Blackjack chord and scale finder slide-rules

No. I'm still not back. :-)

Here are the URLs for the posts I could find containing Blackjack "slide rules". Thanks to Alison Monteith for pointing me to some I missed earlier.

/tuning/topicId_22519.html#22519
/tuning/topicId_22527.html#22535
/tuning/topicId_22532.html#22622
/tuning/topicId_22532.html#22655
/tuning/topicId_22532.html#22715
/tuning/topicId_22527.html#22806

The last contains a brief explanation.

They represent Blackjack as a chain of secors, just as you would represent a meantone as a chain of fifths. That way you can slide any pattern along the chain and it gives the same chord (or subset scale) everywhere that it fits. No wolves. You'll just have to change the notation to match your favourite Blackjack key (the above mostly use degree numbers for 72-tET). And of course they must be viewed in a monospaced font such as Courier.

I give below, a Blackjack chain of secors using the notation that I treat as standard, because it's center (D) matches a center of the Halberstadt keyboard and the center of the meantone universe that all our notation is based on (D is the central note in the chain of natural fifths FCGDAEB). Note that miracle and meantone meet in 31-tET. This key has the same number of sharps as flats. It also happens to suit my Blackjack guitar design, and I think it suits Graham Breed's guitar tuning too.

Note that this key has an A natural in it, which should be tuned to 440 Hz and everything else based on that. The fact that A isn't the center of the chain is irrelevant.

D> E[ F<F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^ B> C] D<

Legend for 72-tET notation:

ABCDEFG#b as in 12-tET
plus the ASCIIfied Sims accidentals
] = 1/4 tone up
> = 1/6 tone up
^ = 1/12 tone up
v = 1/12 tone down
< = 1/6 tone down
[ = 1/4 tone down

Here's the key Joseph Pehrson uses, centered on C.

C> D[Eb< Ev F Gb^ G> A[Bb< Bv C Db^ D> E[ F<F#v G Ab^ A> B[ C<

That's the one Paul Erlich's 3D 7-limit lattices are based on, since he made them for Joseph, except he uses Gbv where it should be F#v. Paul admits this is wrong but at the time he couldn't find a sharp symbol.

Here's another possibility. It maximises the number of naturals. It's centered on the D:A fifth (like Eb to G# in meantone). It contains GDAE naturals. It has a JI major scale with no second, on A, and a JI minor scale with no fourth, on G. Maybe this is what you want Alison.

F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^ B> C] D<D#v E F^
6-----------------3--4---JI-major---7--1--no-second------5
1-----------------5--6---JI-minor---2--3--no-fourth------7

It might also make sense to center it on the C:G fifth, but that won't have an A in it. You could center it on G:D and get both C and A naturals. But why any particular natural has to be there, I'm not sure. Whatever naturals you have you would tune the same as they are in a 12-tET based on A440.

And finally here's Graham Breed's decimal notation.

4> 5> 6> 7> 8> 9> 0 1 2 3 4 5 6 7 8 9 0< 1< 2< 3< 4<

The whole point of the decimal notation is that you can then throw away the slide rule. All you have to remember is that 0< comes after 9 and 9> comes before 0. Then you can transpose chords and scales by simple addition and subtraction.

But in the meantime, choose the sliders for the scales or chords of interest, from the archived posts whose URLs are given above, and paste them above or below a Blackjack chain of secors as notated above. Then slide them along to find all ocurrences.

On another topic, here's a couple of other unrelated things I've posted in the past that I've just recently put up on my website with minor edits.

http://dkeenan.com/Music/NobleMediant.txt
http://dkeenan.com/Music/Miracle/MiracleIntervalNaming.txt

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

David C Keenan wrote:

> No. I'm still not back. :-)
>
> Here are the URLs for the posts I could find containing Blackjack "slide rules". Thanks to Alison Monteith for pointing me to some I missed earlier.
>
> /tuning/topicId_22519.html#22519
> /tuning/topicId_22527.html#22535
> /tuning/topicId_22532.html#22622
> /tuning/topicId_22532.html#22655
> /tuning/topicId_22532.html#22715
> /tuning/topicId_22527.html#22806
>
> The last contains a brief explanation.
>
> They represent Blackjack as a chain of secors, just as you would represent a meantone as a chain of fifths. That way you can slide any pattern along the chain and it gives the same chord (or subset scale) everywhere that it fits. No wolves. You'll just have to change the notation to match your favourite Blackjack key (the above mostly use degree numbers for 72-tET). And of course they must be viewed in a monospaced font such as Courier.
>
> I give below, a Blackjack chain of secors using the notation that I treat as standard, because it's center (D) matches a center of the Halberstadt keyboard and the center of the meantone universe that all our notation is based on (D is the central note in the chain of natural fifths FCGDAEB). Note that miracle and meantone meet in 31-tET. This key has the same number of sharps as flats. It also happens to suit my Blackjack guitar design, and I think it suits Graham Breed's guitar tuning too.
>
> Note that this key has an A natural in it, which should be tuned to 440 Hz and everything else based on that. The fact that A isn't the center of the chain is irrelevant.
>
> D> E[ F<F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^ B> C] D<
>

