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That explains why the circle of fifths is a circle that goes through all keys, but the really interesting thing about the circle of fifths is that a fifth sound
by ktRolster 10y ago
That explains why the circle of fifths is a circle that goes through all keys, but the really interesting thing about the circle of fifths is that a fifth sounds relatively close to the key next to it, and it doesn't really explain that, I guess.
- djaychela 10y agoAny key a fifth away only changes one note - if you go from C Major (CDEFGABC) to G Major (GABCDEF#G) then only the F# has changed, and as a result there are chords which are common between the two keys - any chord without an F in it in C will be common to G as well. Works the other way if you go 'down' a fifth (to F), but has a flat instead. (Bb)
- ngneer 10y agoMore specifically, going up a fifth augments the fourth by a semitone to become the seventh and going down a fifth diminishes the seventh by a semitone to become the fourth. In your example, F the fourth became F# the seventh and B the seventh became Bb the fourth. A fifth away _IS_ a semitone away. Defining the following eight functions: SEMITONE = +1 mod 12; ANTI_SEMITONE = SEVENTH; FOURTH = +5 mod 12; ANTI_FOURTH = FIFTH; FIFTH = +7 mod 12; ANTI_FIFTH = FOURTH; SEVENTH = +11 mod 12; ANTI_SEVENTH = SEMITONE; We ask ourselves why the following holds: FOURTH(X) = ANTI_SEMITONE(SEVENTH(FIFTH(X))) SEVENTH(X) = SEMITONE(FOURTH(ANTI_FIFTH(X))) Substituting, the answer is clear: X + 5 = X + 7 + 11 - 1 X + 11 = X - 7 + 5 + 1 Keys one fifth apart differ by one note because: 1 = 11 + 7 - 5 mod 12 Algebraically it seems to work out...