Post by Tom K.(LJS) I am talking about a set of tones that are considered consonant in an
atonal setting (more specifically I am using 12-tone serial, but it
doesn't have to be) and the tone set creates a perceived or
theoretical consonant harmonic structure and any additional tones
would be the dissonant entities.
(Tom) Still not clear - especially "consonant in an atonal setting"
Since (in music) Consonance = Stability, Dissonance = Instability, the
absence of a pitch center would seem to make these concepts irrelevant.
(see Schoenberg's remarks on the "Emancipation of the dissonance"). The
theoretical instability in 12-tone theory is only the drive to complete the
row statement.
ljs- Keep in mind that I am not talking about music theory from a
perspective of analyzing the piece. I am starting with the Fux
analysis of the early counterpoint and using the concepts of his
thinking and applying them and speculating on ways to apply his
principles to a more modern setting.
Constance/Stability and Dissonance/instability does not have to be
relevant to a pitch center. It usually is, and certainly is in a CPP
setting, but going to the extreme of 12t-serial, the goal is to nave
no pitch center. If it was C/S and D/I were absolutely linked to pitch
center then neither would be able to exist in 12t-serial music. If
consonance is dependent upon a pitch center, how could there be
consonance in 12t-serial? From that perspective, all of 12t-serial is
dissonant and unstable. We can however consider stable to be consonant
or consonant to be stable.
Thus, if we want to establish the a tone set using Fux principles,
this would coincide with the existing concept of "tonal" by Fux to be
equivalent to stability in the 12t-serial setting. To my observation,
without tonality, the tone sets used in a harmonic manner in 12t music
can be considered somewhat dissonant, more dissonant, or the most
dissonant of the ones used in that setting, in other words, somewhat
stable, less stable, or the most unstable. It would be a relative
scale that wold be adjusted to the various sets that are being used at
that particular time.
Post by Tom K.---------------------------------------------------------------------------------------------------------------
Post by Tom K.(Tom)
Or do you mean that a particular 6 pc set with all tones sounding together
would be defined as consonant and the complementary 6 pc set (also sounding
together) as dissonant? If so, I'm hard pressed to think of any pair of
hexachords which would be heard this way.
(LJS) A while back, in this group, we talked about a 12 tone violin
concerto
I think by Webern. I don't have time to look it up now, but I think
you know the one I mean.
(Tom) Webern never wrote a Violin Concerto - perhaps you are thinking of the
Alban Berg work
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(LJS) In this piece, there seems to be three distinct sections of the tone
row that create three separate tone sets used as a harmonic element in
some instances and he divides it into two 6 note sets in other
circumstances. In this piece, there is various ways that the tones are
grouped according to what was happening at the time.
G Bb D F# A C E G# B C# D# F
He constructed it so that every trichord using notes 1~9 is a Triad, and
notes 9~12 comprise the first 4 tones of a Lydian (or whole-tone) scale.
ljs, thanks for the correction, I knew it was one of the disciples and
that he divided them into smaller groups (this damn final stages of
getting my house approved for occupancy is driving me nuts!!!)
The point of the example is that (and if not in this piece, in a
theoretical piece) the "trichords" would produce a harmonic sonority
that would have a certain degree of C/D and the more consonant one
would be considered the most stable and to go back to Fux, this would
make it the more "tonic" or consonant one one of the group.
I do find this interesting and it is a very good question. I ask that
you remember that this is an extreme example of the application of Fux
to 12t-serial and there are other problems with this extreme that
might require a "leap" over some of the changes that would be made in
the quartal harmonic setting that would be more closely related to
tonality or modality. There will be other "leaps" when we get to the
two point counterpoint and overlapping as described by Fux, but I
think that it can still hold up.
