
Piano Tuning - strawcomb
https://sidsite.com/articles/190303PianoTuning/
======
mitchtbaum
Every time we had our piano tuner scheduled to come was a special occasion.
When he'd come, he'd have this aura about him which made his intense
disposition seem fitting for the work he was doing.

My mom felt it important to prepare us for the two day process to be without
our piano and to tread lightly as he worked through his vast toolset of tuning
forks on each key with his most amazing one, his ear.

To watch him act as one with our piano, positioning his head to absorb its
vibrations and set it right for us, made our most prized possession seem like
part of an intricate world of students connected and tuned to the sound
motions of the Universe.

~~~
js2
Two days? Our tuner does the job in about an hour every six months on a modern
upright. I'll allow differnces between tuners and pianos but two days seems a
lot?

------
richardhod
Our old piano tuner explained to me how in practice when tuning you must
stretch the high notes higher and the low notes lower so as to make the piano
sound right. He didn't explain why. It was obvious if you played octaves and
listened to the notes, and he was an excellent piano tuner and the piano did
sound good. The first comment in the article describes it nicely and links to
the excellent Wikipedia section which everybody here ought to read:

[https://en.m.wikipedia.org/wiki/Piano_acoustics#The_Railsbac...](https://en.m.wikipedia.org/wiki/Piano_acoustics#The_Railsback_curve)

~~~
naringas
Indeed, if one tuned a piano like the article describes it wouldn't sound
good.

As far as I undesrtand it has to do with the thickness (i.e. the real world
physicallity) of the lower octave strings.

The strings are not trully one-dimensional. this makes their timbre deviate
from the ideal harmonic series. This is specially true for the thicker strings
of the lower notes.

If we could make a piano using very thin strings we could get away with a less
stretched tuning.

~~~
radiowave
Making the strings (and therefore the piano) longer helps, hence the size of
concert grand pianos.

------
baddox
This is certainly a fun way to introduce twelve-tone equal temperament to
someone who knows enough math to understand logarithms but is new to music
theory. It works well, because the only elementary music theory claims that we
need to accept without explanation are that there are twelve different note
names that repeat in the same order and that each note of a given name is
twice the frequency of the previous note of the same name.

Okay, not quite. You actually also need to know that the frequency ratios of
all pairs of keys n keys apart should be the same, for all n. This article
kind of sneaks that one in silently. But once you’ve accepted that, it leaves
you with only one option: tuning the keys to frequencies spaced evenly along
the logarithmic axis.

Of course, there are so many more details on every side of this topic. Why 12
divisions per octave (this certainly isn’t the case for all musical
traditions)? Why do we want all pairs of notes n steps apart to have the same
ratio (this certainly isn’t the case for some instruments)?

And, most importantly to me, since it’s the question I can find the least
solid information on: why do we take for granted that one note with twice the
frequency of another note sounds so similar that we call both notes by the
same name? I have a pretty good understanding of other details of music
theory, but I’ve never gotten a straight answer on why (and indeed to what
extent) octave equivalence exists.

I’ve always speculated that it has something to do with our auditory systems
evolving to interpret sounds from roughly simple harmonic oscillators, because
those exist in important roles in nature (like the vibrating chords and air
columns of human and animal vocalization).

But that’s still not a great explanation to me. Yeah, there’s some important
noise-makers in nature that have roughly the overtone series. But why would it
be important to hear the first overtone as equivalent (in some strong but not
absolute sense) to the fundamental? Could it have something to with hearing
vocalizations from a distance such that the fundamental would be more
attenuated than overtones? That’s really grasping at straws.

~~~
clarry
> And, most importantly to me, since it’s the question I can find the least
> solid information on: why do we take for granted that one note with twice
> the frequency of another note sounds so similar that we call both notes by
> the same name? I have a pretty good understanding of other details of music
> theory, but I’ve never gotten a straight answer on why (and indeed to what
> extent) octave equivalence exists.

I don't know what the true answer is, but I'd consider the overtones.
Vibrating strings produce overtones whose frequencies are multiples of the
fundamental. So the first overtone is twice the frequency; an octave higher.
When you play that note an octave higher, you're again producing overtones
that perfectly line up with the overtones that were produced by the lower
octave (if we just ignore the effect of string stiffness). So it's like the
same note, only missing the fundamental frequency and odd multiples of it.

This is also why the feedback from a heavily overdriven guitar amp (which
emphasizes overtones) can morph the sound to the same note at a higher octave.
It's simply a matter of letting the fundamental frequency grow quiet in
comparison to the powerful overtones which are further amplified by feedback.
I don't know if that can ever produce a different note; I don't think it
could. That would require actual change in frequencies.

