Class notes are reminders of some of the main points discussed in class. They are not always presented in a rigorous format.
Scales and modes.
Relations of order can be of non-strict or of strict order; here is a comparison:
reflexive
transitive
anti-symmetric
Non-strict ≤ ≥
aRa
a R b, b R c => a R c
a R b b R a only if a = b
Strict < >
not true
transitive
anti-symmetric
Pitch scales are strictly ordered sets, attacks (start times) and durations are also strictly ordered sets. Dynamic marks are
strictly ordered although their perception might not always be. Perceiving a small difference of, let's say a sixteenth
between two very long durations (a whole note or more) is a difficult task due to the fact that our perception uses a
logarithmic scale. In that case the order could become non-strict. Same could be said in the case of very fast attacks of
pitches separated by large intervals: a listener will have difficulty in deciding their exact order.
Tetrachords are ordered sets of four sounds bound by a perfect fourth (4/3) interval. In ancient Greek music there were
three kinds of tetrachords:
diatonic
T T S
or any other combination
chromatic
S m3 S
enharmonic
¼ M3 ¼
However particular tunings should be considered when defining these intervals.
Modes/scales in ancient Greek, Byzantine, and medieval music were the result of combining tetrachords. According to the
number of sounds scales could be described in modern terminology as:
Drones
Pre-pentatonic
Pentatonic
Diatonic
Chromatic
¼ tone scales
ison
scales with 2, 3 or 4 sounds
Byzantine church music
used in ancient ritual, children folklore, etc.
seven sound within an octave
could have coexisting “mobile” sounds (pien)
equal temperament
ex. East European folklore
Alois Haba, Enescu, Xenakis, Penderecki
“Artificial modes”:
Whole-tone scale
Octatonic
Modes with limited transpositions (Messiaen)
Today the term mode is used interchangeably with that of scale. However in older music, a mode meant a scale as well as a
precise mood and certain melodic formulae.