Why Piano Tuning Is So Complicated

This video, via MinutePhysics, takes a quick look at why tuning a piano is so complicated – and summarizes the tuning compromises that are inherent in equal-tempered tuning. 

These compromises are no longer necessary with electronic instruments – but, ironically, equal-tempered tuning is so ingrained in our musical experience that, to many people, anything else sounds ‘out of tune’.

20 thoughts on “Why Piano Tuning Is So Complicated

  1. This video confused more things than it cleared up. I’d like to offer a few comments that might clarify.

    1. Those integer multiples of a frequency (a.k.a. harmonics) are not just different notes, they are the combined components of the sound a single vibrating string or vibrating air in a tube. When a guitarist touches a string to get a harmonic note, they are essentially muting some harmonics and allowing others to ring– but they are all already present in the sound. Yes wind instruments can play notes on those harmonic levels, but then those notes end up having their own harmonics.

    2. When guitars or violins are tuned using those overtones, they are using that non-equally-tempered 5th to tune an equally tempered instrument, so it is off by some small amount. This tuning problem is not unique to pianos.

    3. Most western music is based an scales that are sub-sets of an octave divided into 12 equal-sized steps (equal temperament). If you look at it the other way around, The Harmonic Series only resembles notes within that arrangement– mostly by coincidence. You can pick different equal temperaments to see which division of the octave gets you the most accurate approximation of intervals that are contained in the harmonic series. We went with 12-tone Equal, and it was a good choice.

    4. Tuning a piano is difficult for 3 reasons:
    FIRST: it has lots of strings. Over half of the notes on a piano have 3 unison strings. Some have 2. Only the bass strings have one. You can use a mute/wedge to control which string(s) are vibrating.

    SECOND: The tuning pins themselves require quite a bit of skill to turn, take up string slack, and manage where the tension of the string is distributed over the various physical features of the piano..

    THIRD: Inharmonicity and “stretch”. All stringed instruments have what is called inharmonicity. Remember that all those harmonics are ringing at once. The stiffness of the string at the end-points where it is anchored causes higher harmonics (smaller waves) occupy less than the string’s full length.

    This causes the harmonics to vibrate progressively sharper as you go up in frequency. This is part of what gives a piano string such a complex sound. The overtones are kind of drifting/phasing over each other.

    Tuning an octave involves the question, “Do you make the fundamentals of the notes in tune? Or do you make the octaves sound in tune?” The short answer is the latter. You make the first overtone of the lower note of an octave in tune with the fundamental of the upper note of an octave. The whole piano will be sharper on top, and flatter on the bottom. Google “piano tuning stretch”.

    I think this is a very tough subject to try to spin out in a rapid-fire, sharpie-‘splainin’ vid.

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    1. Great feedback. This topic IS lot deeper than you can cover in a four minute video, this is just the tip of the iceberg.

      Inharmonicity and stretch are interesting topics, especially when you consider that these weird physical limitations have to get imitated in digital virtual instruments in order for them to sound as we expect them to.

      I’d disagree with one comment – that the relationship between notes in an equal-tempered scale and the harmonic series is just coincidence. 12-tone equal temperament was the best solution at the time for creating an equal tempered tuning that allows for scale pitches close to the harmonic series pitches, considering the physical constraints of instrument building. To do better would have required a lot more notes per octave.

      It’s also interesting how our ears are trained to accept intentional deviations from equal tempered tuning by choral and wind performers, but to most people, a keyboard tuned to anything but equal-temperament sounds ‘out of tune’. And also that equal temperament is so ingrained in our musical thinking that anything else is rejected by many synthesists.

      The Microtonal Synthesis is a good resource for synthesists that do want to explore something different:

      http://www.microtonal-synthesis.com/

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      1. Thanks for your response. I chose the word “coincidence” to make a specific point.

        With the Just Intonation scale, we have uneven steps that provide those simpler pitch ratios- BUT you can only play in one key (and it’s related modes).

        In essence we started with a NON-EQUAL 12-tone scale- which led naturally to the 12-equal.

