Piano Impossible to Tune?

[bluefuzz]

Guitars are notoriously difficult to tune and to play in tune.

A guitar string has to be some distance off the fingerboard to have enough space to vibrate. But pressing down on the string to fret a note stretches the string, raising the pitch relative to where the fret is placed. Traditionally, steel string guitars compensate for this string stretch by moving the saddle away from the nut a few millimetres relative to the theoretical scale length. The thicker the string the more compensation it needs. This results in flattening the fretted notes closest to the saddle, thus compensating for the string stretch, but doesn't help that much down around the nut end of the fretboard where it is arguably most needed. Many modern luthiers have begun to compensate the nut as well which basically means moving the nut closer to the first fret a roughly equal distance the saddle is moved away. All this can get the intonation of a guitar as close to 'perfect' equal temperament as the human ear can discern. Of course, as discussed in this thread, equal temperament is a compromise that is still 'out of tune' from just intonation but it's the best we can do with straight frets. At least we can now play our guitars in tune with the piano!

Segovia liked to tell a joke to his audiences while tuning up: Guitarists spend half their time tuning and the other half playing out of tune

Being more stretchy than steel, nylon strings are far less susceptible to string stretch intonation problems than steel strings. Thus classical guitars need far less compensation at the saddle (or nut). I don't know how the fret placement on Segovia's famous Hauser guitar was calculated but before the invention of electronic calculators or spreadsheets frets were commonly placed using the so called 'rule of eighteen'. This entails repeatedly dividing the scale length minus the distance from the nut to the previous fret by 18. If you do the math this results in a scale where the 12th fret is not (even theoretically) half way between nut and saddle! But with the right compensation it actually works pretty well. There are other more or less successful 'rules of thumb'.

The correct calculation for equal temperament is the 12th root of 2 which approximates to 17.817. This can be used similarly to the rule of eighteen for a slightly more accurate placement. But of course a modern spreadsheet can calculate the fret positions to micron accuracy and modern CNC can cut them equally well.

One old 1890s parlour guitar I restored had a scale length I couldn't figure out at first. It didn't seem to fit with any common fret placement methods. And then it dawned on me that it was made with two separate scale lengths. The frets were perfectly placed from the sixth to the 20th fret in one scale length and the first to the fifth fret on a slightly shorter scale. This resulted in a nice 'sweetened' tuning for the lower frets every bit as good as 'modern' spreadsheet-driven compensation algorithms. They knew what they were doing those old fellers ... ;-)

 

[Multicore]

Your post on wanting to learn actually motivated me to go after this childhood dream of playing a "keyboard!" Spent a few weeks reading online reviews and then bought the Kawai stationary electric piano. Bought a couple of online lessons, both of which were useless. Got lucky in that I had seen nice videos from a Piano teacher focusing on technique in youtube and he happened to live 30 minutes from us! After initial interview, I started my lessons a year ago. Progress was quite slow until about 2 months ago when I took a significant step forward. Still at beginner level but for the first time I feel like I can learn this. My teacher had told me that the first year would be the hardest and it was.

This is what you should be making YouTube videos of!

 

[Barrelhouse Solly]

I've been tuning guitars since 1961. I think anyone who plays a string instrument can tell you that it's impossible or at least very highly unlikely that they can be tuned perfectly. There are two problems. First the hardware. Neither friction pegs nor geared pegs can be set to an exact value. Then there's the human factor. Nobody has perfectly precise coordination. When affordable electronic tuners came on the market the first thing I noticed that in tune meant a few cents plus or minus the exact pitch. Most tuners have a green light for in the range. It's a psychophysical thing. Human hearing is not perfect. Two notes a tiny bit apart sound "close enough." When I started high school in 1959 all the new students had to take the music test. We sat in the auditorium and filled out answer sheets for things like "Are these two tones the same pitch?" I dunno. I got into the chorus no problem.

