We know that for each note in a piano's range, there is only one key pertaining to that note. This is in contrast to, say, a guitar where there are multiple ways to play, say, middle C.

Are there other instruments in which there is only way to play notes in its given range?

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    The xylophone/marimba/vibrophone/glockenspiel family, and the harp come to mind. – Duston May 22 '19 at 14:12
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    @Duston A seven pedal harp has different ways of playing the same note doesn't it? – JimM May 23 '19 at 7:11
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    Sorry to be a pedant, harp is a bad example, as you can have lots of enharmonic equivalents, which although written differently sound the same. Cb and B, B# and C, C# and Db etc. – Bob Broadley May 23 '19 at 14:27
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    In fact, pitches being able to be played in multiple ways is an important feature of how pedal harp works. By using enharmonic doublings you can glissando 5 and 6 note chords, rather than just 7 note scales. The only notes that don’t have enharmonic equivalents on pedal harp are D, G and A. – Bob Broadley May 23 '19 at 14:36
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    @BobBroadley Can't every instrument play enharmonic equivalents? – Todd Wilcox May 23 '19 at 16:03

Mainly the one-to-one group includes:

  • Pitched percussion instruments, especially pitched idiophones. This includes metallophones, xylophones, glockenspiel, marimba, celesta, vibraphone, many kinds of bells, and pitched drums like timpani. In many cases, it can be possible to "bend" notes on some of these instruments to a greater or lesser extent, but not often by a semitone.
  • Some chorodophones with one string per note such as harps (that don't have pedals, perhaps some that do) and cimbalons, and I believe dulcimers, but only if we exclude harmonics.
  • Besides pianos, there are some keyboard instruments that are one-to-one, including single-manual harpsichords, clavichords, Hohner Clavinets, electric pianos. Generally, synthesizers and organs (pipe or electronic) are not one-to-one, since using different oscillator settings or stops, respectively, can produce different pitches on the same key. Obviously any keyboard device with more than one manual where the manuals can overlap would not qualify as one-to-one.
  • Other instruments include hurdy-gurdy (I'm pretty sure), I believe some variants of accordion/bandeneon/concertina, melodica, and portative organs, bagpipes, finger pianos, and I expect several other more obscure instruments.
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I guess the most instruments that are able to play some notes multiple ways are string instruments (guitar, violin, cello etc.). Also some instruments using breath are able to do the same, the harmonica for example.

However, even tho it's often basically the same pitch, they can still sound different, for example on a violin, the same pitch played either on a stopped string or an open string sound different and so on...

The most instruments that have each note only once are probably instruments that get hit with a hammer, mallet or the hand (piano, marimba, xylophone, pan/steel drums etc.)

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  • What about wind instruments? I.e. trumpet, saxophone, flute .. – Time4Tea May 22 '19 at 14:17
  • Ok, then maybe those could be added as examples where there is only one way to make a particular note? – Time4Tea May 22 '19 at 14:56
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    @Andy: Yes, you can: there are several notes possible to play with the same position and several positions for the same note - for all brass instruments. But not with the alphorn ... – Albrecht Hügli May 22 '19 at 15:22
  • @AlbrechtHügli Oh ok, great to know - Thanks :) – Andy May 22 '19 at 15:30
  • Clarinets & saxophones have alternate fingerings for a limited number of notes. – Carl Witthoft May 22 '19 at 15:32

I think this comes down to the method by which the instrument produces the pitch.

Some instruments have a mechanical action that simply activates the object that sounds (hitting a piano string for instance) whilst others require that the player "sets up" the object to make a particular sound (putting your fingers over certain holes in a flute for instance).

In the first category you have the piano, xylophone, marimba, church bells etc. as well as tubular bells and (I'm guessing here) the cimbalom. I expect that there are many others.

In the second group you have the violin family, most wind instruments and, judging by other answers and comments, most brass instruments.

I suspect the Hornbostel–Sachs classification system would shed some light on this.

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The triangle only really produces one note (well, you can mute and stuff, but you can't change the fact that the fundamental will be the same every time, obscured by all the clashing harmonics), so it's in one-to-one correspondence with its range of notes. The otamatone is essentially one-to-one, but at the very edges of the fretboard lie notes that can also be covered via the octave switch and moving to the other side of the fretboard (with no frets, I hesitate to call it a fretboard). I believe the Japanese koto qualifies, since every string only really produces one note at once (not counting detuning). Harmonica probably counts if you don't consider bending.

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    Beliefs are not facts. Also a triangle definitely does not "only really produce one sound". – jjmusicnotes May 23 '19 at 15:37
  • @jjmusicnotes What two sounds can a triangle make? Pitchwise, not volume-wise. – user45266 May 23 '19 at 17:10
  • A struck triangle produces a rich harmonic spectrum of pitches; many more than "two" sounds – jjmusicnotes May 23 '19 at 17:35
  • @jjmusicnotes Oh, sorry. I was a little unclear there. I meant that the triangle can only produce one note at a time (including all its harmonics and counting them as the overtones of one singular note, the fundamental). – user45266 May 23 '19 at 23:55

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