increpare games

Hmm, well; I used to write pieces of music as a wee kid; took a break out when doing the whole undergraduate thing – just tried to get back into it again this year – here’s a selection of (piano) stuff from when I was younger, and more recently (chronological order).

So, firstly some pieces from the olden days:

My first piece:

Blue ( ps | pdf | mp3 )

Something a little bangier:

Breaking Through ( ps | pdf )

Some etudes I wrote about the same time (number 9 is the best of them, the first section of which should be played with a sort of mechanical portato (okay, I find it really, really funny that spellcheckers and google insist that portato is a misspelling of potato. Why? Answers on a postcode)):

Study No. 6 ( ps | pdf | mp3 )
Study No. 9 ( ps | pdf | mp3 )
Study No. 14 ( ps | pdf )
Study No. 17 ( ps | pdf | mp3 )

When I decided to give writing a music a try again, I spent an entire weekend bashing away at the keyboard – I chuckle now hearing what I produced, especially given the great grief this output caused me, but I had to start again *somewhere*.

Olive Variations ( ps | pdf )

After this followed a glut of canons:

2-part Canon in the Minor Seventh ( ps | pdf )
2-part Canon in the Fourth ( ps | pdf )
2-part Canon in the Minor Ninth ( ps | pdf )
2-part Canon in the Octave No. 1 ( ps | pdf | mp3 )
2-part Canon in the Octave No. 2 ( ps | pdf | mp3 )
Three-part Canon ( ps | pdf )

I include only the right hand part of the following piece; the left hand is the right’s symmetrical image about middle C.

Mirror about C ( ps | pdf )

This is something pretty trivial. Feel like I should do something with the theme, though.

Modulation ( ps | pdf )

Then came a rather raggedy prelude:

Prelude ( ps | pdf )

Oh, I quite like this; probably my most tolerable pre-Christmas work; certainly the longest.

Henselt Variations ( ps | pdf | mp3 )

I wrote these “lullabies” either side of Christmas, though the first one is really more in the style of these patched-together pieces that come before, or Piece 1, but the other two are a littttle more successful I think.

Berceuse No. 1 ( ps | pdf )
Berceuse No. 2 ( ps | pdf )
Berceuse No. 3 ( ps | pdf )

Ah yes, then came our try at doing some jazz stuff…

Polonaise Sketch ( ps | pdf )
Arctic Sketch ( ps | pdf )

I don’t like this piece. It’s hard to play, and generally quite blah.

Polyrhythm ( ps | pdf )

Hmmm, more of a ricercar, but I suppose that we’ll survive; I’m fond of some of the sonorities in it.

Fugue and Variations ( ps | pdf )

Hmm; I thought that I’d be able to do a lot with this theme, but in the end…didn’t, really.

Piece 1 ( ps | pdf )

Oh! I like this piece (in the last section of the mp3 file, the right hand part can’t be heard; I’ll have fix this some time) .

Piece 2 ( ps | pdf | mp3 )

Hmm…don’t feel much about this piece either way, excepting it’s easy enough that I don’t have to feel bad about putting it up here.

Prelude and Canon ( ps | pdf | mp3 )

Not really enigmatic, but rather based around a password I would rather not forget. As it turned out, my encoding was a little, well, wrong, which caused me some small amount of embarrassment.

Enigmatic Fugue ( ps | pdf )

Hah. Someone used the term “rock epic” in response to one of the jazz sketches; I couldn’t resist rocking this prelude up a little bit. But the small mordant saves it from complete triviality. And what I would like to think is a tolerable fugue.

Prelude and Fugue in Bb – Prelude ( ps | pdf | mp3 )
Prelude and Fugue in Bb – Fugue ( ps | pdf | mp3 )

Hmm…two fugues, based on two arias from the Purcells’ “The Indian Queen”; the first one goes like

“Why, why, why should men quarrel
why should men quarrel here”.

