WHAT IS SET THEORY?
If you are new to set theory or would like to learn more about the topic, please visit Open Music Theory and scroll down to "Post-Tonal Theory." There you can find good introductory resources on set theory analysis.
WHAT THE STR CALCULATOR CAN DO
Through integer notation (see below), the Set Theory Relationship Calculator analyzes pitch class sets and identifies their normal form, prime form, and Forte number.
| Pitch | Integer | Pitch | Integer | Pitch | Integer |
|---|---|---|---|---|---|
| C | 0 | E | 4 | G♯/A♭ | 8 |
| C♯/D♭ | 1 | F | 5 | A | 9 |
| D | 2 | F♯/G♭ | 6 | A♯/B♭ | t |
| D♯/E♭ | 3 | G | 7 | B | e |
Note: A♯/B♭ and B, which are 10 and 11 respectively, are written as "t" and "e."
The STR Calculator also identifies supersets and subsets of each pitch class set. Users can click on any Forte number in the table to highlight corresponding supersets and subsets.
Users can also hover over a pitch class set to learn more information about it including its prime form, interval vector, complement, and Z-related set if applicable.
If more than one pitch class set is entered by the user, the calculator will return common supersets and subsets between the pitch class sets. These are returned under "Related Sets."
WHAT THE STR CALCULATOR CAN BE USED FOR
To demonstrate what the STR Calculator can do, we will use this example from Olivier Messiaen's Couleurs de la cité céleste. At [76], Messiaen identifies four chords as the color "violet." Below is a piano reduction of those chords with the corresponding Forte number listed above.
Using the STR Calculator, we may be able to explore the possible harmonic relationship Messiaen may have associated with the term "violet."
The screenshot below shows all four chords input into the STR Calculator. The calculator returns matching Forte numbers for the first and fourth chords and also illustrates overlapping subsets and supersets between the three unique Forte numbers.
Based on the STR Calculator's "Related Sets," we can clearly see related supersets 8-9, 9-5, and 9-8 and related subsets of 4-9, 3-5, and 3-8. Using this information and further analysis, we may be able to establish links between chords that would have otherwise gone undetected or would have required a tremendous amount of calculation by hand. In this way, the STR Calculator may allow for a new kind of post-tonal, or even tonal, analysis.
ABOUT THE STR CALCULATOR
The Set Theory Relationship Calculator was developed in 2019 by Jonathan Caldwell, assistant professor of music at UNC Greensboro, and Joseph Tolley of SP Global, Inc. Significant data proofing was also done by Logan Epperly, a music education student at Virginia Tech.