Frequencies, cents and ratios of the 12 notes in equal, 5-limit just, Pythagorea...

{ "method": "GET", "queryParams": { "a4": 440, "root": "C4", "temperament": "just" }, "type": "http" }

{ "example": { "a4": 440, "asOf": "2026-10-11T14:38:36.195Z", "degraded": false, "description": "5-limit just intonation (symmetric chromatic scale): small whole-number ratios, pure triads on the root.", "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.", "fifthCents": 701.955001, "majorThirdCents": 386.313714, "maxDeviationFromEqualCents": 17.5963, "minorThirdCents": 315.641287, "notChecked": [ "historical well temperaments (Werckmeister, Kirnberger, Vallotti) and other just-intonation lattices (7-limit)", "the choice of tritone and minor-seventh ratios in just intonation (45/32 and 9/5 here; 64/45 and 16/9 also appear in practice)", "…2 more" ], "notes": [ { "cents": 0, "centsFromEqual": 0, "degree": 0, "equalTemperedHz": 261.6256, "hz": 261.6256, "note": "C", "ratio": 1 }, { "cents": 111.7313, "centsFromEqual": 11.7313, "degree": 1, "equalTemperedHz": 277.1826, "hz": 279.0673, "note": "C#", "ratio": 1.06666667 } ], "reasons": [ "5-limit just intonation (symmetric chromatic scale): small whole-number ratios, pure triads on the root.", "Each frequency is the root's equal-tempered frequency times the tuning's ratio." ], "root": "C4", "rootHz": 261.625565, "source": "Standard definitions of equal temperament, 5-limit just intonation, Pythagorean tuning and quarter-comma meantone, computed locally", "summary": "just tuning on C4 (261.6256 Hz at A4 = 440): fifth 701.955 cents, major third 386.314 cents (equal: 700 and 400).", "temperament": "just", "verdict": "COMPUTED" }, "type": "json" }