Blackjack hexanies

I'm enjoying catching up with the Blackjack threads, such as Joseph's
progression and the commentaries by others. I'm working with the
interlocking hexanies just now, using the triads as a foundation for
slow harmonic movement.

Taking one at random in 'standard' notation, C< , E[ , G< , F#v , A, C#v
(not, I realise, in ascending order), I'd be grateful if anyone can
refresh me with the names of the triads. Major and minor I know, which
leaves six others. I'd imagine that F#v , C#v , E[ has the word
septimal in it. Merci bien.

Kind Regards

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> I'm enjoying catching up with the Blackjack threads, such as
Joseph's
> progression and the commentaries by others. I'm working with the
> interlocking hexanies just now, using the triads as a foundation for
> slow harmonic movement.
>
> Taking one at random in 'standard' notation, C< , E[ , G< , F#v , A,
C#v
> (not, I realise, in ascending order), I'd be grateful if anyone can
> refresh me with the names of the triads. Major and minor I know,
which
> leaves six others. I'd imagine that F#v , C#v , E[ has the word
> septimal in it. Merci bien.

Bv C Db^ D> E[ F<F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^
-----------5*7---1*5------------1*73*5------------3*7---1*3

Here are some possible names.
[To see this with columns lining up when reading on the web, choose
Message Index, then Expand Messages.]

C< E[ G< 4:5:6 major

F#v A C#v 1/(6:5:4) minor

F#v C#v E[ 4:6:7 subminor 7th no 3rd

A C< G< 1/(7:6:4) subminor 7th no 5th
C< G< A 1/(12:8:7) supermajor 6th no 3rd

A C#v G< 4:5:7 major subminor 7th no 5th

F#v C< E[ 1/(7:5:4) subdiminished subminor 7th no 3rd
C< E[ F#v 1/(10:8:7) major diminished

E[ G< C#v 5:6:7 minor subdiminished

C#v E[ G< 1/(7:6:5) subminor subdiminished
E[ G< C#v 1/(12:10:7) minor supermajor 6th no 5th

dkeenanuqnetau wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> > I'm enjoying catching up with the Blackjack threads, such as
> Joseph's
> > progression and the commentaries by others. I'm working with the
> > interlocking hexanies just now, using the triads as a foundation for
> > slow harmonic movement.
> >
> > Taking one at random in 'standard' notation, C< , E[ , G< , F#v , A,
> C#v
> > (not, I realise, in ascending order), I'd be grateful if anyone can
> > refresh me with the names of the triads. Major and minor I know,
> which
> > leaves six others. I'd imagine that F#v , C#v , E[ has the word
> > septimal in it. Merci bien.
>
> Bv C Db^ D> E[ F<F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^
> -----------5*7---1*5------------1*73*5------------3*7---1*3
>
> Here are some possible names.
> [To see this with columns lining up when reading on the web, choose
> Message Index, then Expand Messages.]
>
> C< E[ G< 4:5:6 major
>
> F#v A C#v 1/(6:5:4) minor
>
> F#v C#v E[ 4:6:7 subminor 7th no 3rd
>
> A C< G< 1/(7:6:4) subminor 7th no 5th
> C< G< A 1/(12:8:7) supermajor 6th no 3rd
>
> A C#v G< 4:5:7 major subminor 7th no 5th
>
> F#v C< E[ 1/(7:5:4) subdiminished subminor 7th no 3rd
> C< E[ F#v 1/(10:8:7) major diminished
>
> E[ G< C#v 5:6:7 minor subdiminished
>
> C#v E[ G< 1/(7:6:5) subminor subdiminished
> E[ G< C#v 1/(12:10:7) minor supermajor 6th no 5th
>
> Thanks Dave. Is there consensus on these names?

