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EDIT: CLARIFIED THE QUESTION

Is the circle of fifths also listing the relative dissonance/consonance of notes in a major scale? and not just a list of key signatures?

Consider the solfege ... a method of naming pitches where you can name the notes with their respective 'voice' instead of their letter name... for example the notes of a C major scale such as C-D-E-F-G-A-B-C can be respectively named do-re-mi-fa-so-la-ti-do.

C--D--E--F--G--A--B--C do-re-mi-fa-so-la-ti-do

But notice that the names for C and G are do and so, which rhyme.

This would seem to indicate that G actually sounds closer to C than any other of those major scale notes.

That is, the interval of C to G, a fifth, would be the least dissonant (most consonant).

This would also seem to be the reason keys are built on fifths - because if you're describing some system of values one would want to describe incrementally.

In other words if you wanted to give me a list of all digits you'd give me 0,1,2,3 etc. to show me how the system increments instead of some random list such as 4,9,6,1 etc. If you wanted to show me a collection of all possible colors you'd show me a rainbow spectrum color wheel kind of a picture instead of a picture of random color swatches.

And this is what Leonard Bernstein seems to be implying in this video ... see 3:00 minutes in where he reinforces the importance of the tonic-dominant relationship (I to V).

So all that said doesn't it follow that if C to G is the least dissonant interval that the following, least dissonant interval, would be a fifth of the fifth? ... C to D ... just as keys are built ... and so on?

C - G (C to G is least dissonant)

C - G - D

C - G - D - A

C - G - D - A - E

C - G - D - A - E - B (C to B is most dissonant)

After the B must come F# because, as you might see, every two notes (two fifths) the letter name increases by a whole interval.

C - G ... one fifth C - G - D ... two fifths ... C changes to D

... and two fifths up from D you get E.

C - G - D - A

C - G - D - A - E

That means two fifths up from E you get F# - not F (a half-step).

C - G - D - A - E - B - F#

And this must mean that F belongs on the other side, down a fifth from C.

F - C - G - D - A - E - B

... and this should be a list of dissonance and consonance ... ... *within the tonal system called 'equal temperament' where the musical building block is a half-step ... WWHWWWWH for a major scale ... each W whole is two H halves.

If we number the notes in the key of C from 1 to 7 ...

1-2-3-4-5-6-7

C-D-E-F-G-A-B

... then ...

F - C - G - D - A - E - B

... becomes ...

F - C - G - D - A - E - B

4 - 1 - 5 - 2 - 6 - 3 - 7

If you built the base chords (three notes, every other note) for each of these tones you'd get:

F ... F-A-C ... F to A is WW, A to C is WH ... recipe for Major chord, F Major

C ... C-E-G ... recipe for C Major chord

G ... G-B-D ... recipe for G Major chord

D ... D-F-A ... D to F is WH, F to A is WW ... recipe for minor chord, Dminor

A ... A-C-E ... recipe for A minor chord

E ... E-G-B ... recipe for E minor chord

B ... B-D-F ... B to D is HH, D to F is HH ... recipe for diminished chord, B° (B diminished ... diminished being 'reduced').

So now you can see the first three chords are major, the next three are minor and the last is diminished ... building chords from the fifths also establishes the dissonance of the chords ... harmony.

The first three are major chords ... the 4-1-5 ... the three most common chords of pop-music, the most commercial and most consonant.

The second three are 1-5-2 ... the three most common chords of jazz-music ... a little less consonant, a little more abstract and less commercial appeal.

So, to conclude, is it fair to say the circle of fifths is really also listing the relative dissonance/consonance of the notes of a major scale?

EDIT: ADDENDUM

What I'm claiming is that the interval C to G, a fifth, is the most consonant (least dissonant). Therefore another fifth would denote the note that is the next most consonant.

C-G Most consonant (least dissonant) (a fifth)(5)

C-(G)-D next most consonant ... After C to G, C to D is the most consonant ... the second note (2).

The third most consonant interval would be a fifth up from D, etc.

The result is 4-1-5-2-6-3-7 ... more consonant to the left and more dissonant to the right. Relative to the 1 the 5 is less consonant. Relative to the 1 the D is the next, less, consonant.

If the key was G, G would then be the 1, the D would be the next most consonant, then the A.

And as I noted above you can see the three most consonant chords to the I (the C chord, major, built from the "1" note) are I, IV, V.

