19
Oct
12

Math as Art: Part 3

For the past 3 days, I have been obsessing over the letters: ABCD.

ABACBA

ABADAB

ABCADBA

ABACDAB

AB

AC

BC

CD

Etc.Etc.Etc.

Every axiom I used combined with every “clever” set of rules, produced the most monotonous dribble I have ever heard. I was ready to admit defeat and go back to writing cute little melodies when I realized I had forgotten the most important factor!!!  When I was first conceiving of this project, one of the first thoughts I had was this:

How many unique pitch classes at a minimum will allow a piece of music to be interesting?

My answer? It depends.

One pitch is all that is necessary if the piece is minimalist and the goal is to explore the timbral and sonorous  shades to a single pitch.

Two pitches are all that is necessary if your goal is to exploit the relationship between the two.

However, if your goal is to write a melodic, tonal piece of music inheriting the functions of the classical western tradition….

No less than Five pitches are necessary.

I had assumed this intuitively, but had not performed any experiments to prove it for myself. Well, I can assure you that the last 3 days proved to me without a doubt that no less than 5 pitches are absolutely necessary to create a piece of music that is melodic, tonal, and following in the traditions of western classical music.  With my new assumption, I set out creating a new set of 5 pitch axioms and a set of rules which both imitated formal structures from classical music.  Remember, my goal is to combine classical mathematics and classical music theory in their pure forms to reach my hypothesis that it can be done without threatening either.

So, I chose to use a musical form that is self-referential for the axioms: Rondo

ABACAE

and

ABADAE

For the rules, I used the idea of building harmonic structures:

ruleA = “AE”;
ruleB = “ACE”;
ruleC = “BD”;
ruleD = “CBDAE”;
ruleE = “EA”;
What resulted was a two-voice counterpoint that has a clear tonal center, with clear melodic themes that repeat and interact without ever becoming monotonous.

I’ll let you hear a short excerpt for yourself:

Now, to “wash” it with my human hand, adding intuitive musicality such as dynamics, phrasing, rhythmic variation, and articulation.

-S

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