Yahoo Tuning Groups Ultimate Backup tuning-math Hungarian Scale

On Tue, Mar 15, 2011 at 5:16 PM, Paul <phjelmstad@msn.com> wrote:
>
> I was wondering if the Hungarian scale could be considered a MODMOS. It is the only Fundamental Scale that is not Rothenberg Proprietary (those
> others being Diatonic, Melodic Minor, Harmonic Minor, Harmonic Major and Major Locrian).
>
> This is of course C D Eb F# G Ab B C (0 2 3 6 7 8 11 12) with steps
> 2 1 3 1 1 3 1 Even though you are not adjusting from a MOS, this is a near MOS. Any ideas anyone on how to classify this one? Maybe a MOD2MOS?
> (From Melodic Minor)

Everyone called the Hungarian scale something else. But you could
still consider it a MODMOS. MODMOS's don't have to be only one note
away from the original scale to count as MODMOS's - on the contrary, a
lot of the interesting ones for porcupine are 2 alterations away.

-Mike

🔗genewardsmith <genewardsmith@sbcglobal.net>

🔗Paul <phjelmstad@msn.com>

--- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning-math@yahoogroups.com, "Paul" <phjelmstad@> wrote:
> >
> > I was wondering if the Hungarian scale could be considered a MODMOS.
>
> It is; C D Eb F# G Ab B C' is obtained from CDEFGABC' by single flat or sharp alterations, making it a MODMOS.
>
Excellent --- Then I guess all of these are MODMOS's (or MOS's)

Fundamental Scales (Canvassing hexachords)

Major C D E F G A B C

Mel Minor C D Eb F G A B C

Harm Minor C D Eb F G Ab B C

Maj Locrian C Db Eb F G A B C

Hungarian C D Eb F# G Ab B C

Major #6 C D E F G A# B C

Mel #6 C D Eb F G A# B C

Harm b2 C Db Eb F G Ab B C

Hungr b2 C Db Eb F# G Ab B C

Locrian #6 C Db Eb F G A# B C

Locrian b5 C Db Eb F Gb A B C

To canvass hexachords:

1. Eliminate one note
2. Apply mirror inverse, "M5" mapping, or both, or neither.
3. This will cover all hexads with one or two tritones in them
4. To get remaining hexads there is a simple transform to do

(The region of hexads with one or two tritones, I call the Interzone. The rest is the Outerzone.)

I have to work out how to canvass all septachords, however, taking
Steiner sets (one contained in each scale, will canvass all pentads
so canvass all septachords by complementation).

Six of these scales will also canvass 11 Steiner Sets which in term
canvass all pentads. Sorry left that list at home....You need M1
versions of some of the scales....

PGH

🔗Mike Battaglia <battaglia01@gmail.com>

On Wed, Mar 16, 2011 at 1:10 PM, Paul <phjelmstad@msn.com> wrote:
>
> >
> > It is; C D Eb F# G Ab B C' is obtained from CDEFGABC' by single flat or sharp alterations, making it a MODMOS.
> >
> Excellent --- Then I guess all of these are MODMOS's (or MOS's)
>
> Fundamental Scales (Canvassing hexachords)
>
> Major C D E F G A B C
>
> Mel Minor C D Eb F G A B C
>
> Harm Minor C D Eb F G Ab B C
>
> Maj Locrian C Db Eb F G A B C
>
> Hungarian C D Eb F# G Ab B C
//snip
> Harm b2 C Db Eb F G Ab B C
>
> Hungr b2 C Db Eb F# G Ab B C
> Locrian b5 C Db Eb F Gb A B C

These all look good, although I don't know why you call this "Locrian
br," when Locrian already has a b5...

You also seem to have forgotten this one:

C Db E F# G A B C

This is another MODMOS, but this is why I say you have to be careful -
in 12-tet, the above scale is improper, but it's also a 7-note subset
of the octatonic scale, which is improper. In jazz, if you're playing
over a dom7 b9 #11 nat 13 chord, you'll generally play the octatonic
scale over it and throw in the #9. So sometimes if you move far out
enough, you end up with something that looks more like a subset of a
different scale. Or Locrian Major, of which many modes look like a
whole tone scale with a single extraneous chromatic note added in
(because the pythagorean comma vanishes in 12-equal). So you have to
be careful here.

Above is good so far! There's

> Major #6 C D E F G A# B C
>
> Mel #6 C D Eb F G A# B C
>
> Locrian #6 C Db Eb F G A# B C

OK, now these are the ones which violate the property that I listed in
the other thread - although they are MODMOS's, you can't access them
via the chromatic scale. They require going up 2 levels of MOS to
find. So this doesn't mean that they're NOT MODMOS's, but rather that
they're "second order" MODMOS's in a certain way. Which is fine, and
for many scales (porcupine[7]), the second order MODMOS's will be more
useful than the first order ones. But it's being aware of.

> To canvass hexachords:
>
> 1. Eliminate one note
> 2. Apply mirror inverse, "M5" mapping, or both, or neither.
> 3. This will cover all hexads with one or two tritones in them
> 4. To get remaining hexads there is a simple transform to do
>
>
> (The region of hexads with one or two tritones, I call the Interzone. The rest is the Outerzone.)
>
> I have to work out how to canvass all septachords, however, taking
> Steiner sets (one contained in each scale, will canvass all pentads
> so canvass all septachords by complementation).
>
> Six of these scales will also canvass 11 Steiner Sets which in term
> canvass all pentads. Sorry left that list at home....You need M1
> versions of some of the scales....

