5 ms·

As someone who's tuned my own piano, the inharmonicity in the bass is really noticeably low.

by CarVac 5y ago

felipemnoa 5y ago
For those of us that know nothing about music, is this good or bad?
- LanceH 5y ago
  When played a note will emit overtones -- the same note an at higher octaves. So a low C will also have middle C, high C, etc at different volumes depending on the instrument. This is playing low notes without low volume overtones. In short, the low notes are more purely low.
  - elihu 5y ago
    That's not quite right. The overtones are the harmonic series, not just octaves (1:2, 1:4, 1:8, etc..) but an octave and a fifth (1:3), two octaves and a third, (1:5), etc.. In a piano, the bass and treble strings have a lot of inharmonicity. They don't behave like ideal strings for various reasons, so the harmonics aren't exact multiples of the fundamental frequency. Piano tuners deal with this be stretching the octave, so that the piano sounds in tune even though it kind of isn't. Having a super long bass string instead of a short double-wound bass string probably behaves more like an ideal string (with harmonics that are closer to whole-number multiples of the fundamental), so it should sound like it has a more definite pitch and less like a gong. Interestingly, we don't really perceive the fundamental frequencies of the low notes in a piano much at all in the first place. If you filter them out, the notes will sound about the same -- we take most of our perceptual cues from the higher harmonics, and our brain just inserts the implied bass fundamental. In the same way, playing a major chord sort of implies a bass note a couple octaves below the root of the chord -- if all the harmonics are there, then we expect it to be there.
    - LanceH 5y ago
      Thank you.
    - LeonB 5y ago
      “playing a major chord sort of implies a bass note a couple octaves below the root of the chord” Wow! Of course! Lightbulb moment. This isn’t something that occurred to me independently but makes so much sense I wonder how it hadn’t, and it explains a lot of what chords are really all about.
      - elihu 5y ago
        Yeah, chords are interesting. Major triads are basically a 4:5:6 ratio, which is the 4th, 5th, and 6th harmonic of some low bass note. (Different inversions get you 2:3:5 or 3:4:5 or whatever.) A dominant 7th chord gets you one more step in the harmonic series: 4:5:6:7. That 7th harmonic is way out of tune in 12-tone equal temperament, though. Minor chords are a 10:12:15 ratio, which kind of looks like a bunch of arbitrary chosen numbers, but we could rewrite that as 60/6 : 60/5 : 60/4 and then it sort of make sense that minor would be a sort of mathematical reciprocal of the major. Minor chords can be interpreted either as the 10th, 12th, and 15th harmonics of some bass note or as the first three prime subharmonics that are integer divisions of the fundamental note. Subharmonics don't really occur in nature, though.
        mrob 5y ago
        >That 7th harmonic is way out of tune in 12-tone equal temperament You can sing in any tuning though. If you want to hear just-intonation 4:5:6:7 chords, listen to barbershop music, where this chord is a defining part of the style. See: https://en.wikipedia.org/wiki/Harmonic_seventh_chord https://en.wikipedia.org/wiki/Harmonic_seventh_chord
        elihu 5y ago
        Yep. It's also possible to re-tune a piano to a 7-limit just intonation scale that makes use of that 7th harmonic. https://www.youtube.com/watch?v=D4oKzSRs3sA https://www.youtube.com/watch?v=D4oKzSRs3sA
- retrac 5y ago
  Inharmonicity is when the overtones (frequency multiples) are not whole number multiples of the fundamental frequency. It sounds bad. Discordant, like playing two notes directly next to each other on the keyboard. When designing a string or percussion instrument (or any resonator, in general, I suppose) one of the challenges is ensuring that you aren't creating undesired harmonics. With something like a piano with hundreds or thousands of strings that might be induced to resonate undesirably if even slightly out, or whose own movement might alter other parts and affect them, it becomes a significant challenge.
- duskwuff 5y ago
  It's very good. Normally, the lowest few octaves on a piano all sound a little weird; the individual notes are a little hard to tell apart and multiple low notes played together often blend into a rumbly mess. This is because the strings for those notes are shorter than they should be for their frequencies -- they're artificially made to vibrate at a lower frequency by making the strings heavier. This effect seems to be significantly reduced on the Alexander piano.
  - atwebb 5y ago
    Thanks for the explanation! Is it noticeable at this time stamp? https://youtu.be/nj4fhdiXy48?t=178 https://youtu.be/nj4fhdiXy48?t=178 I feel like the lower notes are much more distinct and separate but might just be imagining it.
    - kmill 5y ago
      Those bass notes are noticeably clearer there! The sound of inharmonicity comes from dispersion -- different frequencies travel through the string at different velocities. The lower the frequency, the less the wave notices the stiffness of the string, so to speak, and the stiffer the string the quicker a wave will travel through it. If you've ever tapped on a wire fence or played with a slinky, you'll be familiar with the "pew" sound. A pure impulse consists of all frequencies at once, but when it's traveled through the fence, bounced off a post, and come back, you hear the high frequencies first, which is why the "pew" descends in frequency. Anyway, I've found that you can notice this on the attacks of bass notes on pianos. Only the very lowest notes of the Alexander piano seem to really have it audible, and even then it's much more slight.
      - mrob 5y ago
        I thought the cause of inharmonicity was that higher frequencies cause steeper bending of the string at the attachment points, which makes the effective length of the string shorter. Sound on Sound's article on synthesizing guitar sounds (which have the same problem) has a good diagram explaining it (see figure 12): https://www.soundonsound.com/techniques/final-attempt-synthesize-guitars https://www.soundonsound.com/techniques/final-attempt-synthe... And this model explains why the inharmonicity is higher on the attacks (higher vibration amplitude increases bending of the string).
