Science Forums

# Mathematics In Music

## Recommended Posts

A thread for the mathematical and scientific study what makes music, music.

example, How string frequency, mixed with body resonance create the sounds they make.

How scale lengths are determined.

How some frequencies interact to create percussive noise cancellation.

etc.

##### Share on other sites

Tymoczko believes that their theory can be used to investigate the differences between musical styles. "Our methods are not so great at distinguishing Aerosmith from The Rolling Stones," he said. "But they might allow you to visualise some of the differences between John Lennon and Paul McCartney. And they certainly help you understand more deeply how classical music relates to rock or is different from atonal music."
http://plus.maths.org/content/geometrical-music-theory

Yet another topic i didn't even know existed, but interesting and appropriate for here. Not too good with words today but I think the very next sentence sums up the purpose of this thread.

If it is mathematical and involves/pertains too music it is welcome to be discussed here.

##### Share on other sites

Pythagoras (582-496 BCE) Greece was the first to try and pin this all down with a mathematical system called the cycle of fifths (or circle of fifths). Start with the tonic. Multiply by a perfect fifth (3/2). Do it again. This puts you into the next octave. Bring it down an octave (multiply by 1/2) so you can keep building your scale. Well …

(3/2)*(1/2) = 3/4

is the inverse of 4/3, an interval with a great deal of consonance. When you completely build the scale, the ratio 4/3 turns out to be the fourth interval in the series of eight that make up an octave. Thus the name fourth. The fifth and the fourth are inversions of one another in an octave. They are the only intervals that work out this way. That makes them special, in my mind, but the adjective that was ascibed to them was perfect. Thus the intervals 4/3 and 3/2 are called the perfect fourth and perfect fifth, respectively.

So here's the plan again: start with the tonic, bring it up a perfect fifth, take it down a perfect fourth, and repeat until the ratio equals an (2/1).

We'll start on C since that's the middle of the modern piano. Behold!

Oh oh. For those of you familiar with the piano, you will note that the errors occur at notes that do not exist on the keyboard.

http://physics.info/music/

Edited by DFINITLYDISTRUBD
##### Share on other sites
• 1 month later...

Suppose you took a recording of a pleasing musical piece, such the "Blue Danube" waltz. And played it backwards.

All the elements of the piece would still be there. All the notes - their pitch, their relative loudness, the intervals, the consonances, the resonances - everything unchanged, and mathematically the same.

But would the "Blue Danube" played backwards, still sound pleasing. If not, why not?

##### Share on other sites
• 1 month later...

Well I'll be dripped.....

I'm not sure it would be the same reversed from a mathematical stand point...this will require a bit of looking into.

Same notes in reverse order same timing and duration.....sound as pleasing....hrmmm....this is easily doable methinks...properly cliping so the notes do not sound backwards seems the most difficult part.

##### Share on other sites

Blue Danube both forwards and backwards...sadly simply reversed....no idea how to get a played backwards recording short of actually playing it backwards with instruments note for note...could be rather pleasing...though it sounds very different (aside from the usual weirdness caused by playing it backwards)

##### Share on other sites
• 1 year later...

Interesting DFINITLYDISTRUBD!

Wiki has a good page on this

http://en.wikipedia.org/wiki/Music_and_mathematics

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.