'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

   

Why Two Notes Played Together Aren't a Chord

Yes.  The old two-note conundrum.  

What is a Chord?

Very often you'll read the following definition of a chord:

'A chord is two or more notes played simultaneously'.  

But this is an incorrect definition.


Why is it incorrect?  Because two notes played simultaneously isn't a chord.  

Of course, it also isn't just a note - as we have two of them.  

The important question is:

Why aren't two notes played together classed as a chord?

We'll get to that - but first let's define what a chord is:

A chord is more than two notes sounded simultaneously.  

I generally use the word 'sounded' rather than 'played', as played can be read to imply a musician physically playing something - whereas 'sounded' is more open, in terms of meaning.  However, either will suffice.

Very, very important point: chords don't have to sound 'good' in order to qualify as chords.  'Chord' is a definition of quantity - not a subjective experience of pleasure.  

When a 5-year old smashes hands/arms/elbows down on the piano - yes, the little one is playing chords!  Possibly not very pleasant chords, but still - chords they are!  

There's a Classical piano piece where the pianist pushes down every piano key by sitting a plank of wood on the whites, and another plank on the blacks.  Is the sound cacophonous?  Possibly.  Is a chord being played?  Yes.  No mention of composer here: do a little digging and see if you can find the piece for yourself.  

If anything, thinking along the above lines should be quite freeing.  Music doesn't have to sound 'good'.  There's a time and a place for everything.  Pleasant music isn't very appropriate during a tense horror scene.    

So - chords don't have to sound 'good' to be chords (and music doesn't have to sound 'good' to be music).  

But chords do have to consist of more than two notes.   

What is an Interval?

In music, interval is an important concept.

The term has nothing to do with everyday use i.e time/duration.

Interval = the distance between two notes.  

We have specific musical terms for certain distances.  It can get rather confusing, as the names for intervals change.

We get semitones/tones/thirds/fourths/fifths etc.


When we have two notes, we have the presence of an interval.

You could think of each note as a house, and the interval as an automatically-created path between the houses.  If we remove one of our two notes and return to only one note, the path disappears.



We'll take our twelve musical notes, and plot them in a circular format:

 


Let us take two notes (we'll take C and E) and plot them on the circle.  We'll also add the 'path' i.e. interval between the notes:

   
As you can see, two notes creates one interval i.e. one 'path':

Psychoacoustically, a chord is the presence/perception of more than one interval.

One note = no intervals.
Two  notes = one interval.

Hence we need more than two notes to have a chord.  We need more than two notes to create more than one interval.


Let's add a note to our previous diagrams.  We'll add G.  The notes we now have are C, E, and G.

Before looking at more diagrams, consider how many intervals you'll now hear:

You'll hear C-E
You'll hear C-G
You'll also hear E-G.

Your ear/mind hears all combinations of the sounds.

Let's add G

As well as hearing C-E, your ear now also hears C-G...

...and it also hears E-G

Three notes = three intervals.  Hence we have a chord i.e. the presence/perception of more than one interval.

It is impossible to perceive exactly two intervals.  We either have one, or three/more than three.


Mathematically, it also isn't a case of simply adding an extra interval for each extra note (for example: a four-note chord has six intervals, not four; a five-note chord has ten intervals etc).  If interested RE the why, on my YT page you'll find a video on the subject of Graph Theory.  Quite a long video, but it explains the mathematical relationship RE the number of notes and the resulting intervallic density of the chord.

The underlying maths isn't too important just now.  What is important is understanding the concept of why we need more than two notes to have a chord.


Remember: any amount of notes greater than two sounded simultaneously is, by definition, a chord, as any more than two notes creates more than one interval.


Three notes sounded simultaneously is a chord.
Forty-two notes sounded simultaneously is a chord.
587 notes sounded simultaneously is a chord.

Note = single, fixed pitch

Interval = *two notes/distance between two notes

Chord = more than two notes.

*Two common words for an interval are dyad, or - if you are familiar with blues - double-stop.  Both mean 'two notes sounded simultaneously'.



As we can see, an interval is an entirely unique category - not an afterthought.



