u/Jdelami

I started with x from 1 to 7.

X^2

I squared the x, yielding 1,4,9,16,25,36,49 I then subtracted each x^2 term from the previous (I.e., 9-4=5, 16-9=7, etc.) I then subtracted those differences a second time (I.e., 5-3=2, 7-5=2, etc.)

On the second time subtraction pass, all the differences were the same: 2

X^3

I again started with x from 1 to 7, then cubed x. Then I made subtraction passes, much like the above. At the third time subtraction pass, all differences were the same: 6

X^4

I yet again started with x from 1 to 7, and then raised to the 4th power. At the fourth time subtraction pass, all differences were the same: 24

I’m wondering about the pattern here: Why does x^2 have all differences the same on the second pass… x^3 has all differences the same on the third pass… x^4 has all differences the same on the fourth pass…

Seems like the exponent is equal to the number of subtraction passes. I imagine if you used, say, x^17, it would take you 17 passes until all the differences are the same?

Why is that?

I started with x from 1 to 7.

X^2

I squared the x, yielding 1,4,9,16,25,36,49 I then subtracted each x^2 term from the previous (I.e., 9-4=5, 16-9=7, etc.) I then subtracted those differences a second time (I.e., 5-3=2, 7-5=2, etc.)

On the second time subtraction pass, all the differences were the same. (2)

X^3

I again started with x from 1 to 7, then cubed x. Then I made subtraction passes, much like the above. At the third time subtraction pass, all differences were the same. (6)

X^4

I yet again started with x from 1 to 7, and then raised to the 4th power. At the fourth time subtraction pass, all differences were the same. (24)

I’m wondering about the pattern here: Why does x^2 have all differences the same on the second pass… x^3 has all differences the same on the third pass… x^4 has all differences the same on the fourth pass…

Seems like the exponent is equal to the number of subtraction passes. I imagine if you used, say, x^17, it would take you 17 passes until all the differences are the same?

Why is that?

Double bass player here. For intonation, I have been doing the following exercise:

I put arms down at my sides, close my eyes, then reach up and try to bow C on the G string. Open eyes and check with a tuner. I do this ten times each for the notes A, C, D and G 8va on the G string. Making very slow progress. Unlike shifting, you have no reference note to shift from. Basically you’re landing on a note without much previous information. Given all the different exercises for intonation, I’m wondering if people think this particular exercise is worthwhile.