 

[Titurel]

After solving the problems of equal temperament, there are two other significant piano tuning challenges. The first is that the overtones of a real world string are increasingly sharper (relative to the fundamental pitch) than the theoretical ratios would predict. In effect, stiffness near the tie-down points makes the effective string length variable. The more energy imparted to the string, the longer the effective length, the lower the pitch*. As the overtones have increasingly less energy than the fundamental pitch, the overtones of a real world string are increasingly sharp. To counteract this, piano tuners "stretch" the tuning, tuning higher notes to the overtones of lower tones, rather than to the fundamentals of lower pitches of the same name. Two octaves and fifth is a common choice. For example, the fundamental pitch of the g two octaves and a fifth above middle C would be tuned to the corresponding overtone of middle C. With a proper "stretched" tuning, the piano sings - harmonic clashes less obvious. Un-stretched, the piano screams - total war.

The other problems are scale (the length and weight of the strings) and the transitions from 1 string notes (the lowest) and 2 strings notes (much of the bass range) and the triple strung notes. These are mostly piano builder concerns, but tuners forced to "marry" pianos of different sizes and manufactures will to need to consider these elements.

* Yes, striking a note violently will lower the pitch, but only momentarily.

 

[Philbo King]

Don - do you mean all the strings for the key in question are tuned slightly sharp or flat - or just 1 of the 2 or 3 string group?

It is common for (real) pianos to employ 'stretch tuning', where the lowest octaves are tuned progressively lower than 'perfect', and the highest notes are tuned higher. This doesn't apply to electronic keyboards, just those with actual strings.
As I understand it, it is because the harmonics of the longest and shortest strings are corrected by this. In other words, the strike transient when key is hit is short enough to be unnoticeable or missed, while the harmonics from the string sustain are much more perceptible. Put another way, the pitch of the strings harmonics are more important than the fundamental note.

I don't bother with it when I tune my piano though. My 100 year old upright piano only stays perfectly in tune for a month or so, with measurable drift happening within minutes. No use beating a dying horse...

Theoretical info:

Stretched tuning - Wikipedia

en.m.wikipedia.org

Edit: Ninja'd by Titurel!

 

[Barrelhouse Solly]

After solving the problems of equal temperament, there are two other significant piano tuning challenges. The first is that the overtones of a real world string are increasingly sharper (relative to the fundamental pitch) than the theoretical ratios would predict. In effect, stiffness near the tie-down points makes the effective string length variable. The more energy imparted to the string, the longer the effective length, the lower the pitch*. As the overtones have increasingly less energy than the fundamental pitch, the overtones of a real world string are increasingly sharp. To counteract this, piano tuners "stretch" the tuning, tuning higher notes to the overtones of lower tones, rather than to the fundamentals of lower pitches of the same name. Two octaves and fifth is a common choice. For example, the fundamental pitch of the g two octaves and a fifth above middle C would be tuned to the corresponding overtone of middle C. With a proper "stretched" tuning, the piano sings - harmonic clashes less obvious. Un-stretched, the piano screams - total war.

The other problems are scale (the length and weight of the strings) and the transitions from 1 string notes (the lowest) and 2 strings notes (much of the bass range) and the triple strung notes. These are mostly piano builder concerns, but tuners forced to "marry" pianos of different sizes and manufactures will to need to consider these elements.

* Yes, striking a note violently will lower the pitch, but only momentarily.

People tune fretted instruments by harmonics too. It was the method I learned for tuning the guitar before inexpensive electronic tuners came on the market.

 

[DonH56]

It is common for (real) pianos to employ 'stretch tuning', where the lowest octaves are tuned progressively lower than 'perfect', and the highest notes are tuned higher. This doesn't apply to electronic keyboards, just those with actual strings.
As I understand it, it is because the harmonics of the longest and shortest strings are corrected by this. In other words, the strike transient when key is hit is short enough to be unnoticeable or missed, while the harmonics from the string sustain are much more perceptible. Put another way, the pitch of the strings harmonics are more important than the fundamental note.

I don't bother with it when I tune my piano though. My 100 year old upright piano only stays perfectly in tune for a month or so, with measurable drift happening within minutes. No use beating a dying horse...

Theoretical info:

Stretched tuning - Wikipedia

en.m.wikipedia.org

Edit: Ninja'd by Titurel!

I mentioned that in my original post, from 2016, earlier in this thread. But I called it "spread" instead of "stretch" tuning, may be a regional thing (or just what I remember, right or wrong). Some sampled and more modern keyboards include the option for stretch tuning, at least the one (Korg or Yamaha, not sure) used by the local music group we play in (she plays it, I am a brasshole).

