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Tag Archives: music

I always like when I can bring (structured) graphs and cohomology into the picture. Yeah. : )

A quick tutorial, and a piece

So, I link two things here; firstly a sort-of tutorial for the counterpoint analysis program (more a worked example):

Counterpoint Analysis Program Tutorial/Fugue in Eb ( PS | PDF )

It should make the program make rather a lot more sense. Oh, and for the record, I don’t dislike the piece as much now as I did when I was writing the tutorial.

and, secondly, a rather dull affair:

Waking ( PS | PDF )

Well, that’s it for now. Have another compositional tool I’ve just finished, but want to see if I can do anything with it before putting it up.

Iz in ur piano
writing u sonataz.

3 new pieces

I actually have written another post before this, but it’s only going to appear in two days time, because, well, the ordering of these things is important, and the contents of this post pre-date those of the one I just wrote, except this disclaimer, so.

Firstly, the worst piece I have written to date in my life; I include it simply because it invokes some Galois theory:

Suite ( ps | pdf )

Secondly, a quick oriental fugue that was to form part of its own suite, but alas I wasn’t able to come up with anything to complement it.

Fugue in F# ( ps | pdf )

Thirdly, I broke the 10-minute time barrier. This is important news for me. It’s also one of my better-sounding pieces, and my first recent attempt at writing a piece in sonata form.

Sonata ( ps | pdf )

As for what’s coming in two days. Well, ye’ll have to wait. (I do not mean to imply that it’s worth waiting for; it’s not, really).

It was a pleasant experience, writing this program.

Counterpoint Analysis Program

Counterpoint Analysis Program

V0.1 as of June 01 2007

So, this is a program that, when you input various melodies, will attempt to find contrapuntal relationships between them. I use something like a slightly weakened version of the 1st species counterpoint rules of Fuchs for this. As you may guess from the version number, this program is chiefly for my own use. However, I think it’s usable enough that it’s conceivable that other people might also use it. Oh, disclaimer: it doesn’t always (or even mostly) give great counterpoint examples, but that wasn’t so much the motivation; I wrote it because I’m never sure when writing fugues that I’m not missing some particular combination of themes that sounds especially nice; with this, I get straight away a bunch of combinations to play about with; many which I wouldn’t have seen without it I think (of course, I won’t limit myself to what this program outputs, but it’s a very good starting point I think), this makes it useful as a compositional tool for me.

No, no no, don’t expect any pictures (yet); it’s a console program (so far), so! And please, if you’ve anything to say about it, don’t hesitate to say it, either here or via email – I’m unlikely to do any work on it otherwise (as it fulfils my personal needs rather well in its current form).

Download Zip – Contains windows binaries, basic documentation, and Haskell source (should you wish to recompile it on a different platform).

Worked Example

Here be bells.

My faux-“Irish” collection

*cough* Yep. Some more. But this time an “Irish”-themed batch.

First is over *gasp* six years old. It fit in to the theme, and has a small charm to it I think, so:

Etude No. 8 ( ps | pdf | mp3 )

Second was written last of all, so that the pieces might fit together and warrant my dredging up the above study; it’s slow and mainly atmospheric in intent (Also it is, shocking, me playing the notes in the recording – it was easy enough and had enough ornamentation that I could without expending any effort do a more convincing interpretation than my computer : ) )

Angelus ( ps | pdf | mp3 )

Thirdly, the piece that made me try put them all together, a short fugue with “Irishy” subjects; I’m pretty happy with the texture I managed to get for the most part. But yeah:

Fugue in Bb ( ps | pdf | mp3 )

So yeah; I can rest easy; three Irish-styled pieces in seven years is probably not anything worth notifying the doctors over, and I doubt I’ll increase my pace any time toooo soon.

She knows what she wants. Do you know what you want?

Prelude & Fugue, Fanfare, and Nocturne

Bah. Another one. There’ll be some non-“musical” content up here before I post up any more of These Sorts Of Things, I promise! It’s a pretty small piece though, shouldn’t cause tooo much offence. If you’re a bit squeamish, just look away and you’ll be fine.

