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Discussion Starter · #1 ·
Hello you all! Nice to be among you again.

Do you too perceive a doubtful height at the highest and lowest notes of a pianoforte, and too small intervals there?

Some theories claim that our height perception is wrong there, keyword "Railsback". I'm not convinced, because we hear the height of a celesta, a glockenspiel or a tuba far better than of a piano. Other attempts want the inharmonicity of the string modes, resulting from the string thickness, let us perceive wrongly the highest notes. But sound syntheses aren't convincing.

My earlier thoughts about hammer mass are in scienceforums on

I experimented on a Yamaha upright piano, here the results.


Using a clothes peg, the plucked highest strings made a true note of clear height, about in tune, while the hammers make an imprecise noise sounding low. So mainly the hammers are to blame, not our perception.

On this piano, the hammers strike near the end of the highest strings. Suppressing the harmonic 11* 2kHz to 4kHz is no good reason as we don't hear it. As a possible and known goal, the heavy hammer rebounds too slowly, and the stiffer string ends improve that. But the felt is far less stiff than the strings. Benade found that the rebound is slower than the half-period of high strings.

  1. Felt is too soft to excite the resonance of the strings, it makes noise instead. A harder material will make a note with clear height.
  2. This hardens the start for the highest notes. No alternative exists, I believe.
  3. Hammers produce near the frame only noise. Nearer to the centre, they vibrate the strings. From pictures, Bösendorfer grand pianos do it, Steinway don't.
  4. For that, the highest hammers should be lighter and faster, for instance from longer shafts or a bigger lever ratio. Parts are less uniform, alas.
I trust better a bigger change at the highest notes: heavy stiff elements replace the strings, keep heavy hammers with cover harder than felt, as on scienceforums on
January 13, 2019 at 05:41 PM - 11:25 PM


I struck the lowest strings with a chisel at its rubber hand protector, and this outperformed the piano hammer, despite the tool was too heavy for the string and the rubber too soft. The sound was more pleasant and the perceived height better defined.

According to my still incomplete theory on scienceforums
we perceive contrabass sound height using several overtones in a limited frequency band around 70Hz. A tuba provides these overtones. A piano with its hammers too light for low strings would make these overtones too faint, the chisel did it better. Striking the string nearer to the centre improved the sound too, but this may result from the too soft rubber.

  1. Make the hammerheads much heavier to excite low string modes.
  2. Make shorter shafts, or reduce the lever ratio, to keep comfortable keys.
  3. Softer felt at the low notes? More pleasant to my ears at least.
  4. Strike low strings nearer to the centre? That's still unclear.
The piano's soundboard and absent soundbox will curb the emission of low sound components, but heavier hammers will improve.

Marc Schaefer, aka Enthalpy
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