Just vs equal temperament API

Compares just-intonation (small-integer 5-limit ratio) and equal-temperament frequencies for an interval above a tonic, with the cents deviation and the audible beat frequency between them. Answers 'What is a just perfect fifth above A4?', 'How many cents sharp is the just major third?'.

Price$0.06per request

MethodPOST

Route/v1/music/just-intonation

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

musicjust-intonationtemperamenttuningcentsratiomicrotuningfrequencyaudio

API URLhttps://x402.hexl.dev/v1/music/just-intonation

Integration docs

Example request

{
  "tonicNote": "A4",
  "semitones": 7
}

Example response

{
  "tonicFreq": 440,
  "semitones": 7,
  "intervalName": "perfect fifth",
  "justRatio": "3:2",
  "justFrequency": 660,
  "equalTemperedFrequency": 659.2551,
  "centsDeviation": 1.955,
  "beatFrequencyHz": 0.7449,
  "note": "JI is pure (small-integer ratio); ET evenly divides the octave into 12 equal cents-steps."
}

Input schema

{
  "type": "object",
  "required": [
    "semitones"
  ],
  "properties": {
    "tonicFreq": {
      "type": "number",
      "examples": [
        440
      ]
    },
    "tonicNote": {
      "type": "string",
      "examples": [
        "A4"
      ]
    },
    "semitones": {
      "type": "number",
      "examples": [
        7,
        4
      ]
    },
    "a4": {
      "type": "number"
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}