Hey guys.

I recently found out numerous musicians have incorporated maths into their music, most commonly the Fibonacci series and the golden ratio. I analyzed and saw how the Fibonacci series was used, but what interests me is the golden ratio. I asked my maths teacher about it and he told me that it is roughly 0.618 (or 1.618 can't remember precisely) and he told me that as you go along the Fibonacci series, dividing a number by the previous number will give you the golden ratio (the further up the series you go, the more accurate your answer will be).

But my question is, how would I use the golden ratio in music - in chord progressions or melodies, and how? How has it been used before, a few examples with analysis would be perfect. So if anyone could enlighten me, I'd appreciate it greatly.

Many thanks, Michal.
My math teacher just told us about the Golden Ratio, and I think the Golden Rectangle is 1 to 1.618 like you said.

But I'm really not too sure about the whole incorporating it into music. I'm interested myself.
my band

dig it.
Quote by bangoodcharlote

"James Tenney reconceived his piece For Ann (rising), which consists of up to twelve computer-generated upwardly glissandoing tones (see Shepard tone), as having each tone start so it is the golden ratio (in between an equal tempered minor and major sixth) below the previous tone, so that the combination tones produced by all consecutive tones are a lower or higher pitch already, or soon to be, produced."

I am not quite sure what that means - each tone started in between the major and minor sixth interval of the last tone?

Apart from that, I see what it is doing, however it is mainly using the Fibonacci series. Thankyou, however, for the link.

"The golden ratio is also apparent in the organisation of the sections in the music of Debussy's Image, Reflections in Water, in which "the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the phi position."

Could you please explain what in this case the phi position would be?

Many thanks
Quote by michal23
I am not quite sure what that means - each tone started in between the major and minor sixth interval of the last tone?
Yes. This isn't something you can easily do on the guitar. You're dealing with microtonality and complex stuff like that. You'll end up playing notes between A and the note between A and A#.

"The golden ratio is also apparent in the organisation of the sections in the music of Debussy's Image, Reflections in Water, in which "the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the phi position."

Quote by michal23
Could you please explain what in this case the phi position would be?
It probably comes from the mathetatical definition of the golden ratio. I don't really know what it means.

However, what I get from this is that you'll have a hell of a time trying to do this on the guitar.

I don't want to discourage you from trying something potentially cool, but I'm afraid that you might be trying something impossible.
Quote by bangoodcharlote
I don't want to discourage you from trying something potentially cool, but I'm afraid that you might be trying something impossible.

Oh well. I like challenges.
You're dealing with microtonality and complex stuff like that. You'll end up playing notes between A and the note between A and A#.

Or it's a superb experiment with note bending. I mean the sitar people who use guitar bend microtones all the time.
Quote by capiCrimm
Or it's a superb experiment with note bending. I mean the sitar people who use guitar bend microtones all the time.
now see, that raises a whole other debate. Exactly how many different micro-tones can be sustained between fretted notes through bending?(realistically that is) We need the world's best chromatic tuner ASAP!

But anyway, this is a good "food for thought" thread.
EDIT:
Quote by bangoodcharlote
It wouldn't be a semitone
fixed it, thx.
Gear:
Inflatable Guitar
Digitech GSP 2101/Mosvalve 962/Yamaha S412V
My Imagination
Last edited by KryptNet at Feb 29, 2008,
It wouldn't be a semitone, as a semitone os the distance beterrn G and G# (or C and C#). However, it could be a microtone (I think).

As far as how many microtones you could achieve, I think there's a huge amount.
Quote by bangoodcharlote

As far as how many microtones you could achieve, I think there's a huge amount.
idk about that. How many realistic tones can be reached using a human finger between a perfectly fretted note and a perfect 1/2 bend? I'd say maybe 4 at the very max. But I'm seriously curious on how far a "golden ratio" progression(obviously non-chordal) could go in a guitar's tonality. It would have to be extremely accurate geetar playing or the mixed-in tones would probably negate the whole purpose of it.

If we could get some actual frequencies for "golden ratio" intervals and an oscilloscope, this really would be an interesting guitar experiment!
Gear:
Inflatable Guitar
Digitech GSP 2101/Mosvalve 962/Yamaha S412V
My Imagination
I know sitar players use 4 microtones between certain notes. So it's definitely possible. I'm going to guess the average human ear kicks out at around 6-8 microtones anyway. (I know that dependent on a lot of things, but I believe that's correct)

I'm guessing the gauge of the guitar string will also affect how much precision you have or how easy it is to hit a note.