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by pge 5573 days ago
One of the music theory things it took me a while to understand is why different major keys matter. In an idealized world, one can start a scale on any frequency and move up in whole and half steps (WWHWWWH) and have a scale. So why talk about the "key of G" vs the "key of C" if all that denotes is the frequency of the note we start on (which can be shifted up or down arbitrarily to suit the range of the instrument or vocalist)? The answer lies the physics of frequencies. The notes are not exactly the same from key to key because the whole and half steps are not exactly the same width. A perfect "fifth" (e.g., C & G played together) from a frequency perspective (meaning the two frequencies that resonate together creating a harmonic one octave above the lower) has a frequency ratio of 3/2 meaning the G is 1.5x the frequency of the C. The octave has a ratio of 2 (the high C is twice the frequency of the C below it). G is 7 half steps above C and the octave is 12 half steps. So if we walk our way up the piano in fifths, after 84 half steps, we would have a note (3/2)^12 = 129.75x the original frequency. But if we do the same on the octaves, we get 2^7 = 128x the original frequency, so the note we need to make all the major fifths sound right is different from the note we need to make the octaves sound right. The two are diverging slightly. So the result is that we can tune an instrument perfectly in one key only or we can tune it in a compromise of all the keys which sounds okay over a short range but sounds worse as we try to cover a wider range. If you're interested, there's lots of good reading on the subject (google "well-tempered" or "meantone").

EDIT: I realized I assumed a key concept in there. When two notes are played together, a third is heard (the "beat" frequency). If f1 and f2 are the frequencies of the notes being played, f2 - f1 = the beat freq. An octave sounds nice because the beat disappears (2f - f = f, so the beat is the same as the lower note of the octave). Other "pleasant" chord combinations are ones in which the beat does not clash with the first two note (e.g., is an octave of one of the notes).

3 comments

Almost every instrument nowdays is tuned in equal temperament. Tuning matters most for old keyboard music, as in, pre-Beethoven.

The reason keys are important is because many instruments have different sound qualities for different notes. Keys close to E minor or G major allow guitarists to get that "twangy" open string sound. You can get a richer sound tuning up, or a thinner "heavy metal" sound tuning down. Keys close to B-flat allow brass players to use more basic tones on their instruments. All singers have certain sound qualities that are only available on certain notes. "Every Breath You Take", for example, would sound different even a semitone off, because Sting's transition from his creepy baritone to his high-pitched whine happens at a very specific part of his range, and the creepy quality of his voice contrasted with the high-pitched pleas for love is one of the most important qualities of the song.

But, yeah, temperament nowdays is almost irrelevant.

If you're really interested in this, I highly recommend checking out the book How Equal Temperament Ruined Harmony (and Why You Should Care) by Ross Duffin.
You'll find that listening to music in a single key for extended periods of time can become extremely tiring. Most (not all people) need fresh tonality, or they get bored. (Obviously all of this depends on what kind/style of music you are listening to, etc., but I would wager that even if you switched from "classical" music to "pop" music and stayed in the same key, most people would find it aurally tiring).