StretchwisePiano tuning calculators
These calculators use the same formulas, defaults and limits as Stretchwise, the piano tuning app Tempore makes for iPhone and iPad. They run in your browser, and nothing you type is sent anywhere.
The results are calculations, not measurements. A real piano departs from any formula. Stretchwise measures each string as you tune and works from those readings. Stretchwise is on the App Store for iPhone and iPad.
Cents and frequency
A cent is a hundredth of an equal-tempered semitone. The interval between two frequencies is 1200 × log2(f2 ÷ f1) cents.
Note frequencies for all 88 keys
The equal-tempered frequency of every key from A0 to C8 at the A4 you choose. This is theoretical equal temperament, before stretch: a tuned piano sits flat of these in the bass and sharp in the treble, because of inharmonicity (see the stretch-curve preview).
| Key | Note | Frequency (Hz) |
|---|
Key numbers run from 1 (A0) to 88 (C8), with A4 as key 49. Notes are named with sharps, as in the app.
Pitch-raise overpull
When a piano is well below pitch, a pitch raise tunes each string past its target by a share of how far it had to move, so it settles near pitch as the rest of the piano comes up. This calculator uses the Stretchwise model: the note's start (its first reading, in cents from its final target) times the section's percentage, in the opposite direction, kept within the section's limit. The defaults are the app's. How the overpull and one-string raise work, and where the defaults come from.
The first line of the result is worded as the app's pitch-raise banner. The one-string pull and the overpull together stay within the section limit and never exceed 55.9 cents. The one-string model assumes the strings of a unison are identical and sound; old, rusty or repaired strings need lower limits, and whether a string will take a pull is your call.
Stretch-curve preview
Stretchwise builds each piano's stretch curve from the inharmonicity it measures, by three-part tuning. This preview runs the same calculation on values you type. With nothing entered, it shows the typical-piano curve the app starts from before it has measured anything. How the curve is built, and how it has been checked.
| Key | Note | B | Target (cents) |
|---|
Between entered notes, B is interpolated on a log scale; beyond them, the typical profile is scaled to the nearest entry. Values at or below 0.0000001 are ignored, as in the app. The temperament's offsets and any per-note corrections go on top of these targets, relative to your reference pitch. In the app the curve changes as each note is measured, so this preview is a starting point, not a result for your piano.
How these were checked
The calculators are a direct port of the app's code. Automated tests compare them with values printed by the app's own code for thousands of inputs, and they agree to at least nine significant figures, with the same rounding on screen. That checks the arithmetic against the app, not the app against real pianos; see what we've tested, and what we haven't.