5 ms·

Piano Tuning

101 points by strawcomb 8y ago

lumens 8y ago
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 8y ago
  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.
  - derriz 8y ago
    Temperament is unrelated/orthogonal to inharmonicity. Temperament deals with picking frequencies for the notes that make up the scale within an octave. Inharmonicity affects how you tune the octaves themselves. The reason a simple doubling rule doesn't work is a result of the properties of real physical strings which are not perfectly elastic causing the harmonics of a single string vibrating to be slightly sharp. To avoid "beating", the ratio of frequencies between two piano notes an octave apart needs to be slightly greater than 2. This article is half of what a "what every musician should know about piano tuning" article should contain - it's the "set-up" part where you derive a nice simple rule that is widely known. The second part would then deal with temperament (first) and then inharmonicity.
  - TheOtherHobbes 8y ago
    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 8y ago
      Note that violinists (and cellists, and others) are not constrained by their instrument and can play in different temperaments depending on the situation.
      - chrisweekly 8y ago
        Right - because they're fretless. Same goes for slide guitar.
        dharma1 8y ago
        And the human voice
      - jancsika 8y ago
        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.
- gjm11 8y ago
  When I saw the article title that's what I expected it to be about. Then I saw your comment and thought "oh, it's going to be about the subtleties of different temperaments and how you get to choose which intervals are how far off from sounding right". Turns out it's actually telling you that there are 12 semitones per octave, all representing the same ratio of frequencies. Ah well.
slashdotdash 8y ago
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/
baddox 8y ago
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 8y ago
  > 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.
robbrown451 8y ago
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)
ramanan 8y ago
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 8y ago
  If you really want to dive deep into historical tuning systems, check out early music sources, https://m.youtube.com/channel/UCJOiqToQ7kiakqTLE7Hdd5g/videos https://m.youtube.com/channel/UCJOiqToQ7kiakqTLE7Hdd5g/video...
jacquesm 8y ago
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.
richardhod 8y ago
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_Railsback_curve https://en.m.wikipedia.org/wiki/Piano_acoustics#The_Railsbac...
- naringas 8y ago
  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 8y ago
    Making the strings (and therefore the piano) longer helps, hence the size of concert grand pianos.
  - richardhod 8y ago
    Indeed it's generally true for thicker strings at all pitches, though perhaps more so for lower ones for this case. The longer the strings, the better the sound in general, too, for related stiffness-timbre reasons. Even a tall upright you can tell can sound better than any short upright, and Grand pianos take this to greater extremes of length.
- tim333 8y ago
  That came up on HN 39 days ago "Why are pianos traditionally tuned “out of tune” at the extremes?" https://news.ycombinator.com/item?id=18988774 https://news.ycombinator.com/item?id=18988774 As an aside I wonder if you could make a digital piano sound better than a real one by correcting for that? And also perhaps auto tuning to the key the music is in, in the manner that a singer will do automatically. So far the digital pianos I've heard don't sound as good as a decent concert grand.
exabrial 8y ago
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 8y ago
  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.
stevehiehn 8y ago
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 8y ago
  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 8y ago
    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 :)
    - stevehiehn 8y ago
      Maybe your point is it 'switches' keys (48*x)
    - jancsika 8y ago
      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.
mitchtbaum 8y ago
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 8y ago
  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?
phlakaton 8y ago
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 8y ago
  I also really appreciated "How Equal Temperament Ruined Harmony (and Why You Should Care)" by Ross Duffin.
mnemotronic 8y ago
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 8y ago
  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.
deleted 8y ago
[deleted]
kazinator 8y ago
Educated guess: Sid has never tuned a piano.
jancsika 8y ago
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?
GuillaumeBrdet 8y ago
Was really hoping to land on an app that would help you tune it.

101 points by strawcomb 8y ago

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 8y ago
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.
- derriz 8y ago
  Temperament is unrelated/orthogonal to inharmonicity. Temperament deals with picking frequencies for the notes that make up the scale within an octave. Inharmonicity affects how you tune the octaves themselves. The reason a simple doubling rule doesn't work is a result of the properties of real physical strings which are not perfectly elastic causing the harmonics of a single string vibrating to be slightly sharp. To avoid "beating", the ratio of frequencies between two piano notes an octave apart needs to be slightly greater than 2. This article is half of what a "what every musician should know about piano tuning" article should contain - it's the "set-up" part where you derive a nice simple rule that is widely known. The second part would then deal with temperament (first) and then inharmonicity.
- TheOtherHobbes 8y ago
  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 8y ago
    Note that violinists (and cellists, and others) are not constrained by their instrument and can play in different temperaments depending on the situation.
    - chrisweekly 8y ago
      Right - because they're fretless. Same goes for slide guitar.
      - dharma1 8y ago
        And the human voice
    - jancsika 8y ago
      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.
gjm11 8y ago
When I saw the article title that's what I expected it to be about. Then I saw your comment and thought "oh, it's going to be about the subtleties of different temperaments and how you get to choose which intervals are how far off from sounding right". Turns out it's actually telling you that there are 12 semitones per octave, all representing the same ratio of frequencies. Ah well.

slashdotdash 8y ago

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/

baddox 8y ago

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 8y ago
> 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.

robbrown451 8y ago

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)

ramanan 8y ago

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 8y ago
If you really want to dive deep into historical tuning systems, check out early music sources, https://m.youtube.com/channel/UCJOiqToQ7kiakqTLE7Hdd5g/videos https://m.youtube.com/channel/UCJOiqToQ7kiakqTLE7Hdd5g/video...

jacquesm 8y ago

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.

richardhod 8y ago

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_Railsback_curve https://en.m.wikipedia.org/wiki/Piano_acoustics#The_Railsbac...

naringas 8y ago
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 8y ago
  Making the strings (and therefore the piano) longer helps, hence the size of concert grand pianos.
- richardhod 8y ago
  Indeed it's generally true for thicker strings at all pitches, though perhaps more so for lower ones for this case. The longer the strings, the better the sound in general, too, for related stiffness-timbre reasons. Even a tall upright you can tell can sound better than any short upright, and Grand pianos take this to greater extremes of length.
tim333 8y ago
That came up on HN 39 days ago "Why are pianos traditionally tuned “out of tune” at the extremes?" https://news.ycombinator.com/item?id=18988774 https://news.ycombinator.com/item?id=18988774 As an aside I wonder if you could make a digital piano sound better than a real one by correcting for that? And also perhaps auto tuning to the key the music is in, in the manner that a singer will do automatically. So far the digital pianos I've heard don't sound as good as a decent concert grand.

exabrial 8y ago

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 8y ago
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.

stevehiehn 8y ago

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 8y ago
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 8y ago
  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 :)
  - stevehiehn 8y ago
    Maybe your point is it 'switches' keys (48*x)
  - jancsika 8y ago
    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.

mitchtbaum 8y ago

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 8y ago
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?

phlakaton 8y ago

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 8y ago
I also really appreciated "How Equal Temperament Ruined Harmony (and Why You Should Care)" by Ross Duffin.

mnemotronic 8y ago

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 8y ago
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.

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kazinator 8y ago

Educated guess: Sid has never tuned a piano.

jancsika 8y ago

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?

GuillaumeBrdet 8y ago

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