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PostPosted: Tue Aug 07, 2007 9:30 pm 
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Location: Ithaca, NY
Further Dialogue on Twelve Tone Music With Mark Gould: A Composer’s Journal Entry, June 18, 2007

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In this Journal entry I have repeated some of our last discussion and given Mark’s new responses - as well as my new comments and questions.

LC: Hmm ... I am not sure that I can separate harmonic movement and melodic movement in that way. Aren’t they intertwined? Unless we are speaking of a single, isolated tone - harmonies, no matter how approximate, will always be implied. But yes, I also see what you mean ...

Have you found that over the years that your basic harmonic progressions or chords have changed?

Mark: I would say that my basic harmonic profile has 'refined' itself over the years. But the essence of the harmonies has not changed. I seem to tend toward four note chords which have a basis either as a kind of seventh chord but altered to be laid out in fourths, or the major chord with an added tritone or major seventh (C E F-sharp and B). Plenty more harmonies still pervade the row, but this one continues to draw my ear.

LC: I think this could be true of many, if not all, great composers. When I first taught the very early works of J.S. Bach, Beethoven, Chopin, Telemann and Mozart, to name a few - and some of the pieces were written when they were six or seven years old - you could already hear the melodic and harmonic frame found in their later, mature works. This was especially intriguing to me because many of these composers, if not all of them, were breaking or redefining or refining the existing musical frames and forms.
You wrote, in your last e-mail: " - namely taking one row and pulling out a few notes that were the same as those from another row -" Could you explain this further, Mark? I am not entirely sure of your meaning.

Mark: Not hard to show:

Schoenberg, Op 37: D C-sharp A B-flat F E-flat E C A-Flat G F-sharp B.

Let us take the 11th 5th and 2nd notes: F-sharp, F, C-sharp. Transpose down a major third: D C-sharp A. Therefore the retrograde transposed down a major third will be:

G D E-flat E A-flat C B C-sharp F-sharp F A B-flat

Extract the D C-sharp A:

D C-sharp A

G E-flat E A-flat C B F-sharp F B-flat

Now make the D C-sharp A the main melodic material. The remaining notes can now be used in the accompaniment, for that melodic fragment. Proceed to the next three notes: B-flat F E-flat. Find these notes in this order in a different transformation of the row. And so it goes. You can extract segments of length only limited by the structure of the row, but every row can handle two notes and most can handle three note segments. As for four or more it becomes harder.

LC: I see. Again, thank you for your very clear examples and explanations. You have a very clear and searching, intelligent mind! I have another question: Are you saying that now harmonic and melodic notes alternate in the construction of your row? Or that now you are considering only the melodic aspect of the row ...

Mark: The melody contains the harmony, as if alternate notes were the harmony. In 2001 I published an article which attempted to derive analogies to the diatonic scale but operating in a microtonal context. It is this work that (along with my long time study of Bartok) led me to believe that twelve notes are inherently imbued with tonality. I rapidly altered my approach to twelve note music - and now attempt to contain tonal elements in my rows.

LC: I see. When you say "twelve notes", I assume you mean the twelve chromatic tones within an octave? How did microtonality lead you to this conclusion, Mark? I could see your conclusion in the sense that there are physical laws that govern the overtone series. And quarter tones, and other microtones, would set up an adjacent harmonic overtone series ... (Hmm ... is "series" both the singular and the plural? In any case, I mean plural.) We could say that each isolated tone has its own place in the harmonic system set up by the fundamental tone. However, we could also say that each isolated tone becomes its own harmonic system, carries within it its own harmonic system - which was more Schonberg’’s view. In any case, please say more about this if you would.

Mark: The twelve-note scale arose out of the necessity of depicting the structure of the diatonic scale as simply as possible, but also to enable greatest richness of harmonic variety. Our notation depicts the variety whilst the keyboard depicts the simplicity.

LC: Well said and well written. By “twelve-note scale”, I assume that you mean the chromatic scale? Hmm ... If so, then are you calling the half steps of the chromatic scale microtones? Generally the term “microtonality” refers to intervals smaller than the half step, i.e. quarter tones and smaller. Are you saying here that the diatonic scale existed before the chromatic scale, and that the chromatic scale was only the result of the transpositions of the Greek modes and of the diatonic scales? I always assumed the chromatic scale grew out of the transpositions. This is a bit off-topic, but when was the chromatic scale “invented”, first used, and by whom - do you know?

LC: The number of possible rows is almost limitless: 12 taken to the 12th power. However, to analyze a finite number of rows would be fascinating, and useful to theorists, composers - and interpreters.

Mark: The Number of Rows is: 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479,001,600. But these are just sequences of the twelve notes. What I was searching for was the number of independent rows, which were independent melodic entities - not retrogrades or inversions or transpositions of one another. I never found what this number was, or a list of rows. I thought of a brute force approach but never wrote the computer program.

Here was the musical shape which I cannot seem to make go away:

C-sharp C A G-sharp B B-flat
E F F-sharp E-flat D G

Play them as pairs of notes, six pairs. Strangely tonal but mournfully lost. There is a work in there, somewhere.

LC: Well, I am sure there is. I was a little confused as to your notation, since you did not number the notes of the row. Therefore, I went to the piano and paired them this way:


C# (1) with the E (2) in bass
C (3) with F (4) in the bass
A (5) with the F# (6)
G# (7) with E flat
B (9) with D (10)
B flat (11) with G (12)

Is this how you thought it?

If so, this pairing does seem to have limitless possibilities. It is a mournful little tune ...

I suggest that you take your fine row and start scribbling down some melodic, rhythmic and harmonic motives. Just keep jotting ideas down and one morning you’’ll find yourself with enough ideas for a new piece. Don’’t impose your ideas on the row, just let the ideas unfold from the row itself. It could be very beautiful, Mark.

Thank you again for this interesting and valuable discussion dear Mark. All the best to you, and keep writing - both words and music.
Laurie[/img]


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