Compare Measured Pitch Ratios in Cents Against a Stated Reference Shift — Free
Hertz differences do not describe equal pitch steps across a range. Use the frequency ratio, keep its signed cents difference, and compare it with your stated reference shift without a musical-quality verdict.
The proof surface
Tempo determines elapsed duration; this compares measured/reference frequency ratios on a logarithmic cents scale without judging a performance.
InputTone code | reference frequency Hz | observed frequency Hz; target shift from the reference (cents)
Rare deviceTempo determines elapsed duration; this compares measured/reference frequency ratios on a logarithmic cents scale without judging a performance.
Output artifactLargest absolute target-relative cents mismatch plus complete labeled working
Cost$0 local core · no account, card, paid key or subscription · filing proposal has no checkout
Sample, not your facts: Invented records: Cedar A tone | 440 | 445; Willow C tone | 261.625565 | 262. Target shift from the reference (cents) = 0; expected Largest absolute target-relative cents mismatch: 19.562175 cents absolute mismatch. These are not quotations, verified observations or personal evidence.
Before using the cent-offset tuning card
Use non-sensitive tone codes and positive finite reference/observed frequencies from the same intended tone and measurement convention. This card has no microphone access, audio upload or pitch tracker; it accepts numbers supplied by you. Cents define a logarithmic ratio scale with 1,200 cents per octave, not a mandate that every performance use equal temperament. The target shift is a deliberate reference offset in cents, applied to every row. It does not alter the measurements. Instrument, style, temperament, harmonic selection and device accuracy matter, so do not convert a precise-looking mismatch into a compulsory adjustment or a judgment of a musician.
Why the flat version breaks
Equal hertz errors are treated as equal pitch errors
A five-hertz difference at a low reference is a different ratio from five hertz at a high reference. The logarithmic cents scale makes the relative pitch step explicit. It does not diagnose an instrument problem or decide the musical acceptability of that step. Keep the original frequencies visible so the ratio can be independently checked.
An octave is silently folded into unison
Pitch class and frequency ratio are not the same question. Doubling frequency is one octave, not zero cents in this model. Wrapping that result would conceal a possibly wrong harmonic or an intentionally different register. This card keeps the full signed ratio and asks you to check the source convention rather than choosing a musically convenient interpretation.
A target offset overwrites observed evidence
Intentional transposition belongs in a separate setting, not in edited observed frequencies. The app calculates the raw ratio first, then subtracts the target in a visible working. A zero mismatch may mean the intended offset was met, not that reference and observed frequency are identical. Do not remove that setting from a shared result or call it a verified universal tuning standard.
How to work the cent-offset tuning card
Identify what frequency was measured
Enter a unique tone code, reference frequency and observed frequency in hertz. Both frequencies must be greater than zero and no more than one million; at most six decimal places are accepted. Units and exponent syntax are rejected to avoid silent parsing mistakes. Check whether a tuner reported the fundamental or a harmonic, and whether the reference was calibrated. The app cannot detect that semantic mismatch from two otherwise valid frequencies.
State any intentional reference shift
The setting accepts a signed target from minus 2,400 through plus 2,400 cents. Zero means compare directly with the supplied reference; 1,200 means the intended tone is one octave above it. It is not a recommended tuning offset. Retain the reason for the shift in your source notes and use the same intention across rows. If different tones have distinct targets, a single shared setting is not a faithful model and the sets should be kept separate.
Convert ratios before subtracting the target
Calculate signed difference as 1,200 times log base two of observed divided by reference. Subtract the shared target shift to obtain signed mismatch. The headline is the largest absolute mismatch, while each row retains its sign, measured ratio and reference convention. Do not add row cents as though they were durations or ordinary frequency changes. The calculation does not wrap octaves or label the largest mismatch as a performance failure.
Check measurement context with a musical professional
Compare the card with the original measurement method and intended tuning system. A brief unstable tone, room noise or a selected harmonic can make an observed number misleading even if the logarithm is correct. Ask a teacher, tuner technician or appropriate musical professional if a consequential adjustment depends on it. The optional filing prototype preserves reference and target assumptions; the unlimited article demo is available for another measurement set without a new sales promise.
What the cent-offset tuning card keeps distinct
Question
Before
Check this working
Equal hertz errors are treated as equal pitch errors
A five-hertz difference at a low reference is a different ratio from five hertz at a high reference. The logarithmic cents scale makes the relative pitch step explicit. It does not diagnose an instrument problem or decide the musical acceptability of that step. Keep the original frequencies visible so the ratio can be independently checked.
State any intentional reference shift
An octave is silently folded into unison
Pitch class and frequency ratio are not the same question. Doubling frequency is one octave, not zero cents in this model. Wrapping that result would conceal a possibly wrong harmonic or an intentionally different register. This card keeps the full signed ratio and asks you to check the source convention rather than choosing a musically convenient interpretation.
Convert ratios before subtracting the target
A target offset overwrites observed evidence
Intentional transposition belongs in a separate setting, not in edited observed frequencies. The app calculates the raw ratio first, then subtracts the target in a visible working. A zero mismatch may mean the intended offset was met, not that reference and observed frequency are identical. Do not remove that setting from a shared result or call it a verified universal tuning standard.
Check measurement context with a musical professional
The cent-offset tuning card replaces this named manual reconciliation, not source verification or the responsible human's decision.