I'm starting to realize that university-level set theory isn't all
that bad: it looks like it's just kind of an overarching theory of
rank-1 scales. We're trying to develop an overarching theory of rank-2
scales here, and I can see that they're about to meet somewhere in the
middle.

-Mike

🔗Mike Battaglia <battaglia01@gmail.com>

🔗Paul <phjelmstad@msn.com>

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Mar 16, 2011 at 1:10 PM, Paul <phjelmstad@...> wrote:
> >
> > >
> > > It is; C D Eb F# G Ab B C' is obtained from CDEFGABC' by single flat or sharp alterations, making it a MODMOS.
> > >
> > Excellent --- Then I guess all of these are MODMOS's (or MOS's)
> >
> > Fundamental Scales (Canvassing hexachords)
> >
> > Major C D E F G A B C
> >
> > Mel Minor C D Eb F G A B C
> >
> > Harm Minor C D Eb F G Ab B C
> >
> > Maj Locrian C Db Eb F G A B C
> >
> > Hungarian C D Eb F# G Ab B C
> //snip
> > Harm b2 C Db Eb F G Ab B C
> >
> > Hungr b2 C Db Eb F# G Ab B C
> > Locrian b5 C Db Eb F Gb A B C
>
> These all look good, although I don't know why you call this "Locrian
> br," when Locrian already has a b5...

Technically Major Locrian b5 is what i meant
>
> You also seem to have forgotten this one:
>
> C Db E F# G A B C

Hmmm okay let me look that up on my grid (Steiner6New.xls) I think is on Files.
Maybe its a better candidate to canvas hexads than another one. Sorry, I can't resist bringing in Steiner theory (and M12) or Polya theory since its such a preoccupation of mine....but that wasn't your point, are you trying to develop a complete list of level 1 and 2 MODMOS's?

> This is another MODMOS, but this is why I say you have to be careful -
> in 12-tet, the above scale is improper, but it's also a 7-note subset
> of the octatonic scale, which is improper. In jazz, if you're playing
> over a dom7 b9 #11 nat 13 chord, you'll generally play the octatonic
> scale over it and throw in the #9. So sometimes if you move far out
> enough, you end up with something that looks more like a subset of a
> different scale. Or Locrian Major, of which many modes look like a
> whole tone scale with a single extraneous chromatic note added in
> (because the pythagorean comma vanishes in 12-equal). So you have to
> be careful here

I love that scale. (octotonic) Messaien and jazz (and Eastern European music) is so rich with it.

The chord G Bb Db Eb Gb A B D F nonachord is also cool

> Above is good so far! There's
>
> > Major #6 C D E F G A# B C
> >
> > Mel #6 C D Eb F G A# B C
> >
> > Locrian #6 C Db Eb F G A# B C
>
> OK, now these are the ones which violate the property that I listed in
> the other thread - although they are MODMOS's, you can't access them
> via the chromatic scale. They require going up 2 levels of MOS to
> find. So this doesn't mean that they're NOT MODMOS's, but rather that
> they're "second order" MODMOS's in a certain way. Which is fine, and
> for many scales (porcupine[7]), the second order MODMOS's will be more
> useful than the first order ones. But it's being aware of.
>
> > To canvass hexachords:
> >
> > 1. Eliminate one note
> > 2. Apply mirror inverse, "M5" mapping, or both, or neither.
> > 3. This will cover all hexads with one or two tritones in them
> > 4. To get remaining hexads there is a simple transform to do
> >
> >
> > (The region of hexads with one or two tritones, I call the Interzone. The rest is the Outerzone.)
> >
> > I have to work out how to canvass all septachords, however, taking
> > Steiner sets (one contained in each scale, will canvass all pentads
> > so canvass all septachords by complementation).
> >
> > Six of these scales will also canvass 11 Steiner Sets which in term
> > canvass all pentads. Sorry left that list at home....You need M1
> > versions of some of the scales....
>
> I'm starting to realize that university-level set theory isn't all
> that bad: it looks like it's just kind of an overarching theory of
> rank-1 scales. We're trying to develop an overarching theory of rank-2
> scales here, and I can see that they're about to meet somewhere in the
> middle.
>
> -Mike

Okay...I"ll drop Steiner theory for now...leave it for another time. I've found some cool things with it....But I can't resist giving a definition: S(5,6,12) (The basis for M12) is
a specialized set of 132 hexachords such that their subsets generate all 792 pentachords exactly once. Noam Elkies found a cool Double Steiner system such that 11 hexads and their inverses, with their 12 transpositions find all pentads exactly
twice. This is the one I use in my colorgrids. PGH
>

🔗Mike Battaglia <battaglia01@gmail.com>

🔗Paul <phjelmstad@msn.com>

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Mar 16, 2011 at 7:01 PM, Paul <phjelmstad@...> wrote:
> >
> > Hmmm okay let me look that up on my grid (Steiner6New.xls) I think is on Files.
> > Maybe its a better candidate to canvas hexads than another one. Sorry, I can't resist bringing in Steiner theory (and M12) or Polya theory since its such a preoccupation of mine....but that wasn't your point, are you trying to develop a complete list of level 1 and 2 MODMOS's?
>
> Sorry, the one I meant was C Db E F# G A Bb C, wth a Bb, not a B.
>
> -Mike
>
Yes, this is a good one, this is my alternate for the Harmonic Minor scale because they both contain 036914 (being blind to mirror inverse here). But in answer to my question are you trying to make a complete list of? If you don't keep me on track I might drift back to my theories:)