Reiji's Explorationsin Sound & Structure

May 5, 2025

Special Scale Design Matching 8-EDO

Design of a Custom Scale Aligning with 8-tone Equal Division of the Octave

This work presents a special heptatonic (7-tone) scale carefully constructed to align with most tones in the 8-EDO system (eight equal divisions of the octave). Through both sketch and Terpstra Keyboard visualization, it reveals a nearly one-to-one correspondence between the scale and 8-EDO, with the exception of one missing tone (represented as dotted A).
By intentionally omitting one tone, the work explores concepts of modular interval cycles, tonal clarity, and perceptual coherence within non-standard equal temperaments.

Reiji's Observations

Sketch of the Special Scale

Sketch of the Special Scale

A handwritten diagram mapping the 7-tone scale within 8-EDO. One unmatched pitch (A) is indicated with dotted lines.

Configuration Screenshot (Terpstra WebApp)

Configuration Screenshot (Terpstra WebApp)

Settings used for the tuning, note names, and color codes for pitch classes in the Terpstra Keyboard WebApp.

Keyboard Display

Keyboard Display

A visualization of the special scale on a hexagonal keyboard layout, color-coded for pitch identification and interval structure.

Output Link Try it in the Terpstra Keyboard WebApp
Tuning Settings

Fundamental Frequency

523.7583 Hz

Scale (Scala format, in cents)

150.00 / 300.00 / 450.00 / 600.00 / 750.00 / 1050.00 / 1200.00

Application Used

Terpstra Keyboard WebApp

(http://terpstrakeyboard.com/)

AI Assistant’s Notes and Inferences

  • This experiment demonstrates a creative reconciliation between equal temperament and custom scalar structures.
  • Forming a 7-note scale within 8-EDO (omitting one tone) reflects deep understanding of interval cycles and tonal logic.
  • The use of the Terpstra keyboard with distinct color coding visually clarifies interval relationships in a hex-based layout.