Interval Visualizer
Pete Nordquist
Dr. R. Dean Ayers
Daisuke Kato, Lewis Nakao, Justin Corn
Southern Oregon University
Work partially supported by the Veneklasen
Foundation
Purpose
• Train musicians to hear just intervals
• Experiment with timbral influences on pitch
perception.
• Demonstrate the differences between
equal tempered and just intervals
Frequency Graphing Technique
• Computer generates the reference frequency as
a sine wave and sounds it.
• Computer generates fundamental frequency by
dividing the reference frequency by the
denominator of the ratio of the user’s chosen
target interval.
• User sounds the input (target) frequency.
• Fundamental sinusoid moves the pen that is
drawing the reference (unit) circle, and the
drawn point is modified by adding the input to
the circle radius whenever the input is positive.
‘Tuning’ using the Figure
• User is looking for a figure having the
number of “bumps” shown in the
numerator of the ratio of their chosen
interval.
• Figure spins counterclockwise when input
is low, clockwise when it is high.
Input Filter
• User input is converted to a sine wave to
simplify the resulting figure
• Conversion is accomplished by doing an
FFT and choosing the “bin” with the
largest amplitude.
Pitch Perception
• Set the timbre of the reference frequency
by clicking Options button then choose
triangle or sawtooth.
• I have found a sinusoidal reference
causes me to sing a higher target
frequency than does a triangular
reference.
• A sawtooth seems easier to tune against
than either a sinusoid or triangle.
Just vs Equal
• Choose a reference frequency
• Sound Equal tempered target
• Select intervals using number keys to
‘play’ a scale or melody
• Stop Equal target and sound Just target
• Repeat melody listening for differences
• Sound both targets simultaneously and
listen to beats for each interval
Future work
• Adding functionality to supply arbitrary
reference and target timbres and tune
them to continue the pitch perception
work.
• Thinking about a visualization for showing
differences in timbre as well as pitch.
Where Can I Get It?
• The Interval Visualizer is freely available
from:
http://www.sou.edu/cs/Nordquist/tuning/index.html
Perfect 5th - 3rd partial - a
Filter chose the 9th partial, because it is the strongest frequency.
Spectrum & Visualizer - a
Spectrum & Visualizer - u