The theme of the second fugue is based on an arias from the last section, a duet, with the lines quoted going,

Wife: My honey, my pug
Husband: My fetters, my clog
Wife: Let’s tamely jog on
Both: Let’s tamely jog on, as many other have done.

The last statement of this theme in the fugue continues the verse with the lines

Wife: And sometimes at quiet
Husband: but oftner at strife
Both: Let’s tug, let’s tug, the tedious, tedious load of our married life.

I find it a terribly, terribly endearing air.

Two Fugues from The Indian Queen No. 1 ( ps | pdf | mp3 )
Two Fugues from The Indian Queen No. 2 ( ps | pdf | mp3 )

Now this is a simple fugue I quite like. It strictly should be included in the 2001 batch of compositions I guess. Actually, I’ll tell the story. So I was all, like, loving all this counterpoint what was going around in the summer of 2001, and decided that it’d be just groovy if I could write a fugue. So I tried, and I was quite proud of my efforts, and I posted it to some website. And the dudes there were, like, “Dude, that’s nice, but it’s not a fugue”, and this frustrated me a little. I found myself remembering it last summer, and thought I’d like to root it out, but all I could find of it were some preliminary sketches of the theme and some other voices. I tried completing it as I remember it, but I wasn’t able to get it right. But there was enough to construct an actual fugue from it; it turned out okay! It was very satisfying.

Fugue in A ( ps | pdf | mp3 )

And now for another bunch of fugues – the first one doesn’t have too much character other than a rhythmically off-putting countersubject really.

Fugue in A minor ( ps | pdf | mp3 )

Another Purcell-related fugue, this time “come come ye sons of art” from his music for the Queen’s birthday; pretty straightforward, if a little long, but nothing too jarringly unpleasant in it.

Fugue in C# major ( ps | pdf | mp3 )

The following fugue was lyrical enough that I couldn’t really resist tacking on a simple prelude based on a variation of that theme. I’m quite fond of some of the harmonies in the fugue.

Prelude and Fugue in G minor – Prelude ( ps | pdf )
Prelude and Fugue in G minor – Fugue ( ps | pdf | mp3 )

I amn’t quite able to decide whether the following fugue isn’t one of the must unmusical things I’ve written – it seems to have a certain dynamism, but…yeah…maybe I should blame it all on the countersubject… .

Fugue in C ( ps | pdf | mp3 )

It is only with the disclaimer that I do not claim the following “fugues” to have any real merits beyond a certain playfulness that I you see them here; they themes (which are, along with the first countersubject, well over four years old) are belonging to a friend of mine who I have no doubt will sue me for billions and billions if he ever sees that I have put them up here; the first theme is clearly not fugue-material and comes out sounding for the most part quite computer-gamey (indeed, it made me feel that there might well be a few fugues lurking about in the megaman soundtracks, that I should check sometime), whilst the second is a little more conventional, but still pretty loosely tossed together.

Fugue on a theme of NS in E ( ps | pdf )
Fugue on a theme of NS in C ( ps | pdf | mp3)

For the sake of posterity, here’s an attempt at humour I might have posted on a (naturally 100% un-illegal) music sharing forum:

There have been a bunch of people just bitching about the complete dearth of satellite sheet-music sharing threads on this forum, and I have to say I totally agree with them; I feel, in fact that we must effect a serious-ass revolution on this here forum.

So, with this in mind, here are my suggestion for some more threads that, whilst slightly specialist (some might say), will still have more than enough followers to ensure a high turnout posts and turnover of participants I anticipate:

——————

Waltzes by composers of the first Vienese school transcribed, by composers of the second Vienese school, for thumb and forefinger of the left hand. (note italics; all other material, however interesting, will be removed by the moderator I’m sure, possibly at the same time as banning you and all of your family members faster than you can say, in as oversized, garishly coloured, and generally obnoxious a font as you can manage, “Could somebody PLS post a version of Pachelbel’s Canon scored for cowbell ensemble?”).

