I’m wondering if there is a piano composition that uses notes from subcontra octave (C0) and five-lined octave (C8) at the same time?
In other words, is there any song there is no way to play without a keyboard that has 88 keys?
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Very few before 1890. Some pianos like the Steinway A still had only 85 notes at that time, and most composers stayed within that range. After that time, many composers pushed the limits.
Olivier Messiaen's piano compositions use the full range. For instance the two-piano piece "Visions de l'Amen" opens with a triad on the lowest A of the piano. Another piece has the left hand playing in the lowest octave and the right in the highest octave.
Ravel, in "Une Barque sur l'Ocean", writes for G below the lowest A on the keyboard. He had a 90-key Erard piano that had that low note. There is a similar 90-key Erard at the Frederick Collection in Ashburnham, Massachusetts.
I have heard that there is a piece by Scriabin that calls for the D above the highest C on the piano, but I don't think any piano was ever made that had that note.
Ligeti's thirteenth piano étude "L'escalier du diable" or devil's staircase, uses the full range of the keyboard. You can see it clearly in this video. The pianist is Francesco Libetta.
Not on top of my head. Some songs will require loads of octaves. The Piano theme by Michael Nyman takes 3 octaves around C3, then jumps down 2 octaves.
But imo the main reason of having so many key (specially since you tagged this question under midi and midi controller) would be for performance reasons.
Most samplers allow you to choose ranges for different presets. So you can actually have 2 blown octaves from a nice sawtooth wave with a huge portamento for your theremin like solo, then 5 octaves of your main rhodes sound :) (I'm speculating, not saying you use those or you want to do this, just putting it into a RL perspective!).
Logic in itself allows you to do this somewhat in environment, etc.
Some compositions will have some information on really really low end (ie. think big, big pipe organs) but again - C1 has it's fundamental at around 32Hz, E1 at 41Hz. C0 it's around 15Hz (see an issue here?)
Uh, I stomped on this the other day - it does play C0 but it's not a keyboard! :P
There's another consideration to take into account with this question:
while a piece may be strictly possible to play without the full 88 keys by moving it up or down an octave, it may not actually sound any good at that point. The lowest and highest octaves have very distinctive sounds about them, and notes written in those ranges are generally written there specifically for this reason.
I would suggest that going beyond just one of these boundaries makes playing the piece 'properly' on a piano impossible, even if not technically so.
John Corigliano, Etude-Fantasy and Concerto for Piano and Orchestra both use a huge range of the instrument.
Fredric Rzewski piano piece #4 (from Four Piano Pieces) starts on the B one note from the top of a full-scale piano and uses the lowest A on the piano. (I have had to "recompose" the piece on the fly when presented at the last moment with a Bechstein whose highest note is the A below the intended starting B)