Talk:Prime harmonic series/WikispacesArchive
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why not start with 2
"2/2" is equivalent to 1. And 1 looks even better than "1/1", I think.
In fact you skip 1 in all the given ratios except for "1/1"
- xenwolf November 05, 2010, 01:06:02 AM UTC-0700
Hi-
not sure what you're saying here...?
- danterosati November 05, 2010, 07:56:27 AM UTC-0700
...let me add a version of yout table, that will show my intention:
| N (primes) | scale |
| 1 (2) | 2/2 |
| 2 (2,3) | 2/2, 3/2 |
| 3 (2,3,5) | 2/2, 5/4, 3/2 |
| 4 (2,3,5,7) | 1/1, 5/4, 3/2, 7/4 |
| 5 (2,3,5,7,11) | 1/1, 5/4, 11/8, 3/2, 7/4 (pentatonic) |
| 6 (2,3,5,7,11,13) | 2/2, 5/4, 11/8, 3/2, 13/8, 7/4 (hexatonic) |
| 7 (2,3,5,7,11,13,17) | 2/2, 17/16, 5/4, 11/8, 3/2, 13/8, 7/4 (heptatonic) |
| 8 (2,3,5,7,11,13,17,19) | 2/2, 17/16, 19/16, 5/4, 11/8, 3/2, 13/8, 7/4 (octatonic) |
- xenwolf November 08, 2010, 04:23:18 AM UTC-0800
am i right in assuming that you want to "start with 2" because then it follows the mathematical definition of the prime number series? Since the attempt here is to relate it to acoustic/musical phenomena, I don't really see why we cannot have a modified series that reflects those concerns. If the point of the mathematical definition of a prime number is that it is not composite, i.e., not derivable from smaller numbers than itself (other than one), in acoustics we must take into account (if we choose to) the phenomena of octave equivalence, which would rule out 2 right away. Also, 1/1 or 1 is so fundamental to the whole concept of just intonation, that it seems silly to do away with it, unless there were a compelling reason to do so. You have suggested 2/2 but have not provided any rationale for it besides that you think it "looks better", which I don't understand either.
- danterosati November 08, 2010, 06:12:21 AM UTC-0800
Oh, sorry, The 2/2 looks silly, indeed. I wanted to suggest to take only 1 instead of 1/1 - so my example table was better written like this:
| N (primes) | scale |
| 1 (2) | 1 |
| 2 (2,3) | 1, 3/2 |
| 3 (2,3,5) | 1, 5/4, 3/2 |
| 4 (2,3,5,7) | 1, 5/4, 3/2, 7/4 |
...but you are right, the prime 2 can be used in any power, the other primes not...
wouldn't it be better to describe the special role of 2 with a further sentence?
- xenwolf November 08, 2010, 07:47:35 AM UTC-0800