Barbelith Underground > Radio & Music > Stupid Music Questions

The notes are intervals in a scale between one A and the next one (at twice the frequency), right?
So how do those intervals work? Are they evenly spaced?

Well, yes and no: no, they're not evenly spaced in the sense that you get a new note every (say) 55 Hz—because, remember, the "distance" between octaves keeps rising as you go up to higher pitch. It's an algorithm. Or a logarithm. Whatever. It's not a specific number, but a ratio.

This means that you can fit the twelve notes of the chromatic scale (black and white keys on a piano) into the 440 Hz range between between A-above-middle-C (440 Hz) and the A above that (880 Hz). But there are also twelve notes between A=440 and the A below middle C (=220Hz), even though the "distance" between the two notes is only 220 Hz. Same is true for the octave between A=220 and low A=110, and for the octave down to the lowest note on an 88-key piano, the gut-rumbling A=55.

*Very Stupid Question Alert* Could you add more notes?

Absolutely. The 12-note scale is a fairly recent Western invention. Many other cultures use microtones—notes that fall between the keys on a piano. Avant-garde composer Harry Partch devised a 33-note scale, which he played by re-tuning a cheap Sears-Roebuck parlor organ. And when you're dealing with fretless stringed instruments, all bets are off. Theoretically, every single-cycle difference between pitches is a different note.

If I set the top string of a guitar to an arbitrary tension, then tune the other strings to that one, will one of those strings make a recognisable 'A' sound?

Not quite sure what you mean here. Although "A" is usually a pretty absolute concept, it's relative in this particular context.

Standard tuning for a guitar's six strings is (low to high) E-A-D-G-B-E. Let's say I tune my guitar's lowest string to C#, and then retune all the other strings to that one. What that means is that the ratios between the strings stay the same, but the starting point is different. In other words, I tune as if that C# were an E.

So my second string, which would ordinarily be tuned to A, is tuned to F#. The ratio between C# and F# is the same as that between E and A—the ratio between "Do" and "Fa." But I might still call that second string, the F#, my "A string"—because that's what it is in standard tuning, and that's how I think of it.

Similarly, when a guitarist talks about a particular chord—"A major," for instance—s/he's usually thinking less about the actual absolute pitches s/he's producing than about the form that s/he's making with hir hands—what strings s/he's pressing down at what frets. The chord that sounds when I press down my third, fourth and fifth strings at the second fret will be an A major when my guitar is in standard E-A-D-G-B-E tuning at A=440: If I'm tuned to C#-F#-B-E-G#-C#, as in the example above, then that same chord will sound as an F# major—but I'll still of the shape my hand is making as "A major."

Musicians can identify the sound of an A, say, in isolation can't they?

Some can—that facility is called "perfect pitch"—but true perfect pitch is pretty rare. But you can get pretty close just by listening and memorizing. If you listen over and over to that A above middle C, then you can memorize the sound of 440 Hz, and when you hear a note you can compare it to the "baseline" A in your head.

I don't really understand how notes can have characteristic sounds if everything is so relative.

Frequencies don't change. 440 Hz is always going to be 440 Hz. But most music is primarily about the relationship between the notes—the simultaneous notes that make up a chord, the sequential notes that make up a melody. It's not terribly important to start from one particular place—as long as you all start from the same place.