Stretch tuning means tuning a piano’s octaves slightly wider than the mathematically pure 2:1 ratio, so the top of the keyboard ends up a little sharp and the bottom a little flat. It is not a flaw or a trick. It compensates for the physical stiffness of piano strings, and without it a piano sounds dull, narrow and strangely out of tune with itself, even when every note matches a tuning fork.
Below, we explain why strings force this compromise, how a technician decides how much stretch to use, what happens with too little or too much, and how digital pianos handle it.
TL;DR
- Piano strings are stiff, so their overtones run sharp of the ideal harmonic series (inharmonicity). Tuners widen octaves to match those overtones.
- The result is a flat bass and a sharp treble relative to equal-ratio pitch, built outward from a temperament set in the middle of the keyboard.
- The right amount differs from piano to piano. Short spinet strings need more stretch than long concert grand strings in some ranges, and the final call is made by ear.
- Too little stretch makes double and triple octaves sound narrow. Too much makes wide intervals noisy and the top unpleasant.
- Digital pianos usually build a stretch curve into their samples, and some models even let you adjust it.
Table of Contents
- Why a piano cannot be tuned to pure octaves
- What stretch does to the sound
- How a technician decides how much stretch to use
- Measuring inharmonicity: electronic tools
- What happens with too little or too much stretch
- Stretch tuning on digital pianos
- A worked picture: how stretch shows up in a tuning session
- Our perspective
- Learn stretch tuning step by step
- FAQ
- Sources
Why a piano cannot be tuned to pure octaves
An ideal string vibrates in a perfect harmonic series: the second partial is exactly twice the fundamental, the third exactly three times, and so on. Two notes an octave apart would then share partials that line up exactly.
A real piano string is a stiff steel wire. Stanford’s CCRMA explains that stiffness stretches the overtone series, so each partial is progressively sharper than the ideal series. The relationship they give is f_n = n f_0 sqrt(1 + B n²), where B is the inharmonicity coefficient. Two things follow from the formula: a higher partial number and a larger B both push the frequency further above the ideal.
There is a physical picture behind the math. The wire is held rigidly at its ends, so it cannot bend freely there. The effective vibrating length is slightly shorter than the speaking length, and the effect grows with higher modes. Short, thick strings, such as those in the bass of a small piano or the lowest notes of a spinet, show the effect most.
The amount is small but audible. A Piano Technicians Guild paper on plain-wire strings reports about 1.2 cents of inharmonicity in the second mode of a middle-C string, roughly doubling every eight semitones above that point. Most partials end up sharp; a few can end up flat.
If you have ever wondered why a piano tuner says every piano is a little “wrong” by design, our post on the mathematical proof that every piano is out of tune covers the related problem of the tuning system itself.
What stretch does to the sound
When you play a note on a piano, you hear its fundamental plus a cloud of partials. When you play an octave, the second partial of the lower note and the fundamental of the upper note should coincide. If the lower note’s second partial is sharp because of inharmonicity and the upper note is tuned to a pure 2:1 ratio, the two do not match. They beat against each other: a slow, wobbling pulse that the ear reads as the octave being narrow.
The tuner’s remedy is to raise the upper note until its fundamental meets the lower note’s sharpened partial. Repeat the logic across the keyboard and each octave is a hair wider than 2:1. Over seven octaves the accumulated difference is considerable. Published measurements of total stretch vary by instrument, and we look at some of them in the digital piano section below.
Mario Igrec, a technician and author of Pianos Inside Out, describes the goal as widening a musical octave so it is richer and more resonant, not simply detuning notes. A slightly wide octave on a well-tuned piano sounds open and alive. A pure one sounds thin.
One common misunderstanding is that stretch is added for brilliance. It is not. Stretch brings partials into agreement that would otherwise clash. Brightness can be a side effect, and some players like it more than others, but the reason for it is acoustic compensation.
How a technician decides how much stretch to use
There is no single number. The amount depends on the scale design, string length, string thickness, the room, and the pianist’s taste. Still, the process follows a reliable pattern.
