Just Major & Minor Scales

Hello, all. In the documentation of several electronic keyboard
manufacturers I've seen references to chromatic 12-tone "Just Major"
and "Just Minor" scales. The minor scale appears to be based upon
major and minor just triads on the I, IV, V degrees of the scale and
would permit the playing of the the natural, harmonic, and melodic
forms of the minor scale.

I'm not sure what is meant by "Just Major" from a 12-tone chromatic
point of view. Using C as the tonic, the just major and minor triads on
C and G are still possible as in the "Just Minor" tuning but the Ab in
that tuning has now become G#. Can someone shed some illumination?
Thanks for the time and comment. Sincerely,

> ----- Original Message -----
> From: <arl_123@hotmail.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, June 19, 2001 5:22 AM
> Subject: [tuning] Just Major & Minor Scales
>
>
> Hello, all. In the documentation of several electronic keyboard
> manufacturers I've seen references to chromatic 12-tone "Just Major"
> and "Just Minor" scales. The minor scale appears to be based upon
> major and minor just triads on the I, IV, V degrees of the scale and
> would permit the playing of the the natural, harmonic, and melodic
> forms of the minor scale.

You're talking about a 12-tone 5-limit JI scale that
can be latticed like this (using "C" as "tonic"):

F# -- C#
\ / \
\ / \
A --- E --- B
/ \ / \ / \
/ \ / \ / \
F --- C --- G --- D
\ / \ / \ /
\ / \ / \ /
Ab -- Eb -- Bb

or

C#
/ \
/ \
A --- E --- B -- F#
/ \ / \ / \ /
/ \ / \ / \ /
F --- C --- G --- D
\ / \ / \ /
\ / \ / \ /
Ab -- Eb -- Bb

I don't know if I ever took note of precisely which tuning my
synths had for "Just Minor Scale". I've looked in my scale
archives and have found no lattices looking exactly like either
of these.

But I *did* examine the "major" tunings... -->

>
> I'm not sure what is meant by "Just Major" from a 12-tone chromatic
> point of view. Using C as the tonic, the just major and minor triads on
> C and G are still possible as in the "Just Minor" tuning but the Ab in
> that tuning has now become G#. Can someone shed some illumination?
> Thanks for the time and comment.

My Yamaha DX-7II and TG-77 had Fogliano's Monochord #2 tuning
(Fogliano, 1529, _Musica theorica_, p 36) programmed in for the
"Just Major Scale":

F# -- C# -- G#
\ / \ / \
\ / \ / \
A --- E --- B
/ \ / \ / \
/ \ / \ / \
F --- C --- G --- D
\ / \ /
\ / \ /
Eb -- Bb

This does indeed do exactly what you describe: moves the Ab which
would be consonant in the "F-minor" triad to a G# which is
consonant in the "E-major" triad (thus enabling a good "V -> I"
in the relative "A-minor" key).

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In tuning@y..., arl_123@h... wrote:
> Hello, all. In the documentation of several electronic keyboard
> manufacturers I've seen references to chromatic 12-tone "Just
Major"
> and "Just Minor" scales. The minor scale appears to be based upon
> major and minor just triads on the I, IV, V degrees of the scale
and
> would permit the playing of the the natural, harmonic, and melodic
> forms of the minor scale.
>
> I'm not sure what is meant by "Just Major" from a 12-tone chromatic
> point of view. Using C as the tonic, the just major and minor
triads on
> C and G are still possible as in the "Just Minor" tuning but the Ab
in
> that tuning has now become G#. Can someone shed some
illumination?

Hello!

I wouldn't be too concerned with these terms -- as long as you can
figure out where the consonant just intervals are, where it seems
you're doing fine. There is no standard "12-tone Just Major" and "12-
tone Just Minor" in tuning theory. Electronic keyboard manufacturers
will tend to include a few just scales, along with the historically
and geographically more important scales, but you aren't likely to
find total agreement between manufacturers on how these scales are
constructed. Monz has latticed a few possibilities out for you; as he
(and probably you) knows, there are many other possibilities that fit
just as well onto a 12-tone keyboard. Generally, these will all be
examples of a 12-tone periodicity block . . .

