The Mathematical Side of Music Theory: Circle of Fifths

This is part of the information I wrote in my report. The music used is Chopin's Prelude "Raindrop"

Category:

Music

Tags:

• Mathematical
• Side
• Music
• Theory
• Circle
• Fifths

[spocksmusic]

I'm not sure this explains the circle of fifths any better than the traditional use of tetrachords or counting scale steps - however a different way of looking at music is always appreciated.

Also, you state that there are only 12 keys but there are in fact 15: one neutral key, 7 flat keys and 7 sharp keys. Visually, on a keyboard, you can think of enharmonic keys as one but on paper (and on certain instruments) there is a difference.

[308813062]

@spocksmusic of course, if you count enharmonic key signatures as independent keys, you can have as many as you want - infinitely many, including keys with double sharps and flats. however, since they are equivalent to the standard 12, you don't need to count them as different keys. in fact, on the circle of fifths, there are 13 different key signatures shown (6 and -6 accidentals are the same key and if you show only one of them, it becomes asymmetrical).

[308813062]

@spocksmusic plus, I have to be honest, I myself don't get the thing about enharmonic notes being off by a fraction of a semitone. We define our key system by dividing the octave into 12 equal steps, and an accidental is defined as altering the pitch by such a step. Hence, I don't see how there could be any imprecision in the pitch. If we don't use 12 tone equal temperament, the whole geometry of the circle of fifths and such collapses

[ambrosiathe1]

I need visuals to accompany these fascinating concepts

[ambrosiathe1]

Oops I meant @zoroastra999

[ambrosiathe1]

Agreed@zorastria!

[zoroastra999]

Whilst we must appreciate the effort made to put this video together - and the quality of the explanation, I think it would be better as a straightforward written post somewhere. I think the animated text is nothing more than a distraction from an otherwise good piece of writing.

[alachabre]

@308813062 Thank you for that excellent explanation, I see I have much more study ahead!

[308813062]

@308813062 if, for example, you decide to write all notes as accidentals, then you can almost always avoid using notes like E# or Ebb. However, if you want to write a piece in, say, F# major, you would have no choice but to use E# instead of F, for that's the diatonic function of the note in the given musical context. There are no simpler alternatives to correctly notate these distant keys.

[308813062]

@alachabre no keys are "artificial", but there are theoretical keys - ones which have double accidentals. keys with 7 accidentals are not theoretical, but they're not great for practical uses either, as they are too hard to sightread and have simpler enharmonic equivalents with 5 accidentals of the opposite kind. But the keys with 6 sharps and 6 flats are a really special case - no matter which notation you use (sharps or flats), they both have 6, and the last one is enharmonic to a natural note