I'm going above and beyond with the following, but here's an interesting way of thinking RE the above definitions:

Note = psychoacoustic perception of a single point within Euclidean Space

Interval = psychoacoustic perception of a line within Euclidean Space

Chord = psychoacoustic perception of shape within Euclidean Space.

Best

Kris

Moog DFAM Custom/Handmade Aluminium End Cheeks

Tasty

I added some custom end-cheeks to the DFAM.  This makes for a good weekend project.  Quick guide below.

200mm x 150mm aluminium is more than enough for both cheeks.  Order 6mm thick.  This piece cost me £10.  Nice.  I used the original cheek as a template: I used a piece of tissue to avoid damaging the original wood

I etched the DFAM shape with a nail.  Good enough as a guide for cutting.  I cut the alu with a jigsaw.  Make sure you use metal blades

When filing the edges, clamp both pieces together in order to have matching pieces

Lots of work on an edge like this.  This edge took around 1 hour of filing

Again, lots of filing work required

...and again!!

Filing out the blemishes

Cheeks almost done

Far smoother

3.5mm drill holes.  Again, I used the original as a template.  PS this part has to be the most accurate

Good trick for polishing the surface of aluminium: fold tinfoil into a ball, dip it in water, and rub across the aluminium.  It works great.  Just be sure to run in the same direction when polshing 

Note I also used silver screws to complement the look.
Order 3.5mm x 16mm.  A pack of 25 cost me £2.

Total cost for project = £12.

But the filing requires much patience!!


Best
Kris

Moog DFAM: Control Customisation

DFAM upgrade.  Or rather, adding knobs where none existed.

A few folks have contacted me on YouTube regarding the modified knobs on the DFAM.

i.e. as of the above image, and as of the video below:

I'll state later exactly where I sourced the knobs from, but it is worth understanding the why.  



Why A Bunch Of Big Knobs on the DFAM?

Very simple, really.  They give greater control of pitch.

The greater the diameter, the greater the distance/turn required between each degree on the circumference.

Therefore, pitching notes is easier.

Note that this has a downside: if you are looking to quickly change from low-high pitch, it'll require more effort.  Whether having a larger diameter is a positive or negative depends more on what your intended use/outcome is.

There are far more unique options than the customisation I've chose for the DFAM (my primary motivator was practicality (i.e. ease of establishing pitch) - the look was secondary.  Not an afterthought - but certainly a secondary thought).



What to Search For?   

You've likely searched for knobs etc over the years for your synth/amps/instruments etc.

Search terms probably go along the lines of:


Moog Control Knobs
Synth Knobs
Knobs for Synth
Synth Dials
Guitar Tone Pots
Guitar Control Pots
Guitar Dials
Amp Dials
Amp Buttons
Volume knob for amp

etc etc you get the idea.  And from music stores, cost can be relatively high.


You'll find an inexhaustible choice of knobs if you search for what the item (at a technical naming convention) actually is:

Potentiometer Knob.

The dials on the DFAM (on almost every synth) are potentiometer dials (potentiometer shafts, to be specific).  Just do a search for potentiometer knobs, and you can narrow in from there.


Look up electronics/components websites and you'll be spoilt for choice.

I purchased the potentiometer knobs from what is probably the best site in the UK for this kind of thing: RS Components.

Here is a direct link to some of the potentiometer knobs you can see on my DFAM unit.

Have a look through the site - there are literally hundreds of knobs available.  You could create a totally unique look.  But be careful - it is a tech geek's dream!!  You may vanish into a vortex for weeks, only to return with sour body odour and a mailbox filled with circuit boards.



DFAM Specifics

The diameter of the potentiometer shafts on the DFAM is 6mm.

6mm for potentiomter knobs would likely work fine (get 6mm if purchasing push-on), but I was looking for knobs with a grub screw as I don't want the knobs to slip position mid-use.  The grub screw is tightened directly against the potentiometer.

The ones I've used (6.35mm shaft) are slightly too large in terms of the internal diameter, but the difference isn't too much of a problem.

Not just a plastic insert.  And a grub screw for securing.  And an indicator line.