The very next set of three digit is 1,2,5 which become the I-II-V chord ... which I'm told by thousands of videos on YouTube, is the core progression of Jazz (and would be more dissonant than the I,IV,V as it's

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    Nope, the thinking is flawed here. I would recommend picking up a theory book instead of trying to "logic" your way through it. Also, the question is a bit unclear (we don't need to be "taught" music theory here). – jjmusicnotes Aug 5 at 14:35
  • Comments are not for extended discussion; this conversation has been moved to chat. – Dom Aug 5 at 22:01
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(Original title:)

Is the circle of fifths also a circle of consonance/dissonance?

What the circle of fifths is is the sequence of pitches you get, going up by perfect fifths. That's all. It also has certain properties, such as how the key signature of each successive pitch gets one more sharp or one fewer flat; composers exploit this to modulate to a "nearby" key.

What a circle of consonance might be hasn't been defined well enough, here or by anyone else, to answer the question with a yes or a no. (Consonant intervals? Consonant chords? Sequences or rankings of either? How dissonance resolves to consonance?) Sure, the perfect fifth is consonant, and if you stack enough of them they become dissonant, but that result isn't deep enough to build a harmonic theory on.

Edit: (Revised title:)

Does the circle of fifths rank the consonance of notes of a major scale?

Not really. Functionally, dissonant means "needs to be resolved to something consonant." In C major, you don't need to resolve the interval C-E to C-A (and then further to C-D and finally to C-G).

  • I clarified the question ... I think my list is showing the relative consonance of the notes of diatonic intervals to the tonic. (But I also admit C-E sounds 'nicer' than C-D. Does Dm to Cmaj have a stronger resolution than Am to Cmaj? – Randy Zeitman Aug 5 at 20:46
  • Yes, you are correct ... as is Rosie, and I posted the answer to be "no". – Randy Zeitman Aug 6 at 19:45
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The circle of fifths certainly gives one way of quantifying the distance between two pitches in a way which means that pitches that make the very consonant interval of a perfect fifth or fourth come out as neighbours. This is fine as far as it goes, but unfortunately that's about as far as it goes. Go two steps C-G-D and you get the interval of a major 2nd, C-D. Which is quite a lot more dissonant.

Where are all the other intervals which are more consonant than a 2nd? The major 3rd and minor 3rd? They are (respectively) 4 and 3 steps away. But they are more consonant than those larger distances would suggest, and the reason is that there's another important reason why pitches can sound consonant together, and just counting steps along the circle of fifths ignores that possibility. This answer goes into some of the theory. In brief: pitches sound consonant together if their frequencies have the same ratio as two small integers; for the perfect 5th, that is 3:2; thus stacking 5ths can only give you a ratio between a power of 3 and a power of 2. This means that your 3-step major 6th (C-G-D-A) is 27:16 and your 4-step major 3rd (C-G-D-A-E) is 81:64. But 3rds and 6ths sound much nicer if a 5:4 major 3rd is used. Now that we're using a factor of 5 in our ratios, we're setting up relationships between pitches for which a line is not adequate: we need something 2-dimensional. Hence the "pitch net" or Tonnetz, to use the German word.

tldr: No because 5ths are not the whole story; you need 3rds too.

  • The four-step interval is only 81:64 if the fifth is 3:2. But if your fifths are 3:2, you don't actually have a circle of fifths but a spiral. If you choose a ratio for four consecutive fifths of 1.49535:1 then the resulting major third will be pretty close to 5:4. – phoog Aug 5 at 16:55
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    @phoog YES! I see that too! It's really only a circle because of equal temperament tuning. In 'Just' tuning it's a spiral. I made this image about a year ago when I was first thinking about this circle stuff. myeasywebaddress.com/Stage/spiral.jpg – Randy Zeitman Aug 5 at 20:27
  • @Rosie Thank you. Your statement has helped clarified what I'm asking... which is... does the circle of fifths show consonance of notes in a major scale relative to the tonic. (As it also would for relative minor scales.) – Randy Zeitman Aug 5 at 20:33
  • @Rosie "Now that we're using a factor of 5 in our ratios, we're setting up relationships between pitches for which a line is not adequate: we need something 2-dimensional." (Why. What is special about a factor of five and 2-dimensional?) – Randy Zeitman Aug 5 at 20:48
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    @RandyZeitman actually, any 12-tone temperament closes the circle of fifths, not only equal temperament. To close the circle of fifths, you must reduce the size of all of the fifths by an average of approximately 1.955 cents (1/12 of the Pythagorean comma). Equal temperament reduces the size of each fifth by the average, but other temperaments reduce some by more than that, while others are reduced less or even increased in size. – phoog Aug 5 at 21:47

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