31edo version of blackjack

i've added a table and lattice-diagram of the
31edo version of blackjack, at the bottom of
my blackjack page:

http://sonic-arts.org/monzo/blackjack/blackjack.htm

-monz
"all roads lead to n^0"

--- In tuning@y..., "monz" <monz@a...> wrote:
> i've added a table and lattice-diagram of the
> 31edo version of blackjack, at the bottom of
> my blackjack page:
>
> http://sonic-arts.org/monzo/blackjack/blackjack.htm
>
>
>
> -monz
> "all roads lead to n^0"

note that the new "standard" for blackjack places its center, the
notes G-D, at the positions labeled 22 and 9 in this lattice. even in
5-limit, but especially in higher limits, these are more connected to
neighboring notes than is the note labeled 0 in your lattice.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> --- In tuning@y..., "monz" <monz@a...> wrote:
> > i've added a table and lattice-diagram of the
> > 31edo version of blackjack, at the bottom of
> > my blackjack page:
> >
> > http://sonic-arts.org/monzo/blackjack/blackjack.htm

you write,

"The central periodicity-block contains most of the blackjack scale"

but of course the central periodicity block contains all of the
blackjack scale, as it contains all 31 pitches of the tuning . . .

some of the adjacencies that you omit, by not drawing more of the
parallel blackjack swaths in the 31-equal lattice, represent 31-
equal's best approximation of the 5:3, a very consonant interval. so
i feel you're not showing 31-equal blackjack's full 5-limit resources
when you're including so little of the parallel swaths. meanwhile, in
72-equal, or even 41-equal, one swath is enough, since this interval
will no longer be the tuning's best approximation of 5:3.

of course, in 31-equal, the 19-note scale (y'know, the usual meantone
one) looks a lot more impressive than blackjack in most respects . . .

--- In tuning@y..., "monz" <monz@a...> wrote:
> i've added a table and lattice-diagram of the
> 31edo version of blackjack, at the bottom of
> my blackjack page:

Wasn't that page supposed to have links to music on it?

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

> note that the new "standard" for blackjack places its center, the
> notes G-D, at the positions labeled 22 and 9 in this lattice.

Why isn't the center the center--the note exactly in the middle of the chain, corresponding to the meantone D?

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
>
> > note that the new "standard" for blackjack places its center, the
> > notes G-D, at the positions labeled 22 and 9 in this lattice.
>
> Why isn't the center the center--the note exactly in the middle of
>the chain, corresponding to the meantone D?

that isn't as good a choice as mapping the neutral third above, and
the neutral third below, the center of the chain, to be your
primary "central" pitches (such as G-D) -- since the latter pitches
participate in more consonant intervals and chords than the true
center of the chain does.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> --- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
> wrote:
> >
> > > note that the new "standard" for blackjack places its center,
the
> > > notes G-D, at the positions labeled 22 and 9 in this lattice.
> >
> > Why isn't the center the center--the note exactly in the middle
of
> >the chain, corresponding to the meantone D?
>
> that isn't as good a choice as mapping the neutral third above, and
> the neutral third below, the center of the chain, to be your
> primary "central" pitches (such as G-D) -- since the latter pitches
> participate in more consonant intervals and chords than the true
> center of the chain does.

actually, this decision was made, if i recall correctly, by alison,
joseph, dave k., and maybe manuel (or others), and not by me at all.
but if it works for them, it works for me!

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

> that isn't as good a choice as mapping the neutral third above, and
> the neutral third below, the center of the chain, to be your
> primary "central" pitches (such as G-D) -- since the latter pitches
> participate in more consonant intervals and chords than the true
> center of the chain does.

