Piano Impossible to Tune?

[amirm]

Would be great to read that.

 

[DonH56]

Couldn't find my old program, but it was easy enough to recreate enough for the fundamentals. Disclaimer: I am NOT a music major! I do play a bit, mostly amateur gigs now.

First a bit of reference from Wikipedia:

Now, A4 on a piano (A above middle C) is defined as 440.0 Hz and is a standard tuning pitch. Notes in a Western scale are spaced 2^(n/12) apart going up from the root. To make things interesting, let's look at a C major chord starting at middle C (C4), so the notes are C4, E4, G4 (and C4 if we want the top note). A bit of math provides the pitches (frequencies) of each note using equal temperament:

Yes, since C5 is an octave above C4, I cheated on the last one and just multiplied C4 by two.

Now, we prefer to hear tones spaced by integer ratios or "even" intervals. If you look at ratios and such, eventually you find a base frequency from which all the notes are integer multiples. Being lazy, and already knowing the answer, I am going to do a bit of hand waving. Look at the multiples from C4 for the E4 and G4 notes in our chord:

Not integers, or even numbers that lead to integer ratios. Now the hand waving; rather than find a common factor (frequency), I know 1.25 and 1.5 lead to common multiples with integer ratios (5/4 and 6/4). If I plug those in, the new (prime, "p") frequencies are:

So the desired pitch, that sounds good to us, is an E that's a little low and a G that's a little high. This is "just" intonation. Musicians playing instruments that allow us to adjust pitch will alter those notes in the chord to make them sound prettier. Can't do that with a piano, alas.

Now, for musicians who are not mathematicians (or even a lowly engineer such as myself), what we see on a tuner are "cents". Remember there are twelve notes in a scale, logarithmicly spaced, and we define 100 cents between each note. The equation is:

# cents = 1200 * log2(P1/P2) where log2 is log to base 2 and P1 and P2 are our pitches (notes)​

Plugging in our notes/pitches:

Note log(x)/log(n) = the log of x to base n

If you read the Wikipedia quote above, or look up a major chord in a music theory book, sure enough the third in a major chord needs to be about 14 cents low, and the fifth about 2 cents high, to create a pleasing sound. The theory and math work the same for other chords, though actual numbers will vary, natch.

Ain't it great when the theory and the reality actually meet?

HTH - Don

 

[amirm]

So the desired pitch, that sounds good to us, is an E that's a little low and a G that's a little high. This is "just" intonation. Musicians playing instruments that allow us to adjust pitch will alter those notes in the chord to make them sound prettier. Can't do that with a piano, alas.

Thanks for the detailed explanation. I have to read it a few times to understand it given my total lack of experience in this area . But did want to ask about this. Can't a piano be tuned differently just like other instruments you mention? Or do you mean due to lack of difficulty relative to something that has its tuning elements within reach all the time?

 

[DonH56]

The problem is that a piano cannot be tuned "on the fly". The E in a C major chord needs to be about 14 cents low, but if the next chord is an E major chord, that same E needs to be dead on pitch. In a major chord the third needs to be 14 cents low, and the fifth a couple of cents high, but the notes in the chord depend upon what chord is being played. Brass players can adjust their embouchure ("lips") and slides to adjust pitch; reeds can adjust embouchure and tension on the reed; strings can adjust finger positions. The piano plays the pitch of the strings the hammer strikes, no easy way to change their length. Note most pianos are tuned so that the (two or three) strings struck by the hammer are tuned a little "off" to help this issue and to provide a "fuller" sound than that of just a single string.

C maj = C, E, G, C -- E (third) needs to be low, G needs to be high
E maj = E, G#, B, E -- E needs to be on pitch, G# low, B high

Amir, is there a way to attach a "wav" file? I created a couple of chord files so you could hear the difference, but VB said it is not an allowed file type. I am able to do this on other fora, just curious.

