## Software

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 spacePC Polygon Assistant is a touch-optimized Web app that uses SVG to render the

polygon notationfor any pc set. It also reports the basic properties of the T_{n}/I_{n}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: Current version: 1.91d

Atonal Assistant

Ratio to Cents:A simple mobile Web app calculator that converts a frequency ratio to centsRatio 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

cis cents, andf/_{2}fis a pitch interval expressed as a frequency ratio. Students typically_{1}enter a frequency ratioderived 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'ssize in centsanddecimal 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

Twelve-Tone Assistant

Atonal Assistant:An atonal theory calculatorWritten with the post-tonal theory novice in mind, this pedagogically-oriented Web-based software application runs in a Web browser (under JavaScript 1.2+). It was designed in the late 1990s for maximal compatibility with Joseph N. Straus's

Introduction to Post-Tonal Theory. Students use the program to check homework exercises, to aid in analysis and composition, and to freely explore the pitch-class set universe. Atonal Assistant can list a a pc set's normal form (Rahn algorithm), set class, prime form, literal complement, abstract complement, Z-correspondent, interval-class vector and index vector. It can also perform the following twelve-tone operations T_{n}, T_{n}I, and M_{n}, and includes a Mod 12 and Interval Calculator (opi, upi, opci & ic). The results of all calculations are generated as ASCII text so that students may copy and paste the output into a word processer.Used in the following courses:Current version: v2.20

The Harmonic Series

Twelve-Tone Assistant:A twelve-tone theory calculator and matrix makerLike 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.Used in the following courses: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.

Download: SLAPI v1.1 for Mac OS | SLAPI v1.1 for Windows | Documentation (pdf)

Used in the following courses:Current version: v1.1

### References

Gann, Kyle. 1997. "Anatomy of An Octave," in

Information on Alternative Tunings. Available online at: http://www.kylegann.com/microtonality.html.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.