Thanks for the replies, Monz and P. Ehrlich. I also did some further
research. As Monz states:

> My Yamaha DX-7II and TG-77 had Fogliano's Monochord #2 tuning
> (Fogliano, 1529, _Musica theorica_, p 36) programmed in for the
> "Just Major Scale":
>
> F# -- C# -- G#
> \ / \ / \
> \ / \ / \
> A --- E --- B
> / \ / \ / \
> / \ / \ / \
> F --- C --- G --- D
> \ / \ /
> \ / \ /
> Eb -- Bb
>

This lattice is also what one obtains using the "Just Major" tuning
given in the Korg MT-1200 multi-temperament tuner manual. Seems
vendors like Fogliano's Monochord #2.

From the "Just Minor" tuning given in the MT-1200 manual we obtain the
following lattice:

A --- E --- B
/ \ / \ / \
/ \ / \ / \
F --- C --- G --- D
\ / \ / \ /
\ / \ / \ /
Ab -- Eb -- Bb
\ / \
\ / \
Gb -- Db

This is like a Mersenne lute tuning except that the Gb-Db fifth has
been moved from the "+1" (Eitz notation) position to the "+2" position.
Sincerely,

> ----- Original Message -----
> From: <arl_123@hotmail.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, June 20, 2001 5:37 AM
> Subject: [tuning] Re: Just Major & Minor Scales
>
>
> Thanks for the replies, Monz and P. Ehrlich.

Typo... it's Erlich.

> I also did some further research. As Monz states:
>
> > My Yamaha DX-7II and TG-77 had Fogliano's Monochord #2 tuning
> > (Fogliano, 1529, _Musica theorica_, p 36) programmed in for the
> > "Just Major Scale":
> >
> > F# -- C# -- G#
> > \ / \ / \
> > \ / \ / \
> > A --- E --- B
> > / \ / \ / \
> > / \ / \ / \
> > F --- C --- G --- D
> > \ / \ /
> > \ / \ /
> > Eb -- Bb
> >
>
> This lattice is also what one obtains using the "Just Major" tuning
> given in the Korg MT-1200 multi-temperament tuner manual. Seems
> vendors like Fogliano's Monochord #2.

Yes, and I've seen it as well programmed into still other keyboards,
I believe the Korg M-1 and an Ensoniq (don't know which model),
and even others which I don't recall. Vendors do indeed have a
preference for Fogliano #2 for their "Just Major scale".

The reason I remembered that this particularly tuning was used
so often is precisely because it *is* so popular (with vendors).

>
> From the "Just Minor" tuning given in the MT-1200 manual we obtain the
> following lattice:
>
>
> A --- E --- B
> / \ / \ / \
> / \ / \ / \
> F --- C --- G --- D
> \ / \ / \ /
> \ / \ / \ /
> Ab -- Eb -- Bb
> \ / \
> \ / \
> Gb -- Db
>
> This is like a Mersenne lute tuning except that the Gb-Db fifth has
> been moved from the "+1" (Eitz notation) position to the "+2" position.

Yes, this looks more typical for a "Just Minor scale" than
the possibilities which I latticed.

The "Gb" gives a 6:5 "just minor 3rd" for the Eb-minor triad,
which would be a minor-mediant relationship with the tonic C-minor,
whereas if it were "F#" it would probably be tuned as the "F#"
which forms a 5:4 "just major 3rd" over "D", so that the "D"
triad would be a nice consonant 4:5:6 V chord resolving to "G",
i.e., the dominant of the dominant.

And the "Db" certainly bears a closer relationship to C-minor
than any kind of "C#" would.

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> Typo... it's Erlich.

A thousand pardons, Paul. Don't know what I was thinking. There are
those surnamed "Ehrlich" in phone books but you are clearly not one
of them. (People constantly want to make my last name plural instead of
singular ;-)) Sincerely,