Prelude and Fugue in Eb ( ps | pdf )

[update: There were some errors in the prelude. oops. fixed now!]


Also, because adding new scores to an existing post isn’t the same as adding a new musical post and so breaking my promise above, two other pieces;

Don’t know what I think about the following piece; should definitely not be played with a metronome.

Nocturne ( ps | pdf )

And this is a piece that was originally titled “Dance” but seemed a little too short and repetitive to really be able to stand with that sort of title hanging off it. However, owing to some Bentzon-inspired inspiration, it appears in this humble post as a Fanfare, a title which, to my ears, suits it just fine!

Fanfare ( ps | pdf )

There. Take a big breath. Good. See? Wasn’t that bad; nothing too it, really.

Yes, I know, not exactly one of my most inspired posting to this site.


Hah. Just a quick call to drop off some scores. And no, no recordings; don’t think any of these are really worth it this time. And, as usual, forgive my lack of dynamical indications.

Firstly, a monophonic fugue on the SOS motive, with a bit of That Other Tune thrown in near the end because, well, I had no other choice.

Also:just realized that this is badly formatted, that there are a heap of empty bars at the end.

Fugue on SOS ( ps | pdf )

Secondly, the worst fugue I have written to date (seriously, don’t bother; it’s just up here For The Record, Because).

Bad Fugue ( ps | pdf )

Thirdly, a prelude & fugue pair, the prelude of which I like (owing to notational laziness, I put the ornaments after the bar lines instead of before, which is what I mean to do), the fugue which isn’t as good as it aught be.

[Also:just realized that this is especially badly formatted, that I left the title out. Oops.: fixed!]

Prelude and Fugue in Am ( ps | pdf )

Fourthly, a wee rag with little to recommend it; it was mainly an exercise – I might try properly to write some another time.

Rag ( ps | pdf )

Fifthly, a song setting; oh yes, I tried. Actually my second attempt: yep, my first try was too bad to put up even *here*, which should tell you something about it. This one is okay though, I think.

Reflections in a Mirror ( ps | pdf )

And lastly (that is to say, sixthly), and most recently, a wee study; haven’t tried something like this in a while…I am a litttttle satisfied with it, though, all things considered.

Etude #23 ( ps | pdf )

[edit: some notes were in the wrong octave (of all places to be!); fixed!]
Anyway. Off with me again. Might be back any minute to finish putting up those wee stories from Way Back, heh.

There are many's the theme from Megaman that I'm rather fond of. Don't want to be One Of Those People, the type that does That Sort Of Stuff, though. That would be terrible, to be sure.

Another Fugue, eh?

Well, it’s better than *nothing*, right? This one is on a theme from a computer game I was might fond of, Mega Man (X3; Blizzard Buffalo’s theme*).

I’ll say no more.

Fugue on Blizzard Buffalo’s Theme ( ps | pdf | mp3 )

*the internet keeps trying to tell me that he is actually called frozen buffalo. I will have to consult my memory more thoroughly to make certain, I guess. You can probably find a decent copy of the theme if you want know what it sounds like here.

Yep. I don't like tooo much the direction I took that particular theme. Not as fun as people might expect. That makes it challenging then, right?

Some new pieces :D

So I’ve made some computer-rendered versions of these piano pieces what I’ve put up. You can check out the compositions page to listen to hear computer interpretations of the pieces I’ve already put up. This means that people can at least get an idea of what they should sound like. I hope nobody is toooo offended by it all.

But. I have three whole new fugues to add here. Now isn’t *that* something.

The first piece is a syncopated fugue I’m rather fond of, though it is a bit brief.

Syncopated Fugue ( ps | pdf | mp3 )

Secondly is a Fugue-version of a canon I did in the octave a while back. I’m not really too fond of it, truth be told. Saying that, I don’t think it’s the worst thing it the *whole* world.

