Re: [MMM] Decatonic Harmony

"Kalle Aho " 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. 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
>
> Hello Kalle

> I'm writing at the moment for 22 tet guitar.

> I've spent some time looking at decatonic modes and related
> progressions, cadences and modulations. To my ears the augmented
> tetrads in tetrad progressions are the most dissonant. They would be
> useful as pivot chords in modulating from one decatonic to another,
> either to the same mode or to another mode. For example, in the
> notation I use, the third tetrad of C standard pentachordal major
> (s.p.m.) is d augmented This same tetrad is the second step of Db
> s.p.m. Modulating to the symmetricals should be easy to work out.

Cadences: I've looked at using the augmenteds minus the fifth, ie 1,3,7.
22 tet has in my opinion a very fine dominant seventh. I find my ears
and fingers are often drawn to dom 7 shapes, patterns and fragments on
the guitar. Many of the structures and motives I collect from
improvisating prior to composition are related to 1357 chords. Obviously
conventional V - I comes to mind, but jazz harmony uses interrupted
cadences where V goes anywhere it likes.

In any one s.p.m. I get the following: -

Full dom 7 tetrads on I, V and VII

Partial (1,3,7) dom 7 on II and III (there's your augmenteds)

Major triad on V

Partial (1,5,7) dom 7 on X

II and III would resolve (as conventional V -I) to decatonic steps VI
and VII respectively, in each case an augmented tetrad or partial dom7
resolving to a major triad.

I've got reams of notes and reflections on practical and theoretical
possibilities in decatonic harmony which I'd be glad to share and
discuss.

Thanks for the opportunity to talk 22.

Kind Regards
a.m.

--- In MakeMicroMusic@yahoogroups.com, Alison Monteith
<alison.monteith3@w...> wrote:

> > Hello Kalle
>
> > I'm writing at the moment for 22 tet guitar.
>
> > I've spent some time looking at decatonic modes and related
> > progressions, cadences and modulations. To my ears the augmented
> > tetrads in tetrad progressions are the most dissonant.

What I find quite interesting about all these dissonant chords is the
fact that they would probably sound even more dissonant in just
intonation. In the tempered intonation of 22-equal the Augmented
tetrad has all its intervals within 9-limit and both Ma-mi and Mi-ma
tetrads have their intervals within 11-limit.

> > They would be
> > useful as pivot chords in modulating from one decatonic to
another,
> > either to the same mode or to another mode. For example, in the
> > notation I use, the third tetrad of C standard pentachordal major
> > (s.p.m.) is d augmented This same tetrad is the second step of Db
> > s.p.m. Modulating to the symmetricals should be easy to work out.
>
> Cadences: I've looked at using the augmenteds minus the fifth, ie
1,3,7.
> 22 tet has in my opinion a very fine dominant seventh. I find my
ears
> and fingers are often drawn to dom 7 shapes, patterns and fragments
on
> the guitar. Many of the structures and motives I collect from
> improvisating prior to composition are related to 1357 chords.
Obviously
> conventional V - I comes to mind, but jazz harmony uses interrupted
> cadences where V goes anywhere it likes.

I don't get a strong cadential feeling if both chords in a dominant-
tonic-progression are complete 7-limit tetrads. But if the tonic is a
5-limit triad, it sure sounds like a normal diatonic cadence.

> In any one s.p.m. I get the following: -
>
> Full dom 7 tetrads on I, V and VII

Shouldn't the V be a VI instead? I guess that's a typo.

> Partial (1,3,7) dom 7 on II and III (there's your augmenteds)
>
> Major triad on V
>
> Partial (1,5,7) dom 7 on X
>
> II and III would resolve (as conventional V -I) to decatonic steps
VI
> and VII respectively, in each case an augmented tetrad or partial
dom7
> resolving to a major triad.
>

That's an interesting and different approach to decatonic harmony. I
have never thought about using partial chords that way!

> I've got reams of notes and reflections on practical and theoretical
> possibilities in decatonic harmony which I'd be glad to share and
> discuss.

Great! I have hoped for some time now that the discussion on
decatonics would go much deeper into the practical issues of music
making.

> Thanks for the opportunity to talk 22.

Thank you!

Kalle

--- In MakeMicroMusic@yahoogroups.com, "Kalle Aho <kalleaho@m...>"
<kalleaho@m...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, Alison Monteith
> <alison.monteith3@w...> wrote:
>
> > > Hello Kalle
> >
> > > I'm writing at the moment for 22 tet guitar.
> >
> > > I've spent some time looking at decatonic modes and related
> > > progressions, cadences and modulations. To my ears the augmented
> > > tetrads in tetrad progressions are the most dissonant.
>
> What I find quite interesting about all these dissonant chords is
the
> fact that they would probably sound even more dissonant in just
> intonation.

it seems to me their tuning in just intonation is "undefined". do you
see it differently? hold on, this isn't really a making microtonal
music question -- reply on tuning.

> In the tempered intonation of 22-equal the Augmented
> tetrad has all its intervals within 9-limit and both Ma-mi and Mi-
ma
> tetrads have their intervals within 11-limit.

well, you don't hear these tempered intervals as 11-limit unless
they're part of larger 11-limit otonal chords, do you?

> > I've got reams of notes and reflections on practical and
theoretical
> > possibilities in decatonic harmony which I'd be glad to share and
> > discuss.
>
> Great! I have hoped for some time now that the discussion on
> decatonics would go much deeper into the practical issues of music
> making.

i'm excited that people are actually making music with my ideas, and
using their ears to guide how they interpret the constructs.
otherwise, they'd go to waste (the ideas *and* the ears *and* the
constructs)!

"Kalle Aho " wrote:

> --- In MakeMicroMusic@yahoogroups.com, Alison Monteith
> <alison.monteith3@w...> wrote:
>
> > In any one s.p.m. I get the following: -
> >
> > Full dom 7 tetrads on I, V and VII
>
> Shouldn't the V be a VI instead? I guess that's a typo.

> Well spotted

>
> Great! I have hoped for some time now that the discussion on
> decatonics would go much deeper into the practical issues of music
> making.
>
> > Thanks for the opportunity to talk 22.
>
> Thank you!
>
> Kalle

One other observation that comes to light looking at cycles. I find it
helpful that in the s.p.m. you have a partial dom7 on III, and of course
a full dom 7 on VII. So within the decatonic you get V7 of V7. Very
funky.

Regards
a.m.

>
>
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