Blackjack subsets

Hi Folks

I was wondering if anyone out there has worked out the best 8 and 6 note
subsets of Blackjack? By best I mean best in terms of the harmonic
capabilities.

Kind Regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> Hi Folks
>
> I was wondering if anyone out there has worked out the best 8 and 6
note
> subsets of Blackjack? By best I mean best in terms of the harmonic
> capabilities.
>
There's no right answer for this, as Blackjack doesn't come into its
own harmonically with this few notes, but I'll give you some
possibilities to try out.

6 notes: the 1-3-5-7 hexany; the JI major scale with no second; a
4:5:6:7:9 chord or 4:6:7:9:11 chord with one note added.

8 notes: the approximate 1/1 9/8 6/5 5/4 4/3 3/2 8/5 15/8; the [3 5
7] Euler-Fokker genus; an otonal and utonal pair, of the 4:5:6:7:9 or
4:6:7:9:11 types, sharing the 3:2 interval.

I'd be happy to spell all these out for you in 72-tET notation, if
you wish.

Paul Erlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> > Hi Folks
> >
> > I was wondering if anyone out there has worked out the best 8 and 6
> note
> > subsets of Blackjack? By best I mean best in terms of the harmonic
> > capabilities.
> >
> There's no right answer for this, as Blackjack doesn't come into its
> own harmonically with this few notes, but I'll give you some
> possibilities to try out.
>
> 6 notes: the 1-3-5-7 hexany; the JI major scale with no second; a
> 4:5:6:7:9 chord or 4:6:7:9:11 chord with one note added.
>
> 8 notes: the approximate 1/1 9/8 6/5 5/4 4/3 3/2 8/5 15/8; the [3 5
> 7] Euler-Fokker genus; an otonal and utonal pair, of the 4:5:6:7:9 or
> 4:6:7:9:11 types, sharing the 3:2 interval.
>
> I'd be happy to spell all these out for you in 72-tET notation, if
> you wish.

Let me try some of these myself and feel free to correct anything. I'm notating everything
starting with A as note 0/72 taking care to begin with the 2-5-2-5 etc. pattern. So my first 6
notes of 72 go A, A^, A>, A] or Bb[ , Bb < , Bb v, Bb, etc. I got the accidentals from an earlier
posting by Graham I think. So my Blackjack notation is: A, A>, Bb^, B[ , B>, C< , C#[ , C#v , D< ,
D, Ebv, Eb^, E, E> , F^, F] , F#> , G< , G] , G#v , A<

6 notes - the 1 -3 -5 -7 hexany = A, C#[ , E, G<
- the JI major scale with no second = can't find a good 5:3 starting on A. Does this
start on the A>?
- a 4:5:6:7:9 = A, C#[ , E, G< , B[ (assuming that the :9 is an approximate 8:7?) plus
one other note.
- a 4:6:7:9:11 = A, E, G< , B[ , can't figure out the :11. Starting on A> gives a
better :11 but a funny :7.

Not doing too well here, particularly with the 9 and 11.

8 notes - I understand the approximate 1/1 9/8 6/5 5/4 4/3 3/2 8/5 15/8; and the [3 5 7]
Euler-Fokker genus, but not the otonal and utonal pair.

I'd be interested to see the 6 and the 8 note examples in BJ steps. Thanks for the help.

Kind regards.

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> 6 notes - the 1 -3 -5 -7 hexany = A, C#[ , E, G<

That's only four notes. The hexany is the six-tone scale that
Robert Walker keeps talking about, with the wind chimes and all.

> - the JI major scale with no second = can't find a good
5:3 starting on A.

The scale doesn't start on A.

> - a 4:5:6:7:9 = A, C#[ , E, G< , B[ (assuming that the :9 is
an approximate 8:7?)

This is strange notation and doesn't correspond to any of those
proposed so far. But in any case, the chord in question doesn't
start on A, and is within 4 cents of a pure 4:5:6:7:9.

> I'd be interested to see the 6 and the 8 note examples in BJ
steps. Thanks for the help.

I'll do that when I get back to the office. In the meantime, you can
take my lattice and transpose all the notes down a 12-tET minor
third, so that we'll have the scale centered on A as you desire it.
Then you'll easily find the hexanies (geomtrically, they're
octahedra) and the JI major scales with no 2nd.

>
>
> Kind regards.

