The Unknown Dimensions of Time and Pitch

Music evolves simultaneously in three worlds: TIME, PITCH, and ENERGY.
     TIME represents the "when" of each musical event while
     PITCH represents the "what" and
     ENERGY represents the “how much”.

The three dimensions of physical space (the "where")
are evidently useful in musical performance
but are not truly pertinent to musical structure.

Since TIME cannot be stopped and music can be made without variations in PITCH (or ENERGY),  TIME seems the most fundamental of the three. The "when" will always affect the "what" and the “how much”.

Structure of TIME
The structure in the World of TIME is found in RHYTHM.
     The Quantitative Dimension of TIME, Duration,
          measures the length of a note.
     The Qualitative Dimension of TIME, Alternation (of Beat and Off-beat)
          defines the "rhythmical flavor" of a note.

This concept of Alternation (of Beat and Off-beat) is familiar to all of us at its smaller levels,
but is almost totally unknown, or at least unappreciated, at the larger levels.

Structure of PITCH
All structure in the World of PITCH is built in the Series of Fifths (its back-bone).
     This applies to both HARMONY and MELODY.
          The scale itself is built in this series.
     The Quantitative Dimension of PITCH measures the frequency of a note
          (its absolute position).
     The Qualitative Dimension of PITCH measures the "Chrominicism" of a note
          (its degree of relative "flatness" or "sharpness").

This dimension of Chrominicism has only recently been identified
and will come as a surprise to just about everyone.

Structure of ENERGY
The structure of the World of ENERGY includes
     the Quantitative dimension of VOLUME which indicates the total energy involved, and
     the Qualitative dimension of TIMBRE which indicates the proportions
               in which this total energy is distributed in the Natural Harmonics.
          The more energy there is in the upper harmonics, the more the Timbre is “nasal” and bright.
          The more energy there is in the fundamental harmonic (#1) the more the timbre is "fluted" and dark.

The dimensions in the world of ENERGY affect performance far more
than they affect the basic structure of a piece of music.
Changing the orchestration of a piece (transcribing a piano piece for orchestra, for example)
does not, and certainly should not, basically change the essence of the original.

We have started examining these dimensions of Energy in a chapter called Orchestration.

We now suggest that you see the
or the
Process of Quantification

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