Kind Regards

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_31593.html#31609

> Here are some possible names.
> [To see this with columns lining up when reading on the web, choose
> Message Index, then Expand Messages.]
>
> C< E[ G< 4:5:6 major
>
> F#v A C#v 1/(6:5:4) minor
>
> F#v C#v E[ 4:6:7 subminor 7th no 3rd
>
> A C< G< 1/(7:6:4) subminor 7th no 5th
> C< G< A 1/(12:8:7) supermajor 6th no 3rd
>
> A C#v G< 4:5:7 major subminor 7th no 5th
>
> F#v C< E[ 1/(7:5:4) subdiminished subminor 7th no 3rd
> C< E[ F#v 1/(10:8:7) major diminished
>
> E[ G< C#v 5:6:7 minor subdiminished
>
> C#v E[ G< 1/(7:6:5) subminor subdiminished
> E[ G< C#v 1/(12:10:7) minor supermajor 6th no 5th

Hi Dave!

Well, these seem servicable, but I do have some questions about them.

Why, for instance would one call a simple minor derived from the
OTONAL direction 4:6:7 F#v C#v E[ a SUBminor 7th no 3rd...

Wouldn't it make sense to have everything in an OTONAL direction
a "super" rather than a sub?

Or am I just confused?

Similarly, C< G< A or 1/(12:8:7) is a SUPERmajor 6th, no 3rd....

Wouldn't that be better as a SUB... going in that direction.

Or am I just confused?

I found it a little ironic that, for these simple examples, you
started on a variant of "C," a C< which would lend credence to my
predilection for "C" as a starting point!

Also, it seemed ironic that the simple examples, for all the emphasis
on the *naturals* of the "standard" Blackjack key, only had *ONE*
natural, "A."

Even the simple triad, the very first one, was entirely "elaborated."

C< E[ G<

What a sad thing to do to that triad... :)

Are you sure you don't want to "rethink" the standard again?? :)

Joseph

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> Dave Keenan wrote:
> > Here are some possible names.
> > [To see this with columns lining up when reading on the web,
choose
> > Message Index, then Expand Messages.]
> >
> > C< E[ G< 4:5:6 major
> >
> > F#v A C#v 1/(6:5:4) minor
> >
> > F#v C#v E[ 4:6:7 subminor 7th no 3rd
> >
> > A C< G< 1/(7:6:4) subminor 7th no 5th
> > C< G< A 1/(12:8:7) supermajor 6th no 3rd
> >
> > A C#v G< 4:5:7 major subminor 7th no 5th
> >
> > F#v C< E[ 1/(7:5:4) subdiminished subminor 7th no 3rd
> > C< E[ F#v 1/(10:8:7) major diminished
> >
> > E[ G< C#v 5:6:7 minor subdiminished
> >
> > C#v E[ G< 1/(7:6:5) subminor subdiminished
> > E[ G< C#v 1/(12:10:7) minor supermajor 6th no 5th
>
> Thanks Dave. Is there consensus on these names?

There don't seem to be any objections to the interval names.
http://dkeenan.com/Music/Miracle/MiracleIntervalNaming.txt
Provided certain logical alternatives are allowed.

But the chord names have never really been put to the test. Some of
those names are very long for triads. Maybe we can do better.

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> /tuning/topicId_31593.html#31609
>
> > Here are some possible names.
> > [To see this with columns lining up when reading on the web,
choose
> > Message Index, then Expand Messages.]
> >
> > C< E[ G< 4:5:6 major
> >
> > F#v A C#v 1/(6:5:4) minor
> >
> > F#v C#v E[ 4:6:7 subminor 7th no 3rd
> >
> > A C< G< 1/(7:6:4) subminor 7th no 5th
> > C< G< A 1/(12:8:7) supermajor 6th no 3rd
> >
> > A C#v G< 4:5:7 major subminor 7th no 5th
> >
> > F#v C< E[ 1/(7:5:4) subdiminished subminor 7th no 3rd
> > C< E[ F#v 1/(10:8:7) major diminished
> >
> > E[ G< C#v 5:6:7 minor subdiminished
> >
> > C#v E[ G< 1/(7:6:5) subminor subdiminished
> > E[ G< C#v 1/(12:10:7) minor supermajor 6th no 5th
>
> Hi Dave!
>
> Well, these seem servicable, but I do have some questions about
them.
>
> Why, for instance would one call a simple minor derived from the
> OTONAL direction 4:6:7 F#v C#v E[ a SUBminor 7th no 3rd...
>
> Wouldn't it make sense to have everything in an OTONAL direction
> a "super" rather than a sub?