Different notes, by comparison, produce overtones that only sometimes (or
never) line up with the overtones of another note. I'm not sure but I think
that also explains why some notes together sound dissonant while other
combinations make good chords. If you're trying to transcribe a piece of music
by analyzing its spectrogram (which I do because my ear isn't very good),
you'll find that the notes that are usually hard to tell apart are the ones
that harmonize well and have overtones that line up.

~~~
baddox
That’s the usual explanation I read, but I don’t fully buy it. Yes, two notes
an octave apart have lots of overtones in common. But that’s true of two notes
a perfect fifth apart as well. Or even better, two notes an octave and a fifth
apart.

~~~
stfwn
For this exact reason, in music theory, the perfect fifth is seen as a note
that amplifies/emboldens the root note of a chord and does not add a
particular harmonic color.

In jazz it's often left out to open up chords more (i.e. not muddy the
frequency distribution with too many adjacent notes unless you explicitly want
the powerful sound). In pop the nondescript nature is used to create a strong
sense of grounding in the scale; the root note of the scale and its fifth fit
over every possible diatonic root note (play c-g in your right hand with root
notes c,f,a,g in the left one after the other, it will sound familiar). In
rock they literally call the perfect fifth a 'power chord' and they play
melodies with it. It fattens up the melody note without adding any harmonic
identity that would create tension with the rest of the harmonic content of
the song.

~~~
baddox
For sure. It still doesn't explain why the octave is the specific point where
the cycle of pitch perception repeats. The perfect fifth is very consonant,
for sure, but there is no "perfect fifth equivalence" in any musical
traditional as far as I know.

~~~
kazinator
Note that there is no harmonic that is a perfect fifth above the fundamental;
the first harmonic is the octave. So if cycles of perception have to be based
on harmonics (multiples of frequencies), the next plausible one after octaves
(2f) would be based on the perfect 12 (3f), rather than the 5th (3f/2). The 4f
based cycle is really just octaves again, except we're skipping every other
octave. It gets too distant after that. Maybe the 3f progression _does_
contain a cycle of pitch perception; I will try giving that a listen.

~~~
kazinator
I tried this! Eerily, I'm able to convince my ear/brain that this 12th
interval is an octave-like relationship; that the two notes have a sameness
(that I don't perceive in the case of the perfect fifth that we normally
consider enharmonic with the 12th, giving it the same letter name).

Come to think of it, a lot of western harmony is based on a two-octave
"gamut". Like for instance alterations to chords such as dominants take place
close to this "3f octave" (dodecade?) 12th interval, like the like 11th, 13th.
The usual explanation is that if these alterations are in the higher octave,
it prevents certain dissonances. But from the "3f octave" view, we can just
regard them as different notes; that the 13th is not simply the 6th, only one
octave higher, but rather an "augmented dodecave" interval.

------
slashdotdash
Anyone who enjoyed this article might also like “Music for Geeks and
Nerds”[1]. It’s a free eBook describing musical structure using Python code.

[1] [https://pedrokroger.net/mfgan/](https://pedrokroger.net/mfgan/)

------
jacquesm
Once, long ago I landed in a house in Poznan, Poland which had the wreck of a
Bosendorfer baby grand piano sitting in one of the rooms. I had a lot of time
on my hand and tried to figure out the story behind the piano. After tracing
the owner it turned out that he was trying to 'restore' the piano but in the
process had butchered it and had sent parts all over Poland for refurbishing.
For some strange reason the Action was in Gdansk but the hammers were in
Warsaw, and the dampers were in yet another location.

I bought the piano and bit by bit collected all the other pieces from wherever
they had ended up. What really didn't help is that they had ripped out all of
the strings except for the basses, and in the process had scratched the
soundboard quite badly.

Over the course of a year I rebuilt it bit by bit with a lot of knowledge
gleaned from a local piano tuner, Marek Koczy (he died some years ago).
Finally at the end of all that I had a really nice piano, except for one
little detail: it had to be tuned up from scratch.

Tuning up a piano from zero is a lot harder than it seems. As the tension on
the cast iron frame increases it deforms a bit, enough to de-tune everything
you've done up to that point. So the only way to get this done is to tune the
whole thing up gradually and to pace yourself so you don't end up
overstretching part of the frame or end up in a never ending cycle of de-
tunings.

It took me a month, I could probably do it much faster a second time. Never
realized that your ears could be tired either, after a couple of hours of
tuning I was unable to hear the subtle beats that tell you that you are
getting close, very low frequency and soft you need to really pay attention.

Keeping the rest of the piano quiet (especially when it is still a mess) with
sympathetic resonances each of which will have their own harmonics is also
quite a trick, in the end I used strips of felt woven through the strings that
were not 'in scope'.

All in all a fantastic experience and I would be happy to just work on
restoring musical instruments. The piano when it was done got donated to the
Conservatory of Poznan where it still is in use today, with my lack of skills
in play I did not feel that keeping it was right, an instrument like that
should be used as much as possible.

edit: HAH! I am so happy. So, the message that Marek had died reached me in a
pretty roundabout way through friends from long ago, I did not verify in any
way that it was true. So, after writing this little bit above I decided to
type his name into google to see if there was an obituary, but instead I found
he's alive and well!! [https://spsf.pl/pl/marek-
koczy/](https://spsf.pl/pl/marek-koczy/)

I will definitely send him a message and maybe go visit, he's one of the
nicest people I ever met and had endless patience teaching me all the tricks
of the trade.

