by tpinto on 11/25/10, 4:04 PM with 30 comments
by gjm11 on 11/25/10, 4:29 PM
What's special about those simple rational-number ratios? Answer: on most musical instruments, notes whose frequencies are in simple rational ratios sound nice together. This turns out (surprisingly, at least to me) to be a fact about the instrument and not merely about the notes; when you play a given note on a given instrument, you get (kinda) sine waves whose frequencies are those of the given note, plus some higher frequencies; exactly what the higher frequencies are and how much of each you get depends on the instrument. For most instruments, the higher frequencies are integer multiples of the fundamental frequency, and that turns out to mean that the good-sounding combinations of notes are ones with simple rational frequency ratios; but there are instruments that behave differently (e.g., a tuned circular drum; or you can make a synthesized instrument that does anything you like) and different chords will sound good on them.
For much more on this, see William Sethares's book "Tuning, Timbre, Spectrum, Scale" and his web pages at http://eceserv0.ece.wisc.edu/~sethares/ttss.html where you can find, e.g., some music in unorthodox scales performed on (synthetic) instruments designed to make the harmony sound good.
For instance: listen to http://eceserv0.ece.wisc.edu/~sethares/mp3s/tenfingersX.mp3 and hear how out-of-tune it sounds. Now try http://eceserv0.ece.wisc.edu/~sethares/mp3s/Ten_Fingers.mp3 which has exactly the same notes but played on a synthetic instrument designed to make the harmonies work.
by extension on 11/25/10, 7:03 PM
Musical culture seems to resist illumination, perhaps fearing that the "magic" will somehow be broken. The irony is that music is, in a sense, a mathematical illusion, but revealing the trick only makes it more fascinating.
I will add one important point that hasn't really been made: The purpose of equal temperament may have originally been to "change keys without retuning", but it also essentially allows you to play in 12 different keys at the same time. This has been exploited to great lengths as source of musical novelty and is absolutely fundamental to modern music.
by kainhighwind on 11/25/10, 8:01 PM
Just a bit funny to come across it here, it'd be a bit like finding out musicians were talking on a forum going 'wow, computer programs are written using structured text files!' or something of the like. Not trying to be rude..
by hasenj on 11/25/10, 7:12 PM
I recently bought a Oud[1], a classical stringed middle eastern instrument, it's not fretted, it's portable, and adjustable. To me, when I compare it to the piano, the Oud feels like the Unix of musical instruments. It's a bit hard to get used to at first, but it's designed to be lite-weight (portable) and adjustable, allowing power users to be very creative and expressive. Most other users will stick to a standard tuning and placement of fingers.
I'm not super-bothered by the way the piano is layed out, to me it's just a simplified instrument that works for 95% of the cases.
What I don't understand is why do all the middle eastern scales (maqam[2]) have 7 tones. The fact the western C major scale also has 7 tones is just another example of yet another scale with 7 tones (and it happens to correspond to the Ajam maqam[3]).
There are some middle eastern scales not really playable on a piano, like the Rast[4], unless the piano is somehow adjustable.
[1]: http://en.wikipedia.org/wiki/Oud
[2]: http://en.wikipedia.org/wiki/Arabic_maqam
by cletus on 11/25/10, 5:12 PM
What came much later was equal temperament. The 12 steps don't match up exactly. Equal temperament changes the notes slightly by changing the ratio slightly (to factors of the 12th root of 2). I believe it was Bach who first discovered this.
Not all cultures use equal temperament but it is overwhelmingly dominant in the West.
The series also explains chords, keys and so on. For someone like me who is more mathematically inclined it was fascinating. Give it a look if you can.
Oh also it wasn't the BBC as you might expect. It was Channel 4.
by fxj on 11/25/10, 5:49 PM
http://en.wikipedia.org/wiki/19_equal_temperament
there are also some mp3 files using 19 tone scale: e.g. http://www.harrington.lunarpages.com/mp3/Jeff-Harrington_Pre...
by hugh3 on 11/25/10, 4:38 PM
On one level, the white notes are the notes of the C major scale, and the black notes are the semitones which are left over. Why not put all the semitones in one row? That would be much harder to play. Why split it into "C major" and "leftovers"? A bunch of semi-arbitrary decisions made by early harpsichord manufacturers, I guess, which happen to make the instrument easier to play than most alternatives.
If you're looking for an explanation of why the notes of the major scale sound good together whereas most alternative modes sound weird, that's a more difficult question.
by cturner on 11/25/10, 6:47 PM
http://www.amazon.co.uk/How-Music-Works-listener%C2%92s-harmony/dp/1846143152/ref=sr_1_1?ie=UTF8&qid=1290710570&sr=8-1
by JonnieCache on 11/26/10, 12:23 AM
http://www.worldsciencefestival.com/video/notes-neurons-full
by edanm on 11/25/10, 5:03 PM
Haven't read it, but it looks good.
by wzdd on 11/25/10, 4:53 PM
I like the above example because it always starts by sounding "off" to me but seems okay by the end of the piece. It's a matter of what you're used to.
by stupidsignup on 11/25/10, 8:17 PM
by MrJagil on 11/25/10, 6:16 PM
The highly emotional associations I get of rock musicians and metal concerts when thinking about music could not be further from the science of music.
by jacquesm on 11/25/10, 8:11 PM