When doing Fux's exercises, if you extend the melodies longer between
cadences than his examples, you will likely find passages that could
be considered non-tonal in a pan-diatonic manner if only for short
periods of time. Without the use of altered tones, or musica ficta,
the resulting counter point could be often be considered to be in any
of a number of modes. Without a strong cadence in the composition, we
can find many different temporary centers if we just let the music run
its course until a cadence is reached.
Post by Tom K.----------------------------------------------------------------------------------------------------------
(LJS) In serial music, the shift of dissonance is extreme.
(Tom) I don't know what you mean by this. Dissonance (see definition above)
is normally irrelevant in a serial piece. The pitch movement is toward row
completion, not from an unstable structure to a stable one. And although
the Berg Concerto uses the row as a thematic force, it is not atonal -
being mostly centric around G and Bb (in parts, perhaps even tonal in G
Minor - Bb major).
Yes, but remember, I am only using the Berg as an example of creating
tone sets from the row to be used as harmonic sonorities to give us a
point of reference. That sonority can be major, minor, or atonal. IF a
section is in G, than that wold create a more easily recognized tone
set that suggested the G as a tonic and that set would be the "tonal"
base or the "stable"part of that section and the tones from another
sonority built on other parts of the row wold be the unstable or
dissonant aspects in that setting and this clash wold be the tones
that needed to be resolved.
Post by Tom K.If you are simply trying to say that music using a tone row (probably
somewhat loosely) may be pitch-centric and therefore contain
consonance/dissonance relationships, Berg proved this nearly 80 years ago,
but these exceptional examples are not atonal.
That is not what I am trying to say. I think we are still not in the
context at all about what I am trying to say and I am beginning to see
why. As I mentioned earlier, this is the really extreme example of
using Fux as a compositional tool for more modern settings. Thre are a
lot of skips required to go from Fux to Berg. It might be necessary to
use the intermediate step of something like tone sets being drawn from
quartal harmonic music to see how to handle the type of questions that
you are asking. (very good questions, by the way, and I think that I
can account for them if we go through the steps of evolution that
happened between Fux and Berg.
My question to you would be, (for purposes of discussion) Can you see
the use of Fux in music through the Romantic Period? If you can, I
would like to try this again with out the large leap of context from
Romantic to Serial. I would like to go through this being used in the
a quartal setting that may or may not have an atonal base. I think
that I could do better to explain how I see using the tones sets as a
basis of reference from a fixed set of C/D rules as in Fux to a more
loose set of tones. I think I might be able to explain where I think
we are not connecting better and will be able to give real examples
that can be explained more easily.
Post by Tom K.So if you want to answer my original question and provide the particular
pitches for your "something like a tone set of say 6 unique tones as
consonant, and the other 6 tones as dissonance", I'd be interested. And
please, no more lengthy meanderings on Fux, I'm asking about your statement
on (atonal) consonance/dissonance, not counterpoint.
Tom
Well, my statement is really about counterpoint, and the C/D is
important to understand. I did not isolate that as the main focus of
your question, I apologize.
I don't know if I can give a good definition of this in the 12t
setting that wold be understandable at this time. I will try with the
quartal context to see if I can explain it that way first and if I
can, then we can proceed. If not, I will do more work on it.
Take two quartal sonorities. A =A D G C F and B = F Bb Eb Ab Db.
Both are of equal dissonance and consonance of course as they are the
same "chord" transposed. But I will be using the A as the given or
"cantus firmus". The B will be the "resultant" melody.
A also = the F pentatonic chord. B also = the Db pentatonic scale
( and all of the enclosed pentatons)
Any tone in A would assume that it was part of the A set and any tone
in B would assume to be part of the B set. Thus when a tone from the
set of A is in the melody and the counter melody is also in A you can
go static and go to another tone in A with the melody movement, OR you
can go to any tone in B to create the dissonance (except the common
tone in this instance of F.) and then the counter melody will resolve
this dissonance by going to a note in the B tone set. and then this
consonance can move the following note to note and switching or not
switching dependent upon the desire to be active or static in the
harmony.
