Posers and Puzzles
13 Sep 06
13 Sep 06
Originally posted by sonhouseA scale made of PI'th root of 2 is one way to desrcibe our 12 tone system.
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.
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.
13 Sep 06
Originally posted by FabianFnasThe 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.
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.
15 Sep 06
Originally posted by sonhouseUm. 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 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.
16 Sep 06
Originally posted by jimslyp69The pure scales make mathematically perfect beats which sound best, the original Pathy scales. But they are only good for one scale, say Do.
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.
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.
17 Sep 06
Originally posted by sonhouseHave you read this?
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...
17 Sep 06
Originally posted by HindsteinThanks for the link. I see they talk about guitars with 25 frets per octave. Have you ever seen such a guitar? It would seem to me they would be so close together as to be difficult to finger. It would definitely intimidate me and I am an expert guitarist. I would love to give it a go though. It is really annoying never to be in tune. I spend a lot of time tuning before I am satisfied I have comprimised it as best as can be done. I can't get comfortable playing till its as perfect as I can get it. Like when you play a G chord then try a E, it doesn't sound right so I keep going back and forth to get a decent compromise between them. You can do a lot by simply bending notes a bit when they are out, which works a lot better if the note needs to go UP in frequency. If it has to go down, you are screwed. Well that covers half the changes anyway!
Have you read this?
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...