Aren't you telling your grandma how to suck eggs here? We can leave to the composer what he or she chooses to use as a tonic. Meanwhile, the center is just the center, isn't it? I find the central mode to be just fine, incidentally.

hi paul,

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, November 01, 2002 12:23 PM
> Subject: [tuning] Re: 31edo version of blackjack
>
>
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
> wrote:
> > --- In tuning@y..., "monz" <monz@a...> wrote:
> > > i've added a table and lattice-diagram of the
> > > 31edo version of blackjack, at the bottom of
> > > my blackjack page:
> > >
> > > http://sonic-arts.org/monzo/blackjack/blackjack.htm
>
> you write,
>
> "The central periodicity-block contains most of the blackjack scale"
>
> but of course the central periodicity block contains all of the
> blackjack scale, as it contains all 31 pitches of the tuning . . .
>
> some of the adjacencies that you omit, by not drawing more of the
> parallel blackjack swaths in the 31-equal lattice, represent 31-
> equal's best approximation of the 5:3, a very consonant interval. so
> i feel you're not showing 31-equal blackjack's full 5-limit resources
> when you're including so little of the parallel swaths. meanwhile, in
> 72-equal, or even 41-equal, one swath is enough, since this interval
> will no longer be the tuning's best approximation of 5:3.

ah, good point. i'll update that graph to include all the
blackjack chains which occur ... i was originally going to
do it that way anyway but changed my mind.

> of course, in 31-equal, the 19-note scale (y'know, the usual meantone
> one) looks a lot more impressive than blackjack in most respects . . .

i had made a bingo-card-lattice of this, but never uploaded it
to the website, so i just did. it's at the bottom of the 31edo
section of the Tuning Dictionary "bingo-card" entry:

http://sonic-arts.org/dict/bingo.htm

-monz
"all roads lead to n^0"

Looking at the 21 from 31 blackjack,

can those working with it confirm or deny the following statements

1. Pitch class 30 feels like a focus or 'tonic'
2. Pitch class 31 feels like a focus or 'tonic'

An equaivalent in 53 I can also determine:

0,2,5,7,10,12,15,17,20,22,25,27,30,32,35,37,40,42,45,47,51,(0

Mark

--- In tuning@y..., Mark Gould <mark.gould@a...> wrote:
> Looking at the 21 from 31 blackjack,
>
> can those working with it confirm or deny the following statements
>
> 1. Pitch class 30 feels like a focus or 'tonic'
> 2. Pitch class 31 feels like a focus or 'tonic'

Can you explain what you mean in terms of the chain of secors?

>
> An equaivalent in 53 I can also determine:
>
> 0,2,5,7,10,12,15,17,20,22,25,27,30,32,35,37,40,42,45,47,51,(0

I like the 22-tone orwell MOS as an analogy.

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

> > of course, in 31-equal, the 19-note scale (y'know, the usual
meantone
> > one) looks a lot more impressive than blackjack in most
respects . . .
>
>
> i had made a bingo-card-lattice of this, but never uploaded it
> to the website, so i just did. it's at the bottom of the 31edo
> section of the Tuning Dictionary "bingo-card" entry:
>
> http://sonic-arts.org/dict/bingo.htm

you say it tiles the plane, but it doesn't -- tiling implies no holes
or spaces.

the diagram could be explained more clearly. are the shaded cells the
ones not included in the scale?

p.s. i really meant "impressive" in the 7-limit, not just the 5-
limit . . .

--- In tuning@y..., Mark Gould <mark.gould@a...> wrote:
> Looking at the 21 from 31 blackjack,
>
> can those working with it confirm or deny the following statements
>
> 1. Pitch class 30 feels like a focus or 'tonic'

definitely not.

> 2. Pitch class 31 feels like a focus or 'tonic'

it can be projected that way, but pitch class 22 is even more
comfortable as a tonic.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
>
> > that isn't as good a choice as mapping the neutral third above,
and
> > the neutral third below, the center of the chain, to be your
> > primary "central" pitches (such as G-D) -- since the latter
pitches
> > participate in more consonant intervals and chords than the true
> > center of the chain does.
>
> Aren't you telling your grandma how to suck eggs here?

alison, joseph, dave k., manuel and others went through a lengthy and
thorough investigation to choose this standard . . . it's all in the
archives. i don't know what that has to do with my grandma or eggs.

We can leave to the composer what he or she chooses to use as a
tonic. Meanwhile, the center is just the center, isn't it? I find the
central mode to be just fine, incidentally.