- hug 5y ago
  The harmonic series is a really neat thing to learn about -- one of those "art is math" kind of moments. This video does a good job of explaining it in a relatively short and simple way, but goes in-depth enough that even people with an understanding of music might learn something: https://www.youtube.com/watch?v=Wx_kugSemfY https://www.youtube.com/watch?v=Wx_kugSemfY
- CarVac 5y ago
  It's good. Due to the stiffness of real strings, the overtones do not occur at even multiples of the fundamental frequency. This means that when tuning a piano, you need to compromise between tuning so that the fundamentals are in tune with distant notes but having the overtones sound discordant with nearby notes, or having sweet overtone matching with nearby notes, causing notes to be very far off when harmonizing at longer distances across the keyboard. With my upright, I've had more success tuning more based on the fundamental than on the overtones, because it has enough inharmonicity that tuning to the overtones causes right-hand-to-left-hand harmonies to sound noticeably off. But this makes single-hand chords sound messier. A piano with looooooooooooooooong bass strings can have skinnier strings that are flexible and behave closer to ideal, so you don't have to compromise as much when tuning.
  - leephillips 5y ago
    Excellent explanation. We can get a little quantitative if we remember that the fundamental frequency of a vibrating string is sqrt(T/μ)/(2L), where T is the tension, μ is the linear density, and L is the length. So if we make the string twice as long, (T/μ) has to be increased by a factor of four; if we keep the tension the same we can use a string with 1/4 the linear density, which I guess would decrease the inharmonicity significantly. The square root magnifies the effect of increasing the length, so you get a lot from making the piano a bit longer. The project is a wonderful idea.
  - munificent 5y ago
    For anyone curious, the name for this tuning technique is "stretch": https://en.wikipedia.org/wiki/Piano_tuning#Stretch https://en.wikipedia.org/wiki/Piano_tuning#Stretch https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning Software synthesized pianos implement this too because it's part of how we expect piano-based instruments to sound.
elihu 5y ago
I think the low strings usually get tuned about half a semitone or more lower just to sound in tune with the rest of the instrument. It'd be interesting to know what the railsback curve looks like for this long piano; I'd expect it to be a lot flatter. I imagine you could also flatten out the curve on the treble end by using thinner gauge wire, but I suppose there's probably a trade-off in terms of volume or durability, otherwise all pianos would use thin wire for the treble strings. (I think most pianos use wire that's a little thinner in the treble, but not by much. I might be wrong about that, though.) https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_curve https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_...
prvc 5y ago
Yet the timbre on this is quite different from that of an ordinary piano. Which make the experiment worth doing on its own (and successful)!
nyanpasu64 5y ago
Chrono Trigger is a SNES game with short samples. Normally that would result in significant quality degradation, but one interesting side effect is that its short looped low piano sample (found in songs like Lavos's Theme[1]) has no inharmonicity. When the attack ends and the sample loops, it almost sounds like the harmonics go a bit flat. [1]: https://fi.zophar.net/soundfiles/nintendo-snes-spc/chrono-trigger/205%20Lavos%27%20Theme%20%28Extended%29.mp3 https://fi.zophar.net/soundfiles/nintendo-snes-spc/chrono-tr...
marcan_42 5y ago
This is why I love Pianoteq. It's a plug-in that virtually models a piano, so if you want 10 meter long strings, you can have that. Or you can go crazy with other parameters and get very strange pianos. As someone who enjoys playing piano but doesn't have the space nor acoustic insulation for a real one, it's great being able to not just get the sound of different pianos whenever I want, but also virtually design my own. Modeling technology has really come a long way. That's not to say that if I ever own a large enough house I wouldn't want an acoustic piano :-)
- HPsquared 5y ago
  I searched this thread to see if anyone mentioned Pianoteq. :) It's also fun to play around with alternative tuning systems, try different hammers, soundboard characteristics, etc etc.
- yboris 5y ago
  I second Pianoteq as a recommendation. It can run on Linux, so I have it on a Raspberry Pi attached to my digital piano. As a bonus, it also drives some addressable (programmable) LEDs: https://github.com/whyboris/Digital-Piano-LED https://github.com/whyboris/Digital-Piano-LED To install Pianoteq on a Raspberry Pi, it's a single script that sets everything up: https://github.com/youfou/pianoteq-pi https://github.com/youfou/pianoteq-pi
- myself248 5y ago
  Thank you! Reading the original article, I was wondering if exactly this sort of physical modeling was possible or being done yet. I'm still not sure what _sort_ of modeling it's doing (surely not full FEA of the entire vibrating system), but I'm sure we'll get there in another few years of GPGPU...
  - marcan_42 5y ago
    If I had to guess, they probably have a fairly accurate single-string model and then model energy coupling across strings. Another neat thing it does is it lets you position virtual microphones around the piano (and open and close the lid), so they definitely have full-instrument spatial awareness in their modeling. One curious thing I noticed from the (simpler) string modeling synth in my keyboard is that if you up the dispersion it starts sounding like a bell... and indeed Pianoteq also has a very nice tubular bells patch. Explains what that's doing in a piano synth :)
Synaesthesia 5y ago
I once pitched up a sample of a very low note plated on piano, it sounds so weird! The inharmonicity manifests as all kinds of weird whistling sounds.

