Re: [MMM] 34 Equal Wins The Gyaling Award

> From: jacky_ligon <jacky_ligon@...>
> To: <MakeMicroMusic@yahoogroups.com>
> Sent: Sunday, January 13, 2002 11:52 AM
> Subject: [MMM] 34 Equal Wins The Gyaling Award
>
> Step 13 of 34 EDO comes in a little sharp,
> but this would seem to be the lowest number
> ET which approximates this tuning.

Hey, how did you do that so fast?! I was looking into
it -- and still working on my post -- but you beat me
to it!

I found this:

146-cET (= ~8.22-EDO) is an ET of very low cardinality which
gives pretty good approximations to 5 of the intervals in the
Gyaling scale (at 146, 292, 438, and 876 cents), one that's
rather farther away (730 cents), and one oddball pitch
that's not even close (584 cents).

Note that 17-EDO also gives a good approximation of 5 of the notes.

-monz

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monz wrote:

>
> 146-cET (= ~8.22-EDO) is an ET of very low cardinality which
> gives pretty good approximations to 5 of the intervals in the

What does low cardinality mean? Would that make this scale a poor catholic?

GZ

G,

{you wrote...}
>What does low cardinality mean? Would that make this scale a poor catholic?

I'm sorry, but this belongs on tuning-humor-(in-short-supply)@yahoogroups.com.

ROFLMAO!

Cheers,
Jon

> From: Jonathan M. Szanto <JSZANTO@...>
> To: <MakeMicroMusic@yahoogroups.com>
> Sent: Sunday, January 13, 2002 12:22 PM
> Subject: Re: [MMM] 34 Equal Wins The Gyaling Award
>
>
> G,
>
> {you wrote...}
> >What does low cardinality mean? Would that make this scale a poor
catholic?
>
> I'm sorry, but this belongs on
tuning-humor-(in-short-supply)@yahoogroups.com.
>
> ROFLMAO!

Yeah, that was a good one, George!

In case you really did need to know the answer:
cardinality simply refers to the number of distinct degrees in a scale.

When Jacky suggested finding a Gyaling-equivalent ET, he wrote:

> From: jacky_ligon <jacky_ligon@...>
> To: <MakeMicroMusic@yahoogroups.com>
> Sent: Sunday, January 13, 2002 10:48 AM
> Subject: [MMM] Re: Gyaling Tuning: The Diamond Path
>
> Might be interesting to see which ET best approximates this tuning.
> I'd bet without looking that it'd be a pretty numerous division of
> the octave.

IOW, he was guessing that an ET with rather high cardinality
would be required to represent the Gyaling scale. So I took
that as a challenge to find one of only a few notes.

-monz

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Joke aside, I did need to know.

Thanks Monzadelic!

G

>
>
> In case you really did need to know the answer:
> cardinality simply refers to the number of distinct degrees in a scale.

> From: jacky_ligon <jacky_ligon@...>
> To: <MakeMicroMusic@yahoogroups.com>
> Sent: Sunday, January 13, 2002 11:52 AM
> Subject: [MMM] 34 Equal Wins The Gyaling Award
>
>
> Gyaling Tuning:
>
> 0
> 139
> 280
> 450
> 493
> 707
> 884
> Step 13 of 34 EDO comes in a little sharp,
> but this would seem to be the lowest number
> ET which approximates this tuning.

Assuming that "8ve"-equivalence is OK, your Gyaling scale
gives an interval matrix (in cents) of:

| 139 280 450 493 707 884
----+------------------------------
884 | 455 596 766 809 1023 0
707 | 632 773 943 986 0 177
493 | 846 987 1157 0 214 391
450 | 889 1030 0 43 257 434
280 | 1059 0 170 213 427 604
139 | 0 141 311 354 568 745
0 | 139 280 450 493 707 884

where the number from the left column is subtracted from the
number in the top row, mod 1200.

Then using this more stringent criteria for finding an
ET equivalent, I took a look at 34-EDO and again it seems
to be the winner.

-monz

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