The Mathematical Side of Music Theory: Circle of Fifths

[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.

[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

[alachabre]

Could you help me with what appears to be an inconsistency in your presentation? I am not a music theorist, I only study music with an eye to improving my hobby of guitar playing. Your grasp of English is impressive, and I hope I can present this question well. The subject is modern Western even-tempered scales, and, as you state, there are seven primary and five secondary notes in each octave. However, you go on to list seven sharps and seven flats as you go up and down the circle of fifths.

[alachabre]

@alachabre I believe you should represent the progression up and down as including only five sharps and five flats, as the notes C and F have no flat, and B and E have no sharp. There is, as with any rule, an exception to this, and that is the somewhat artificial key of F#/Gb, where there is E# (in F# key) and Cb (in Gb key). I hope this makes sense, and if I am wrong, I appreciate your correction. I like your choice of music.

[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

[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 oh, that's because the last two sharps and flats that appear in the key signature are enharmonically equivalent to natural notes: E# = F, B# = C, Cb = B, and Fb = E. I meant that, in the standard model of a diatonic scale (which requires no accidentals, setting aside the raised leading note in harmonic minor scales and such), there are 5 notes that HAVE TO to be spelled as raised or lowered degrees of the scale, depending on their function in the particular musical context.

[alachabre]

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

[buildsbest]

THANK YOU FOR THIS EXCELLENT VIDEO. I'M HUNGRY FOR MORE....

[308813062]

@buildsbest thanks

[Bogdan036]

привет

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[308813062]

@Bogdan036 щас я уже не работаю. да я и не работал, просто задавал вопросы и отвечал. пойди на сtpаницу /partners

[ipadharmony]

GREAT shall forward to my Programmers

[aldriagen01]

tnx for it..

[308813062]

no problem

[jhuneo5]

tnX!

[mergatroidal]

Though I'm not familiar with the vocabulary (I'm not schooled in music) your presentation is "over my head." I've learned that the biological brain is wired with a mathematical bias, and this bias is why birds tweet melodies, and humans can appreciate aesthetically the melody and harmony of sounds.

I envision the first (computer) systems mimicking biological cognition employing some type of a mathematical framework. It will use this framework for learning, and appreciating the world. Math, yes.

[308813062]

feel free to ask me about any vocabulary that was difficult to understand. I'll explain it