As someone who's tuned my own piano, the inharmonicity in the bass is really noticeably low.

by CarVac 5y ago

As someone who's tuned my own piano, the inharmonicity in the bass is really noticeably low.

felipemnoa 5y ago

For those of us that know nothing about music, is this good or bad?

LanceH 5y ago
When played a note will emit overtones -- the same note an at higher octaves. So a low C will also have middle C, high C, etc at different volumes depending on the instrument. This is playing low notes without low volume overtones. In short, the low notes are more purely low.
- elihu 5y ago
  That's not quite right. The overtones are the harmonic series, not just octaves (1:2, 1:4, 1:8, etc..) but an octave and a fifth (1:3), two octaves and a third, (1:5), etc.. In a piano, the bass and treble strings have a lot of inharmonicity. They don't behave like ideal strings for various reasons, so the harmonics aren't exact multiples of the fundamental frequency. Piano tuners deal with this be stretching the octave, so that the piano sounds in tune even though it kind of isn't. Having a super long bass string instead of a short double-wound bass string probably behaves more like an ideal string (with harmonics that are closer to whole-number multiples of the fundamental), so it should sound like it has a more definite pitch and less like a gong. Interestingly, we don't really perceive the fundamental frequencies of the low notes in a piano much at all in the first place. If you filter them out, the notes will sound about the same -- we take most of our perceptual cues from the higher harmonics, and our brain just inserts the implied bass fundamental. In the same way, playing a major chord sort of implies a bass note a couple octaves below the root of the chord -- if all the harmonics are there, then we expect it to be there.
  - LanceH 5y ago
    Thank you.
  - LeonB 5y ago
    “playing a major chord sort of implies a bass note a couple octaves below the root of the chord” Wow! Of course! Lightbulb moment. This isn’t something that occurred to me independently but makes so much sense I wonder how it hadn’t, and it explains a lot of what chords are really all about.
    - elihu 5y ago
      Yeah, chords are interesting. Major triads are basically a 4:5:6 ratio, which is the 4th, 5th, and 6th harmonic of some low bass note. (Different inversions get you 2:3:5 or 3:4:5 or whatever.) A dominant 7th chord gets you one more step in the harmonic series: 4:5:6:7. That 7th harmonic is way out of tune in 12-tone equal temperament, though. Minor chords are a 10:12:15 ratio, which kind of looks like a bunch of arbitrary chosen numbers, but we could rewrite that as 60/6 : 60/5 : 60/4 and then it sort of make sense that minor would be a sort of mathematical reciprocal of the major. Minor chords can be interpreted either as the 10th, 12th, and 15th harmonics of some bass note or as the first three prime subharmonics that are integer divisions of the fundamental note. Subharmonics don't really occur in nature, though.
      - mrob 5y ago
        >That 7th harmonic is way out of tune in 12-tone equal temperament You can sing in any tuning though. If you want to hear just-intonation 4:5:6:7 chords, listen to barbershop music, where this chord is a defining part of the style. See: https://en.wikipedia.org/wiki/Harmonic_seventh_chord https://en.wikipedia.org/wiki/Harmonic_seventh_chord
        elihu 5y ago
        Yep. It's also possible to re-tune a piano to a 7-limit just intonation scale that makes use of that 7th harmonic. https://www.youtube.com/watch?v=D4oKzSRs3sA https://www.youtube.com/watch?v=D4oKzSRs3sA
retrac 5y ago
Inharmonicity is when the overtones (frequency multiples) are not whole number multiples of the fundamental frequency. It sounds bad. Discordant, like playing two notes directly next to each other on the keyboard. When designing a string or percussion instrument (or any resonator, in general, I suppose) one of the challenges is ensuring that you aren't creating undesired harmonics. With something like a piano with hundreds or thousands of strings that might be induced to resonate undesirably if even slightly out, or whose own movement might alter other parts and affect them, it becomes a significant challenge.
duskwuff 5y ago
