Guitar 4 Flashcards
You may have heard of “sharps” and “flats.” Where do they come from? The scale of tones shown above is “in the key of C” because the fractions were applied with C as the starting note. If we were to start the fractions at D, with a frequency of
297, then we would be “tuned to the key of D” and the frequencies would look like this:
297 Hz, D, do (multiply by 9/8 to get:)
334.1 Hz, E, re (multiply by 10/9 to get:)
371.3 Hz, F, mi (multiply by 16/15 to get:)
396 Hz, G, fa (multiply by 9/8 to get:)
445.5 Hz, A, so (multiply by 10/9 to get:)
495 Hz, B, la (multiply by 9/8 to get:)
556.9 Hz, C, ti (multiply by 16/15 to get:)
594 Hz, D, do (multiply by 9/8 to get:)
And the sequence repeats.
The notes at 297 Hz (D), 396 Hz (G) and 495 Hz (B) in the key of D match the same notes in the key of C exactly.
The E note in the key of D (at 334.1 Hz) is pretty close to the E note in the key of C (330 Hz). The same applies for the A note.
F and C, however, are distinct in the two keys. F and C in the key of D are therefore referred to as F# (F sharp) and C# (C sharp) in the key of C. (Note that F sharp is also known as G flat, and C sharp is also known as D flat.)
If you apply the fractions to several different keys, merge together all the identical and pretty-close notes and then look at the unique sharps that fall out, you realize that you need A#, C#, D#, F# and G# to handle all the keys.
You can see that, with all of these mergings of keys, the major scale can leave you with some pretty arbitrary decisions to make when you tune an instrument.
For example, you can tune the major notes to the key of C, and then the sharps for F and C to the key of D, and the sharps for D and G to… It can get pretty messy.
Over time, most of the musical world came to agree on a scale called
the tempered scale, with the A note set at 440 Hz and all of the other notes tuned off of that.
In the tempered scale, all of the notes are offset by
the 12th root of 2 (roughly 1.0595) instead of the fractions we saw above. That is, if you take any note’s frequency and multiply it by 1.0595, you get the frequency for the next note.
