Useless theory news

Over on tuning-math we found a "spooky" periodicity in the graph
of "good" ETs for the 7-limit. The graph seemed to cycle from high to
low to high again every 1664 ETs.

Mystified, we looked at 5-limit, and found the same pattern every 612
ETs.

Familiar with 612-tET as the good old "scale of schismas", it hit be
that there must be an important 7-limit tiny interval that is 1/1664
octave.

Indeed there is: 2401:2400, with which Graham Breed created the now
famous "Blackjack pump" chord progression some time ago . . .

What stopped us is that 1664-tET does not itself look like an
especially good 7-limit ET, nor does anything in its vicinity . . .

. . . more useless theory news over at tuning-
math@yahoogroups.com . . .

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, December 14, 2001 5:14 AM
> Subject: [tuning] Useless theory news
>
>
> Familiar with 612-tET as the good old "scale of schismas", it hit
> be [_sic_: me] that there must be an important 7-limit tiny interval
> that is 1/1664 octave.
>
> Indeed there is: 2401:2400, with which Graham Breed created the now
> famous "Blackjack pump" chord progression some time ago . . .

More useless theorizing...

Here's the prime-factorization of the 2401:2400 ratio:

2^-5 * 3^-1 * 5^-2 * 7^4

So in "8ve"-invariant terms (i.e., ignoring prime-factor 2),
it's the difference between 7^4 (= 2401:2048 = ~275.3036259 cents)
and 3^1 * 5^2 (= 75:64 = ~274.5824286 cents), which amounts to
only ~0.721197281 (just a bit more than 5/7) cent.

My voicing and mp3 file of Graham's theoretical "Blackjack pump"
progression is near the bottom of:
http://www.ixpres.com/interval/monzo/blackjack/blackjack.htm

Is there some information I should have for a Dictionary entry
for the "breedsma"?

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In tuning@y..., "monz" <joemonz@y...> wrote:
> Is there some information I should have for a Dictionary entry
> for the "breedsma"?

Just put a picture of Graham's mother and be done with it. :)

Time for bed,
Jon

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_31549.html#31573

>
> My voicing and mp3 file of Graham's theoretical "Blackjack pump"
> progression is near the bottom of:
> http://www.ixpres.com/interval/monzo/blackjack/blackjack.htm
>
>

Hi Monz!

I like the new "click on" effect for Graham's progression. I still
love that blackjack progression... maybe it's the "funky" timbre... I
don't know, but real magic there.

You can compare and contrast that with my recent "extended blackjack
progression" details of which I recently posted:

/tuning/files/Pehrson/

JP