This piece is a sonification of all of the possible filled Tic Tac Toe games, whether possible by the rules or not.  In other words, you are hearing a particular sonification of every way to fill a Tic Tac Toe grid with X's and 0"s, assuming X always goes first.  

While teaching Algebra II one summer, a student asked if we could just play Tic Tac Toe all day.  Of course, I said "No," but I did offer for us to "analyze the game of Tic Tac Toe all day!"  As it turned out, we had to cover some mathematical probability anyway, so it turned into a really cool two-day lesson in probability - all focused on the game of Tic Tac Toe.  

As to the precise way in which I sonified these arrangements, I'll have to get back to you on that!  It was several years ago at this point...but suffice it to say it had a whole lot to do with first converting every Tic Tac Toe arrangement into binary.  

Tic Tac Toe [All Possible Games]

"Squares and Cubes Mod 12 [Pure Variation]" is, well, a sonification of the sequences of the perfect squares and cubes, including zero, all over modulo 12.  

First, the squares.  Then the cubes.  Then both.  

That repeats.  

Each time, however, a next generation of degeneration plays simultaneously along with each line.  Well, at least until the four such voices for each line are met.  

Then it begins to disintegrate, i.e. each line disappears in the opposite order it came.  Then it builds back up again, now from the bottom to the top.  

Then it breaks down again, losing each lower layer, as it slowly becomes what it once was.

It is a symmetrical piece.  Well, there's actually two conflicting lines of symmetry occurring simultaneously which breaks the symmetry...even right in the middle of what might have been a symmetrical center of sorts.  

Anyways...I've been wanting to sonify the perfect squares and cubes again for quite some time.  Plus, I've been in need of more abstract pieces for exploring mathematics.  So here's the dry/pure variation.

- - -

Also, on the musical side of things, there are several goings ons.  

First of all, each sound for each line (squares and cubes) begins with a pure sine wave, then slowly becomes a square wave from voice to voice.  Believe it or not, this did not occur to me as appropriate till later.   

The undulations between conflicting voices between the two lines occur primarily due to the fact that each are set in precisely the opposite phase of one another.  This creates a rather super pleasant means of hearing their interactions.  

The degeneration from voice to voice within each line is more of an accentuation of each sequence.  Essentially, peaks and troughs are highlighted, whilst the middle grounds fade away.  The details, in other words, are slowly subtracted out as each line descends into the a-bass...heh.  As in abyss...never mind.  

Puns aside, I am most pleased with the way each of these sequences fit together, particularly the fact that the former repeats every six terms, while the latter repeats every 12.  Subsequently, this piece was arranged in 3/4 meter....though related meters could also be used I suppose.  For this variation, however, it provides the perfect simplicity.     

Squares And Cubes Mod 12 [Pure Variation]

nice and slow...nice and soft...peaceful? eerie? hard to say...it's either way.  I see it as beautiful.  

This mix was a little last mini-mix I just had to do...after a 2 hr mix.  This one is, if anything, even more "experimental" than the mix that preceded it. 

The piano excerpts heard are, indeed, just excerpts...from one of my countless freeform piano improvisations - my main performance-based instrument.   

"Why does this keep happening to me?!"  I'd love to see if any of you can figure out who that is...and from what show.  ~_~

Beautiful music, this.   

Oak 510 II PS [Mix 12]

The Abstractician, aka Swircle 987, aka Rotozane, aka Swirculations, aka Will Beazley...is here to represent the more ... abstract ... musical creations/discoveries of the latter entity who is the prior entities.  

~_~

