Xenharmonic recordings and a common generator pattern )was Re: The blackjackisma)

Gene wrote:

>> 250/243~3125/3087~3136/3125 fairly cries aloud to get used, but I don't >> know
>> that it ever has been.

Okay, here's a try.
First the familiar porcupine:
http://dl.dropbox.com/u/8497979/pp_xenharm_250.mid
Next, tempering out 3136/3125 and period is 7/3:
http://dl.dropbox.com/u/8497979/pp_xenharm_3136.mid
Next, tempering out 3125/3087 and period is 1/3 as the mapping is inverted:
http://dl.dropbox.com/u/8497979/pp_xenharm_3125.mid

Petr

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:
>
> Gene wrote:
>
> >> 250/243~3125/3087~3136/3125 fairly cries aloud to get used, but I don't
> >> know
> >> that it ever has been.
>
> Okay, here's a try.
> First the familiar porcupine:
> http://dl.dropbox.com/u/8497979/pp_xenharm_250.mid
> Next, tempering out 3136/3125 and period is 7/3:
> http://dl.dropbox.com/u/8497979/pp_xenharm_3136.mid
> Next, tempering out 3125/3087 and period is 1/3 as the mapping is inverted:
> http://dl.dropbox.com/u/8497979/pp_xenharm_3125.mid

I'm not sure what you mean here. You could, for instance, replace the approximate 10/9 period with an approximate 28/25 or 25/28 to temper out 3136/3125. Can you relate this to what you did?

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> I'm not sure what you mean here. You could, for instance, replace the approximate 10/9 period with an approximate 28/25 or 25/28 to temper out 3136/3125. Can you relate this to what you did?

Let me expand on this. If you take (10/9)^3, it is equivalent mod the 250/243 porcupine comma to 4/3, and (10/9)^5 is equivalent to 8/5. Similarly, (28/25)^3 is equivalent mod 3136/3125 to 7/5, and (28/25)^5 to 7/4. Finally, (25/21)^3 is equivalent mod 3125/3087 to 5/3, and (25/21)^5 to 7/3. Hence 1-4/3-5/3 ~ 1-7/5-7/4 ~ 1-5/3-7/3. The corresponding subgroups of the 7-limit are 2.3.5, 2.5.7 and 2.5/3.7/3.

Gene wrote:

> 1-4/3-5/3 ~ 1-7/5-7/4 ~ 1-5/3-7/3.

I assume you wanted to say 1-4/3-8/5.

> The corresponding subgroups of the 7-limit are 2.3.5, 2.5.7 and 2.5/3.7/3.

Aha, you're leaving the period at 2/1, that's where it was different.
The reason why I changed the period was that
A) I wanted to somehow involve the prime 3 even though 3136/3125 doesn't include it, and
B) When you say 3125/3087 to me, the first thing which immediately comes to my mind is the non-octave temperament supported by, among others, 13 equal divisions of 3/1.
So the periods were different, but the rest, I think, is in accordance with what you're saying.

Petr

I wrote:

> So the periods were different, but the rest, I think, is in accordance > with
> what you're saying.

And that's also why I had to invert the mapping in the case of 3125/3087.
For porcupine, the generator numbers "0, 2, 5" approximate the JI chord of "5:6:8". For 3136/3125, they mean "4:5:7". But for 3125/3087, they mean "15:21:35" which is much more difficult to recognize than "3:5:7". Therefore, I viewed it as "7:5:3" and understood the generator as a tempered 21/25 rather than 25/21. For this reason, I then also used a period of 1/3 instead of 3/1.

Petr