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Music of Aging
Ever feel like a sloppy derivative of your former self? This song's for you. | |
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...
[link]
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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. |
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You "change" a little every day. Then, one day, you stop
changing... |
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Trying to understand your scale - are those chromatic
notes (is 12 the octave of 1)? |
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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. |
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Derivative of y=2 is defined, I think. I dunno. Like I said, a
sloppy derivative. |
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What note to you play on the 0? A rest? |
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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. |
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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. |
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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). |
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9 10 8 1 5 -> 1 1 7 4 -> 0 6 3 -> 6 3 -> 3 |
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[fishboner], what you meant is an absolute value of a difference, not a derivative. |
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[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
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and you take the derivative? |
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[tatterdemalion] why would zero be a rest? Then again, why
not? Sure. It's a rest. Or, it's b. |
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I just like the name "fishboner". |
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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... |
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I like your name, too. My fav is beanangel, though. |
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// 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...// |
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I don't know about the others, but I got a phone call... |
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