Run it on the samples, right here
FIRST-LOAD
HYPOTHESIS / PROTOTYPE — checkout unavailable. Calculation is local. A draft is saved automatically in this browser profile when storage is available; Reset to sample clears it. Optional Pro history stores only five summaries and has its own deletion control. State links encode your inputs and can remain in browser history, clipboard or recipients’ records; share only non-sensitive rows. Optional external AI formatting leaves this device. The required site analytics beacon reports page activity; shared URLs contain encoded inputs. Do not treat an encoded URL as private. The calculator has no input-collection endpoint.
Supplied-frequency arithmetic only: no audio analysis, device calibration, performance judgment or universal tuning prescription. Confirm harmonic/reference conventions and any consequential adjustment with an appropriate music teacher or tuner technician.
Data note: This cent-offset tuning card calculates in the tab from Tone code | reference frequency Hz | observed frequency Hz. No input-collection endpoint, AI request or file upload is built into it. Drafts may be saved locally; explicit input-state links and optional external formatting can disclose the records. Use non-sensitive codes and clear the draft when finished.
Go deeper: the companion app files the same reading as a index card with a stamped header
The article demo above runs without limits. The companion app keeps a local history, exports the rows as CSV, prints the cent-offset tuning card reading, and holds your drafts on this device — one complete free app run; the proposed $4 one-time filing layer is not for sale.
Keep the complete cent-offset tuning card answer free; optional filing proposes its boundary-preserving print, row-and-summary CSV and five local reading summaries. The $4 one-time prototype is not for sale; another calculation remains free in the article demo.
Supplied-frequency arithmetic only: no audio analysis, device calibration, performance judgment or universal tuning prescription. Confirm harmonic/reference conventions and any consequential adjustment with an appropriate music teacher or tuner technician.
What this is built on
Declared local method: Calculate signed difference as 1,200 times log base two of observed divided by reference. Subtract the shared target shift to obtain signed mismatch. The headline is the largest absolute mismatch, while each row retains its sign, measured ratio and reference convention. Do not add row cents as though they were durations or ordinary frequency changes. The calculation does not wrap octaves or label the largest mismatch as a performance failure.
Every sample code, measurement, date, price, fingerprint and scenario is invented. Artifact checks do not verify reader data, policies, actual files, tickets, votes or health/accessibility outcomes.
Google’s official Gemini pricing page, fetched 2026-10-01, lists AI Studio access in its Free section, limited model access and free input/output tokens. Free-tier content may be used to improve products. Optional external formatting may require an account; limits/access can change. Manual local entry needs none. Do not send sensitive records.
Before: raw hertz differences looked like comparable tuning errors. After: signed frequency-ratio cents and the intentional reference shift have separate, explicit roles.
Three worked readings, with different inputs
Sample A — typical inputs
Cedar A tone | 440 | 445
Willow C tone | 261.625565 | 262
Setting: Target shift from the reference (cents) = 0. Expected summary: 19.562175 cents absolute mismatch.
Cedar is about 19.562175 cents above its supplied reference, while Willow is about 2.475948 cents above its reference. With a target shift of zero, the largest absolute mismatch is Cedar’s. A five-hertz change does not have the same pitch size at every reference frequency: cents use the ratio. Neither difference is labeled a bad performance or a mandated tuning correction.
Sample B — changed plan
Harbor octave tone | 220 | 440
Orchard unison tone | 330 | 330
Setting: Target shift from the reference (cents) = 0. Expected summary: 1200 cents absolute mismatch.
Doubling frequency produces exactly 1,200 cents; unison produces zero. The headline retains the octave mismatch rather than wrapping it into a pitch-class unison. If your task is pitch-class comparison or a different tuning convention, that is a different model. Reference and observed frequencies must describe the same intended tone or harmonic for this ratio to answer the question.
Sample C — boundary convention
Exact-reference tone | 432 | 432
Setting: Target shift from the reference (cents) = 0. Expected summary: 0 cents absolute mismatch.
Matching frequencies give zero cents difference and zero mismatch at the entered zero-shift target. This arithmetic equality does not verify measurement calibration, sustain, intonation over time or a musical standard. Changing the shared target shift changes the mismatch while leaving the measured frequency ratio intact; the card prints both quantities so that deliberate transposition is not confused with measurement error.
Optional AI formatting, never the calculation
Manual entry completes this cent-offset tuning card for free without signup. If available to you, the free AI Studio interface linked in the sources may format fictional or non-sensitive notes; external access may require an account. No API key or AI call is built into this tool. Free-tier content may be used to improve products. Review each cell and transcribe it to the labeled row schema; do not paste the JSON object into the row box.
Format only these fictional or non-sensitive notes for a cent-offset tuning card. Return strict JSON shaped as {"rows": [{"label": "string", "cells": ["string", "string"]}], "setting": "string"}. The columns are Tone code | reference frequency Hz | observed frequency Hz; the setting is Target shift from the reference (cents). Keep all supplied strings and quantities exactly; do not calculate, infer missing entries, invent dates or add advice. If any required value is missing, return an empty rows array and ask me for it separately. I will verify every cell against my source and manually transcribe rows using vertical bars before running the local calculator.
An AI response is not executed, fetched or trusted as a result. Missing values remain questions; the strict local parser checks the rows you actually enter.