~ sequence and permutation ~

'all of life is sequential yet we continually permutate it our own ways :)

~ nutshell ~

~ baroque ~

~ sequence ~

~ a permutation ~

~ by the numbers ~

~ and other options ~

In a nutshell. For some reading here, these two artistic elements, sequence and permutation, become the basis of a lifetime of musical invention, and artistic invention in general in all of the various 'arts' we love. Using our smarts, our own elevated sentient thought process, we create and recognize a series of pitches as a sequence, and devise ways to rearrange or permeate them to create new art.

wiki ~ sequence music
wiki ~ permutation music

For improvising musicians, these two techniques become mainstays for creating our variations of whatever motifs we're given to work with, from any song or musical setting. Musical elements that are sequenced can be permutated. Improvising artists 'sift through' ideas, find their gems, and filter them through various forms and patterns. Examine the following idea of major triads. Thinking 'C' major. Example 1.

Cool? These vocab / theory terms go way deeper into academia as the shedding evolves. Once the jazz frontier is crossed on the style spectrum, a whole new universe can blossom for the evolving artist. So ... got these triads under your fingers yet ? In a couple of keys even ?

A Baroque sequence. This next idea comes to us from a couple of hundred years ago now, from an era of stately sounding, majestic music whose composers just love to sequence a bass line, chord changes and create 'written out' orchestrations and permutations in the lead lines.

Click the music. Do you by recognize this Euro 'top 10' hit from the early 1700's ? It's become a winter holiday classic, still to this very day. In this first pass we use an upper pedal for our melody. Without a key signature, thinking in 'D' major. Example 2.

wiki ~ Pachebel's Canon

Sound familiar? Cool. No? Well, another first :) Baroque style music and sequencing / permutation go hand in hand. Composers and players loved to sequence their ideas, mostly following along diatonic pathways. Let the melody permuations begin. First motif sequenced through the changes keeping mostly the same melody rhythm pattern. Example 2a.

wiki ~ Baroque music

Simply permutating the pitches of the last idea into a new melody line. Example 2b.

Simply permutating the pitches of the last idea with more a 'leap and stepwise' formula. Example 2c.

Cool ? There's a ton of ways this all can go really ... but have a sense of the process here ? Becoming a classically trained Americana improvisor ? Want to try out a few more baroque sequences ?

a classical improvisor

A sequence.

A sequence can be thought of as an order of events that form a closed loop. In music, these events are the pitches of course.

And does a sequence always have to close ? No.

A permutation.

A permutation is simply a re-arranged version of the elements, the pitches, in a sequenced loop of musical sounds.

And can the permutation of the elements of a sequence evolve its elements, and retain the essence of the sequence? Absolutely. Ever hear of the blues hue ? Let's 'bluesify' the 'A' and 'D' triads thinking blues in 'A.' Example 2.

wiki ~ musical sounds

New melody. In this next idea we combine the above 'theory machinations' and create a motif we can organically grow into a song. Here's the motif. Ex. 3.

And here's the song. Pretty sure this was a 'break tune' some where along the way :) Example 3a.

A group of pitches / by the numbers. In our basic philosophies here, we can think of a scale or mode as a group of pitches from which we can create our melodic ideas. Thus, we can swap pitch letter names with numbers and create a way to facilitate understanding and energizing our sequences and permutations. Examine the following numerical evolution of the pitches. Thinking 'C' major. Example 4.

Cool ? Making this leaping transition to our music / math basis of all things theory? Surely a potential giant step in understanding as we look to order up the whole tamale.

Permutation by the numbers. If the last bit is cool, then this next idea is the potential game changer. Thinking 'C' major. Example 4a.

Cool ? So our permutation of an idea can be rhythmic too yes? U bet. Pitches, rhythms, phrasing, accents, sequencing a permutation through cycles of root pitches, chords. On and on really. And with the five note pentatonics ... no 'bad' pitches. Just like wind chimes :)

Well that's all for this discussion folks. Have a sense now of the musical term 'sequence?' And how we 'permutate' the components of a sequence into new configurations?

Other options. Blending chord progressions and sequence, we can see in song's harmonic motion a sequence with a beginning and an end. Once the song starts, the chord sequence 'progresses' along to its finish, where if needed for the arrangement, it will begin again. In modern jazz stylings, there's the idea that a chord progression doesn't necessarily have to proceed in the sequence that the chords were written.

So we can permutate a progression's elements. Rare for the most part, Coltrane's 'sheets of sound' styling falls under this 'permutation' of a chord progression. Though in this approach, chord substitution, and what V7b9 can bring with its multiple leading tones, must be factored in. In a word; complex, in theory and performance.

So: C7 A7 D7 G7 can be A7 G7 C7 D7 etc.

Review. A sequence is an order of events that form a loop. A permutation is simply a re-arranged sequencing of the elements of its original loop. Artists use these two techniques to expand on their motifs, create themes and variations, call and response and the interplay found in the improvised performance formats of a lot of our Americana musics.

Further sequencing and permutation studies included in this book include, the interval studies, loops of pitches, working with arpeggios, the #15 arpeggio and diatonic and non-diatonic chord progressions.