Hex-head grub screw.  Ideal for securing

On amazon you'll find the likes of 50 6mm potentiometer knobs for £5!  Definitely worth a look.  I ordered a bag, so I'll write up here how they are.  They are push-on, hence I had some doubt & went for screw-on.

Note - be sure to get potentiometer knobs with Indicator Lines, otherwise you won't know what side of 12 o' clock the potentiometer is sitting at!!

Perhaps the best thing about RS components is they include spec sheets for every product (accessible on the product page).  Click Here to access the spec sheet for the knobs I have on the DFAM.



Knob Diameter

The base diameter of my potentiometers is 16.2mm.

Here are some close-up photos to show you how this looks in-situ:

Slightly overhanging the pitch/velocity text 

Only ever so slightly over the sequence step numbering

Again, only a slight overhang

As of the captions, you can see the base is slightly covering the lettering.  But I didn't consider this a problem/too much of an issue.

20mm would likely be bordering on knobs touching each other.  Or you wouldn't fit your fingers between them.  Probably the best would be a straight/continual 15mm shaft (rather than a taper).



Attaching the Potentiometer Knobs

If you put the potentiometer directly on the DFAM and lock it down, there's every chance when you turn it you'll scrape the surface of the DFAM.

I'd suggest using small shims when locking down.

A thin piece of card will do the job fine.  I used piano shims - simply because I have them lying around from pianos I've destroyed modified/dabbled with over the years:

Small bag of piano shims: felt & paper/card, of varying thicknesses

Note the shims.  I used one at either side, and simply pulled them out once the knob was secured.  The shims give the necessary clearance to avoid scraping against the Moog surface

Word of Warning

The knobs I used have the grub screw relatively high.  It only just bites the potentiometer:

Slight damage to the top of the potentiometer

Be sure to measure up the grub screw height when purchasing.

One other thing worth mentioning is colour choice.  When the cheap push-on knobs come through, I'll likely change the VCO & noise knobs (white for noise, and yellow or blue for VCO's).  But consider intended use i.e. if playing live, account for stage lighting, as it can drastically alter colours.  You may lose colour distinction.

For now I'm using the DFAM in the studio, hence I'm not too bothered RE colours.


Hopefully the above helps DFAM owners & the general synth community.  Modification/personalisation certainly has its appeal!!

On RS Components you'll find everything from 5p knobs to silver £15 per unit knobs.  If in the US, there are likely 10 times the availablilty/ordering options.


All best
Kris

Tokyo Expressway (Matrixbrute)

On the Tokyo Expressway.  Despite entering one of the busiest areas in one of the world's busiest cities, traffic runs smoother than in the likes of, say, Bolton!!  (note the side barriers.  These are to shield apartments from noise pollution)

Presently I'm working on a (rather tricky) piano/synth piece that takes part of its inspiration from Koji Sujuki's fantastic 'Ring' series of novels.  The other day I revisited 'Spiral'; I had all but forgotten how well Suzuki describes journeying around Tokyo, whether by foot, car, or train.  

As downtime from the piano piece, I thought it was time to have some fun again with the Matrixbrute :)  And in a decidedly Japanese manner.  

This short work was originally going to be titled 'Tokyo Threeway' - as in 'freeway', and in the three-part nature of the recording.  Yes, the pun is appalling!!  However, part of me is proud of such a terrible pun.

Individual Tracks/"Unbaking the Cake"

As with many in the synth community, I could happily listen to a sequencer part for hours.  I'm perfectly content with a good sequence line on its own i.e. no drums/pads/solo etc.  

I've uploaded individual tracks for you to have a listen to.  I set up a page on Soundcloud (literally set up 5 minutes ago!) - click Here to head over to the page (link opens in new window), where you'll find the individual tracks.

The individual tracks also demonstrate the true analog nature of the Brute.  Great to hear them individually.  I was going to let the sequence parts run for c.10 minutes, but short & sweet will do just fine.  

By all means play with the included - but just for fun ;)  Don't go adding one of these parts to a commercial track!!!

On the Japanese front...

I assume anyone reading this specific article is probably a synth/electronics geek.  If so, visit Akihabara when in Japan.  It's the area famous for maid cafes/manga etc.

