Comment by tracnar
2 days ago
To give an example, this it of course not true:
> Only a limited set of frequencies is used in music. All these frequencies (that exist in music) can be played by a piano.
2 days ago
To give an example, this it of course not true:
> Only a limited set of frequencies is used in music. All these frequencies (that exist in music) can be played by a piano.
Yeah, I think a good discussion on music theory is starting from first principles, explaining Pythagorean tuning, then explaining 5-limit just intonation, the explaining we compromised on 12-tone equal temperament because it made tuning and changing keys a lot simpler, at the expenses of some notes being slightly out of tune (e.g. the minor and major thirds deviate by about 15 cents from their 5-limit just intonated “ideal” tunings).
You're saying its not possible to tune a piano to an arbitrary set of 88 pitches?
Aside from that not being what was said (the parent’s pull-quote is wrong in multiple ways), it is in fact not possible to tune a piano to any arbitrary set of 88 pitches without changing the design so dramatically and fundamentally that it would no longer be a piano. The triangular shape of a grand determined by the strings lengths, the placement of the pins, the use of double/triple strings in some frequency ranges, and design of the sound board, all permit only a very limited range of frequencies for each key on the keyboard. You very obviously cannot take an existing piano and tune it to 88 keys of A0, nor to 88 keys of C9.
That's clearly not what was meant, even without the context of this following bit:
> To describe tones that exist in music, we can describe tones that exist on a piano. There are only two rules:
> the first key must play a tone of 27.5 Hz each next key must play a tone 6% higher than the previous key
(This is not to mention that at a 1.06x increase per half step you're going to be sharp by 1 cent / octave which starts to add up).
Of course you can, but that's not what's implied by the quote.
In addition to microtonality, many instruments (and the human voice) are capable of infinite tuning, and musicians will deviate from the "correct" note (as played by an even-tempered instrument) based on chord structure, voice leading, etc.
That's not what "tuning" means. Yes, fretless string instruments, the human voice, instruments like the trombone are all capable of being played with arbitrary or semi-arbitrary pitch. But they are still either tuned in some way, or never tuned at all. Performance is not tuning.
Also quarter step bends in guitar and vibrato in general.
there are absolutely pitches that an arbitrary piano cannot be tuned to. it is also non-trivial to tune a piano.
Since an "arbitrary piano" is tuned by turning screws, like simpler string instruments, the only pitches that it cannot be tuned to are those that fall outside the range of each string. Departing from the usual inharmonically tempered 12-EDO tuning would just sound strange, possibly outside some piano tuner's professional comfort zone.
https://www.modartt.com/pianoteq_overview :) Very high quality and affordable software modeled piano. It is rather easy to tune via Scala KBD formatted files.
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