Consider this melody: 1, 12, 3, 5, 6, 5, 12, 1
the derivative is: 11, 9, 2, 1, 1, 7, 11
The second derivative is: 2, 7, 1, 0, 6, 3
the third derivative is: 5, 6, 1, 6, 3
fourth: 1, 5, 5, 3
etc...-- fishboner, Jan 08 2010 the series of numbers is a piecewise defined function in short- hand. Each number is a note that plays for some interval. The second series is just the difference of each note from the one next to it. It's the slope from one note to the next. Then it's the slope of the slope. More and more alienated from the original function until it turns into 0 at the end.
You "change" a little every day. Then, one day, you stop changing...-- fishboner, Jan 09 2010 Trying to understand your scale - are those chromatic notes (is 12 the octave of 1)?-- tatterdemalion, Jan 09 2010 Tatter, yes. Chromatic. You could start with any sequence. I wrote that one spontaneously. It is so youthful and full of hope before the mathematics of change slowly ravage its glowing visage.-- fishboner, Jan 09 2010 fifth: 4, 0, 2
sixth: 4, 2
seventh: 2
eighth: undefined-- Inyuki, Jan 09 2010 Derivative of y=2 is defined, I think. I dunno. Like I said, a sloppy derivative.-- fishboner, Jan 09 2010 What note to you play on the 0? A rest?
1, 12, 3, 5, 6, 5, 12, 1 - Assuming a root of C: C, c, Eb, F#, Ab, F#, c, C. It's quite Mixolydian.
If you change the 12s to 8s and make it a major scale, it's quite pleasant and happy sounding, even the derivatives. But chromatic allows for too many dissonant notes, I think.
I can't think of any purpose for this other than idle musical curiosity. And possibly mathematical, it creates a way to represent a melody with a single digit (though it can't be derived in reverse).
9 10 8 1 5 -> 1 1 7 4 -> 0 6 3 -> 6 3 -> 3-- tatterdemalion, Jan 09 2010 [fishboner], what you meant is an absolute value of a difference, not a derivative.-- Inyuki, Jan 09 2010 [inyuki] what do you get if you have a piecewise-defined function: y= 1 from x=0 to x<1 4 from x=1 to x<2 9 from x=2 to x<3 7 from x=3 to x<4
and you take the derivative?-- fishboner, Jan 09 2010 [tatterdemalion] why would zero be a rest? Then again, why not? Sure. It's a rest. Or, it's b.-- fishboner, Jan 09 2010 I just like the name "fishboner".-- doctorremulac3, Jan 09 2010 Thanks [doctorremulac]. I read halfbakery for months before joining. This was the only place having discussions about sail blimps, which I was really into at the time. Later, I came upon it again and I noticed a conversation about a solar concentrator (backyard death Ray). There was a little talk about a secondary focusing lens to extend the focus to more distant locations, but, like everywhere else in the net, when the conversation gets to that point, it myseriously ceases...
I like your name, too. My fav is beanangel, though.-- fishboner, Jan 09 2010 // There was a little talk about a secondary focusing lens to extend the [backyard death Ray] to more distant locations, but, like everywhere else in the net, when the conversation gets to that point, it myseriously ceases...//
I don't know about the others, but I got a phone call...-- ldischler, Jan 09 2010 random, halfbakery