Physics of a novel method of identifying
dichords: Interference Pulsation
Marianne Ploger and Frank Block, Jr.
From the Blair School of Music, Vanderbilt University, and the Department of
Physics and Astronomy, Vanderbilt University
Background
Approaches and Findings
Future Directions
Traditional musical ear-training involves
repetitive drills to teach the recognition of
two-note musical chords (dichords). We
have observed three subjective
teachable characteristics of dichords
which lead to rapid learning: The three
characteristsics are (1) Interference
Pulsation (a perceived vibration of the
two pitches), (2) Looking Up or Looking
Down (whether the upper note is tending
toward the lower note or toward the
octave above), and (3) Harmonicity
(which is defined in a slightly different
fashion from the usual).
The traditional teaching of physics suggests that when two notes are played simultaneously, one will
hear the frequencies of the two notes, the sum of the frequencies, and the difference between the
frequencies. The Interference Pulsations at approximately 8, 4, and 2 Hertz do not fit the traditional
teaching.
Future work will determine the physical
frequencies that are observed here, and
their causes. Auditory perception of the
frequencies may not be the same as the
physical frequencies. Elucidating this
mechanism will permit a better
understanding of how the dichords are
perceived by the ear and brain.
Interference Pulsation is a perceived
vibration at approximately (1) 8 Hertz
(cycles per second) for musical 2nds and
7ths, (2) 4 Hertz for musical 3rds and
6ths, and (3) 2 Hertz for musical 4ths,
5ths, and the tritone. The physical basis
for Interference Pulsation has not been
previously identified.
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We used a program written in MATLAB® (The MathWorks, Inc., Natick, Massachusetts) to obtain
graphics of the sound envelopes of the dichords. The included figures represent two-second plots of
several dichords, all in even tuning (as on a modern piano): Shown are a minor 2nd (C and C#) on
the left, a Major 3rd (C and E) in the center, and a Perfect 4th (C and F) on the right.
In each case, a vibration is seen – a vibration that is not explained by the traditional teaching of
physics. Similar vibrations are seen in other tuning systems, such as the Pythagorean system (in
which the notes are in exact mathematical ratios). The vibration is indeed fastest on the 2nd, slowest
on the 4th, and intermediate on the 3rd.
Acknowledgements
The Vanderbilt Department of Hearing
and Speech Sciences (Wes Grantham,
Dan Ashmead (who created the
MATLAB® program), and others).
Roy Patterson, University of Cambridge..