Decatonic Harmony

Hi Paul and Alison!

I'm wondering how you understand the "function" of the 4 dissonant
tetrads Major-minor, Minor-major and the two Augmented ones occurring
in the pentachordal decatonic modes.

For example, I find the progression from Major-minor tetrad (in
second inversion) to the tonic (in root position) in the standard
pentachordal major mode to be a most satisfying cadence. The Minor-
major tetrad can be used similarly in the standard pentachordal minor
mode.

But what kind of uses you find for the two Augmented tetrads?

Kalle

--- In MakeMicroMusic@yahoogroups.com, "Kalle Aho <kalleaho@m...>"
<kalleaho@m...> wrote:
> Hi Paul and Alison!
>
> I'm wondering how you understand the "function" of the 4 dissonant
> tetrads Major-minor, Minor-major and the two Augmented ones
occurring
> in the pentachordal decatonic modes.
>
> For example, I find the progression from Major-minor tetrad (in
> second inversion) to the tonic (in root position) in the standard
> pentachordal major mode to be a most satisfying cadence.

indeed! this progression embodies the "strong tonality" of the scale,
since you have the unique characteristic dissonance resolving in
contrary motion through the rare-sized steps to notes of a consonant
chord -- just as the classical dominant seventh-to-tonic progression
does for the diatonic scale.

> The Minor-
> major tetrad can be used similarly in the standard pentachordal
minor
> mode.

yup!

> But what kind of uses you find for the two Augmented tetrads?
>
> Kalle

i presume you're asking about the pentachordal scale here, let me
know if you meant this question to ask about the symmetrical scale
too. anyway, here's the progression of my piece "decatonic waltz",
performed at the first microthon. it's in the standard pentachordal
minor modem and uses all ten tetrads:

--
..
Imin
IIImaj
Vmin
Imin
Imin
IIImaj
Vmin
Imin
IVmaj
VIIImaj
IIma-mi (or V[VI]ma-mi)
VImin
Xaug
IXaug
Vmin
VIImi-ma
..
--

at least that's how i think it goes -- my instruments aren't here,
and i came down with a really bad case of food poisoning (leading to
a mistaken appendectomy two days later, and not actually diagnosed
for over a week after that -- thank you somerville hospital) during
this 1999 performance (reviewed here:

http://sonic-arts.org/monzo/spider/The%20Village%20Voice%20ArtsMusic%
20Micro%20Breweries.htm

).

Paul wrote:

> indeed! this progression embodies the "strong tonality" of the
scale,
> since you have the unique characteristic dissonance resolving in
> contrary motion through the rare-sized steps to notes of a
consonant
> chord -- just as the classical dominant seventh-to-tonic
progression
> does for the diatonic scale.

Is the fact that the motion is *contrary* somehow important?

> > The Minor-
> > major tetrad can be used similarly in the standard pentachordal
> minor
> > mode.
>
> yup!

One could also substitute the Minor-major and Major-minor chords for
each other in these progressions but I hear them as stronger this
way. Must be the simpler root relationships.

> > But what kind of uses you find for the two Augmented tetrads?
> >
> > Kalle
>
> i presume you're asking about the pentachordal scale here, let me
> know if you meant this question to ask about the symmetrical scale
> too.

I was asking about the pentachordal scale. But I suppose that the
Augmenteds could have cadential uses in the symmetrical scale.

One thing that came to my mind is a progression from one Augmented to
the other Augmented and then to the tonic. This goes through all
tones of the scale. It might be an easy way to establish the key and
works with both standard pentachordal modes.

> anyway, here's the progression of my piece "decatonic waltz",
> performed at the first microthon. it's in the standard pentachordal
> minor modem and uses all ten tetrads:
> --
> ..
> Imin
> IIImaj
> Vmin
> Imin
> Imin
> IIImaj
> Vmin
> Imin
> IVmaj
> VIIImaj
> IIma-mi (or V[VI]ma-mi)
> VImin
> Xaug
> IXaug
> Vmin
> VIImi-ma
> ..
> --

You like to connect chords with common notes, don't you? :)
Thanks for this! Is there a recording of Decatonic Waltz in existence?

> at least that's how i think it goes -- my instruments aren't here,
> and i came down with a really bad case of food poisoning (leading
to
> a mistaken appendectomy two days later, and not actually diagnosed
> for over a week after that -- thank you somerville hospital) during
> this 1999 performance (reviewed here:
>
> http://sonic-arts.org/monzo/spider/The%20Village%20Voice%
20ArtsMusic%
> 20Micro%20Breweries.htm
>
> ).

Yuck!!! What did you eat?

Kalle

--- In MakeMicroMusic@yahoogroups.com, "Kalle Aho <kalleaho@m...>"
<kalleaho@m...> wrote:
> Paul wrote:
>
> > indeed! this progression embodies the "strong tonality" of the
> scale,
> > since you have the unique characteristic dissonance resolving in
> > contrary motion through the rare-sized steps to notes of a
> consonant
> > chord -- just as the classical dominant seventh-to-tonic
> progression
> > does for the diatonic scale.
>
> Is the fact that the motion is *contrary* somehow important?

yes, i believe it is. take a look at this paper:

http://www.music-cog.ohio-
state.edu/Huron/Publications/huron.voice.leading.html

and look at

[D16.] Semblant Motion Rule. Avoid similar or parallel pitch motion
between concurrent voices.