Symphonic etudes with the object of increasing the flexibility of the second violist’s rehearsal schedule.

Music minus one versions of 4’33”.

Postings of scalar passages of Mozart sonatas running from G flat to B in the fourth octave.

Scans of photocopies of the third measure of the dover edition of das Rheingold.

In a similar vein, a thread for Instructions on how to fold an origami edition of Die Meistersinger von Nuernberg, ideally from a single square of the third measure of the dover edition of das Rheingold.

——————

In any event, as the great Oscar Wilde once said, “If you want to live in a World where there are many, many satellite threads, post lots of satellite threads and you’ll live in that sort of world”.

If you are interested in establishing, please send me your answers on a postcode with robust promptitude, and, indeed, entirely loxodromically.

Ho ho ho, I’m sure you’ll agree.

I posted the following on sci.math.research in response to something, but I think I’ll put it here as well, because I think it’s pretty interesting:

Here’s a question for you, that you might want to know the answer to: *Historically*, why are there twelve notes in the scale? And why are seven white and five black?

The answer is that one that ties in lots of stuff about continued fractions, but goes along these lines: one is looking at the octave, and divides it up by looking at the first n fifths (in our scale c,g,d,a,e,b,…) – this divides up the scale.

Pythagoras et al. thought that one should try to keep the variety of intervals between consecutive notes as small as possible – in the end, deciding that the fewer different intervals present the better. Scales generated by fifths that have only two intervals present between side-by-side notes are called Pythagorean. None have just one interval, and the first three Pythagorean scales have 5,7, and 12 notes. 12 was thought pretty much enough, I’m guessing, and it can have nicely embedded into it the two smaller scales (as white and black notes).

I should have a reference for the original article where I read this (some Irish maths society bulletin I think), but I’ve said enough that the material should be findable online. Ah yes, here it is: IMS BULLETIN Number 35 Christmas 1995, p24, “Musical Scales”, María José Garmendia Ridríguez, Juan Antonio Navarro González , for all the good it’ll do you.

Stephen Lavelle

Messiaen was a fair-sound composer with some fair-sound ideas.

I’m basing the body of this analysis around one of the things he was big into, though I’m approaching it from a
mathematical point of view.

I won’t speak of him again in this article.

ok, here’s the notation:

That’s how I’m going to represent the scale, I’m not going to put the sharps above the other normal notes or anything.

Ok, most scales we use don’t have any transformational symmetries. Why? very simple – we know where we stand. Here’s the major scale (x mark the notes):

It has no symmetries.

So you always know exactly where you are and where the main note should be. You feel secure.

Look at the whole tone scale however:

Because the scale looks the same whether you start it on C or D or F# or whatever, you can’t tell where you are – it leaves you feeling very confused and helpless.

Or, in other words, it has transformational symmetries.

I’m going to try and see if i can catalogue these symmetris now if i can. (I’m just seeing what happens as i go along).

The 12 note scale has 12 different symmetries, so when you’re listening to the scale, you can’t tell absolutely where you are, you could be in any one of twelve positions:

The 11 note scale, though it’s hard to differentiate it from a 12 note scale unless you have some really explicit runs, has no symmetries. It is non-symmetrical.

The following 10 note scale has two symmetries, so you can’t tell whether you’re in the top group of five or the bottom group.

The 9-note scale has symmetries too, three of them, (you see now the niceness inherant in having a 12 note scale? so many divisors!).

The 8-note scale has a fair few symmetries, but there are lots of different possible 8-note scales, but they all have the same two symmetries as the 10-note one, except for one version:

This one has two symmetries

the following one has four symmetries! (innit it great?)