Paul Erlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > 6 notes - the 1 -3 -5 -7 hexany = A, C#[ , E, G<
>
> That's only four notes. The hexany is the six-tone scale that
> Robert Walker keeps talking about, with the wind chimes and all.

Oops, yes I see that now. Wasn't concentrating.

>
> > - the JI major scale with no second = can't find a good
> 5:3 starting on A.
>
> The scale doesn't start on A.

Well, whatever it starts on would be my A. I've chosen this because I want A to be without accidentals
and to be A440. This makes sense with the ranges of the instruments I've built.

>
> > - a 4:5:6:7:9 = A, C#[ , E, G< , B[ (assuming that the :9 is
> an approximate 8:7?)
>
> This is strange notation and doesn't correspond to any of those
> proposed so far. But in any case, the chord in question doesn't
> start on A, and is within 4 cents of a pure 4:5:6:7:9.
>
> > I'd be interested to see the 6 and the 8 note examples in BJ
> steps. Thanks for the help.
>
> I'll do that when I get back to the office. In the meantime, you can
> take my lattice and transpose all the notes down a 12-tET minor
> third, so that we'll have the scale centered on A as you desire it.
> Then you'll easily find the hexanies (geomtrically, they're
> octahedra) and the JI major scales with no 2nd.

Many thanks

Best wishes

>
>

Paul wrote:

> This is strange notation and doesn't correspond to any of those
> proposed so far. But in any case, the chord in question doesn't
> start on A, and is within 4 cents of a pure 4:5:6:7:9.

I think I've worked out the notation, and the lattice is

A>
/
/
C<----Eb^
/ \/
/ /\
B[----D--/--F]-\--A
/ \ / / \
/ \ / / \
A>----C#v---E>----G#v---C<----Ebv
/ \/ \/ /
/ /\ /\ /
C<----Eb^/--G<-\--Bb^/--D<----F^----A<
/ \ / / \ /
/ \ / / \ /
B[----D-----F]----A-----C#[---E-----G]
/ \/ \/ /
/ /\ /\ /
A>----C#v---E>-/--G#v\--C<-/--Ebv---F#>
/ \ / / \ /
/ \ / / \ /
Eb^---G<----Bb^---D<----F^----A<
\/ \/ /
/\ /\ /
A--\--C#[/--E-----G]
\ /
\ /
Ebv---F#>

A<

Graham

graham@microtonal.co.uk wrote:

> Paul wrote:
>
> > This is strange notation and doesn't correspond to any of those
> > proposed so far. But in any case, the chord in question doesn't
> > start on A, and is within 4 cents of a pure 4:5:6:7:9.
>
> I think I've worked out the notation, and the lattice is
>
> A>
> /
> /
> C<----Eb^
> / \/
> / /\
> B[----D--/--F]-\--A
> / \ / / \
> / \ / / \
> A>----C#v---E>----G#v---C<----Ebv
> / \/ \/ /
> / /\ /\ /
> C<----Eb^/--G<-\--Bb^/--D<----F^----A<
> / \ / / \ /
> / \ / / \ /
> B[----D-----F]----A-----C#[---E-----G]
> / \/ \/ /
> / /\ /\ /
> A>----C#v---E>-/--G#v\--C<-/--Ebv---F#>
> / \ / / \ /
> / \ / / \ /
> Eb^---G<----Bb^---D<----F^----A<
> \/ \/ /
> /\ /\ /
> A--\--C#[/--E-----G]
> \ /
> \ /
> Ebv---F#>
>
> A<
>
> Graham

Yes, that's what I'm using. And thanks for the lattice Graham.

Kind Regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
>
> Paul Erlich wrote:
>
> > > - the JI major scale with no second = can't find a
good
> > 5:3 starting on A.
> >
> > The scale doesn't start on A.
>
> Well, whatever it starts on would be my A.

Ah! Well, that's news!

> I've chosen this because I want A to be without accidentals
> and to be A440. This makes sense with the ranges of the instruments
> I've built.

You mean you want to have the following pitches:

A unaltered
C# lowered by 1/12-tone
D unaltered
E unaltered
F# lowered by 1/12-tone
G# lowered by 1/12-tone

?

There are two ways to acheive this -- center the Blackjack scale on

C raised by 1/4-tone

or on

C lowered by 1/3-tone

Are you sure this is what you want? Is the JI major scale with no 2nd
that important to you, over and above all the other scales, and
having it on A rather than D or G or C?

Once you decide on this, I'll be happy to show you where all the
chords and scales I was talking about are.