Software

PC Polygon Assistant

PC Polygon Assistant: Allows students to display the polygon notation for a pc set and 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 (Toussaint 2013) for any pc set. Moreover, it reports the basic properties of the Tn/In set class (Straus 2016) and cyclic interval array of the prime form (Morris 1987), and allows the student to explore transformations (Tn & I) and relations (C) in pc space. Playback is available via Web Audio API. This program is currently in beta testing. For more information, see my ATMI 2016 presentation.

Current version: 2.03

Ratio to Cents

Ratio to Cents: Allows students to convert an interval frequency ratio to cents

Ratio to Cents is a simple mobile Web app that allows students to convert an interval frequency ratio to cents on their 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:
  1. MUSC 725 Contemporary Styles II
  2. MUSC 726B Mathematics & Music
    MUSC 726T Tuning Theory

Current version: v2.03

Twelve-Tone Assistant

Twelve-Tone Assistant: A twelve-tone theory calculator and matrix maker

Like its companion program Atonal Assistant, this pedagogically-oriented JavaScript application was written in the late 1990s for maximal compatibility with Joseph N. Straus's Introduction to Post-Tonal Theory. It performs basic 12-tone row operations and generates matrices useful in the composition and analysis of twelve-tone music.

Current version: v2.4

Used in the following courses:

  1. MUSC 525 Post-Tonal Theory
    MUSC 725 Contemporary Styles II
The Harmonic Series

The Harmonic Series: A Web-based multimedia introduction to the harmonic (overtone) series for musicians.

Used in the following courses:
  1. MUSC 215 Music Theory III
  2. MUSC 726B Mathematics & Music
    MUSC 726T Tuning Theory

Current version: v2.0

News: I am in the process of developing a mobile-friendly version of these resources

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.

Used in the following courses:
  1. MUSC 215 Music Theory III
  2. MUSC 726T Tuning Theory

Current version: v2.0

News: I am in the process of developing a new version of this program using Max 8.

References

Campbell, Murray and Clive Greated. 1987/2001. The Musician's Guide to Acoustics. New York: Oxford University Press.

Gann, Kyle. 2019. The Arithmetic of Listening: Tuning Theory and History for the Impractical Musician. Urbana, IL: University of Illinois Press.

Morris, Robert. 1987. Composition with Pitch Classes. New Haven: Yale University Press.

Rahn, John. 1908. Basic Atonal Theory. New York: Longman.

Straus, Joseph N. 2016. Introduction to Post-Tonal Theory, 4th ed. New York: Norton.

Toussaint, Godfried T. 2019. The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good?, 2nd ed. Boca Raton, FL: CRC Press.

Tymoczko, Dmitri. 2011. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. New York: Oxford University Press.