Well, that could suit my notational requirements. Can anyone remind me how to work out frequencies from this with A at 440Hz? I'm not yet there with tuning Blackjack by ear.

> Here's another possibility. It maximises the number of naturals. It's centered on the D:A fifth (like Eb to G# in meantone). It contains GDAE naturals. It has a JI major scale with no second, on A, and a JI minor scale with no fourth, on G. Maybe this is what you want Alison.
>
> F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^ B> C] D<D#v E F^
> 6-----------------3--4---JI-major---7--1--no-second------5
> 1-----------------5--6---JI-minor---2--3--no-fourth------7

That would do as well, if I could work out the frequencies.

>
>
> It might also make sense to center it on the C:G fifth, but that won't have an A in it. You could center it on G:D and get both C and A naturals. But why any particular natural has to be there, I'm not sure. Whatever naturals you have you would tune the same as they are in a 12-tET based on A440.
>
> Regards,
> -- Dave Keenan
> Brisbane, Australia
> http://dkeenan.com

Many thanks if you're there Dave.

Best Wishes

>

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

> > Note that this key has an A natural in it, which should be tuned
to 440 Hz and everything else based on that. The fact that A isn't
the center of the chain is irrelevant.
> >
> > D> E[ F<F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^ B> C] D<
> >
>
> Well, that could suit my notational requirements.

It does? I thought you insisted that there be a JI major scale with
no second built upon A-440. As you can see, this arrangement doesn't
even have E in it.

> > Here's another possibility. It maximises the number of naturals.
It's centered on the D:A fifth (like Eb to G# in meantone). It
contains GDAE naturals. It has a JI major scale with no second, on A,
and a JI minor scale with no fourth, on G. Maybe this is what you
want Alison.
> >
> > F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^ B> C] D<D#v E F^
> > 6-----------------3--4---JI-major---7--1--no-second------5
> > 1-----------------5--6---JI-minor---2--3--no-fourth------7
>
> That would do as well, if I could work out the frequencies.

I'd be happy too, if you're sure this is what you want to use. Dave
is right, though, that centering on D is prettiest notationally.

If you center on C, I won't have to redo my lattices for you :)

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

> > Here's another possibility. It maximises the number of naturals.
It's centered on the D:A fifth (like Eb to G# in meantone). It
contains GDAE naturals. It has a JI major scale with no second, on A,
and a JI minor scale with no fourth, on G. Maybe this is what you
want Alison.
> >
> > F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^ B> C] D<D#v E F^
> > 6-----------------3--4---JI-major---7--1--no-second------5
> > 1-----------------5--6---JI-minor---2--3--no-fourth------7
>
> That would do as well, if I could work out the frequencies.

72 frequency
not. in Hz
.
.
.
A 220.0000
A> 224.2769
Bb^ 235.3366
B[ 239.9117
B> 251.7424
C< 256.6364
C] 269.2918
C#v 274.5270
D< 288.0646
D 293.6648
D#v 308.1461
Eb^ 314.1367
E 329.6276
E> 336.0357
F^ 352.6065
F> 359.4614
F#v 366.4496
G< 384.5201
G 391.9954
G#v 411.3257
Ab^ 419.3222
A 440.0000
.
.
.

