3 ms·

There's quite a lot of discussion about how it was made (which is pretty interesting, and impressive for a 15 year old!) but not very much discussion about the

There's quite a lot of discussion about how it was made (which is pretty interesting, and impressive for a 15 year old!) but not very much discussion about the results. My understanding is that it has a normal range of notes, but with a different type of string - is that true? Or can it go lower than a normal piano? How is the experience of playing it? Is it the same? Or does it respond differently (eg a different relationship between key force and sound). I guess as a complete piano novice my question is why would you want this over a normal piano?

wirrbel 3y ago
for string instruments, there are optimal ranges for string-length, tension and thickness that vary with its frequency. Which is why for example a violin has shorter strings than a cello or a contra bass. Similarly, acoustic (non-electric) bass guitars don't work so well, etc. To my understanding in a piano, the lower strings are "too short", this includes grand pianos at a concert hall for example. There is a compromise in the construction. The Alexander Piano has an adequate length of strings, so in principle it has better sounds in the lower frequency ranges.
mrob 3y ago
The difference is reduced inharmonicity in the bass notes. A sound we hear as a single pitch is made from multiple different sine waves playing simultaneously, called "partials" in general, or "harmonics" when those sine waves are integer[0] multiples of the lowest frequency, which is called the "fundamental". In an string instrument, the ends of the strings are fixed in place. This means any standing wave in the string must have "nodes" (points where the wave has zero amplitude) at the ends. When you pluck or strike the string, you induce multiple different standing waves at once. In a mathematically ideal string (modeled with zero thickness), these standing waves are sine waves. Because the ends are always nodes, and because nodes and anti-nodes (points of maximum amplitude) of a sine wave are evenly distributed along the length of the wave, there will always be an integer number of anti-nodes. The frequency of the wave is proportional to the number of anti-nodes, so you end up with a harmonic sound, where the upper partials are integer multiples of the fundamental. Music played in standard Western tuning sounds the most consonant when it uses harmonic sounds. But a real string instrument is not mathematically perfect. The strings have thickness, which makes them resist bending. Higher frequencies cause sharper bending of the string, so they are more affected by the bending resistance. This results in a standing wave that's very close to a sine wave, but with the end nodes shifted slightly towards the center of the string. The higher harmonics are effectively played on shorter strings, so their frequency is increased. They are no longer integer multiples of the fundamental, so the sound is "inharmonic". Bass strings are typically thicker, so this effect is most noticeable in the bass. It's a big enough problem in a traditional piano that a special tuning technique ("stretched tuning") is used to try to hide it, but it still results in a kind of muddy/blurred sound. The only alternative to making the bass strings thicker is to make them longer, which is what the the Alexander piano does. The result is an unusual clarity in the bass. [0] In practice people use "harmonics" to mean approximately integer multiples too.
- pclmulqdq 3y ago
  As I understand it from my own tuning career, octave stretching is more about correcting dissonances that result from equal temperament than correcting anything about the dynamics of a physical piano. When you tune with octave stretching, you will also widen the high octaves, which are the correct size to hold a standing wave on almost every piano with standard "piano wire" strings. This helps to bring the 2nd overtone of a string more in line with the note a 12th above at a cost of making the 1st and 3rd overtone (one and two octaves up) slightly imperfect. On the lower, wound strings, the thickness of the string causes the string to also hold a standing wave at the fundamental frequency in the short length that the string has, but it amplifies the higher-order harmonics and adds some secondary effects that cause the note to be less "clean" sounding. It doesn't cause the frequency to change. By the way, I am not a fan of octave stretching on my own piano, so I usually ask piano tuners not to do it. It's completely optional.
  - Jeff_Brown 3y ago
    I don't believe that's it. The problem of tuning higher notes to the stretched harmonics of lower notes would still be present even in a piano tuned using just intonation. Suppose for instance the 2nd harmonic of C2 is 2 cents sharp of where it "ought" to be (which is twice the frequency of C2 itself). Then if you tune C3 (the C in the next octave) to be similarly 2 cents sharp of where it ought to be, it will not clash against the 2nd harmonic in C2 -- but the result is that the distance from C2 to C3 is a little more than an octave. (I don't know whether 2 cents is anywhere ballpark -- I've studied the theory but haven't performed measurements.) Incidentally, if you want to play microtonal music on an equally tuned piano, this is an argument for selecting a sharp system, such as 27-edo or 58-edo -- that is, a system whose approximations to the harmonics you're interested in are sharps. (12-edo gives an approximation 2 cents flat of the 3rd harmonic and 14 cents sharp of the 5th harmonic. It ignores the other harmonics. 27-edo gives a sharp approximation to harmonics 3, 5 and 7. 58-edo gives a sharp approximation to 3, 5, 7, 11, and 13 -- nirvana, as far as I'm concerned.)
    - pclmulqdq 3y ago
jacquesm 3y ago
There are some videos at the bottom where it is played. It sounds beautiful. The range is like a normal 88 key piano, no extra keys but what matters is the difference in timbre in the low notes. Your 'regular' piano has what is called an overwound string, a steel string that is covered with one or two layers of copper. This results in a string that sounds less pure. The Alexander piano is special in that it uses no overwound strings, all the bass notes are simply simplex strings at their natural length without added weight to reduce their period of oscillation. It also has a huge soundboard, so presumably it is quite loud, but the main difference is in how the bases sound.
- calf 3y ago
  I listened to the Clara Schumann piece and I thought the low notes have a "perfectly tinny" sound, as if they were computer-generated on MATLAB. Or like a harpsichord. I assume that's the difference?
  - jacquesm 3y ago
    I wouldn't call it tinny, I would call the alternative 'muddy'. It's a much more pure tone than you would get from a 'normal' bass string (which is actually quite a complex piece by itself).
    - calf 3y ago
      Well I can hear a repetitive rattling sound on the low bass notes, but it is rattling very fast and evenly. So I call that tinny. A pure treble note like from a computer wave form does not rattle like that, to my ears. A normal piano is supposed to have impure frequencies, it's part of the timbre and what gives it warmth. Like a chocolate or winey kind of muddy. Artistically I much prefer that.
      - dsubburam 3y ago
        FWIW I've noticed that "rattling" (which I think I hear in the Liszt Funerailles video) in some K-pop videos featuring electronic low bass at the ~40Hz level. I think it might be natural and not an artifact or flaw.