It can't be a "simple" minor if it has ratios of 7 in it.

super and sub don't refer to otonal or utonal but to whether the
interval to which they refer is narrower or wider than the usual
diatonic one.

In this case it refers to the 4:7 which can only be called a
supermajor 7th or an augmented 6th.

A minor 7th chord has both a minor 3rd and a minor 7th.
A major 7th chord has both a major 3rd and a major 7th.
So a subminor 7th chord should have both a subminor 3rd (6:7) and a
subminor 7th (4:7). Of course they all have perfect fifths.

A minor major 7th chord has a minor 3rd and a major 7th. So a 4:5:6:7
would be a major subminor 7th chord.

But a 4:6:7 chord has no 3rd so we don't need to qualify the 3rd. It
can just be a subminor 7th no 3rd.

> Similarly, C< G< A or 1/(12:8:7) is a SUPERmajor 6th, no 3rd....
>
> Wouldn't that be better as a SUB... going in that direction.

Same reasoning. A 7:12 is a supermajor 6th (or a wide? diminished 7th
I think)

> I found it a little ironic that, for these simple examples, you
> started on a variant of "C," a C< which would lend credence to my
> predilection for "C" as a starting point!

Hee hee. This was Alison's "random" hexany. Not my choice.

> Also, it seemed ironic that the simple examples, for all the
emphasis
> on the *naturals* of the "standard" Blackjack key, only had *ONE*
> natural, "A."

The most naturals you can have in a 7-limit hexany is 2. There are 6
7-limit hexanies in Blackjack. It doesn't matter whether you use FCG
or CGDA, only two of these hexanies can have 2 naturals. In both
cases, one choice gives naturals for (the root and fifth of) the major
triad, the other for the minor.

> Even the simple triad, the very first one, was entirely
"elaborated."
>
> C< E[ G<
>
> What a sad thing to do to that triad... :)

In the standard key one hexany makes it G Bv D. Another makes the
minor triad G Bb^ D.

> Are you sure you don't want to "rethink" the standard again?? :)

I think we should just use decimal. :-)

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_31593.html#31631

>
> super and sub don't refer to otonal or utonal but to whether the
> interval to which they refer is narrower or wider than the usual
> diatonic one.
>

Hi Dave!

Oh! Well your usage is perfectly clear in your examples once I
understood that. I guess I should have inferred that from the diads
you posted... I guess that makes sense as a terminology.

Do other people use that system of "super" and "sub" in that way??

Just curious...

>
> In the standard key one hexany makes it G Bv D. Another makes the
> minor triad G Bb^ D.

Why sure... since the basic "key" is G... that would make sense as
the "starting place."

I guess that pretty much conforms to Partch's idea of G as the
starting point as well, which might be nice.

>
> > Are you sure you don't want to "rethink" the standard again?? :)
>
> I think we should just use decimal. :-)

I look forward, Dave, to watching you teach and train the musicians
to do that... I want to be there to see it when it happens! :)

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> /tuning/topicId_31593.html#31631
>
> >
> > super and sub don't refer to otonal or utonal but to whether the
> > interval to which they refer is narrower or wider than the usual
> > diatonic one.
> >
>
> Hi Dave!
>
> Oh! Well your usage is perfectly clear in your examples once I
> understood that. I guess I should have inferred that from the
diads
> you posted... I guess that makes sense as a terminology.
>
> Do other people use that system of "super" and "sub" in that way??

It goes back to Fokker, and, I think, Helmholtz.