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:

/tuning/topicId_29923.html#29923

> No. I'm still not back. :-)
>
> Here are the URLs for the posts I could find containing
Blackjack "slide rules". Thanks to Alison Monteith for pointing me to
some I missed earlier.
>
> /tuning/topicId_22519.html#22519
> /tuning/topicId_22527.html#22535
> /tuning/topicId_22532.html#22622
> /tuning/topicId_22532.html#22655
> /tuning/topicId_22532.html#22715
> /tuning/topicId_22527.html#22806
>
> The last contains a brief explanation.
>
> They represent Blackjack as a chain of secors, just as you would
represent a meantone as a chain of fifths. That way you can slide any
pattern along the chain and it gives the same chord (or subset scale)
everywhere that it fits. No wolves. You'll just have to change the
notation to match your favourite Blackjack key (the above mostly use
degree numbers for 72-tET). And of course they must be viewed in a
monospaced font such as Courier.
>

Thanks so much, Dave, if you're still browsing here for posting this
compendium again. Finally, I've printed it up and put it all in one
place. And, also, finally, I understand what you mean by "sliding
the chord along..." This same kind of procedure would even work with
a meantone chain of fifths as you mention above...

Of course, it's a matter of setting the actual "scale" or pitch
notation... but that's not rocket science here....

Thanks so much again for your patience!

Quit doing profitable work, and come back here soon!

best,

Joseph

Paul Erlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > > Here's another possibility. It maximises the number of naturals.
> It's centered on the D:A fifth (like Eb to G# in meantone). It
> contains GDAE naturals. It has a JI major scale with no second, on A,
> and a JI minor scale with no fourth, on G. Maybe this is what you
> want Alison.
> > >
> > > F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^ B> C] D<D#v E F^
> > > 6-----------------3--4---JI-major---7--1--no-second------5
> > > 1-----------------5--6---JI-minor---2--3--no-fourth------7
> >
> > That would do as well, if I could work out the frequencies.
>
> 72 frequency
> not. in Hz
> .
> .
> .
> A 220.0000
> A> 224.2769
> Bb^ 235.3366
> B[ 239.9117
> B> 251.7424
> C< 256.6364
> C] 269.2918
> C#v 274.5270
> D< 288.0646
> D 293.6648
> D#v 308.1461
> Eb^ 314.1367
> E 329.6276
> E> 336.0357
> F^ 352.6065
> F> 359.4614
> F#v 366.4496
> G< 384.5201
> G 391.9954
> G#v 411.3257
> Ab^ 419.3222
> A 440.0000
> .
> .
> .

Excellent - howdyoudothat?

Regards

Paul Erlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > > Note that this key has an A natural in it, which should be tuned
> to 440 Hz and everything else based on that. The fact that A isn't
> the center of the chain is irrelevant.
> > >
> > > D> E[ F<F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^ B> C] D<
> > >
> >
> > Well, that could suit my notational requirements.
>
> It does? I thought you insisted that there be a JI major scale with
> no second built upon A-440. As you can see, this arrangement doesn't
> even have E in it.
>

No, the JI major scale with no second was only one possible option for a Blackjack subset. Sorry,
as usual, for not being clear on this. I want to tune everything to A440 and it makes sense to me
to have A notated without accidentals. So I worked out a notation starting on A but since then
have been guided (by your good self and others) to other possible notations with a 'clean' A, such
as the one below. Now I have the frequencies I can tune up.

>
> > > Here's another possibility. It maximises the number of naturals.
> It's centered on the D:A fifth (like Eb to G# in meantone). It
> contains GDAE naturals. It has a JI major scale with no second, on A,
> and a JI minor scale with no fourth, on G. Maybe this is what you
> want Alison.
> > >
> > > F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^ B> C] D<D#v E F^
> > > 6-----------------3--4---JI-major---7--1--no-second------5
> > > 1-----------------5--6---JI-minor---2--3--no-fourth------7
> >
> > That would do as well, if I could work out the frequencies.
>
> I'd be happy too, if you're sure this is what you want to use. Dave
> is right, though, that centering on D is prettiest notationally.
>
> If you center on C, I won't have to redo my lattices for you :)
>

Well, the lattices are fine as they are. I'd never have worked out the spellbinding beauty of two
'modulating' hexanies without the visual representation. I showed the lattice, enlarged, to a
pianist and teacher, explaining that this was the future of musical theory. He gave me the
'two-headed alien' look and seemed to be severely hacked off. But he had the good sense to ask
more and I've no doubt it has set him thinking and possibly moving out of his comfort zone.

It'll be a good mental exercise to work with different notations, and already I'm thinking in
terms of sounds and shapes with notation an afterthought. It's when I eventually muster the
players that I'll have to do a hard sell on whatever notation I choose.

Kind Regards

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

> Excellent - howdyoudothat?

In Matlab, with this command:

220*2.^(sort(mod(116.666667/1200*[-13:7],1)))'

(since I saw the chain of secors extending from 13 secors "below" A
to 7 secors "above" A)