 

[JohnnyAudio]

No idea what I am talking about but watch these nice minute videos on physics:

We have two piano's in our home, just recently tuned, they chorus a bit when played together.
The children complained so I gave them an experiment.
I gave them a paint set and asked them to mix the same color, they tried and realized it was impossible.

 

[Multicore]

A zombie topic risen from the grave! My favorite kind.

We did a whole podcast episode on YouTube 'Splainers like this. When you survey the typical features of them, it's a window onto the zeitgeist.

Did you spot the deliberate error in this particular video? The one that the video's seemingly-contradictory premise is based on? It's at 2:00 and involves the word "should". Why should six 9:8 harmonic whole tone intervals stack up to a 2:1 octave? It also says "is supposed to". Both are a deliberate con. YouTube has loads of 'splainers that use a similar sleight of hand.

 

[Multicore]

Amir, is there a way to attach a "wav" file? I created a couple of chord files so you could hear the difference, but VB said it is not an allowed file type. I am able to do this on other fora, just curious.

I asked the same recently

How to share uncompressed audio with player on ASR etc.?

I want to share uncompressed PCM audio clips that you can play with one click/touch here on ASR and other such forums (and DL if you want). Does anyone know a service that does that like YouTube does for video or Imgur does for images? Soundcloud comes close but 1) requires an account to...

www.audiosciencereview.com

It can be done but would require a change to the forum, perhaps something that can be done with a config in the admin console to render a player given an audio URL.

 

[Bob from Florida]

Note most pianos are tuned so that the (two or three) strings struck by the hammer are tuned a little "off" to help this issue and to provide a "fuller" sound than that of just a single string.

C maj = C, E, G, C -- E (third) needs to be low, G needs to be high
E maj = E, G#, B, E -- E needs to be on pitch, G# low, B high

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?

 

[Ported]

Strange things with tunings apply to other instrument sets too. I have probably recorded a couple of dozen horn sections and only 3 sounded like they were spot on pitch with each other throughout the range .. a couple that weren't still sounded good for reggae!
I also had a piano that would not tune but for physical reasons .. the tuning block had shrunk so would move slightly in the metal frame so by the time a tuner had gone from bottom to top the bottom was out of tune again! Fixed it by injecting epoxy in the gaps..

 

[Multicore]

Strange things with tunings apply to other instrument sets too.

How true.

Guitars are notoriously difficult to tune and to play in tune. I heard a story that 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. Imagine the polite chuckle rippling through the quieted room.

There's a good deal of truth in it. It's evident to anyone who like me is very sensitive to off tuning. And I discovered through extensive research that this explains why guitarists feel compelled to play very fast, usually as fast as possible. In a blizzard of notes coming at you so fast that you can't know one from another, you won't notice tuning problems at all.

I actually like to play very slowly. Not always but I really taking the time to listen to how a chord sounds. This is when off-tuning becomes most obvious. So I've been trying to integrate re-tuning into the music itself. It doesn't work at all in an audio-only recording but if the audience can see what you're doing and you can win their indulgence then maybe.

Another funny story is that for nearly 40 years I believed that guitars were not really equal temperament instruments. I came up with a few tricks to minimize the problem, one of which is the CG3 tuning I still use for some music. Only in recent years when I got a couple of really well made acoustic guitars did I learn the truth. I now have a new method for fine tuning a guitar in standard tuning but I wouldn't use it on a guitar that doesn't have a well adjusted nut.

Sigh. I guess it's all part of the fun.

 

[DonH56]

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?

I am not a tuner, though I have spoken with a few (my wife plays and has a baby grand that we have tuned yearly'ish). It is definitely not all, that would make it always out of tune, so 1 or 2 of the 2 or 3 strings per key are adjusted to better allow the piano to play "just intonation" instead of "even (or equal) temperament". See my earlier post; having tones (pitches) in a chord be exact 1/12 octave divisions, does not sound as good as having them be integer ratios in the chord, so they are in the harmonic('ish) series. By "detuning" (my word) a string or two from the primary frequency you introduce beat patterns that allow a piano to sound more in tune in a group of instruments that normally use just intonation. That requires adjusting the pitch on the fly to suit the chord being played, something many (not all) instruments (and musicians) can do, but nearly impossible with a piano, thus tuning is a compromise. It is an art with science behind it, cool stuff!

