Tuning Temperament

{
  "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"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://audio-calc.x402tookit.com/tuning-temperament?a4=440&root=C4&temperament=just'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://audio-calc.x402tookit.com/tuning-temperament?a4=440&root=C4&temperament=just' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Faudio-calc.x402tookit.com%2Ftuning-temperament
const res = await pay("https://audio-calc.x402tookit.com/tuning-temperament?a4=440&root=C4&temperament=just");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://audio-calc.x402tookit.com/tuning-temperament?a4=440&root=C4&temperament=just")
    print(res.status_code, res.text)