Interesting.
I went to bed last night and woke up this morning thinking about harmony, more specifically harmonic ratios and overtones. For example, if I start with the note C and say this corresponds to the pitch that sounds at 256hz, then the first overtone which this note generates would be 512hz, or C2, being that it's oscillating at twice the rate (I'm using made up values for the number of oscillations; this would be a very flat C in the musical world) . The next overtone would be 768hz, or 3 times the initial rate of vibration, producing a G, relative to our original C. The next overtone 1024hz would be another C, at 4 times the initial rate and 1280hz would be the next overtone, at 5 times the initial rate, giving a relative E.
Anyway, that's the basics of overtone harmonics, so last night I was thinking about this, reducing the problem to just the ratio's themselves, not really thinking about hz or whatever, so:
1=C, 2=C, 3=G, 4=C, 5=E, 6=G, 7=Bb, 8=C...
Thus are new pitches generated from an initial starting pitch, through this sequence of overtones that can be described as ratios.
So, I start thinking this morning, what if I just use
prime numbers to generate my pitches?
1 2 3 5 7 11 13 17 23...
C C G E Bb F# A Db Gb...
I'm not even sure if the notes to overtone ratios are matching up because I really haven't explored enough in this area, but for some reason this morning I spent about 4 hours thinking about this stuff. I started making a table, like the multiplication tables from grade school....
1____3_____5____7
__C_____G____E___Bb
3____9 ____15___21
__G_____D____B____F
5____15___25___35
__E_____B____G#___D
7____21___35___49
__Bb____F____D___Ab
Well, I didn't realize 2 was considered prime and that 1 was not, but I also quickly realized that a 2-d table wasn't gonna do it for me so I started working on a 3-d table. Actually I was still using pencil and paper so it became 2-d cross-sections or slices of a 3-d grid. Each slice looks similar to the grid above, but I won't bother posting cause I don't feel I got anywhere with it. For one thing the axes were (1 3 5 7) by (1 3 5 7) by (1 3 5 7), when they I know now that they should be (2 3 5 7) by (2 3 5 7) by (2 3 5 7) if I'm going to be consistent in my exploration of prime numbers. Except that I started to think about the fibonacci sequence (yes, rather inexplicably) and soon left my prime numbers grid behind. I began using the sequence as the basis for selecting the overtones that would serve as my functional pitches:
0=? 1=C 1=C 2=C 3=G 5=E 8=C 13=A 21=F
And then through octave multiplication/reduction (simply doubling) I was constructing harmonies, using these ratios.
F A C = 168hz 208hz 256hz
(An F Major chord)
These values were reached by multiplying the given ratios by powers of 2, which are in themselves pretty interesting-- 21x2^3=168, 13x2^4=208, 8x2^5=256, etc.
Pretty strange sounding stuff. Anyhoot, at this point I let it go for the day....
Until about an hour and a half ago when I saw this thread and '
prime numbers' once again invaded my mind. Funny thing is that some one posted a link to that video last week and I just blew it off as some flakey new age stuff about 3 secs in. Well, seeing all the talk about prime and fibonacci numbers gave me a reason to stay engaged for the duration.
It's really interesting and has lots of interesting implications, as well as focusing on some numbers that had come up for me this morning. Honestly, though, that information is totally lost on me. I don't understand how to use any of those relationships or how they can be applied to my thought experiments, much less the technical problems of our world. Looks like a few of you know what to do with all this info, and I'm really excited about that. Can't wait to see some action birthed from this strange experience.
I myself just wanted to share how strange and extra-ordinary this thread is, especially from my personal perspective of having spontaneously began the day in overtone-series-harmonics-ratios-prime-numbers-fibonacci-sequence-head-space only to, hours later, discover that others were thinking about the same stuff, if for entirely different reasons.
Well, that's cool. Wow.
Great Love,
John