A Compositional Tool For Music Theory Exploration & Calculation

If you have any questions, need support with Pitch Kit, or would like to share feedback and suggestions, please feel free to reach out to us at jaybeardmusic@gmail.com.

How To Use The Pitch Kit:

1. Start by tapping on the virtual keyboard to input pitches.

This will display your selected scale as sheet music at the top of the screen and output key information below, including the colloquial name of the scale, intervals it contains, number of unique transpositions, Forte number, and more.

2. To modify the scale, tap the Transpose button to shift the scale up or down to any pitch, or tap the Mode button to cycle through different permutations of the scale.

3. Hold a pitch down to shift the bass to that note, which changes the mode of the scale.

If you know a specific Forte or Spread number (e.g. 7-35 for the major scale), tap the Forte or Spread button to input it directly, and the app will load the corresponding scale.

Key Concepts Explained:

Mode

Modes are permutations of the same scale, sharing a similar interval pattern but reordered to start on different pitches. They are labeled in order from the most spread out (1st mode) to the most compact, based on the span distance compared to other modes.

Pitch Kit allows you to select a mode by its ranking with the Mode button, shift permutations by moving the first/last pitch to the back/front using the up/down arrows, or hold a pitch on the keyboard to switch to the mode starting with that pitch in the bass.

Interval Pattern

The sequence of intervals between consecutive notes in a scale measured in semitones (e.g. whole-half = +21)

Interval Vector

The total amount of each interval type in a scale. The first digit counts half steps and major 7ths, the second counts whole steps and minor 7ths, and so on, with the last digit showing the total number of tritones in the scale.

Forte #

The original labeling system for musical sets in set theory. The 1st number indicates the total number of pitches in the set, while the 2nd number denotes its rank among sets with the same pitch count.

Spread #

A new labeling system for musical sets based on evenness. The 1st number indicates the total number of pitches in the set, while the 2nd number denotes its rank in terms of distance from the perfectly equal division of the octave among sets with the same pitch count.

STDR

Self Transposition Displacement Ranking is a system that measures how efficiently a musical set transposes to itself across all 12 transposition levels, ranking those with the least movement highest. This system compares sets of any size, with consonant sets typically ranking highest (sets with transpositional symmetry being an exception).

Complement

The remaining pitches not included in the scale. For example, the complement of the first 6 pitches (C, C#, D, D#, E, F) is the last 6 pitches (F#, G, Ab, A, Bb, B).

Unique Transpositions

The number of distinct ways a scale can transpose before mapping onto itself with the same pitches. Most scales can be transposed uniquely to all 12 positions, while sets with transpositional symmetry, such as the diminished chord, are limited to fewer unique positions (3).