# Music theory idea:

sonhouse
Posers and Puzzles 13 Sep '06 17:45
1. sonhouse
Fast and Curious
13 Sep '06 17:45
The scale used today is derived from the 12th root of 2. Can a musical scale be made from the PI'th root of 2? Pi number of notes per octave.
2. 13 Sep '06 18:05
Originally posted by sonhouse
The scale used today is derived from the 12th root of 2. Can a musical scale be made from the PI'th root of 2? Pi number of notes per octave.
A scale made of PI'th root of 2 is one way to desrcibe our 12 tone system.
Another way is to find the nearest fraction p/q of each tone with as smallest integer possible. Pythagoras did that.

But of course you can form any series of tones with arbritrary frequencies. The problem is to find it enjoyable.
3. sonhouse
Fast and Curious
13 Sep '06 20:41
Originally posted by FabianFnas
A scale made of PI'th root of 2 is one way to desrcibe our 12 tone system.
Another way is to find the nearest fraction p/q of each tone with as smallest integer possible. Pythagoras did that.

But of course you can form any series of tones with arbritrary frequencies. The problem is to find it enjoyable.
The pythy method is the best one for pure chords but they are pure only for a given scale. So the 12th root of 2 was invented to be fairly close in all scales, or slightly off everywhere but the octaves. Octaves remain pure. I have to drag out my trusty HP 48G and see what the Pi root does.
4. 15 Sep '06 19:33
Originally posted by sonhouse
The pythy method is the best one for pure chords but they are pure only for a given scale. So the 12th root of 2 was invented to be fairly close in all scales, or slightly off everywhere but the octaves. Octaves remain pure. I have to drag out my trusty HP 48G and see what the Pi root does.
Um. I never knew that notes would be slightly out. I thought scales were devised so that the resultant beat frequency of two over lapping frequencies would fall nicely on a peak or trough to make it sound 'nice'. I thought also that dischords were when the beat frequency fell out of synch which made it sound so horrible. All of this , of course, is my own thinking and not what I've read.
5. sonhouse
Fast and Curious
16 Sep '06 19:50
Originally posted by jimslyp69
Um. I never knew that notes would be slightly out. I thought scales were devised so that the resultant beat frequency of two over lapping frequencies would fall nicely on a peak or trough to make it sound 'nice'. I thought also that dischords were when the beat frequency fell out of synch which made it sound so horrible. All of this , of course, is my own thinking and not what I've read.
The pure scales make mathematically perfect beats which sound best, the original Pathy scales. But they are only good for one scale, say Do.
If you go to Fa, for instance, the intervals are wrong and will sound like it, the chords will be off. Thats where the 'Tempered scale' comes in. It was invented before JS Bach's time and he is the first to use it extensively. It is actually a bit off everywhere but the octaves but close enough that all the scales can be used and it takes a purist to know the differance.
6. 16 Sep '06 20:25
But the the 12th root of 2 scale sounds somewhat artificial, don't you think...? Where is the charm of music with total perfection?
7. Hindstein
Finish Him!!!
17 Sep '06 00:27
Originally posted by sonhouse
The scale used today is derived from the 12th root of 2. Can a musical scale be made from the PI'th root of 2? Pi number of notes per octave.

http://www.harmonics.com/lucy/lsd/chap1.html

I must admit to not really caring about the intricacies of microtones and the like - though I have a degree in music, it does seem to have little appeal outside the walls of the houses of physicists and mathmaticians...
8. sonhouse
Fast and Curious
17 Sep '06 05:31
Originally posted by Hindstein