wirrbel 3y ago

for string instruments, there are optimal ranges for string-length, tension and thickness that vary with its frequency. Which is why for example a violin has shorter strings than a cello or a contra bass. Similarly, acoustic (non-electric) bass guitars don't work so well, etc. To my understanding in a piano, the lower strings are "too short", this includes grand pianos at a concert hall for example. There is a compromise in the construction. The Alexander Piano has an adequate length of strings, so in principle it has better sounds in the lower frequency ranges.

mrob 3y ago

The difference is reduced inharmonicity in the bass notes. A sound we hear as a single pitch is made from multiple different sine waves playing simultaneously, called "partials" in general, or "harmonics" when those sine waves are integer[0] multiples of the lowest frequency, which is called the "fundamental". In an string instrument, the ends of the strings are fixed in place. This means any standing wave in the string must have "nodes" (points where the wave has zero amplitude) at the ends. When you pluck or strike the string, you induce multiple different standing waves at once. In a mathematically ideal string (modeled with zero thickness), these standing waves are sine waves. Because the ends are always nodes, and because nodes and anti-nodes (points of maximum amplitude) of a sine wave are evenly distributed along the length of the wave, there will always be an integer number of anti-nodes. The frequency of the wave is proportional to the number of anti-nodes, so you end up with a harmonic sound, where the upper partials are integer multiples of the fundamental. Music played in standard Western tuning sounds the most consonant when it uses harmonic sounds. But a real string instrument is not mathematically perfect. The strings have thickness, which makes them resist bending. Higher frequencies cause sharper bending of the string, so they are more affected by the bending resistance. This results in a standing wave that's very close to a sine wave, but with the end nodes shifted slightly towards the center of the string. The higher harmonics are effectively played on shorter strings, so their frequency is increased. They are no longer integer multiples of the fundamental, so the sound is "inharmonic". Bass strings are typically thicker, so this effect is most noticeable in the bass. It's a big enough problem in a traditional piano that a special tuning technique ("stretched tuning") is used to try to hide it, but it still results in a kind of muddy/blurred sound. The only alternative to making the bass strings thicker is to make them longer, which is what the the Alexander piano does. The result is an unusual clarity in the bass. [0] In practice people use "harmonics" to mean approximately integer multiples too.