The lowest keys are at low enough pitches that the harmonics dominate the sound we hear (equal loudness curves again).

We have an ancient piano at church (not the main one, fortunately) that I swear goes out of tune in a week. My wife's Boston grand holds tuning pretty well.

 

[Multicore]

People tune fretted instruments by harmonics too. It was the method I learned for tuning the guitar before inexpensive electronic tuners came on the market.

I do that for CG3 tuning but not standard since tuning a stack of perfect fourths leads to too much error. It's ok for some but too much for me.

 

[Sal1950]

Sorry if this has been mentioned before but,

You can tune a piano.
But you can't tune-a-fish.

 

[Titurel]

I mentioned that in my original post, from 2016, earlier in this thread. But I called it "spread" instead of "stretch" tuning, may be a regional thing (or just what I remember, right or wrong). Some sampled and more modern keyboards include the option for stretch tuning, at least the one (Korg or Yamaha, not sure) used by the local music group we play in (she plays it, I am a brasshole).

The lowest keys are at low enough pitches that the harmonics dominate the sound we hear (equal loudness curves again).

We have an ancient piano at church (not the main one, fortunately) that I swear goes out of tune in a week. My wife's Boston grand holds tuning pretty well.

I once had to retune a piano (one note only) during intermissions, with just a pair of channel locks and a ball peen hammer borrowed from a stagehand. The piano was brand spanking new and had come from the factory with one of the tuning pins slightly undersized. After that, I always toured with a tuning wrench and dampers in my luggage.

 

[Multicore]

After solving the problems of equal temperament, there are two other significant piano tuning challenges. The first is that the overtones of a real world string are increasingly sharper (relative to the fundamental pitch) than the theoretical ratios would predict. In effect, stiffness near the tie-down points makes the effective string length variable. The more energy imparted to the string, the longer the effective length, the lower the pitch*.

* Yes, striking a note violently will lower the pitch, but only momentarily.

That is very interesting. On guitar and bass the problem is reversed. It's only really a problem on guitar in the bass but if you drop the E2 down to D or C then it becomes obvious. The note starts sharp and drifts flat and it's easy to demonstrate.

Trying to follow what you're saying here, seems there's two things. "stiffness near the tie-down points makes the effective string length variable" Variable with respect to what? With respect to the overtone I can imagine since at the fundamental there's less deflection at the string ends than at high overtones. With respect to loudness: it isn't so clear how that works. In the simplistic physics model, greater deflection (loudness?) means greater tension and higher pitch.

 

[Leporello]

It is common for (real) pianos to employ 'stretch tuning', where the lowest octaves are tuned progressively lower than 'perfect', and the highest notes are tuned higher. This doesn't apply to electronic keyboards, just those with actual strings.

My father (87 yrs) is a very good amateur pianist who used to play an acoustic upright piano. But for the last ten years he has played a Yamaha Clavinova.
He has told me a couple of times that one of the keys has gotten out of tune. I have been quite skeptical of this since it is a digital device after all. Then we've done a "factory reset" by switching the piano off, the back on while pressing down the highest white key. And - according to him - this has resolved the issue.

Is my old man imagining things or is there something that actually could put a digital piano out of tune? He also purchased a pair of Sennheiser HD599 headphones for the piano but does not use them because he feels that through them the piano also sounds out of tune.

 

[Julf]

Is my old man imagining things or is there something that actually could put a digital piano out of tune?

Only accidentally activating one of the alternative tunings.

He also purchased a pair of Sennheiser HD599 headphones for the piano but does not use them because he feels that through them the piano also sounds out of tune.

That is a clear one - there is no way headphones could change the pitch of a signal.

 

[Bwmr]

I just added more context to my previous post after thinking back. My wife was lucky in her tuner (now retired ); he tuned concert pianos for local and statewide schools and universities as well as some large show venues. I am hoping he'll tune hers again so we can talk; I have time to be there now I've retired instead of a few words on his way out the door. I wish I had been able to load that old .wav file as it clearly showed the difference in chords for just vs. even frequencies. Some classical guitarists I have known/seen/heard/read about use fretless or what they called "widely-spaced frets" guitars to allow them to tweak the pitches to the chords. I am not a guitar player so know no more than that. In bands/orchestra stuff, somebody (often enough me) was always asking the conductor for the chord so we could determine where to place the note (straight on, lower, or higher in pitch). One of my biggest regrets was not being able to take a music theory course in college (tried, couldn't, long story summarized by "music prof wanted nobody but music students in his classes").

