'Aviary': Polytemporal, Polymetric, Prime-Palindromic Music

Yes, the title is quite a mouthful!  

The included refers to my work Aviary.  Link below:  

The work plays with time.  Time slows down and speeds up - we observe.

My idea with the work was floating through space amongst a flock of birds ('Aviary' isn't the most appropriate title (as it implies 'caged') - but I like the sound of the word/it is good enough) - and as with a flock of birds, some speed up, others slow down, and others maintain a steady pace.  The idea with the sound was to create the effect of birds vanishing into a wormhole (hence the very deep 'gulps'), only to reappear in a different temporality.  

I'm not a big fan of movies, but a while ago I seen Interstellar at a friends house.  It had an interesting scene where some people descended to a planet - for a minutes max. - and upon returning to their ship, the crew member who chose to remain on the ship was many years older due to the time displacement.  With this piece I'm imagining a similar kind of perceptual experience - but we are the multi-dimensional beings observing the fluctuations of time - we are 'outside of time'.

PS If you don't like 'the cake unbaked', it is probably best simply to enjoy the music without reading the information below, as it plunges into compositional structure.  Decoding can spoil.  

It can also enlighten, so I'll leave it for my readers to decide.

Ultimately, the function of all this structure is to create something very expressive.  The structures themselves may be relatively 'hard', but I see these as leading to freedom - much like the chicken breaking out of the egg into a new world.

So - despite the technical focus below, it is worth keeping in mind the primary function is to create a new kind of beauty.

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Poly-Palindromic Melodic Phrasing

This is something you'll likely have to be actively listening for to notice.  Otherwise, it can slip by with the listener completely unaware.  

If you listen to the melody, you'll hear there is a phrasing pattern.  Think of each phrase ending when I remove my hand from the keys (it should be obvious in the video).  

The number of notes in each phrase is always prime - with a palindromic prime pattern.  

For example:  

Phrase 1 = 2 notes long

Phrase 2 = 3 notes long

Phrase 3 = 5 notes long

etc etc

See the image below for the full phrasing pattern/sequence:  

Melodic phrasing sequence

The entire melody is a 31-step palindrome (31 is, of course, also prime), consisting of three (also prime) stacked palindromes.  

The central prime of the work (indicated in yellow) is also the 'master' time signature (explained in more detail further on in this article).

Have a look/listen again to the piece and you should be able to spot the pattern in the melody.  

What is the point of the above?  Many reasons.  The exploration of something new, of course.  

The palindromic sequencing also gives a very natural, organic feel.  The melody seems to act as a form of 'bellows' - the phrases grow/recede in a very natural manner.  

What could be more natural than prime numbers?

It is very interesting to give a listener a piece of music which is, on one level, a piece of music, but is also at a deeper level something else; something more.  I find a great beauty in this.  

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Polymetricism

Yes, another mouthful!  The easiest way to imagine 'polymetric' is to think of two sequencer parts of different lengths running together (at the same tempo).  

Imagine a sequence of 5 notes long playing whilst a sequence of 4 notes long is also playing.  

The result would be as of the number sequence below (consider the vertical alignment as beat alignment):

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

  

The next step of the above sequence would be a return to the beginning of the sequence (i.e '1-1' alignment).  

At the simplest level, simply multiply the sequence lengths to generate the Latch Point (i.e how long before the repeat/sync). 

This, however, isn't always true.  There are some exceptions, notably common factors.  

If we have two sequences where one sequence is a common factor of the other, the Latch Point is the longest sequence.  

Assume we have a sequence of 8 and a sequence of 2.  The Latch Point isn't 16 (i.e we aren't multiplying), but rather, 8:

1 2 3 4 5 6 7 8 1 2 3 etc.

 1 2 1 2 1 2 1 2 1 2 1 etc. 

Latch Point indicated in yellow.  

With Aviary, three sequences are running.  The sequences are polymetric.  

They are:

1)  11 notes long

2)  13 notes long

3)  17 notes long 

i.e all sequences are prime, and also prime-consecutive, and there are a prime number of sequences.  

