Fractal music

I remember someone telling me about fractals and explaining using a coastline. If you only have a very long ruler - say 50 kilometres - (OK bear with me) then as you measure, all the bits less than that - like say Anglesey - get lost as noise. Take it down to a five km ruler, and suddenly you can measure a little bit more, and the distance increases as a result.

Then go down to 500m - more again, and so it goes. Your measurement is longer, because eventually you are twisting and turning round every separate grain of sand. Until you get down to the Planck length - at which point - something else happens I think. (Actually you can't find rulers measuring 10 to the power -35 metre lengths, so I am not worrying about it.)

Where on earth am I going here? Music. I was at a rehearsal this afternoon for an audition for a big classical piece. And the audition pieces are about as clichéd as you can get. O Fortuna (the creepy bit from the Omen), the Hallelujah Chorus, and Zadok the Priest (pretty much the Champions League theme but without the Continental Tyres bit).

Three pieces that are basically strings of note, largely in one key, and with minimal dynamic subtlety - they are either LOUD or quiet and nothing in between. And at one level, we got them pretty good. They started at the same place, and ended together etc. But the tricky little runs that Handel apparently loved were often just a sort of smear from the start to the end. So at one level the piece was fine, but when it got into details it really was the 50 km ruler effect.

Now, everyone's hearing is not the same., but I recall seeing something about the shortest musical time that can be perceived - known as a Tatum (after Art Tatum). And there must be a division of pitch that at least the average person cannot tell the difference between. Again I recall watching a program which talked about how concert pitch had varied across the years - and it played some examples which I thought were distinct. The person listening with me however needed to get pretty much to A flat before she heard a difference. That's I think about 25Hz different - where as I could hear a difference of 2 or 3Hz (or thought I could). [Plus when really close there's a beat effect that helps, so perhaps I couldn't really hear it.]

And our tempered scale, which allows us to play every piece without retuning the piano in between, makes sacrifices. Some intervals are effectively bashed into shape with a big hammer to fit where they belong. So in some keys the true note really feels some way off the note the piano gives you. (If you are a non-musician you will have lost this two paragraphs ago - sorry - I'll write about something else tomorrow.)

But I am guessing computers could play things with such tight intervals and such short times that we can't spot the difference. After all, the Hertz is just a measure of frequency - the number per second. A note doesn't have to be precisely an integer number of Hertz in frequency - so it can have an infinitely long decimal string. And likewise time is thought to be continuous (there's some dissent about a thing called a chronon but that's not viewed as sound science right now). So a note can be shorter, and shorter still.

Yep - the set of people following this blog has now been reduced to musical mathematicians. Sorry!

So to a sentient computer listening to our music, even the finest tuning and timing that a human can produce could be 'off' by 'miles'.

So I need to be a bit more forgiving - at some level, literally nobody is perfect.