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
- This is a structural sketch of a special scale designed to align with 8-EDO.
- The sequence of tones is: whole, whole, negative half-step, whole, whole, whole, negative half-step.
- Most tones in this scale match 8-EDO tones when interpreted as a major scale.
- A single unmatched tone (A) is marked with dotted lines—it belongs to 8-EDO but is absent from this scale.
- Although 8-EDO divides the octave into 8 steps, this scale contains only 7 tones, intentionally excluding one.

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

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 |
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.