Blackjack in 52 EDO

Let's try again.

0,2,5,7,10,12,15,17,20,22,25,27,30,32,35,37,40,42,45,47,50,(0

which of course, is 21 from a 52 card pack. Sadly, the tuning is awful,
except for some 7 limit ratios, but there's an awful pair of 3/2s one at
692.3cents and the other at 715.4. There's a reasonable 5/4 at 392.3, but
6/5 is poor, with one at 300 and the other at 323.1.

apologies for previous error-riddled posts.

Mark

> From: "Mark Gould" <mark.gould@argonet.co.uk>
> To: <tuning@yahoogroups.com>
> Sent: Monday, November 04, 2002 11:56 PM
> Subject: [tuning] Blackjack in 52 EDO
>
>
> Let's try again.
>
> 0,2,5,7,10,12,15,17,20,22,25,27,30,32,35,37,40,42,45,47,50,(0
>
> which of course, is 21 from a 52 card pack. Sadly, the
> tuning is awful, except for some 7 limit ratios, but there's
> an awful pair of 3/2s one at 692.3cents and the other at
> 715.4. There's a reasonable 5/4 at 392.3, but
> 6/5 is poor, with one at 300 and the other at 323.1.
>
> apologies for previous error-riddled posts.

as i explained before, to be a blackjack tuning (and thus
part of the MIRACLE family of temperaments), when latticed
on a 5-limit diagram the tuning must temper out ampersand's
comma 3^7 * 5^6.

the EDOs of lower cardinality than 72 which do this are
31 and 41.

-monz

--- In tuning@y..., "Mark Gould" <mark.gould@a...> wrote:
> Let's try again.
>
> 0,2,5,7,10,12,15,17,20,22,25,27,30,32,35,37,40,42,45,47,50,(0
>
> which of course, is 21 from a 52 card pack. Sadly, the tuning is
awful,
> except for some 7 limit ratios, but there's an awful pair of 3/2s
one at
> 692.3cents and the other at 715.4. There's a reasonable 5/4 at
392.3, but
> 6/5 is poor, with one at 300 and the other at 323.1.
>
> apologies for previous error-riddled posts.
>
> Mark

hi mark.

you finally got it.

52-equal is indeed capable of supporting some sort of blackjack
scale. if you look at xoomer.gif again, you'll see that there is a
straight line connecting 10(&one of the 20s), one of the 51s, the 41,
the 72, the 31, one of the 52s, and one of the 21s, and one of the
11s. this is the line along which ampersand's comma vanishes. in 21-
equal, blackjack is just the whole tuning, and of course the fifths
are extremely flat . . . in the first tuning, it collapses to 10-
equal (as the smaller steps reduce to 0), and the fifths are quite
sharp . . . in 11-equal, it's the *larger* steps that reduce to 0, so
you have a really bizarre representation of blackjack . . .

--- In tuning@y..., "monz" <monz@a...> wrote:
>
> > From: "Mark Gould" <mark.gould@a...>
> > To: <tuning@y...>
> > Sent: Monday, November 04, 2002 11:56 PM
> > Subject: [tuning] Blackjack in 52 EDO
> >
> >
> > Let's try again.
> >
> > 0,2,5,7,10,12,15,17,20,22,25,27,30,32,35,37,40,42,45,47,50,(0
> >
> > which of course, is 21 from a 52 card pack. Sadly, the
> > tuning is awful, except for some 7 limit ratios, but there's
> > an awful pair of 3/2s one at 692.3cents and the other at
> > 715.4. There's a reasonable 5/4 at 392.3, but
> > 6/5 is poor, with one at 300 and the other at 323.1.
> >
> > apologies for previous error-riddled posts.
>
>
>
> as i explained before, to be a blackjack tuning (and thus
> part of the MIRACLE family of temperaments), when latticed
> on a 5-limit diagram the tuning must temper out ampersand's
> comma 3^7 * 5^6.

that's why mark is correct!

> the EDOs of lower cardinality than 72 which do this are
> 31 and 41.

and, depending on which 5-limit approximation is used, so do 51 and
52 -- it's just that those are 5-limit inconsistent, so you have to
be careful to use the right 5-limit approximation -- the one that
lies on the ampersand line in xoomer.gif.

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, November 05, 2002 12:41 PM
> Subject: [tuning] Re: Blackjack in 52 EDO
>
>
> --- In tuning@y..., "monz" <monz@a...> wrote:
> >
> > > From: "Mark Gould" <mark.gould@a...>
> > > To: <tuning@y...>
> > > Sent: Monday, November 04, 2002 11:56 PM
> > > Subject: [tuning] Blackjack in 52 EDO
> > >
> > >
> > > Let's try again.
> > >
> > > 0,2,5,7,10,12,15,17,20,22,25,27,30,32,35,37,40,42,45,47,50,(0
> > >
> > > which of course, is 21 from a 52 card pack. Sadly, the
> > > tuning is awful, except for some 7 limit ratios, but there's
> > > an awful pair of 3/2s one at 692.3cents and the other at
> > > 715.4. There's a reasonable 5/4 at 392.3, but
> > > 6/5 is poor, with one at 300 and the other at 323.1.
> > >
> > > apologies for previous error-riddled posts.
> >
> >
> >
> > as i explained before, to be a blackjack tuning (and thus
> > part of the MIRACLE family of temperaments), when latticed
> > on a 5-limit diagram the tuning must temper out ampersand's
> > comma 3^7 * 5^6.
>
> that's why mark is correct!
>
> > the EDOs of lower cardinality than 72 which do this are
> > 31 and 41.
>
> and, depending on which 5-limit approximation is used, so do 51 and
> 52 -- it's just that those are 5-limit inconsistent, so you have to
> be careful to use the right 5-limit approximation -- the one that
> lies on the ampersand line in xoomer.gif.

OK, i see it now. mouse-over 51 and 52 at
http://sonic-arts.org/dict/bingo.htm#tile-applet

comparing 51 and 52 with 31, 41, and 72 shows that all of them
temper out ampersand's comma.

-monz
"all roads lead to n^0"