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Golden Ratios
Previous | Next by ludwig616 19 January, 2005 - 6:53 PM

I've been reading "The Golden Ratio" and thought to myself, "If Phi is such a divine number, why hasn't it been used to create a musical scale?"

If a musical scale is based on ratios, like 3/2 is a fifth and 2/1 is an octave, why not use the Mother Of All Ratios to create a musical scale?

Can anyone out there link to a website that allows you to hear tones based on a given frequency?

1/20/2005 >> ben

yeah, i don't know enough about music to be much help on this one... sorry

1/20/2005 >> Septimus

There are bunch of different kinds of scales currently used. The four biggies are major, minor, chromatic and modal. (The modal scales get pretty pretty fucking esoteric with names like Lydian, Ionian, Mixolydian
Dorian, Aolian and Phrygian)

Within the 4 biggies, the frequencys of the notes in a given scale are usually related by some simple mathematical law. Scales in traditional Western European music are eight notes starting on one given note and working its way up to the first octave of the starting note going through whole and half steps.

Basically, a scale is a division of an acoustic frequency range in an interval [f,2*f] with a finite number of steps which are defined by their relation to the root of the scale, the note with frequency f.

Scales can begin in any key and to stick with the whole-whole-half-whole-whole-whole-half format and accidentals are placed on certain notes to keep the format consistant.

The simplest system is to name each degree after its numerical position in the scale, for example: the first, the fourth. Because intervals are inclusive, a fifth describes a note which is four notes after the tonic.

Can you tell my dad got his masters degree in musical theory?

1/20/2005 >> ben

hehe, i stopped my musical education pretty much in the 2nd grade, after taking Suzuki violin lessons for 4 years

1/20/2005 >> Casey

"a fifth describes a note which is four notes after the tonic."

Is it notable if I have my fifth with my tonic?

1/20/2005 >> ralph

ben, one more thing we have in common.

1/20/2005 >> Septimus

"Is it notable if I have my fifth with my tonic?"

I think it's vastly preferred. Makes musical thery go down muuuuuch easier.

1/20/2005 >> ben

no way, really? damn, that's one of the more scary ones...

1/20/2005 >> ludwig616

Septimus: Yes, but the current ratio is 3/2 to define a fifth, and on from there. I'm postulating a new musical basis, not necessarily constrained by the current pattern of wwhwwwh, based on 1:1.618 and tempered for continuity.

According to my calculations, it would have 9 scales, and I have yet to see how many notes. But 9 scales is starting to freak me out a little. More on that when I finish my calculations.

I'm gonna ramble for a second... It's not as organic as regular music, in that the harmonics wouldn't necessarily jive, but it's mathematically significant, so theoretically should sound good. I wish I had a place to go where I could test this out...

Anyway, if you think outside of the box, as it were, and discard your 12-step chromatic scale based on the circle of fifths, which is based on the ratio of 3/2, and instead think about a new circle based on Phi, it's interesting.

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