{"uid":"cap_vtp5M7V1zqFPUNf6S4UFX","slug":"audio-calc-interval-ratio-converter-58df4e1a","name":"Audio Calc – Interval Ratio Converter","description":"Convert a frequency ratio (3:2) to cents and semitones or back, name just and Pythagorean intervals and commas, apply to Hz.","url":"https://audio-calc.x402tookit.com/interval-ratio?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":[],"properties":{"cents":{"type":"number","description":"Interval size in cents (1200 per octave)"},"ratio":{"type":"string","description":"Frequency ratio such as 3:2, 5/4 or 1.5 (use this, or cents)"},"baseHz":{"type":"number","description":"Optional starting frequency in Hz to apply the interval to"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"asOf":{"type":["null","string"]},"cents":{"type":["null","number"]},"ratio":{"type":["null","number"]},"baseHz":{"type":["null","number"]},"source":{"type":["null","string"]},"octaves":{"type":["null","number"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"resultHz":{"type":["null","number"]},"semitones":{"type":["null","number"]},"disclaimer":{"type":["null","string"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"intervalName":{"type":["null","string"]},"simpleFraction":{"type":["null","string"]},"nearestSemitones":{"type":["null","number"]},"nearestNamedRatio":{"type":["null","string"]},"octaveReducedCents":{"type":["null","number"]},"nearestNamedInterval":{"type":["null","string"]},"nearestNamedCentsAway":{"type":["null","number"]},"centsFromEqualTemperament":{"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_n_OlayLt62XXhBNmVIExu","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":"Converts a frequency ratio or cent value to cents, semitones, and octaves, names the just/Pythagorean interval, and optionally applies the interval to a base frequency in Hz.","exampleAgentPrompt":"What is the 3:2 frequency ratio in cents and semitones, what just or Pythagorean interval is it named, and what Hz does it land on if I start from 440 Hz?","exampleUseCases":[{"title":"Identifying a just intonation interval","prompt":"I have the ratio 5:4 — can you tell me how many cents that is, how many semitones, and what just intonation interval it corresponds to?"},{"title":"Checking equal-temperament deviation","prompt":"How far off from equal temperament is a Pythagorean major third (81:64)? Give me the cents value and how many cents it differs from the nearest equal-tempered semitone."},{"title":"Applying a ratio to a root frequency","prompt":"If my root note is 261.63 Hz (middle C), what Hz do I get by applying a just perfect fourth (4:3 ratio) above it?"}],"resultDescription":"Returns a JSON object with the computed cents value, number of semitones, octaves, octave-reduced cents, deviation from equal temperament in cents, the recognized interval name (just or Pythagorean), nearest named ratio and interval with how many cents away, a simple fraction form, and optionally the resulting frequency in Hz when a base frequency is supplied.","failureModes":["Invalid or unparseable ratio string returns an error or null fields","Providing both cents and ratio may cause ambiguity or only one to be used","Very large ratios may fall outside named interval tables, returning null for intervalName","Missing required input parameter returns a 400-level error","baseHz of 0 or negative may produce undefined resultHz"],"whenToPreferThis":"Choose this endpoint when you need precise musical interval arithmetic — converting between ratio, cents, and semitones representations — or when you need to identify whether an interval belongs to just intonation or Pythagorean tuning and quantify its deviation from equal temperament. Prefer it over general music theory lookups when you have a numeric ratio or cent value and need computation, not just a table lookup.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-29T13:11:25.818Z","isFirstParty":false,"canonicalSlug":"audio-calc-interval-ratio-converter-58df4e1a"}