God’s Scales

[whitesynth]

God’s Scales: Design any scale with one perfectly pure interval—fifth, fourth, octave, tritave—and near-perfect Pythagorean harmony everywhere else.

Here is a tuning system that bridges ancient Pythagorean harmony and modern equal temperament in a way I haven’t seen before.

The core idea:
You can build a scale where one interval of your choice is mathematically perfect—whether it’s the perfect fifth (3/2), perfect fourth (4/3), octave (2/1), tritave (3/1), major second (9/8), etc.—while every other interval stays within 1–3 cents of Pythagorean purity (inaudible deviation).

And the best part? It’s not theoretical. You generate these scales using a simple, repeating “skip pattern” (like 4‑9‑9‑9 or 4‑5‑4‑5-4-5-4) applied to specific high-resolution temperaments (e.g., 31-EDO for perfect fifths, 22-EDO for perfect fourths, 53-EDO for perfect octaves, 84-EDO for perfect tritaves, etc.).

This means:
- Want a 12-note scale with an exact perfect fifth and near-just thirds? → Use 31-EDO + skip pattern.
- Want an 11-note tritave scale with a perfect tritave (3:1)? → Use 84-EDO + skip pattern.
- Want a 7-note diatonic scale with a perfect major second? → Use 9-EDO per 9/8 + skip pattern.

The same skip logic works across all these systems because they’re all approximations of the same Pythagorean spiral—just “anchored” to a different perfect interval.

[Read the PDF here]

God’s Scales.zip

This could be useful for:
- Synth designers creating adaptive tuning tables,
- Composers wanting modal purity without comma drift,
- Microtonal explorers seeking structured yet flexible frameworks.

[Scoops]

Nothing is perfect in this world, hence God's Scale, while fun in concept, is a poorly conjured up name

[planetearth]

It might be helpful if you posted an example of a piece using "God's Scale". Perhaps something you feel best demonstrates the "perfect fifth", "perfect tritave", or "perfect major second".

And as @Scoops suggests, it might be better to avoid suggesting any one supreme deity had a hand in this scale. Maybe just call it the "Perfect" Scale (with, of course, the understanding that nothing is perfect).

Also, if I wanted this "Perfect" Scale (See? That name is already catching on!) to have a 12-note scale with an exact perfect fifth and near-just thirds, but someone else (such as that troublemaker, @Scoops) wanted an 11-note tritave scale with a perfect tritave, how would we denote that? We obviously couldn't call both of them the "Perfect" Scale.

I've heard some very interesting micro-tuning pieces in the last few years, and I'm not suggesting this might not be equally impressive. But like many people, I'd probably get more out of hearing examples than reading the logic behind them.

Steve

[stoopicus]

I'll take a look after I have exhausted 12-tet

[jancivil]

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