Start in the middle
PTG author Kent Swafford describes the usual sequence: the technician lays the temperament in the middle register, then uses octave and other interval checks to extend the tuning across the keyboard. Virginia Tech’s FFTuner documentation says the same thing in other words: central octaves are tuned first, then lower notes go somewhat flat and higher notes somewhat sharp, so their inharmonic partials line up with the central scale.
The middle is a good anchor because inharmonicity there is modest. Errors made in the temperament get carried outward, which is one reason a careful temperament matters so much. If you are new to the idea, our post on why pianos need to be tuned sets out the basics.
Choose which partials to match
There is a real choice here. A technician can match the second partial of the lower note to the fundamental of the upper note (a 2:1 octave), the fourth partial to the second (a 4:2 octave), or tune a double octave so that the fourth partial meets the fundamental (4:1). Swafford’s procedure uses 2:1, 4:2 and 4:1 checks and recommends strip muting so a single string per note can be heard while tuning.
The tradeoff is simple. Matching low partials gives a narrower stretch and cleaner single octaves. Matching higher partials gives a wider stretch that sounds purer across double and triple octaves but can make single octaves feel wide. A Piano Technicians Journal article on stretch describes using beat-speed windows and check-note comparisons to set octave sizes, including a choice between narrow 6:3 octaves and purer relationships among higher partials.
Listen to the beat rates
Even with a clear plan, the beat rates tell the truth. Swafford notes that beat rates progress differently from piano to piano because inharmonicity varies through each scale. Experienced technicians compare the beat rates of fourths, fifths and octaves and adjust until the progression is smooth, with no sudden jumps as you move up the scale.
This is why the ear stays central even when devices are used. A good beat progression is a pattern you learn to hear with practice. If you worry about that skill, our article on whether you need perfect pitch to be a piano tuner addresses it directly.
Measuring inharmonicity: electronic tools
Electronic tuning devices measure what the ear estimates. The FFTuner documentation explains that a spectrum display can reveal and measure inharmonicity by comparing at least two harmonics of a note, and the measured values can guide stretch note by note.
The research goes further. In a study in the Journal of the Acoustical Society of America, Lattard measured fundamental and partial frequencies, fed them into a mathematical tuning simulation, and used the calculated frequencies to tune a particular piano. The lesson is that a piano’s own measured partials can set its targets, instead of applying one fixed curve to every instrument. Modern tuning software works along these lines.
Even so, the Virginia Tech documentation treats such tools as measurement and visualization aids. The final choice stays perceptual, because the best compromise depends on the piano’s actual spectrum and on what sounds harmonious. A device gives a starting curve; a technician judges whether the result sings.
What happens with too little or too much stretch
| Situation | What you hear |
|---|---|
| Too little stretch | Double and triple octaves sound narrow; narrow intervals such as thirds and tenths become objectionably beatful |
| About right | Octaves sound open and resonant, with smooth beat progression across the scale |
| Too much stretch | Wide intervals become noisy and the top of the keyboard sounds sharp and unsatisfying |
These effects are described in Igrec’s Pianos Inside Out: insufficient stretch makes double and triple octaves sound narrow, while overstretching the top is something most pianists do not find satisfying.
In practice, the symptoms of poor stretch are easy to hear. Play a bass note and its octave plus two octaves above. If the top note sounds like it is dragging flat, the stretch is too small. If the treble sounds shrill and the highest octaves seem to float away from the middle of the piano, it is too large. Playing against a fixed-pitch instrument or recording can expose both.
Stretch tuning on digital pianos
A digital piano has no strings, so physics does not force inharmonicity on it. Virginia Tech notes that electric pianos could in principle have zero inharmonicity, yet people like a little anyway. For that reason, many digital pianos copy an acoustic piano’s tuning curve, usually baked into the recorded samples or applied as a stretch table.
The amounts differ by instrument. Stanford CCRMA lists measured total tuning stretch of about 35 cents on a Kurzweil PC88, 45 cents on a Steinway Model M, and 60 cents on a Steinway Model D. So a digital piano can be a bit more modest than a large grand. Some models let you switch the stretch on or off, which matters if you play with other instruments tuned to a fixed scale, since a stretched bass or treble can clash with them.