pclmulqdq 3y ago
As I understand it from my own tuning career, octave stretching is more about correcting dissonances that result from equal temperament than correcting anything about the dynamics of a physical piano. When you tune with octave stretching, you will also widen the high octaves, which are the correct size to hold a standing wave on almost every piano with standard "piano wire" strings. This helps to bring the 2nd overtone of a string more in line with the note a 12th above at a cost of making the 1st and 3rd overtone (one and two octaves up) slightly imperfect. On the lower, wound strings, the thickness of the string causes the string to also hold a standing wave at the fundamental frequency in the short length that the string has, but it amplifies the higher-order harmonics and adds some secondary effects that cause the note to be less "clean" sounding. It doesn't cause the frequency to change. By the way, I am not a fan of octave stretching on my own piano, so I usually ask piano tuners not to do it. It's completely optional.
- Jeff_Brown 3y ago
  I don't believe that's it. The problem of tuning higher notes to the stretched harmonics of lower notes would still be present even in a piano tuned using just intonation. Suppose for instance the 2nd harmonic of C2 is 2 cents sharp of where it "ought" to be (which is twice the frequency of C2 itself). Then if you tune C3 (the C in the next octave) to be similarly 2 cents sharp of where it ought to be, it will not clash against the 2nd harmonic in C2 -- but the result is that the distance from C2 to C3 is a little more than an octave. (I don't know whether 2 cents is anywhere ballpark -- I've studied the theory but haven't performed measurements.) Incidentally, if you want to play microtonal music on an equally tuned piano, this is an argument for selecting a sharp system, such as 27-edo or 58-edo -- that is, a system whose approximations to the harmonics you're interested in are sharps. (12-edo gives an approximation 2 cents flat of the 3rd harmonic and 14 cents sharp of the 5th harmonic. It ignores the other harmonics. 27-edo gives a sharp approximation to harmonics 3, 5 and 7. 58-edo gives a sharp approximation to 3, 5, 7, 11, and 13 -- nirvana, as far as I'm concerned.)
  - pclmulqdq 3y ago

jacquesm 3y ago

There are some videos at the bottom where it is played. It sounds beautiful. The range is like a normal 88 key piano, no extra keys but what matters is the difference in timbre in the low notes. Your 'regular' piano has what is called an overwound string, a steel string that is covered with one or two layers of copper. This results in a string that sounds less pure. The Alexander piano is special in that it uses no overwound strings, all the bass notes are simply simplex strings at their natural length without added weight to reduce their period of oscillation. It also has a huge soundboard, so presumably it is quite loud, but the main difference is in how the bases sound.

calf 3y ago
I listened to the Clara Schumann piece and I thought the low notes have a "perfectly tinny" sound, as if they were computer-generated on MATLAB. Or like a harpsichord. I assume that's the difference?
- jacquesm 3y ago
  I wouldn't call it tinny, I would call the alternative 'muddy'. It's a much more pure tone than you would get from a 'normal' bass string (which is actually quite a complex piece by itself).
  - calf 3y ago
    Well I can hear a repetitive rattling sound on the low bass notes, but it is rattling very fast and evenly. So I call that tinny. A pure treble note like from a computer wave form does not rattle like that, to my ears. A normal piano is supposed to have impure frequencies, it's part of the timbre and what gives it warmth. Like a chocolate or winey kind of muddy. Artistically I much prefer that.
    - dsubburam 3y ago
      FWIW I've noticed that "rattling" (which I think I hear in the Liszt Funerailles video) in some K-pop videos featuring electronic low bass at the ~40Hz level. I think it might be natural and not an artifact or flaw.