Fugue on Canon Theme ( ps | pdf | mp3 )

Oh, and finally, a bit of fun. Yep.

Fugue on Pinky and the Brain Theme ( ps | pdf | mp3 )

He had peppers on the mind. Don't...don't we all?

My favourite calculation: Combination tones

Hmm, so in the interest of subscribing to this mathematical carnival what’s doing the rounds now, I’m writing something specifically mathematical in nature, my favourite elementary derivation. I’m trying to make it understandable and brief – if anyone is having trouble following, I can help in the comments.

Okay, so lets say we’re hearing a signal given by f(t); let’s assume it’s periodic. Now, to monitor what we hear, we have to view this as a sum of sine waves

f=a*sin(t)+b*sin(2t)+c*sin(3t)+ …

so a,b,c represent the frequencies we hear of frequency 1,2,3, etc, and the bigger the coefficient the bigger the amplitude.

Lets look at two really simple sounds, pure sine waves of different frequencies sin(at), and sin(bt). SO, they each have exactly one frequency present.

Now, so what if there were some non-linearity of our hearing system. That is what if, when someone plays f=sin(at)+sin(bt), we don’t actually hear this, but rather something more complicated.

So, the simplest way of such a thing being non-trivial is to introduce a quadratic non-linearity (ignoring coefficients…we’re thinking that because “all” functions can be taylor expanded as f(t)+f(t)2/2+f(t)3/3!+…, the next best thing to having just f(t) is to having the first two terms).

So, anyway, now when someone plays a signal f(t), we don’t hear f(t), but rather f(t)+f(t)2

So, what results from this? Well, we have to break down f(t)+f(t)2 to being a sum of sine waves first.

f(t)+f(t)2=sin(at)+sin(bt)+ (sin(at)+sin(bt))2

looking up trig tables and decomposing further we get (ignoring coefficients)


Ah, so look at this. We might be led to deduce from this that, if non-linearities were present, when someone plays two frequencies at the time, we will also perceive sounds playing at double either frequency, their sum, and their difference.

Now, the multiples of a and b can be reasonably expected to be masked by overtones (though it is possible to bring them out), but the difference (and, to a lesser extent, the sum), on the other hand, can be controlled very easily, just by bringing the two source sounds closer together or further apart. And, indeed, we can quite easily hear them.* Which is darnedly neat.

I like this calculation so very, very much because it’s surprisingly fruitful; whenever I feel like I’m loosing my faith in the power of Taylor expansions, I go through this derivation again.

The phenomenon was first noted by Tartini, the derivation was by Helmholtz, and these extra tones are sometimes called Tartini tones or, more commonly combination tones.

What’s also interesting, by the by, is that these effects are actually quadratic: I remember, the first time I heard an example (they can be found on the interweb quite easily, here for instance), I was listening to them with earphones, and the strength of the combination tone totally overwhelmed the two base ones. But, when I played it on speakers, it was much weaker relative to these tones, and if I went too far away, I couldn’t hear it at all.

*okay; this is a lie, actually the third order terms are the easiest to hear, corresponding to things like 2a-b…and there’s an explanation for this (check out Dave Benson’s notes if you want to know more).

I've been well-Fuxed, oh yeah.

I’ve put up what some music yeah

Oh yes. Well then, as a break from this story-telling what I’ve been doing after a long put-off, I’m going to break what by putting up some of these compositions what I’ve written that’ve emerged from this composition group that formed itself at the start of the academic year within the maths department.

The scores of my efforts can be found here.

No recordings though. And I’d rather stay away from using this icky Sibelius plugin the one what’ll let you listen to midi files as you watch the score. So, not the most accessible of musical archives. Of course, if you actually want to hear any of them, then you should come along to this composition group what we have (get in touch with me if you want to know more details).

I’ve also been trying to get rid of some of these absolutely bizarre problems some people other than myself have noticed about links behaving quite naughtily. But in a way that leaves some of the less-important areas of the site unformatted. But OH WELL, right?

Right, bitch.