Comment by tehwalrus | Hacker News Reader

Comment by tehwalrus | Hacker News Reader

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> I suppose it’s possible to change the sound of an entire piece of music just by changing the key signature, but does anyone actually do that?

Much more interestingly, this touches on the reason why different pieces were given keys at all by their composers (think "foo in B flat minor by Chopin").

Musical instruments have to be tuned to a particular key. This is because of the frequency ratios: the circle of fifths is a lie, (3/2)^N != 2^M for any N and M, you can't be an in-tune fourth in one key and third in another, the frequency values are slightly off.

Thus, some instruments (e.g. Piano) are tuned to be in C, and the other keys sound different played on that instrument, because the ratios are slightly different. Other instruments are in B flat (e.g. Trumpet) and the combination of them with C-tuned instruments sounds interesting. Indeed, stringed instruments are tuned to N different keys where N = number of strings!

The mathematics of music is so cool, I found the dismissive tone in the article to be quite unnecessary and irritating.

EDIT: thanks to replies informing me that I'm wrong about instrument tuning. This means I've been tuning my guitars wrong all these years!

REEDIT: but perhaps I'm right about old-school music with a key in the name? Since instruments would have been tuned with a tuning fork and then harmonics pre-20th century according to one reply.

Instruments haven't been tuned to a particular key in a very long time. Pretty much all instruments are built with equal temperament, meaning the pitches are a compromise between what would be otherwise be perfect ratios in different keys.

When an instrument is said to be in B-flat (or any other key), this only means that written music is notated in an alternate key so that it is likely to fit on the treble or bass clef without too many ledger lines. It has nothing to do with ratios between pitches or sounding better/worse in that key.

Is that true? I thought most instruments (or at least most pianos) these days were tuned to be equal tempered, so each scale would sound the same (modulo a pitch scaling).

Pianos actually often even employ a form of stretch tuning ( https://en.wikipedia.org/wiki/Stretched_tuning ) - which gets even more complex, as the OP only refers to sinus tones, which don't have any melodic overtones. Things get even more fun with this.

Otherwise, you're right. Historic tunings often tried to optimize for a certain base scale (often times C major), while leaving behind a really bad sounding tuning at the other side of the circle of fifths ( https://en.wikipedia.org/wiki/Wolf_interval ).

Modern pianos are usually equal tempered, which is the strategy of leaving every scale equally bad off - but on the other hand being able to play in all keys without sounding too bad (The famous "well-tempered piano" is referring to this historic change in tuning strategies with small pieces written in all different kinds of keys, all of which would have sounded weird before).

The more I learned about tuning, the more complex, beautiful and sad this topic became for me: http://blogs.scientificamerican.com/roots-of-unity/the-sadde...

It's fascinating and even a little philosophical that we can get so close to perfection with the 12 step tuning - but never, ever completely attain it.

By the way - That's part of the reason why choirs and orchestras often sound so good: As most other non-fixed-string instruments are able to do a slight adjustment in pitch, they can actually play perfect intervals in any chord, dynamically adjusting to any scale.

You're correct. Most instruments that lack real time tuning capabilities use equal temperament tuning, which is a 20th century development.

Wind instruments are necessarily tuned to a specific key, due to the nature of the harmonic series. But most talented wind instrumentalists are capable of modifying pitch to be in tune in any key or chord.

Down the rabbit hole, read on at your own peril:

Even string instruments are tuned to a key, to a certain extent, due to the use of harmonics. It is possible to fine tune the pitch of a harmonic by shortening the string as usual, but it is exceedingly difficult, since shortening the string changes the position of the nodes (the spots on the string that must be touched in order to produce harmonics).

That's the ideal, given infinitely long and infinitely bendable strings. Reality is that a tuner works from a certain key and tunes in equal temperament the other keys. Since the piano and the tuning is a compromise and there is limited time, the piano will always sound slightly better in one key than another. As most people play in keys close to the C major scale, this usually gets most attention.

Also, pianos rely on resonation. I would not be surprised that the sound board and resonant cavity is designed to favour certain tones. I'm not certain about this though.

I think the "dismissive" tone is entirely sarcastic, and really helps to de-emphasize the very intimidating complexity of music theory. I've always been curious about music theory, but have really failed to get anywhere close to learning it because of how formidable the field is. This article made that complexity feel a little less untouchable for someone who was not trained in music, and the sarcastically "dismissive" tone helped a lot.

Check out:

http://www.truetemperament.com/

I can't say I understand any of this, but it's fascinating.

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