It's very good. Normally, the lowest few octaves on a piano all sound a little weird; the individual notes are a little hard to tell apart and multiple low notes played together often blend into a rumbly mess. This is because the strings for those notes are shorter than they should be for their frequencies -- they're artificially made to vibrate at a lower frequency by making the strings heavier. This effect seems to be significantly reduced on the Alexander piano.
- atwebb 5y ago
  Thanks for the explanation! Is it noticeable at this time stamp? https://youtu.be/nj4fhdiXy48?t=178 https://youtu.be/nj4fhdiXy48?t=178 I feel like the lower notes are much more distinct and separate but might just be imagining it.
  - kmill 5y ago
    Those bass notes are noticeably clearer there! The sound of inharmonicity comes from dispersion -- different frequencies travel through the string at different velocities. The lower the frequency, the less the wave notices the stiffness of the string, so to speak, and the stiffer the string the quicker a wave will travel through it. If you've ever tapped on a wire fence or played with a slinky, you'll be familiar with the "pew" sound. A pure impulse consists of all frequencies at once, but when it's traveled through the fence, bounced off a post, and come back, you hear the high frequencies first, which is why the "pew" descends in frequency. Anyway, I've found that you can notice this on the attacks of bass notes on pianos. Only the very lowest notes of the Alexander piano seem to really have it audible, and even then it's much more slight.
    - mrob 5y ago
      I thought the cause of inharmonicity was that higher frequencies cause steeper bending of the string at the attachment points, which makes the effective length of the string shorter. Sound on Sound's article on synthesizing guitar sounds (which have the same problem) has a good diagram explaining it (see figure 12): https://www.soundonsound.com/techniques/final-attempt-synthesize-guitars https://www.soundonsound.com/techniques/final-attempt-synthe... And this model explains why the inharmonicity is higher on the attacks (higher vibration amplitude increases bending of the string).
hug 5y ago
The harmonic series is a really neat thing to learn about -- one of those "art is math" kind of moments. This video does a good job of explaining it in a relatively short and simple way, but goes in-depth enough that even people with an understanding of music might learn something: https://www.youtube.com/watch?v=Wx_kugSemfY https://www.youtube.com/watch?v=Wx_kugSemfY
CarVac 5y ago
It's good. Due to the stiffness of real strings, the overtones do not occur at even multiples of the fundamental frequency. This means that when tuning a piano, you need to compromise between tuning so that the fundamentals are in tune with distant notes but having the overtones sound discordant with nearby notes, or having sweet overtone matching with nearby notes, causing notes to be very far off when harmonizing at longer distances across the keyboard. With my upright, I've had more success tuning more based on the fundamental than on the overtones, because it has enough inharmonicity that tuning to the overtones causes right-hand-to-left-hand harmonies to sound noticeably off. But this makes single-hand chords sound messier. A piano with looooooooooooooooong bass strings can have skinnier strings that are flexible and behave closer to ideal, so you don't have to compromise as much when tuning.
- leephillips 5y ago
  Excellent explanation. We can get a little quantitative if we remember that the fundamental frequency of a vibrating string is sqrt(T/μ)/(2L), where T is the tension, μ is the linear density, and L is the length. So if we make the string twice as long, (T/μ) has to be increased by a factor of four; if we keep the tension the same we can use a string with 1/4 the linear density, which I guess would decrease the inharmonicity significantly. The square root magnifies the effect of increasing the length, so you get a lot from making the piano a bit longer. The project is a wonderful idea.
- munificent 5y ago
  For anyone curious, the name for this tuning technique is "stretch": https://en.wikipedia.org/wiki/Piano_tuning#Stretch https://en.wikipedia.org/wiki/Piano_tuning#Stretch https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning Software synthesized pianos implement this too because it's part of how we expect piano-based instruments to sound.

