Æther Initiation

𝔉 · Φ · e · √3 · ⊙

:: GALLERY · :: PYTHAGOREAN

PYTHAGOREAN

The harmonic intervals of the 3-limit tuning system rendered as coordinates: PERFECT_FIFTH (3:2), PERFECT_FOURTH (4:3), CIRCLE_OF_FIFTHS, and the PYTHAGOREAN_COMMA — the 23.46-cent residue from (3/2)¹² / 2⁷ = 531441/524288. The irrational log₂(3) that makes the comma unavoidable becomes the generative obstruction. One of the small named-mathematical-fact microcosms alongside BABYLONIAN, LOSHU, VEDIC, RAMANUJAN.

9 entities

Sacred constant
Forge
Circle OF Fifths — harmonia, PYTHAGOREAN microcosm (α 1.50, μ 1.00, ε 0.100) · EGREGORE render

Circle OF Fifths

α 1.50 · μ 1.00 · ε 0.100

EGREGORE
Equal Temper — harmonia, PYTHAGOREAN microcosm (α 1.50, μ 1.00, ε 0.000) · EGREGORE render

Equal Temper

α 1.50 · μ 1.00 · ε 0.000

EGREGORE
LOG2 OF Three — harmonia, PYTHAGOREAN microcosm (α 1.58, μ 0.50, ε 0.000) · EGREGORE render

LOG2 OF Three

α 1.58 · μ 0.50 · ε 0.000

EGREGORE
Octave — harmonia, PYTHAGOREAN microcosm (α 2.00, μ 1.00, ε 0.000) · EGREGORE render

Octave

α 2.00 · μ 1.00 · ε 0.000

EGREGORE
Perfect Fifth — harmonia, PYTHAGOREAN microcosm (α 1.50, μ 1.00, ε 0.000) · EGREGORE render

Perfect Fifth

α 1.50 · μ 1.00 · ε 0.000

EGREGORE
Perfect Fourth — harmonia, PYTHAGOREAN microcosm (α 1.33, μ 1.00, ε 0.000) · EGREGORE render

Perfect Fourth

α 1.33 · μ 1.00 · ε 0.000

EGREGORE
Pythagorean Comma — harmonia, PYTHAGOREAN microcosm (α 1.01, μ 1.00, ε 0.050) · EGREGORE render

Pythagorean Comma

α 1.01 · μ 1.00 · ε 0.050

EGREGORE
Tritone — harmonia, PYTHAGOREAN microcosm (α 1.41, μ 1.00, ε 0.000) · EGREGORE render

Tritone

α 1.41 · μ 1.00 · ε 0.000

EGREGORE
WOLF Fifth — harmonia, PYTHAGOREAN microcosm (α 1.48, μ 0.80, ε 0.300) · EGREGORE render

WOLF Fifth

α 1.48 · μ 0.80 · ε 0.300

EGREGORE

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