> > > The Minor-
> > > major tetrad can be used similarly in the standard pentachordal
> > minor
> > > mode.
> >
> > yup!

>
> One thing that came to my mind is a progression from one Augmented
to
> the other Augmented and then to the tonic. This goes through all
> tones of the scale. It might be an easy way to establish the key
and
> works with both standard pentachordal modes.

cool! try to avoid similar motion from 14/22 oct. to 13/22 oct if you
can, for the voice-leading reasons above (of course, this is a great
progression in *oblique* motion, but that requires microchromaticism).

> > --
> > ..
> > Imin
> > IIImaj
> > Vmin
> > Imin
> > Imin
> > IIImaj
> > Vmin
> > Imin
> > IVmaj
> > VIIImaj
> > IIma-mi (or V[VI]ma-mi)
> > VImin
> > Xaug
> > IXaug
> > Vmin
> > VIImi-ma
> > ..
> > --
>
> You like to connect chords with common notes, don't you? :)

it helps, but of course Xaug -> IXaug works on a different
principle . . .

> Thanks for this! Is there a recording of Decatonic Waltz in
>existence?

probably somewhere. so far johnny has dug up the tapes from the
second microthon, but not the first. ara and i will get back to this
piece someday. i'm looking forward to having more than two weeks to
develop some *real* 22-tone ensemble skills.

> Yuck!!! What did you eat?

never quite figured that out. got camphylobacter.

> > Is the fact that the motion is *contrary* somehow important?
>
> yes, i believe it is. take a look at this paper:
>
> http://www.music-cog.ohio-
> state.edu/Huron/Publications/huron.voice.leading.html
>
> and look at
>
> [D16.] Semblant Motion Rule. Avoid similar or parallel pitch motion
> between concurrent voices.

Yes, I have already red this paper. I am a lurker at SPEC MUSIC :)
I consider these "rules" to be more like tips than rules.

Kalle

Kalle,

{you wrote...}
>I consider these "rules" to be more like tips than rules.

Good - rules were meant to be broken.

Cheers,
Jon

Greetings:

Sorry to interrupt but is there a good music theory
dictionary on line or which one should I buy? If I
plan to stay in this company I'll need to scramble to
catch up.

Also what's up with 17 step Arabic scales? Are there
any note worthy compositions being performed or
recorded presently? I would like to see them have a
renaissance in music.

"Are other scales associated with Arab music; do they
have their own system of music notation", these are
questions perhaps better left until I have studied it
out for myself more.

Sincerely yours.
Jim Nagy

--- "Jonathan M. Szanto" <JSZANTO@...> wrote:
> Kalle,
>
> {you wrote...}
> >I consider these "rules" to be more like tips than
> rules.
>
> Good - rules were meant to be broken.
>
> Cheers,
> Jon
>
>

__________________________________________________
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Jim,

{you wrote...}
>Sorry to interrupt but is there a good music theory dictionary on line or >which one should I buy? If I plan to stay in this company I'll need to >scramble to
>catch up.

Try this (its free):
http://sonic-arts.org/dict/index.htm

Joe Monzo's tuning dictionary is probably by far the most current accounting of the terminology you might want. Joe is a member of the tuning forums and a lot of the terms he documents are only used here. In fact, some of the terms might only be used by a couple of people, but there you have it anyway.

Cheers,
Jon

jim,

to understand what is being discussed in this thread ("decatonic
harmony"), you'll need to read my paper.

do a web search for "tuning, tonality, and twenty-two tone
temperament", and read the .pdf (not the .html).

if that doesn't work, i can print out a copy of the paper and mail it
to you -- let me know!

-paul

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:
> Jim,
>
> {you wrote...}
> >Sorry to interrupt but is there a good music theory dictionary on
line or
> >which one should I buy? If I plan to stay in this company I'll
need to
> >scramble to
> >catch up.
>
> Try this (its free):
> http://sonic-arts.org/dict/index.htm
>
> Joe Monzo's tuning dictionary is probably by far the most current
> accounting of the terminology you might want. Joe is a member of
the tuning
> forums and a lot of the terms he documents are only used here. In
fact,
> some of the terms might only be used by a couple of people, but
there you
> have it anyway.
>
> Cheers,
> Jon

Paul,

{you wrote...}
>to understand what is being discussed in this thread ("decatonic >harmony"), you'll need to read my paper. do a web search for "tuning, >tonality, and twenty-two tone
>temperament", and read the .pdf (not the .html).

Gad, man, don't you even keep a copy of a link to your own paper???

http://www-math.cudenver.edu/~jstarret/22ALL.pdf

Cheers,
Jon