elihu 5y ago

I think the low strings usually get tuned about half a semitone or more lower just to sound in tune with the rest of the instrument. It'd be interesting to know what the railsback curve looks like for this long piano; I'd expect it to be a lot flatter. I imagine you could also flatten out the curve on the treble end by using thinner gauge wire, but I suppose there's probably a trade-off in terms of volume or durability, otherwise all pianos would use thin wire for the treble strings. (I think most pianos use wire that's a little thinner in the treble, but not by much. I might be wrong about that, though.) https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_curve https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_...

prvc 5y ago

Yet the timbre on this is quite different from that of an ordinary piano. Which make the experiment worth doing on its own (and successful)!

nyanpasu64 5y ago

Chrono Trigger is a SNES game with short samples. Normally that would result in significant quality degradation, but one interesting side effect is that its short looped low piano sample (found in songs like Lavos's Theme[1]) has no inharmonicity. When the attack ends and the sample loops, it almost sounds like the harmonics go a bit flat. [1]: https://fi.zophar.net/soundfiles/nintendo-snes-spc/chrono-trigger/205%20Lavos%27%20Theme%20%28Extended%29.mp3 https://fi.zophar.net/soundfiles/nintendo-snes-spc/chrono-tr...

marcan_42 5y ago

This is why I love Pianoteq. It's a plug-in that virtually models a piano, so if you want 10 meter long strings, you can have that. Or you can go crazy with other parameters and get very strange pianos. As someone who enjoys playing piano but doesn't have the space nor acoustic insulation for a real one, it's great being able to not just get the sound of different pianos whenever I want, but also virtually design my own. Modeling technology has really come a long way. That's not to say that if I ever own a large enough house I wouldn't want an acoustic piano :-)

HPsquared 5y ago
I searched this thread to see if anyone mentioned Pianoteq. :) It's also fun to play around with alternative tuning systems, try different hammers, soundboard characteristics, etc etc.
yboris 5y ago
I second Pianoteq as a recommendation. It can run on Linux, so I have it on a Raspberry Pi attached to my digital piano. As a bonus, it also drives some addressable (programmable) LEDs: https://github.com/whyboris/Digital-Piano-LED https://github.com/whyboris/Digital-Piano-LED To install Pianoteq on a Raspberry Pi, it's a single script that sets everything up: https://github.com/youfou/pianoteq-pi https://github.com/youfou/pianoteq-pi
myself248 5y ago
Thank you! Reading the original article, I was wondering if exactly this sort of physical modeling was possible or being done yet. I'm still not sure what _sort_ of modeling it's doing (surely not full FEA of the entire vibrating system), but I'm sure we'll get there in another few years of GPGPU...
- marcan_42 5y ago
  If I had to guess, they probably have a fairly accurate single-string model and then model energy coupling across strings. Another neat thing it does is it lets you position virtual microphones around the piano (and open and close the lid), so they definitely have full-instrument spatial awareness in their modeling. One curious thing I noticed from the (simpler) string modeling synth in my keyboard is that if you up the dispersion it starts sounding like a bell... and indeed Pianoteq also has a very nice tubular bells patch. Explains what that's doing in a piano synth :)

Synaesthesia 5y ago

I once pitched up a sample of a very low note plated on piano, it sounds so weird! The inharmonicity manifests as all kinds of weird whistling sounds.