February 28, 201016 yr I would have done something like this myself if I had the ability to, however, until I reach a level where I'd be able to do something like this well, here is a challenge for all of you: Harmonize Pi I've been going through music theory where I'm becoming comfortable with the use of roman numerals representing chord progressions. As I became well versed with this, the numerical aspect of my mind has begun to wonder what mathematical progressions such as pi (3.1415926535...) or e (2.7182818...) would sound like as a tonal progression. The first 50 digits of pi are 31415926535897932384626433832795028841971693993751. It's seems strangely coincidental that the last two numbers there are 5 1, aka V I (pac). Inverting chords to preserve tonality, try and make a 4-part tonal piece following the above progressions.
February 28, 201016 yr Author Well that's a trippy idea! Can we tonicize other keys or modulate? Sure, I tried that a little myself. I'm not too experienced in that area, though, I'm sure you could do better. :)
February 28, 201016 yr Sorry - you mean using the digits of pi as scale degrees for a bass line and then adding chords above to create a tonal progression? How do you qualify 9 and 0? Also 1 and 8 - those would be the same. Also - you chose 50 digits, so it's not really coincidental at all that it ends with a 5 and 1. I mean - if it was a finite number, then you could maybe call it coincidental - but pi goes on and on.
February 28, 201016 yr Author Sorry - you mean using the digits of pi as scale degrees for a bass line and then adding chords above to create a tonal progression? How do you qualify 9 and 0? Also 1 and 8 - those would be the same. Also - you chose 50 digits, so it's not really coincidental at all that it ends with a 5 and 1. I mean - if it was a finite number, then you could maybe call it coincidental - but pi goes on and on. I see 8 and 9 as being the 1 and 2 an octave above the tonic. I see 0 as being a rest. But, I'm not being strict. Interpret the scale degrees as you will. Perhaps coincidental was not the right word, I just thought it was interesting that at a round number like 50 we would see pi end with 5-1.
March 2, 201016 yr I did something similar with the fibbonacci sequence. And surprisingly if you correspond each number relative to its diatonic distance from the root (i.e. 8 = I, and 13 = VI because it is 5 above the octave), the phrase repeats every 16 numbers... or 16 measures musically if you assign each number to a measure. The equation i used came out with 0's which I equated to the 7th because it is one before the root (I). Also each half of the sequence ended with the 7th (measure 8 and measure 16) and each half started with 2 consecutive measures of the same note. I made a short metal bit based entirely off of it and it was rather neat sounding. To make things easier to understand here is the sequence broken up into its two halves root root 2nd 3rd 5th root 6th 7th 6th 6th 5th 4th 2nd 6th root 7th This set was repeated consistently. i went as far as 1.72x1013 Pi would be another interesting project, though much less organized.
March 8, 201016 yr I used pi as the scale degrees in the bass and harmonised chords over top. I treated 8 as 1, and 9 and 0 as wildcards (rest, or note of choice). The first fifty numbers I harmonised as such: http://img534.imageshack.us/img534/8876/ss20100308014114.png Yes, I ignore the fact that the value pi actually begins with the number 3 and I didn't bother with proper voice leading. Sue me. With slight adjustments, here's a MIDI sound sample: http://cid-831123e954ae1fef.skydrive.live.com/self.aspx/.Public/pi.MID?ccr=6495
November 23, 201015 yr You could interpret pi as a frequency ratio. (odviously a terminating, pi approximation, as pi is irational.) This makes it (approximatley) 1981.79536 cents Phi is: 833.0903 cents I made a 16 tone scale based on Phi that repeats at 3/1.
March 12, 201115 yr It's Pi Day again two days from now... anybody else wanna take up the challenge? You could make it a serial row. xDD
March 13, 201115 yr Okay, I'd really like to do it, but can I write a melody above it? Thanks! Heckel
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