Re: [TUNING] Re: The mil: 1/1023 of an equal-tempered semitone

(To tuning, tuning-math)

On Sun, Mar 22, 2015 at 5:59 PM, Gavin R. Putland <grputland@...> wrote:

> Wilson's work substantially reduces the originality of my article
> (although some remains). I shall acknowledge it at
> http://beta.briefideas.org/ ASAP.

That's done at http://t.co/swOBXVyHBM .

(Pity about the single quotes in the title, which were displayed
correctly in the preview but not in the final article!)

--
Gavin R. Putland
http://www.grputland.com .

On Sun, Mar 22, 2015 at 1:32 AM, kraiggrady@... [TUNING]
<TUNING@yahoogroups.com> wrote:

> the 12276 division of the octave was proposed by Erv Wilson in 1995.
> see http://anaphoria.com/sieve.PDF

Thanks for this information.

Wilson's work substantially reduces the originality of my article
(although some remains). I shall acknowledge it at
http://beta.briefideas.org/ ASAP.

--
Gavin R. Putland
http://www.grputland.com .

Suppose the Cantor Set mapped across an octave. Any thoughts on how to hear a polyphony of every note at once? (Assume each point in set corresponds to a pitch).

How are the points in the Cantor Set mapped to pitches? Are we looking at logarithms of frequencies, frequencies, or string length?

1) Logarithms of Frequencies (octave):
[0\3, 1\3] U [2\3, 3\3]
[0\9, 1\9] U [2\9 3\9] U [6\9, 7\9] U [8\9, 9\9]
...

2) Frequencies:
[3/3, 4/3] U [5/3, 6/3]
[9/9, 10/9] U [11/9, 12/9] U [15/9, 16/9] U [17/9, 18/9]
...

3) String Length:
[3/6, 3/5] U [3/4, 3/3]
[9/18, 9/17] U [9/16, 9/15] U [9/12, 9/11] U [9/10, 9/9]
...

For instance:

0 -> sine wave @ 440 Hz
n/m -> sine wave @ 440 * 2^(n/m) Hz
1 -> sine wave @ 880 Hz

On 8/31/2015 9:14 AM, gedankenwelt94@... [tuning-math] wrote:
>
> How are the points in the Cantor Set mapped to pitches? Are we looking > at logarithms of frequencies, frequencies, or string length?
>
>
> 1) Logarithms of Frequencies (octave):
>
> [0\3, 1\3] U [2\3, 3\3] ===>
>
> [0\9, 1\9] U [2\9 3\9] U [6\9, 7\9] U [8\9, 9\9]
>
> ...
>
>
> 2) Frequencies:
>
> [3/3, 4/3] U [5/3, 6/3]
>
> [9/9, 10/9] U [11/9, 12/9] U [15/9, 16/9] U [17/9, 18/9]
>
> ...
>
>
> 3) String Length:
>
> [3/6, 3/5] U [3/4, 3/3]
>
> [9/18, 9/17] U [9/16, 9/15] U [9/12, 9/11] U [9/10, 9/9]
>
> ...
>
>