Seven-note scales arn’t symmetrical, they have no symmetries, and are the scales we use mostly (eg. the major/harmonic-minor scales)

Six-note scales have a fair few symmetries, the main one being the whole-tone scale from the beginning. It has 6 symmetries:

These ones have two symmetries:

And this one has three:

I hypothesise that given a scale with n notes (in this case 12), and a subscale of k notes, the number of
symmetries depends on the number of common factors of the two numbers. I won’t prove it till I’ve slogged through the rest of the scales.

Five note scales don’t have any symmetries.

Four note scales have lots of symmetries and possible scales. This one has four symmetries:

These ones have only 2:

Three note scales arn’t that common (or versatile!)but there’s one scale that fits the bill with three symmetries:

There’s only one two-note scale with a symmetry(it has two transformational symmetries):

And the one note scale has none.

Right!, that’s the scales done out. Now to look for a pattern :)

see that there’s a sort of pattern emerging? :)

Notice how scales with a length that has no common factors with 12 (eg. 5 or 7) have no symmetries, and how no scale has a number of transformational symmetries equal to a number that doesn’t divide into 12.

The reason that, say, a scale with 7 notes doesn’t have any symmetries in the 12 note system is that it has to be able to divide the 12 notes into pieces of equal sizes. But it can’t. So it has no symmetries.

Here’s a rewritten version of the same table:

(I left out the 12 note scale because it’s not part of the pattern. Also, i dount count scales with 6 symmetries as also having 2 and 3 (though they do))

Given a segment of 12 notes, it can be divided into lengths of its factors greater than 1, i.e.2,3,4,6 (we’ll ignore 12).

Each of these segments can be filled in many different ways, though we won’t count some of them (i.e. xx– is same as –xx, and x–x is same as -xx- when they’re
stuck beside eachother). So given a length n, and k “x”s to put in it, there are (n-1)!/(k!(n-k)!) ways to fill it up. (! means factorial.
e.g. 5!=5*4*3*2*1)

Now, lets say you’re counting the scales with 6 notes. You know that you can get at least one scale with 3 symmetries because 3 divides 12 and 6. The question is, “how many can you get?”. The answer is pretty simple. You have 6 notes, and three identicle areas, each of length 4, each with 6/3 notes in it.

So this tells me that there are 3 different scales with 6 notes and 3 symmetries. But my table only hints at two…why? because a scale with 6 symmetries also has two so it must also be included.

Here’s a modified version of the original table taking this into account:

So, given an L note superscale (in this article L=12), and a subscale of length l, for each common factor f of L and l,
the number of different scales S, of symmetry f is:

I didn’t explain every step in the proof but it generates the grid above … basically if you don’t understand how i deduced it by this stage you wouldn’t
understand the proof. (all to do with cyclic permutations, nothing too interesting).

Some Formalizations in Musical Set Theory PDF or Postscript

An Introduction to Forms and Denotators (Mazzola Stuff) PDF or Postscript

Recordings

Here’s a small selection of what stuff still survives of my recordedmusic. Some of it’s fairly entertaining :)

I’m sorry about the dodgy quality of them – all the ones below were recorded via a minidisk player, copied to a computer, copied back ot a minidisk player, copied back to a computer, compressed, etc., then put up here. The ones recorded were also recorded with *very* *very* dodgy recording equipment. I did try to touch them up a little, but to little effect.

Sleeping Scared : Electronic , 2:29, 1.7mb

Beepy : Electronic , 1:09, 1.7mb

Improvisation: Gathered
Round : Piano, 1:05, 0.7mb

Improvisation in three parts : Piano 36:35
Part 1 13:34, 9.3mb
Part 2 12.29, 8.6mb
Part 3 10.32, 7.2mb

Improvisation around Dies Irae (very rough) : Piano, 4:00, 2.8mb

Lento: synthesized strings, 4:25, 3.2mb

It’s a pity all of my better electronish stuff is long gone (it’s a pity for me anyway ). I did have some entertaining stuff though! I do have lots of midi files of piano stuff I wrote also, but they’re…well – not really for listening to.