perspiration" aspect of this opening axiom. Whether the composed music is written out and perfected by rewrite or spontaneously improvised and perfected by practice, similar principles for thematic development are involved. To create refreshing melodic ideas and develop them into stories is part of the challenge for the composing artist. Improvising minded artists of American music can perhaps prepare themselves for developing in time the spontaneous emergence of nice ideas by internalizing fundamental concepts of permutation and sequencing. So that when the nice melodic idea arrives via "10% of inspiration", we hope that there is still potentially 90% more coolness via "perspiration" to extract out of the idea.

First a few definitions. In this text, to permutate means to simply to take an idea and recreate other ideas from it. This is done by simply rearranging the elements of the original idea. Sequence is defined here simply as an "order of successive events", each event musically termed an "episode" within the sequence. Lets apply these ideas using letters of the alphabet first, then move into using musical pitches. Example 1.

In the above chart we have simply remixed the order of the elements, creating a permutation of the original idea. We then sequenced this idea by creating a series of episodes, each of which mirror elements of the original components. Lets create the above remixing of elements with pitches and rhythms. Example 1a.

Let's take these spin-offs from the original idea and try to create a bit of art. Example 1b.

So, a basic remixing of the principle elements yes? The newly permutated idea oftentimes retains a semblance of both its theoretical structure and emotional / intellectual direction, so one idea can organically lead to the next? That's the basic idea. When composing, this developing of musical elements from a principle idea is often termed theme and variations. Linking or mirroring two or more occurrences of a theme, variation or permutation together potentially becomes a sequence. Cool? Are these new terms and definitions for you? Cool, read on.

So why are the theoretical principles of melodic permutation / sequence potentially so important for the creative musician? Well, depending on one's artistic direction, the principles associated with permutation and sequence can infinitely expand the resources provided by the equal temperament system. Exploring permutation and sequence ideas is oftentimes the next logical step for the emerging player who has a number of different colored scales under their fingers and are looking to develop and expand this on core of resources. Is there perhaps a finite number of scales and chords within equal temper? Perhaps yes. Is there an infinite number of possible recombination's of the colors? Yes, I think so. Why? Well, simply put, as no two of us are exactly alike one another, so is usually our approach to the musical resources, especially when our individual uniqueness is encouraged, as is so often the case in the American styles of music. Sure, we can all potentially play a C major scale or the melody of a song, but rarely if ever do we sound exactly the same. Is this idea part of the tenants of creating American music? Individuality? Could be. This natural, individually unique and artistic approach provides the basis for our own unique expressions, and when we add in the principles of permutation and sequence, we can exponentially expand the potential variations of the resources dramatically.

For whatever reasons, each of us are drawn to particular musical colors. As we explore the artistic potential of a color and become more and more familiar with it, we sort of naturally begin to experiment and reshape the components. Can augment this natural reshaping process by the music we hear around us? You betcha, for not only do we get new ideas on how to manipulate the resources, we can also begin to sense our own potentials and limitations as we try to recreate what we think is cool, helping to define our own directions and hinting at what we need to do ( practice ) to get there. Cool with this? I call it the big picture. A searching of oneself so to speak. So, bottom line, that the reshaping principles of permutation and sequence can dramatically expand the basic melodic and harmonic resources, and that how this reshaping is achieved, lays the ground work for our own searching and development of our own artistic signature.

The overall format which follows for exploring various melodic permutation / sequence techniques simply creates melodic ideas ideas from various melodic resources contained within this text and permutates them through various filters. Resource wise, the main focus in the following examples is given to the major / Ionian mode, major pentatonic color, the natural minor / Aeolian mode and their major and minor triads. These popular and distinctive groups create the major and minor tonal environments and countless melodies we love. Triads are oftentimes a big part of these melodies, are an essential structural component, and once under our fingers, relatively easy and fun to work with. The filters are various diatonic, chromatic or intervalic treatments which we "permutate" or pass our melodic idea through, searching for new versions of coolness. Here is a chart listing potential melodic resources ( scales ) and permutation / sequence "filtering" possibilities. Of course, any of the following components / filters can be mixed, matched and rematched any way you choose to do. Example 2.

With this in mind, lets start by looking at diatonic permutations and sequences created from major scale / Ionian group of pitches. Here is an ascending C major scale in major and minor 2nd's. Example 3.

Sound familiar? Cool. Here is the above idea permutated through the filter of major and minor thirds. Example 3a.

Sound like an interval studies? Let's create a permutation of the above idea. Simply changing pitch directions of every other episode of the sequence. Example 3b.

Permutation of the above idea, simply combining elements of the two lines. Look to the interval studies section for more intervalic ideas as above. Example 3c.