Back in 2016 when I posted, I might have remembered more, but right now (8 years later) I confess I've forgotten the details. I also remember that the upper and lower octaves are sometimes "stretched" to go a little higher or lower in frequency (pitch) to make smaller pianos sound "bigger". It is a fascinating subject but one I know little about, sorry.

 

[gwing]

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?

In principle the three strings are tuned to the same frequency however you can’t actually tune anything with ultimate precision so they are all tuned to around the same measured value. A good piano tuner will tune one string to the nominal value as accurately as possible and then tune the other two strings to the first by ear until they sound best, an exceptional tuner will do this also taking into account how the note sound in the context of common chords. I’m not really a piano tuner and find this incredibly hard, when a note on my piano goes sour I just listen to find which of the strings has remained in tune the best, measure the pitch of it an then tune the other two as close to it as I can. Then after having to do this patch up for a few notes I get the real piano tuner in for a nice fresh tune.

 

[Sal1950]

I am not a tuner, though I have spoken with a few (my wife plays and has a baby grand that we have tuned yearly'ish). It is definitely not all, that would make it always out of tune, so 1 or 2 of the 2 or 3 strings per key are adjusted.

The best reasons for a quality electronic keyboard!
Only thing is, none sound as good as a true acoustic.
A good stage amp goes a long way to make them sound better though.
It's so hard to get the bottom octaves sounding right.

 

[DonH56]

The best reasons for a quality electronic keyboard!
Only thing is, none sound as good as a true acoustic.
A good stage amp goes a long way to make them sound better though.
It's so hard to get the bottom octaves sounding right.

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.

 

[kelesh]

I know a professional piano tuner who told me this years ago - without going into too much detail - that the best you can do with a complex instrument like the piano, even with a ridiculously expensive Peterson tuner worth a few grand, is an approximation. Lots of tiny adjustments and aim for the margins of tolerance of human hearing.

 

[antcollinet]

We have two piano's in our home, just recently tuned, they chorus a bit when played together.
The children complained so I gave them an experiment.
I gave them a paint set and asked them to mix the same color, they tried and realized it was impossible.

That is some necromancy you've pulled off there

Still, I got to watch an interesting video as a result and learned my thing for the day.

 

[amirm]

The best reasons for a quality electronic keyboard!
Only thing is, none sound as good as a true acoustic.

It is stunning how bad my $5000 Kawai sounds compared to my teacher's Chinese Pearl River piano. His puts a smile on my face every time I use it. I do need to put proper studio monitors on it and see if it improves.

 

[Sal1950]

It is stunning how bad my $5000 Kawai sounds compared to my teacher's Chinese Pearl River piano. His puts a smile on my face every time I use it. I do need to put proper studio monitors on it and see if it improves.

I didn't know you were taking piano lessons, hope your doing better than me.
Progress has been very slow over the last 3 years, but then at 74, I'm pretty slow at everything. LOL
I bought a Behringer keyboard amp for my Roland and it made a tremendous improvement over the onboard amp and speakers, specially in the bottom octaves. A pretty cheap upgrade

https://www.sweetwater.com/store/detail/KXD15--behringer-ultratone-kxd15-600w-15-inch-keyboard-amp

 

[amirm]

I didn't know you were taking piano lessons, hope your doing better than me.

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.

 

[Sal1950]

Still at beginner level but for the first time I feel like I can learn this.

That's great !
I haven't gotten near as accomplished as I would have hoped, but on the other hand
I enjoy my time stumbling thru a good hour or more each day. I know in the long run I'll
never be a "musician" but what I can do brings me pleasure.
I would encourage everyone who has an interest to go for it. what have you got to lose?