~~~
sureaboutthis
I had a friend, Jim, who was blind. He went to school to become a piano tuner.
Once, we were at another friend's house who had a piano. The friend played a
short piece on the piano and Jim mentioned that it could use some tuning and
went on to claim he had perfect pitch hearing. Well, of course, we had to test
him.

We hit one key. "That's D!", he said.

We hit another. "That's G!"

With a smirk, my friend pressed three keys at once.

"Uh, Uh, B, D and F#!"

We were amazed.

~~~
bloak
Of course, once he'd got the first note right, he didn't need perfect pitch to
get the second one. Is there a reset procedure for testing perfect pitch? Some
confusing sequence of slidey trombone sounds? Just listen to Shepard tones for
a while?

~~~
criddell
One of my kids has perfect pitch and it's very weird. I used to randomly test
her with things and she was never wrong. I'd ask what note the microwave beeps
or her toothbrush buzzes and she could easily say answer the question (or at
least say what two notes the noise falls between).

------
exabrial
Equal temperament just means equally out of tune.

Minute physics does a great video on it:
[https://youtu.be/1Hqm0dYKUx4](https://youtu.be/1Hqm0dYKUx4)

~~~
kazinator
Equal temperament is certainly not "equally out of tune". It has terrific
octaves and very good fourths and fifths, compared to some other intervals.

It really does mean equal geometric steps between successive tones.

Each key is equally "out of tune" under equal temperament; e.g. C# minor and D
minor are basically the same, modulo pitch.

------
lumens
yeah, great, but what about adjusting for inharmonicity in the overtones?
(partially /s)

a good explanation:
[https://www.youtube.com/watch?v=b_fU6yVxDZs](https://www.youtube.com/watch?v=b_fU6yVxDZs)

~~~
veli_joza
I've been down that rabbit hole. Math and music aren't really in such harmony
as advertised. Yeah, equal tuning gives your instrument ability to play in any
key, but it will always be slightly off.

For more enjoyable tuning, your frequency ratios should actually be fractions
of small integers. For example, note E to note C ratio should be 5/4\. This is
called "just intonation", you can hear some examples on youtube when compared
to equal temperament described in article. It sounds much better to trained
ear, but doesn't work for changing keys.

It would be nice for your digital instrument to be aware of key you are in
(much harder than it sounds) and to re-tune all notes into just intonation.
This would give you best of both tunings.

~~~
TheOtherHobbes
It's easy to set up just intonation digitally.

The problem is that most classical music modulates to other keys. So why not
just set up some switches or programmed changes?

Because as you modulate there's a grey area in which you're not fully in one
key or the other. If you interpolate the intervals as you go through this
area, it sounds wrong. If you switch to a new tuning when you land in the new
key, that sounds wrong too.

Equal temperament solves the problem by being a good-enough compromise. All
the intervals are slightly off, but they're off by a consistent amount, so -
paradoxically - key changes become smoother.

~~~
isolli
Note that violinists (and cellists, and others) are not constrained by their
instrument and can play in different temperaments depending on the situation.

~~~
jancsika
_Can_ and _do_ are two different things. I rarely hear string players talk
about more than "sweetening" a note that is an important arrival in a phrase.

I've also never heard about a systematic strategy string players use to a)
analyze a tonal piece for pivot points in a modulation, b) temper all the
notes going forward from that pivot to fit whatever tuning system they are
using.

I've seen various approaches for microtones and idiosyncratic tunings for
single pieces of modern music, but those are fairly static things that the
players practice and perform. It's not a system they apply dynamically to the
standard rep.

Also keep in mind that string players have an added constraint that the
keyboard does not-- if you give a cellist a sudden, large leap it can be
difficult for them to even find the note at all.