Here is a simple three note "core" created from the major scale grouping of pitches sequenced diatonically by step. Example 3d.

Sequencing motives diatonically has long been popular in all of the musical styles we love. Georgeous sequences characterize the sound of music from the Baroque era of classical music, are you hip to the Baroque sounds? Permutation of the above idea. Example 3e.

Permutation of the above idea. Example 3f.

Here is a common diatonic four note group ( 5, 4, 3, 1 ) from the major scale moved upward diatonically by step. Example 4.

Permutation of the above idea. Example 4a.

Permutation of the above idea. Here we repeat an idea three times before moving on. Example 4b.

Three times and out? Could be a golden rule of thumb for the permutating and sequencing creative musician. Along these lines, to musically permutate and sequence melodic ideas while avoiding redundancy is a real challenge, especially if the cool idea comes along while playing live, that’s always fun. Perhaps the idea of creating one melodic idea per chorus and permutating and sequencing that idea through the format of the tune? Big challenge, big rewards. To continually develop the idea we just played while telling a story which builds and climaxes. Yes! Tis very cool indeed. Is this what the classical players have written out for them? Probably.

Lets extract just the major pentatonic group from the major scale color used above, create a melodic idea, extract a core idea and run it through various filters. Example 5.

Our core idea comes from the first bar above, which is then diatonically sequenced. Example 5a.

Here the above core is sequenced through the cycle of fourths. Example 5b.

Permutating and sequencing the core idea upward chromatically. Example 5c.

The above permutation opens up a new dimension to our ideas, that of using non-diatonic pitches in our variations. Continuing in this vein, permutating and sequencing the core idea downward by whole step. Example 5d.

Permutating and sequencing the core idea downward by half step. Example 5e.

Lets move to the minor tonal environment and create some ideas from the various minor scale configurations available. Here are the pitches of the natural minor / Aeolian scale, in 3/4 time, using the pitch A as the root. Example 6.

From the above group of pitches we recreate the motif of "Scarborough Fair" in A minor. Example 6a.

Do you know this tune? It is a very old "English Air." In the next permutation we create a sequence using the first rhythm and pitches of our melody and extend it diatonically through the natural minor scale. Example 6b.

In this idea we combine the two rhythmic motives from our theme and permutate scalewise in a ascending fashion. Example 6c.

This line was created by singing possible combinations of our motifs. Example 6d.

Extracting a motif from the above idea and moving it up chromatically. Example 7d.

Lets take a look at the triad structure and create some common diatonic and non-diatonic permutations and sequences. With it’s three part structure, this powerful building block is ideally suited for endless permutation and sequencing possibilities. Played confidently, triads can always work as a part of one's improvisations. The following examples build triad configurations on the diatonic scale degrees of the C major / Ionian group of pitches, thus both the major ( I, IV, V ) and minor ( ii, iii, vi, vii ) triads emerge. Starting with diatonic triads ascending stepwise. Example 8.

Permutation of above idea, simply reversing direction of every other arpeggio. Example 8a.

New idea, starting on the third of the chord, triad or arpeggio, moved upward diatonically. Example 8b.

Permutation of the above idea. Very popular model. Example 8c.

New idea, starting on the fifth of the chord, triad or arpeggio. New triplet rhythm. Example 8d.

Permutation of the above idea. Example 8e.

The following ideas sequence major triads through various filters. These filters are interval based and simply move major triads around non-diatonically. Lets start with ascending triads by half step, i.e., chromatically. Example 9.

Just like out at the ballpark eh? Same idea as above but now descending. Example 9a.

Ascending pitches of triads moving downward by whole step. Example 9b.

Re-sequence this idea moving upward. Example 9c.

Major triads moving upward by perfect fourth. Example 9d

Re-sequencing of the above idea, using the triad in the cycle of fifths and moving downward. Example 9e.

Cool minor 3rd / fourth / 1/2 step resolving cadential motion. Common triadic turnaround. Example 9f.

Triads play a huge part in all styles of American music. Jazz melodies such as "In the Mood", "All of Me", "Cherokee", "Air Mail Special", "Spring Can Really Hang You Up the Most", "Birdland" and "Giant Steps" are just a few compositions that have melodies that are clearly structured around tonic major triad pitches. From basic blues to Bebop, dance tunes to complex harmonic and melodic organization, triads are a key melodic component. So cool and emotionally powerful, yet potentially so simple in theory. 

Cool with the concepts of permutation and sequence? Perhaps begin to see how they can begin to expand the resource potential of any of our scales already under your fingers? Cool. Here are a few links to other pages within this text that expand along the of permutation and sequence.

"Half this game is ninety percent mental." Yogi Berra