The practical rule: if you play a digital piano alone, the built-in stretch will sound natural. If you combine it with a synthesizer, backing track or tuned instruments, try the setting that matches them.
A worked picture: how stretch shows up in a tuning session
Imagine tuning an ordinary upright. You set the temperament around the octave that includes middle C, checking thirds, fourths and fifths for smooth beat progression. Then you tune outward by octaves. At each step, you choose between a clean 2:1 match and a slightly wider octave, and you check it against the 4:2 and 4:1 relationships. By the time you reach the top octaves, the stretch has accumulated. The bass goes flat in the same way in the other direction.
If the piano is a small spinet with short strings, inharmonicity rises quickly and you accept more stretch in the bass, since the pure-sounding choice would leave those notes buzzy against the middle. A larger grand has longer strings and less inharmonicity at the same pitch, but the same logic holds. That is why the same stretch curve does not suit every piano, and why a technician who measures first and listens second usually gets better results than one who applies a standard pattern.
The cost of a professional tuning also reflects this judgement. If you want to understand what you are paying for when you hire a tuner, see our guide to piano tuning prices in the U.S.
Our perspective
We teach stretch early in a student’s training, because it sits at the heart of why tuning is a skill rather than a procedure. Students sometimes arrive believing that an electronic device is simply right, and that a tuner’s job is to follow it. We tell them the opposite: a device measures, an ear decides.
Our advice for anyone learning is to practise on one piano until the beat progression across octaves becomes familiar. Tune the temperament, check it, then extend outward and listen for where the progression turns rough. Do not chase a number. The best stretch is the one that makes thirds, fifths and octaves sound settled together on that specific instrument, and you only learn that by hearing many pianos.
We also encourage students to think of inharmonicity as information. A piano with high inharmonicity in the bass is telling you something about its scale design, and good technicians use that to decide where to compromise. Since 2009, our course has been built around that way of thinking, with a path toward the Piano Technicians Guild RPT exam.
— Michael
Learn stretch tuning step by step
Reading about stretch helps, but hearing it is what makes it stick. Our Piano Tuning and Repair Online Course is a fully online, self-paced program that covers tuning from the basics to advanced technique, and is designed to prepare you for the Piano Technicians Guild RPT exam. The course is $1,800 as a one-time purchase. You can see this and the other options on our courses page, or browse the full course index first.
If you are still weighing whether to train online, our overview of an online piano tuning school and our article on how much piano tuners make are good places to start. You will also need a proper kit; we stock tuning tools for students.
FAQ
Is stretch tuning the same as being out of tune?
No. A stretched piano is deliberately set so that its inharmonic partials agree with each other. A pure 2:1 octave on a real piano actually produces beating between partials, which the ear hears as out of tune. Stretch removes that beating.
How many cents of stretch does a piano need?
It depends on the instrument. Published measurements show roughly 45 cents of total stretch on a Steinway Model M and 60 cents on a Model D, according to Stanford CCRMA. A smaller piano, with shorter strings, may need a different curve. A technician settles on the amount by measuring and listening.
Do electronic tuning devices handle stretch automatically?
They can calculate a stretch curve from measured inharmonicity, and that is a useful starting point. Virginia Tech’s documentation, however, treats them as aids, since the final choice remains perceptual. Most professionals check the result by ear using octave and interval tests.
Do digital pianos use stretch tuning?
Many do, because they imitate the tuning curve of an acoustic piano. Measurements on a Kurzweil PC88 showed about 35 cents of total stretch. Some digital models let you turn the stretch off, which helps when playing with fixed-pitch instruments.
Sources
- Dispersion Filter Design, Stanford CCRMA
- Stiff Piano Strings, Stanford CCRMA
- Inharmonicity of Plain Wire Piano Strings, Piano Technicians Guild
- The Stretching of Octaves, Historical Tuning
- Fundamentals of Piano Practice: What is Stretch?
- Pianos Inside Out, Mario Igrec
- Kent Swafford, Piano Technicians Guild tuning procedure
- Piano Technicians Journal article on stretch
- FFTuner documentation, Virginia Tech
- Influence of inharmonicity on the tuning of a piano, Journal of the Acoustical Society of America