        If we just took the harmonic series notes in a list and asked: Which division of the octave will give us the most closely in-tune notes from the harmonic series? As you suggest, we might end up with an impractical number of divisions of the octave, with LOTS of useless notes included. 12- was a very good compromise. But it just worked out that way due to coincidence. Dividing the octave into 12 parts has no mathematical relationship to the harmonic series (other than the octave). Your point that more than 12 would be impractical is true, but it means that this particular coincidence was also practical in terms of usability.

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  2. BTW, the Hermode tuning system that is included with Logic and others, is a cool system that analyzes the current chord you are playing and makes adjustments to the notes in the chord to make them more like the harmonic series. This system works very well, especially if you are playing in a single key.

    It is possible to “break” the hermode system if you play certain sequences of chords where the adjustments just keep getting further out of the normal scale and it eventually the Hermode can’t keep up and has to come back to center. Otherwise, it’s pretty great.

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  3. You know what’s easy to tune? The Yamaha Reface series.

    Building on Yamaha’s 40-year heritage of creating some of the most heralded and renowned electronic keyboards in music history, reface reimagines the interface of four classic Yamaha instruments – some of which are difficult to find in the vintage market and weigh too much to carry around. The new series offers thick, booming sound, built-in speakers, 37 keys with professional-grade HQ-Mini action (derived from the flagship Motif XF professional synthesizer) and battery-powered portability for making music on the go. But more than mere travel companions, these versatile keyboards connect with external speakers, smartphones, tablets, MIDI devices and computers for use on stage and in the studio.

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    1. That comment might be SO tongue-in-cheek.. such that the tongue pokes through the cheek, not unlike an alien bursting from a hapless abdomen.

      Reface palm.

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    1. You caught yet another mistake in the video.

      There’s no wha-wha-wha, because the example chord was made up of sine waves. Had the chord been made up of complex tones (like saws, or plucked strings, or piano notes) you would have heard the overtones of lower notes “beating” against those of higher notes. With sine waves, there aren’t any overtones to beat.

      For those who don’t know, “Beating” is the term used by tuners to describe the alternating loud and soft (tremolo?) that comes from two unison pitches that are slightly out of tune. As two slightly different frequencies drift in and out of phase (like one wave “lapping” the other) they alternate between reinforcing and canceling each other. Slower beats means more in-tune.

      When tuning a piano, sometimes the “unison” waves that are beating are overtones rather than the fundamental frequencies. Tuners strategically use the speed of beats to calibrate the temperament.

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  4. The third reason given by stub (inharmonicity & stretch) could lead to another video: “Why it’s more difficult to tune an upright piano than a grand piano”. In an upright piano, the low strings cannot be as long as in a grand piano; to get the low pitches, the strings have to be thicker; the increased stiffness leads to more inharmonic spectrums.

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  5. In this day of incredibly fast processing, why can a keyboard not adjust the tuning of each key as it is being played so that that note, at that instant, is perfectly harmonic? Each octave could be wider or narrower than the actual octave, and slide up and down virtually to place the perfect harmonic under the proper key as it is played. Has anyone ever experimented with keyboards that have other than twelve keys per octave?
    I just read the comment above about Logic’s system, but that appears to have limits that can break a performance. If it were done with dedicated hardware, could the adjustment always outperform the player, eliminating the possibility of harmony crashes?

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    1. The Hermode system does exactly what you describe and does it pretty well. What breaks it is a kind of unusual circumstance where you keep shifting your chords to new tonalities, it keeps adjusting, but because it doesn’t know where you might be going, it makes its best guess about what notes to adjust without causing problems in future chords, it isn’t a very common issue and otherwise works incredibly well.

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      1. From the original comment it sounded as if it could last a few minutes before giving out. Depending on your definition of “it isn’t very common” it could be a good example, then. But, how to get it into all keyboards? That is the question.

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        1. Yea, when I put “breaks” in quotes, its really not breaking, it is just showing that it is limited.

          It doubt if the chord analysis is very CPU intensive. It just has to look at the currently sounding notes and follow some rules about what might be the chord. Then the DSP would just do some Poly AT type pitch manipulation to each note.

          But imagine if I play a chord where the 3rd is in the bass, the hermode would flatten it. But If I change one upper note, the chord interpretation could change and something would have to bend.

          As a side note, when I had an Ensoniq EPS which had poly AT, I’d set it to drop pitch by 5-10 cents. Then when I played a major chord, I’d press on the third to drop it. Worked great.

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