A Unison tuning guide
Stretch tuning explained: why piano octaves need room
Stretch tuning adjusts a piano’s note targets to account for stiff strings: bass notes generally sit below, and treble notes above, a simple equal-temperament table. The amount depends on the instrument’s inharmonicity and the intervals you want to balance. It is a tuning choice grounded in measurements, not a fixed correction for every piano.
Why exact frequency ratios are not enough
Inharmonicity means a string’s partials are not exact whole-number multiples of its fundamental. An ideal flexible string would have partials at 1, 2, 3 and 4 times the fundamental frequency. A real piano string has stiffness, which pushes the upper partials progressively sharp of that ideal pattern.
When you compare two notes an octave apart, you hear several partials interacting. Setting the higher fundamental to exactly twice the lower one does not necessarily align the partials that dominate your listening. A wider octave can align a chosen pair more closely, even though a generic chromatic tuner calls the upper note sharp.
The familiar Railsback curve plots the resulting note offsets against an equal-temperament reference. Its broad shape is flatter in the bass and sharper in the treble. A curve is a description of targets, not proof that every note already matches them.
What do 2:1, 4:2 and 6:3 mean?
These labels identify the partials being matched across an octave. In a 4:2 octave, the fourth partial of the lower note is matched to the second partial of the upper note. They do not mean stretching an octave to four times the frequency or adding a fixed number of cents.
| Octave type | Lower note | Upper note |
|---|---|---|
| 2:1 | Second partial | Fundamental (first partial) |
| 4:2 | Fourth partial | Second partial |
| 6:3 | Sixth partial | Third partial |
Different pairs need not agree perfectly on a real piano. Choosing a style means deciding which relationships to favor in each register, then checking how the whole instrument sounds. Unison includes selectable bass, middle and treble stretch styles; its Classic style uses 4:2 octaves.
As an illustration, suppose a lower note’s fourth partial is measured at 884 Hz. A 4:2 octave seeks an upper note whose second partial is also 884 Hz. That does not automatically put the upper fundamental at 442 Hz: its own inharmonicity affects the relationship between its first and second partials.
How many cents of stretch should I use?
There is no universal cents table that is correct for every piano. Measure the instrument, select an appropriate style, and check intervals by ear. Copying another piano’s curve ignores differences in string scale and stiffness. Adding more stretch simply because the treble looks flat can make the overall balance worse.
A cent is one hundredth of a semitone. To apply a cents offset to a reference frequency, use target Hz = reference Hz × 2^(cents / 1200). For example, a hypothetical 440 Hz reference with a +5-cent offset becomes about 441.273 Hz. This illustrates the calculation; it is not a recommendation to stretch A4 by five cents.
Zero cents depends on the target. A tuner can show zero deviation from its stretched target even when that target differs from a plain equal-temperament table. In Unison, the active piano’s measured curve contributes to the tuner’s target. Keep the reference pitch, temperament, stretch and any custom offsets in mind when comparing readings.
How to use measured stretch in Unison
- Select the piano and reference pitch. Use the intended A4 and temperament for this instrument. Changing the reference and changing the stretch solve different problems.
- Measure inharmonicity in the Stretch tab. Follow the suggested notes, isolate a string when appropriate, and capture a clear sustained sound. Avoid treating a noisy or uncertain reading as a reliable measurement.
- Review the curve and style. Unison builds a curve from the measurements and applies it to the active piano’s tuner targets. The Classic 4:2 style is one starting point; other styles and extra bass or treble adjustments are available.
- Tune to the targets, then listen. Check octaves and other intervals across the keyboard. Finish the strings of each note as a unison, and recheck stability after striking the key again.
Follow the separate unison-tuning steps for matching strings on one key. A clean unison can still be at the wrong overall pitch, and a correct stretch curve cannot fix strings that disagree with one another.
Stretch, temperament and pitch raise are different
Temperament sets the relationships between pitch classes. Stretch adjusts targets for partial relationships across the instrument. Pitch raise compensates for settling during a larger change in overall pitch. These settings can interact, but they should not be substituted for one another.
A piano that is substantially below its intended pitch may need an initial pitch correction before fine tuning. Unison offers a pre-measurement and overpull workflow, but the app cannot assess string condition or decide whether a neglected piano can safely reach a higher pitch. That decision needs physical inspection and tuning experience.
Read further and try the tools
The TuneLab iOS manual explains partials and stretch workflows; PianoMeter’s technical overview describes measured inharmonicity and balancing several interval types. These explain the shared acoustics, although each app’s tuning method differs.
Unison is a free piano tuner for iPhone and iPad with measured stretch, unison beat-rate guidance, temperaments, strobe and pitch raise. All 88 keys are included, with no ads or account.