The best electronic keyboards IME/IMO (and that of my wife and various keyboardists who's opinions should be weighted far more than mine!) most closely mimic acoustic pianos. Keyboards have evolved significantly over time from simple tone generators to various waveform algorithms to sampled keyboards to advanced waveform generation engines.

I am not sure how a stage amp, good or otherwise, allows them to change pitch on the fly?

Few people realize the lowest key on a standard 88-key piano is 27 Hz, compared to 41 Hz or so for a bass guitar's lowest note. Or that beat notes appear much lower than that, into the single digits -- though in the audience you can't really hear beats, just the difference between a group in tune or even a little out of step.

How interesting! I am in the process of shopping for a keyboard. Any recommandation for one that sounds closest to an acoustic piano? Budget is ~$3,000. I intend to play mostly classical. Thanks.

 

[DonH56]

Sorry if this has been mentioned before but,

You can tune a piano.
But you can't tune-a-fish.

I thought about liking this for a second, but just couldn't...

 

[DonH56]

How interesting! I am in the process of shopping for a keyboard. Any recommandation for one that sounds closest to an acoustic piano? Budget is ~$3,000. I intend to play mostly classical. Thanks.

Sorry, no, not my field. I am not even sure what model the orchestra uses, I just set it up for my wife (and am usually focused on hooking up the monitor and making sure it makes noise when I press a key). Hopefully one of the other ASR musicians can help; playing trumpet does not give me great competence to judge a piano (of any sort).

 

[Titurel]

That is very interesting. On guitar and bass the problem is reversed. It's only really a problem on guitar in the bass but if you drop the E2 down to D or C then it becomes obvious. The note starts sharp and drifts flat and it's easy to demonstrate.

Trying to follow what you're saying here, seems there's two things. "stiffness near the tie-down points makes the effective string length variable" Variable with respect to what? With respect to the overtone I can imagine since at the fundamental there's less deflection at the string ends than at high overtones. With respect to loudness: it isn't so clear how that works. In the simplistic physics model, greater deflection (loudness?) means greater tension and higher pitch.

Remember that strings on a piano have hard tie downs on both ends, whereas this is only true for open strings on guitar, bass, etc. When you "drop" to a lower pitch, you lengthen the string (a new pitch), but the string will initially carry the previous pitch until the string re-stabilizes in its new tuning (length).

When I wrote variable, I meant that a string's nominal length is not necessarily it's effective length, and that because of increasing stiffness near the tie down points, the overtones, being weaker than the fundamental, would deflect less of the string's length, thus producing pitches sharper than a mathematically ideal string of the same fundamental pitch. How much sharpening occurs depends on a combination of string length, tension, weight, and stiffness. Size matters. This is one of the reasons why huge concert grands like the Boesendorfer 290 sound sweeter (more harmonious) than an Acrosonic spinet.

 

[Titurel]

My father (87 yrs) is a very good amateur pianist who used to play an acoustic upright piano. But for the last ten years he has played a Yamaha Clavinova.
He has told me a couple of times that one of the keys has gotten out of tune. I have been quite skeptical of this since it is a digital device after all. Then we've done a "factory reset" by switching the piano off, the back on while pressing down the highest white key. And - according to him - this has resolved the issue.

Is my old man imagining things or is there something that actually could put a digital piano out of tune? He also purchased a pair of Sennheiser HD599 headphones for the piano but does not use them because he feels that through them the piano also sounds out of tune.

"Madamina, il catalogo e questo..."

The fact that Yamaha provides a mechanism for resetting the keyboard suggests to me that your old man is not imagining things.

 

[Sal1950]

I thought about liking this for a second, but just couldn't...

Hey Don, I thought about not posting that for a second,
but just had to. LOL

 

[Leporello]

"Madamina, il catalogo e questo..."

Indeed. Greetings to Monsalvat! Looking forward to meeting the knights in Bayreuth this summer.