synopsis of microtonal Protopopoff

Anton Rovner was kind enough to write up a synopsis of the microtonal
aspects of Protopopoff's music, which I thought the list might
appreciate:

Dear Joseph,

I did some reading of the Protopopoff book yesterday, and I can give
a few insights about it now, which will probably as detailed as it
could get. The reason that Protopopoff brought up the subject of
microtonality in the first place was because he wanted to show that
Yavorsky's theory is applicable for all types of music - folk music,
tonal (Bach, Chopin, Liszt), chromatic (showing examples chiefly from
late Scriabin, as well as Protopopoff's own music) and microtonal -
the latter, obviously, having no repertoire as of yet.

The principle for Yavorsky's theory in microtonality is the same as
in the standard twelve-equal scale - resolving dissonant tritones
into consonant intervals. As you remember from the article, in
tonal/atonal music, the two important progressions are the dominant
to tonic (B-F resolving to C-E and B-E# resolving into A#-F#) and the
subdominant to tonic (D-A passing through D#-Ab and resolving into E-
G as well as the same thing transposed up or down a tritone).

In the microtonal realm, there are also dominant and subdominant
intervals resolving to tonics, however microtonal intervals are used.
The principle is very interesting: in the dominant to tonic
resolution, the dissonant interval remains the same: the unchangeable
tritone (the "basis" of all intervals). However, since the
intervallic movement is microtonal, the "consonant" intervals end up
being different from those in the 12-equal scale. In the quarter-tone
realm, the dominant-to-tonic resolution is B-F resolving to C
<quarter-tone flat> - E <quarter-tone sharp), so the result
is a tritone resolving to a perfect fourth. It can also be B <quarter-
tone sharp> - F <quarter-tone sharp> resolving to C-E#. Likewise, the
inversion would be B-E# resolving to B <quarter-tone flat> - F
<quarter-tone sharp>.

The subdominant to tonic resolution is a bit more complicated - he
has to alter some things to make it zany. The standard progression
would be, for instance D-A <quarter-tone flat> (in between a tritone
and a perfect fifth)passing through D <quarter-tone sharp> and
resolving into Eb-G <quarter-tone sharp> and the inversion,
transposed up or down the tritone is of the same principle.

As a result, new "modes" are produced - just like in the standard
twelve-note scale several of these dominant and subdominant
progressions produce the "harmonic modes", likewise
microtonal "harmonic modes" are produced here, for instance: B
<quarter-tone sharp> - F <quarter-tone sharp> resolving to C-E# || C#-
E resolving to D <quarter-tone flat - F <three quarter-tone sharp> ||
D <quarter-tone sharp> - A <quarter-tone flat> resolving to Eb-G# ||
E-Bb resolving to F <quarter-tone flat> - A <quarter-tone sharp>. You
can use this "harmonic mode" to write a whole composition or a
section of a composition. Protopopoff cites eight possible "harmonic
modes", depending on the configurations of dominant and subdominant
progressions. These can be inturn joined with their tritone
transpositions to produce "double - modes", each of which would have
an abundance of pitches and relationships betwen "consonant"
and "dissonant" pitches and intervals to produce a harmonically
saturating piece or section of piece.

Then, Protopopoff applies this principle towards third-tones (18-tone
temperament) where the same principle is used: in the dominant
progression the tritone remains intact, while the "consonant"
interval is altered. Thus, C-Gb would resolve to C <third-tone
sharp> - Gb <third-tone flat>. A subdominant progression would be
more complex: C-Gb <third-tone sharp> would pass through C <third-
tone sharp> - Gb and resolve into D-G <third tone flat>.

Finally, he applies the principle towards the sixth-tone scale (or the
36-tone temperament). A dominant progression would be C-Gb resolving
to C <sixth-tone sharp> - Gb <sixth tone flat>, while a subdominant
one would be C - G <sixth-tone sharp> passing through C <sixth-tone
sharp> - Gb and resolving into C# <sixth-tone flat> - Gb <sixth-thone
flat>. Now you can build harmonic modes out of these third-tone and
sixth-tone progressions and use them to write microtonal
compositions, which would follow Yavorsky's theory - just like
Protopopoff's three Piano Sonatas, being quite adequate musical
compositions in themselves, strictly follow Yavorsky's theory, as
expressed within the standard 12-note equal temperament.

--Anton Rovner

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_29850.html#29850

>
> Then, Protopopoff applies this principle towards third-tones (18-
tone
> temperament) where the same principle is used: in the dominant
> progression the tritone remains intact, while the "consonant"
> interval is altered. Thus, C-Gb would resolve to C <third-tone
> sharp> - Gb <third-tone flat>. A subdominant progression would be
> more complex: C-Gb <third-tone sharp> would pass through C <third-
> tone sharp> - Gb and resolve into D-G <third tone flat>.
>
> Finally, he applies the principle towards the sixth-tone scale (or
the 36-tone temperament). A dominant progression would be C-Gb
resolving
> to C <sixth-tone sharp> - Gb <sixth tone flat>, while a subdominant
> one would be C - G <sixth-tone sharp> passing through C <sixth-tone
> sharp> - Gb and resolving into C# <sixth-tone flat> - Gb <sixth-
thone flat>. Now you can build harmonic modes out of these third-
tone and
> sixth-tone progressions and use them to write microtonal
> compositions, which would follow Yavorsky's theory - just like
> Protopopoff's three Piano Sonatas, being quite adequate musical
> compositions in themselves, strictly follow Yavorsky's theory, as
> expressed within the standard 12-note equal temperament.
>
> --Anton Rovner

I guess one obvious aspect of Protopopoff's theory is how easily it
fits into 72-tET.... I wonder if that has any relationship to the
Russian scales that were in 72... I'll ask Anton offlist until he
comes back on again...

_______ _______ _____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
>
> I guess one obvious aspect of Protopopoff's theory is how
easily it
> fits into 72-tET.... I wonder if that has any relationship to the
> Russian scales that were in 72... I'll ask Anton offlist until he
> comes back on again...
>
> _______ _______ _____
> Joseph Pehrson

I think the theory is a little silly and rather historically blind. The
diatonic scale predates the use of the tritone to define the
dominant-tonic progression, which in turn predates the tuning of
the tritone as the half-octave. To promote this half-octave to the
"basis of all harmony" is absurd. And where does it leave
19-tET?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

> To promote this half-octave to the
> "basis of all harmony" is absurd. And where does it leave
> 19-tET?

Half of the 38 et? :)