This would be the application of one species. Start on say the common
tone of F on both voices ( called 1 and 2 ) and then work the
pattern.
1&2 begins on the common tone of F. (could be any two notes one from
each set (A or B).
Then 1 can move to either another tone in A making a static move, or 1
can move to a B note creating the dissonance.
Then 2 will follow suit. with the same options. Where ever 1 goes,
the choices will be the same. Either to go to a static note in the
same set or to an active note in the other set.
Then 1 will respond in kind and the process continues with the same
choices until it comes to a cadence. One would presume in the A set
(the implied tonality in this case, but in a different set of tones,
there may be other options for cadence notes depending on the
intention of the composer.
This process is the best way that I know to explain the concept as it
relates to your question. If this makes sense to you as a workable
process that the composer can follow, then you should be able to see
the application if it was in a more serial technique.
Any 12 tone set can be split into two groups of 6. You might want to
start on any tones in the two sets. OR you might want to start on the
O note and then 1 would go to either an active tone from the B set
(the last 6 tones of the row, or to the A set (the first 6 tones of
the row. Then 2 would follow the same rules as above with the two
pentatonic scales and then 1 to create the same species as in the
above example.
You see, what I am saying is that the analysis of Fux created
procedures that ruled the counterpoint of the day according to the
accepted tools of the day. I am saying that we can take these
procedures and create different rules (of consonance/dissonance) and
still do the process in these different contexts. I
I am not presenting an analysis tool, I am using Fux's analysis to
create a composition tool or process that uses the tone sets as if
they were the definition of C/D. The actual sounding traditional (and
true definition ) def, of C/D would still be a choice to be made by
the composer as he crafted his rows or his quartal tone sets or
quintal tone sets or tertian or what ever tone sets and the composer
also has control over traditional C/D by his choice of tones from the
other set of tones.
So the compositional plan uses Fux to guide the movement of the voices
with the direction and the choice of tones that are "C/D" but the
choices of the tones from the other set or the same set in combination
with the choices of the same from the other set, allows a wide range
of true Consonance and Dissonance while the Process is still a result
of a process that was defined by Fux in is GaP.
I hope that this answers your question. I did some improvising here on
my piano with the two voices using the Quartal Example. I really don't
have the time to actually try to put together a composition, at
present, but when my house if finished and if the SS checks come in on
time and with good value, and I can get get back to working and still
have time, (actualy it should work that way) I will try to put
something together as an example but my contribution with this is not
really intended to be a composition. My contribution is intended to be
a way to use a process in a different context that will allow anyone
to follow it and come up with something that is organized and
multilevel and the variations are so great that the possibilities
provide the opportunity for anyone to have their own unique sound
using this same process that we learned with Fux.
This is about as much as I think I can explain the overall concept
without some questions as to the process itself but I really only hope
that you understand what I am saying. Its difficult to answer your
question directly as there is not one single answer that I know to
address it. The tones in the rows MAY be serieal and they MAY be half
serial and even tonal in the other, or any combination of any elements
that the composer chooses to group together and he "redefines them as
consonant" and he "redefines the other to be dissonant". The
terminology is not literal. The terminology is only important so that
one can follow the rules of Fux with ease. The resultant piece can
actually be Pacific Island static and consonant and tonal. OR it can
be very dissonant and completely atonal. I am presenting a process and
not a composition. The process will work only as well as the creative
composer can manipulate the process to create what he wants it to
sound like. The nice thing is that he has a process to give him rules
and direction just as if he was writing a fugue or a canon or what
ever.
Let me know if you understand what I am saying and if so we can talk
about its value, merit or usability. If not and you are still
interested, I can answer questions.
Hey, thanks for the reply. I hope that it is interesting enough for
you to pursue it a bit more, you are helping me to bring in the
abstract ideas into a more concrete process that Is starting to
formulate in my head. Tell me what you understand and what you think.
LJS