{"uid":"cap_PnFtOk3-6YOv4fRUF-6WQ","slug":"audio-calc-tuning-temperament-frequencies-a082b001","name":"Audio Calc: Tuning Temperament Frequencies","description":"Frequencies, cents and ratios of the 12 notes in equal, 5-limit just, Pythagorean or quarter-comma meantone tuning.","url":"https://audio-calc.x402tookit.com/tuning-temperament?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method"],"properties":{"type":{"type":"string","const":"http"},"method":{"enum":["GET"],"type":"string"},"queryParams":{"type":"object","required":["temperament"],"properties":{"a4":{"type":"number","description":"Reference pitch for A4 in Hz (default 440); sets the root's frequency by equal temperament"},"root":{"type":"string","description":"Root note with optional octave, for example C4 (default), D3, F#4, Bb2"},"temperament":{"enum":["equal","just","pythagorean","meantone"],"type":"string","description":"equal, just, pythagorean or meantone"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"a4":{"type":["null","number"]},"asOf":{"type":["null","string"]},"root":{"type":["null","string"]},"notes":{"type":["array","null"],"items":{"type":"object","properties":{"hz":{"type":["null","number"]},"note":{"type":["null","string"]},"cents":{"type":["null","number"]},"ratio":{"type":["null","number"]},"degree":{"type":["null","number"]},"centsFromEqual":{"type":["null","number"]},"equalTemperedHz":{"type":["null","number"]}}}},"rootHz":{"type":["null","number"]},"source":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"disclaimer":{"type":["null","string"]},"fifthCents":{"type":["null","number"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"description":{"type":["null","string"]},"temperament":{"type":["null","string"]},"majorThirdCents":{"type":["null","number"]},"minorThirdCents":{"type":["null","number"]},"maxDeviationFromEqualCents":{"type":["null","number"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_umHXMzVuGJfUwcAfJjQiJ","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Returns frequencies, cents, and ratios for all 12 chromatic notes in equal, 5-limit just, Pythagorean, or quarter-comma meantone tuning, relative to a specified root and A4 reference pitch.","exampleAgentPrompt":"Can you give me the frequencies, ratios, and cent deviations for all 12 chromatic notes in Pythagorean tuning, rooted at C4 with A4 = 440 Hz?","exampleUseCases":[{"title":"Just intonation synth tuning table","prompt":"I'm building a synthesizer patch in just intonation — can you give me the Hz frequencies and ratios for all 12 chromatic notes rooted at A4 = 432 Hz using 5-limit just tuning?"},{"title":"Comparing meantone vs equal temperament","prompt":"Show me how quarter-comma meantone tuning compares to equal temperament — I want the cent deviation for each of the 12 notes, rooted on C4 at standard A4 = 440 Hz."},{"title":"Historical tuning for early music recording","prompt":"I'm recording a Baroque piece and need Pythagorean tuning frequencies for all 12 notes starting from D3 with A4 at 415 Hz — can you calculate that for me?"}],"resultDescription":"Returns a structured list of all 12 chromatic notes with their: note name, scale degree, frequency in Hz, frequency ratio relative to root, cents value, cents deviation from equal temperament, and equal-tempered Hz equivalent. Also returns summary metadata including the temperament name, root note, A4 reference, fifth/major-third/minor-third cents, max deviation from equal, and a human-readable description of the temperament.","failureModes":["Missing required 'temperament' query parameter returns an error","Invalid temperament value (not one of equal/just/pythagorean/meantone) causes rejection","Malformed root note string (e.g. unrecognized accidental or octave) may return an error or fall back to default","A4 value outside a reasonable audio range may be rejected or produce unexpected results","Payment not included or insufficient USDC causes HTTP 402 response"],"whenToPreferThis":"Use this endpoint when you need precise, mathematically correct frequency tables for historical or alternative tuning systems — particularly equal, just, Pythagorean, or quarter-comma meantone. Prefer it over generic music theory APIs when you need the full 12-note chromatic set with ratios, cents, and deviations all in one call, or when comparing how a tuning system diverges from equal temperament. It is especially useful for instrument tuning, musicology research, audio synthesis, and early music performance contexts.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-30T00:30:45.869Z","isFirstParty":false,"canonicalSlug":"audio-calc-tuning-temperament-frequencies-a082b001"}