Actual buildings.  Not a level in Super Mario.

The reason for mentioning this area: here you'll find shops that sell the likes of only connector cables (literally!).

Brilliant.  

Or terrible if you're dragging a woman around with you.  Leave her at home.

  

Recording/Mulitracking

OK, you'll see in the vid I'm using my trusted Tascam DR-100.  

Connection is with a 2-1, 1/4" stereo - single 3.5mm.  Great for running two channels into the one device.  Works perfectly.

The cable I'm using is by a company called Nordell.  You'll find the cables at a site called 'Dangleberry Music'.  Good gear.  They also have an ebay shop.  If you buy any of their stuff, tell them Kris sent you :)   

Unfortunately the specific cable I'm using only comes in a 1.5m length.  3m would be great.

Nordell noiseless lead.  Nice wee bit of kit.  But guys - double the length of it if you get the chance.

In terms of the sequencer parts: both were recorded separately, then aligned in a DAW.  When this was ready, I set up the lead patch and played along with the sequencer parts.  Simple & easy enough to do.

All best

Kris

AKB48.  They have their own floor (in Akihabara, hence 'AKB' !!), and perform... every day (no joke)

Piano: Voicing Exercise #1

This article is primarily for some students I'm working with at present.  For anyone else, the piece should be self-explanatory, despite my covering of certain aspects relatively quickly (i.e. already discussed with students, no need to write up here).  

Video illustration Here.

Exercise is in the manner of Tausig/Thalberg/Liszt etc.

Repeats on YT vid are x4; when performing the exercise with full musical variations, x2 is likely more useful.

I'll make another recording, with the first 24 fingering variations (see the bottom of the article): dull, but it'll illustrate the point/will be useful for reference.  

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I'm sitting on the blacks (beginning on Gb) purely for illustration purposes - but the best method of practise is to start in C position (C D E F G), and play the pattern on:

C major, C minor, C diminished

After this, repeat the sequence one semitone lower (i.e. B major, B minor, B diminished etc).  No break when transitioning.

The image below illustrates the positioning:

  

Continue the descending pattern through every semitone until reaching C one octave lower from where you began.  

This is what we'd class as the Musical/Harmonic Variation. 

 - Remember - only do this for the first exercise.  The final exercise on the video is a technical variation.  

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Technical Variations

There are 120 fingering sequences in total for this exercise.

Included below is every exercise beginning on finger 1 (RH fingering only included below, but the LH fingering can be derived i.e. mirror it):

1 - 2 - 3 - 4 - 5

1 - 2 - 3 - 5 - 4 

1 - 2 - 4 - 3 - 5

1 - 2 - 4 - 5 - 3

1 - 2 - 5 - 3 - 4

1 - 2 - 5 - 4 - 3

1 - 3 - 2 - 4 - 5

1 - 3 - 2 - 5 - 4

1 - 3 - 4 - 2 - 5

1 - 3 - 4 - 5 - 2

1 - 3 - 5 - 2 - 4

1 - 3 - 5 - 4 - 2

1 - 4 - 2 - 3 - 5

1 - 4 - 2 - 5 - 3

1 - 4 - 3 - 2 - 5

1 - 4 - 3 - 5 - 2

1 - 4 - 5 - 2 - 3 

1 - 4 - 5 - 3 - 2

1 - 5 - 2 - 3 - 4 

1 - 5 - 2 - 4 - 3

1 - 5 - 3 - 2 - 4

1 - 5 - 3 - 4 - 2

1 - 5 - 4 - 2 - 3

1 - 5 - 4 - 3 - 2

* The final exercise in the video is actually exercise #24 (i.e. the last exercise from the above list).

Remember to practise the other 100 fingering variations.

3 per day for the entire set (i.e. including the above variations) = just under 1 1/2 months to play through all variations.  Add to your warm-up.

Exercises up until this point in history haven't utilised mathematics to yield every possible variation.  Therefore, it could be said that there has been no 'complete pianist' - mathematical oversights lead to technical oversights (i.e. omitted sequences).  

Regards

Kris