Therefore, we have three options when ascribing a time signature to the piece.  The piece could be described as 11/16, 13/16, or 17/16.  All are correct.

Given the above are prime, they have no common factors.  The Latch Point for the triple polymetric sequence above is 11 x 13 x 17.  

It would take 2431 beats for the pattern to latch (!).  Yes, a long sequence!  

All possible sequences can very easily be generated - included below is the generative algorithm for polymetric sequencing (shown below for triple-polymetric sequences):

The above algorithm is, in one sense, the foundation for Buchla's 252e module (I plan to write an article on this module soon).  Unfortunately the Buchla module isn't as all-inclusive as the above.  Which is very unfortunate, as it is potentially a stunning module.

We can infer from the above that there are 4096 possible triple-polymetric sequences for a 16-step sequencer (i.e 16 x 16 x 16).  

The above statement isn't fully accurate, as we can also add rests/empty steps.  And ties.  

The plot thickens...!!  

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Polytemporal Music

In simple terms, polytemporal music is a piece of music where two or more tempi occur simultaneously i.e a piece where one player performs at, say, 112 BPM, whilst another player performs a second part at, say, 115 BPM.

Simultaneous tempi of 120 BPM/60 BPM wouldn't in the strictest sense be polytemporal, as the listener would perceive one player simply playing double/half the speed of the other (i.e quavers against crotchets).  Both players are still 'locked in' to a beat.

In Aviary, the 13/16 sequence line is, on average, running at 173 BPM.  There are slight fluctuations: this is compensation to allow the three sequencer parts to sync when there is a change of mode.  The fluctuations aren't a sudden change of tempo, but rather, a very gradual drift to the temporal latch point.

The tempo of the other two sequences is in a state of flux, ranging from 137 BPM through to 191 BPM (again, both prime.  The upper bound, being palindromic, is a structural reference to the palindromic nature of the melody).  

I'm not manually altering the tempo (as the beat-matching would fall apart) - I pre-programmed multiple LFO's (summed) to create a waveform that acts as a modulator for the tempo/clock.  

In 'normal' music, tempo is as of image 1 below.  When using LFO's, we could/can create a tempo wave such as image 2:

I latched multiple triangle-wave LFOs to create the tempo oscillations for the piece (certain summing values can create a 'flat' wave i.e even tempo).  The low 'gulp' is also LFO-tempo controlled. 

This is essentially a form of Harmonic Analysis.  The very simple way to think of Harmonic Analysis is 'summing waves to make patterns'.   

Basic algorithm below outlining the process for Aviary.  It only shows the basics (and no values), but should give an idea of the scale of the task:

VCO's 4 & 5 are producing the 'gulp', with the other three producing the polytemporal sequencer lines.

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Aviary Deconstructed

Below is the audio for Aviary, but only the sequencer parts.  I've also included a basic visual map of tempo/time domain.

Modal transitions are also indicated on the temporal map (as changes of colour).

In terms of listening: I've removed the delays and hard-panned the voices.  Following the parts should be easier:

17/16 sequencer line = Left ear

11/16 sequencer line = Right ear

13/16 sequencer line = Centre  

PS I'd personally think of the work as 13/16, as this is the (most) constant throughout.  But I'd be happy for others to argue the case against.

Take note that all three sequencer parts are playing simultaneously (i.e don't read the music in the manner of a normal score, from L-R).

  

      

Hopefully the included sheds some light on the structure of this work.  No discussion of harmony here as the focus of this short article is structure rather than harmony, but I'm sure some listeners will spot certain tools of the trade i.e pitch-axis modal transitions etc.  

Note also the axis-scale degree transition in the final mode (i.e altering enharmonic degrees - hence the 'freshness' of the sound).  Also keeping prime with the mode count (5 modes).

PS the melody being performed on the Vermona: very difficult to keep in time, given there are multiple tempi running!  Key to the structure of the melody is having the central 13-note phrase (highlighted in yellow on the melody image early in the article) at the centre of the piece, temporally.  This is the 13-note run that occurs during the F# overtone section.    

All best

Kris