Ratio to Cents
PC Polygon Assistant: Displays the polygon notation for any pc set, and allows students to explore basic transformations, properties and relations in pc space
PC Polygon Assistant is a touch-optimized Web app that uses SVG to render the polygon notation for any pc set. It also reports the basic properties of the Tn/In set class and successive interval-array for the prime form. Playback is available via Web Audio API. This program is currently in development. For more information, see my ATMI 2016 presentation.Used in the following courses:
Ratio to Cents: A simple mobile Web app calculator that converts a frequency ratio to cents
Ratio to Cents is a simple mobile Web app that allows students to convert a frequency ratio to cents on a smartphone. Built with jQuery Mobile, the program utilizes the following conversion formula:
where c is cents, and f2/f1 is a pitch interval expressed as a frequency ratio. Students typically enter a frequency ratio derived from the harmonic series, or a tuning system like Pythagorean intonation,
e.g., 1/1, 2/1, 3/2, 4/3, 5/3, 5/4, 6/5, 9/8, 7/4, 81/64, 22/7, 81/80, etc.and the program reports the ratio's size in cents and decimal equivalent. Decimal values (e.g., 1.618/1, 3.14/2, etc.), reciprocal frequency ratios (e.g., 1/2, 2/3, 3/4, etc.), and frequency values in Hz (e.g., 466/440, 660,440, 880/440, etc.) may also be entered. All values are rounded to 3 decimal places. For example, enter the just (5-limit) perfect fifth 3/2 and the program will report its decimal equivalent as 1.5 and its size in cents as 701.955 cents. For more information, see my ATMI 2012 presentation. Used in the following courses:
Current version: v2.03
Atonal Assistant: An atonal theory calculator
Current version: v2.20
The Harmonic Series
Twelve-Tone Assistant: A twelve-tone theory calculator and matrix maker
Current version: v2.4
The Harmonic Series: A Web-based multimedia introduction to the harmonic (overtone) series for musicians.Used in the following courses:
Current version: v1.0
News: I am in the process of developing a mobile-friendly version of these resources using Bootstrap.
SLAPI: A harmonic series interval player for Mac OS and Windows.
String Length and Pitch Interval (SLAPI) is a harmonic series interval player. It provides my students with a convenient way to compare the size of pitch intervals within the octave (Gann 1997) based on integer frequency ratios. The student enters a ratio (e.g., 3/2) and SLAPI calculates the frequency above A4 that corresponds with that ratio and plays the interval (e.g., 440 & 660 Hz) using a Karplus-Strong plucked string tone sample. The program reports the ratio's decimal equivalent (1.5), size in cents (702), and difference from the nearest equal-tempered interval (+2). The equal-tempered counterpart is played using a sampled piano tone.
Current version: v1.1
Straus, Joseph N. 2016. Introduction to Post-Tonal Theory, 4th ed. New York: Norton.
Campbell, Murray and Clive Greated. 1987/2001. The Musician's Guide to Acoustics. New York: Oxford University Press.