~~~
Tor3
> Also keep in mind that string players have an added constraint that the
> keyboard does not-- if you give a cellist a sudden, large leap it can be
> difficult for them to even find the note at all.

A professional cellist? No. They'll find the note. And that goes for all pro
(or just good) string players, fretless instrument or fretted instrument.

------
phlakaton
For those of you that want to go deep on this subject (of which this article
only superficially covers), I commend Stuart Isacoff's entertaining book
_Temperament_ (Vintage 2009) to your attention.

A wonkier, somewhat more no-nonsense treatment is J. Murray Barbour's _Tuning
and Temperament_ (Dover 2004).

~~~
frankhorrigan
I also really appreciated "How Equal Temperament Ruined Harmony (and Why You
Should Care)" by Ross Duffin.

------
robbrown451
Since the frequency doubles every 12 half steps, that means that the frequency
of any note is the twelfth root of two times the frequency of the one before
it. That's really all you need to know.

(of course this doesn't account for octave stretching that is typically done
on acoustic pianos)

------
mnemotronic
I think that knowing frequencies and hearing frequencies still leaves one a
long way from being able to tweak a string to match that frequency.

Question for piano tuners: Does tuning the piano require multiple iterations?
When re-tuning my 12-string to or from an open (where some or all of the
strings are tuned to a specific chord) I sometimes have to go back and tweak
each string a couple times. I think this is due to the change in stress on the
top and neck of the guitar.

~~~
yarosv
It does. When I tune (warning - I am novice) I tune middle octaves, then go up
and down the scale with octave intervals. And then check the whole instruments
tuning notes that sound off. String itself stretches and loses the pitch a
little sometimes, especially if it was out of tune by quarter tone. But more
importantly string peg that holds the string is just screwed into the hardwood
board. So when you tune it, you still have some room for it to settle. Even
slight press with tuning hammer on the peg can result in big difference in
tune. Especially on high notes.

------
jancsika
Hm... here's a question:

The G# minor fugue in Book II of Bach's WTC has a rather long sequence around
the circle fifths. It starts on E# minor.

Did the well-tempered tuning system open up the possibility for Bach to start
writing longer chromatic sequences like that? Would that sequence have sounded
out of tune in the meantone tuning system?

------
stevehiehn
Reminds me of Bach's 'The Well-Tempered Clavier' It's written in all 24
major/minor keys so your keyboard needs to be well tempered :)

[https://en.m.wikipedia.org/wiki/The_Well-
Tempered_Clavier](https://en.m.wikipedia.org/wiki/The_Well-Tempered_Clavier)

~~~
jancsika
It's 48 because Bach did it all again in book II of the Well-Tempered Clavier.

And really, it's 96 because there is both a prelude and a fugue for each key.

And if you think about it, it's 48 + (48 * x) where x is the average number of
voices in the fugue.

And then at least a few of those are double and triple fugues, so I guess a
forEach statement in there to multiple by 2 or 3 for those cases.

So if you were an organist who was opposed to this tuning method, you'd have a
pretty difficult time making a persuasive counterargument against all that.

~~~
stevehiehn
Hmm, I think there is only 24maj/min keys in traditional western harmony. If
you write 100 different pieces using 2 keys: C or G, you've still only used 2
keys. But I don't want to argue about set theory :)

~~~
jancsika
Ah yeah, I wrote that incorrectly. I meant that Bach went back and did "it"
again for a grand total of 48 prelude/fugue pairs.

------
ramanan
minutephysics had a nice video about the mathematics that go behind piano
tuning too.

"Why It's Impossible to Tune a Piano"
[https://www.youtube.com/watch?v=1Hqm0dYKUx4](https://www.youtube.com/watch?v=1Hqm0dYKUx4)

~~~
kzrdude
If you really want to dive deep into historical tuning systems, check out
early music sources,
[https://m.youtube.com/channel/UCJOiqToQ7kiakqTLE7Hdd5g/video...](https://m.youtube.com/channel/UCJOiqToQ7kiakqTLE7Hdd5g/videos)

------
GuillaumeBrdet
Was really hoping to land on an app that would help you tune it.

------
kazinator
Educated guess: Sid has never tuned a piano.

