# Audio Calc: Tuning Temperament Frequencies

> Audio Calc: Tuning Temperament Frequencies is a paid API for AI agents from audio-calc.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).

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.

## Facts

- Endpoint: GET https://audio-calc.x402tookit.com/tuning-temperament?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-30
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/audio-calc-tuning-temperament-frequencies-a082b001
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_PnFtOk3-6YOv4fRUF-6WQ

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability audio-calc-tuning-temperament-frequencies-a082b001
```

Example prompt: 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?

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

Frequencies, cents and ratios of the 12 notes in equal, 5-limit just, Pythagorean or quarter-comma meantone tuning.

## Output

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.

## Request schema (JSON Schema)

```json
{
 "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"
       ]
    
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/audio-calc-tuning-temperament-frequencies-a082b001/health.json
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