Fruit Loop Discussions - the Circle of 5ths

[fearfaoin]

After ruminating on it for 2 years my main thought is: "Hm".
It reminds me of the lesson a fiddle teacher gave me once
that laid out the circle more linearly by constructing each
major scale starting with the 5th note of each previous
scale and copying the notes, looping back to the beginning
and sharping the 7th note each time.

Code: Select all

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

No we start having too many sharps. We have to switch over to
flats. F# is the same as Gb:

Code: Select all

Gb Ab Bb Cb Db Eb F
            Db Eb F Gb Ab Bb C
                       Ab Bb C  Db Eb F  G
                                   Eb F  G  Ab Bb C  D
                                               Bb C  D  Eb F  G  A
                                                           F  G  A  Bb C  D  E
                                                                       C  D  E  F  G  A  B

And we're back! Now, take the first note of each in order and you
have constructed the circle of fifths.



This method is also going up 7 semitones each time, but it started
with the Major and stayed there. I wonder what other patterns are
there starting with different modes.

[I.D.10-t]

Code: Select all

Gb Ab Bb Cb Db Eb F
            Db Eb F Gb Ab Bb C
                       Ab Bb C  Db Eb F  G
                                   Eb F  G  Ab Bb C  D
                                               Bb C  D  Eb F  G  A
                                                           F  G  A  Bb C  D  E
                                                                            C  D  E  F  G  A  B
                                                                                        G  A  B  C  D  E  F#
                                                                                                    D  E  F# G  A  B  C#
                                                                                                                A  B  C# D  E  F# G#
                                                                                                                            E  F# G# A  B  C# D#
                                                                                                                                        B  C# D# E  F# G# A#
                                                                                                                                                    F# G# A# B  C# D# E#

This is the first time that I have seen this in a way that is intuitive to me, thank you. Start with Gb and only F Nat, rotate five notes and sharpen the end. Anything on the minors? Minors, someone, please think of the minors!

[Bloomfield]

F# is the same as Gb:

Is it though?

[fearfaoin]

This is the first time that I have seen this in a way that is intuitive to me, thank you.

It was the same for me.

Anything on the minors? Minors, someone, please think of the minors!

Let's find out.

Code: Select all

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

etc.

Looks like with the minors, you have sharpen the second
note each time (which is the seventh of each relative major).

[fearfaoin]

F# is the same as Gb:

Is it though?

I don't know, you tell me.
As far as the circle is concerned, it seems to be.
Certainly easier to switch from all sharps to all flats
than to go around the circle backwards for the other
half.

[Denny]

F# is the same as Gb:

Is it though?

on a piano

[Bloomfield]

F# is the same as Gb:

Is it though?

I don't know, you tell me.
As far as the circle is concerned, it seems to be.
Certainly easier to switch from all sharps to all flats
than to go around the circle backwards for the other
half.

Denny is right, on a piano F# = Gb. But some pretty significant tuning compromises are required to make these notes be enharmonic equivalents; for example, on a piano thirds sound dissonant, but naturally thirds are consonant. Listen to the pipes (or a good fiddler) to hear a true third.

[fearfaoin]

Denny is right, on a piano F# = Gb. But some pretty significant tuning compromises are required to make these notes be enharmonic equivalents; for example, on a piano thirds sound dissonant, but naturally thirds are consonant. Listen to the pipes (or a good fiddler) to hear a true third.

I wasn't saying "F# is the same note as Gb".
I was saying "F# occupies the same slot on the
circle as Gb". i.e., they are overlapping major
scales.

[Bloomfield]

Denny is right, on a piano F# = Gb. But some pretty significant tuning compromises are required to make these notes be enharmonic equivalents; for example, on a piano thirds sound dissonant, but naturally thirds are consonant. Listen to the pipes (or a good fiddler) to hear a true third.

I wasn't saying "F# is the same note as Gb".
I was saying "F# occupies the same slot on the
circle as Gb". i.e., they are overlapping major
scales.

Point is, the circle isn't a circle unless you make F#=Gb, as in the same note.

[talasiga]

The artifice of equal temperament allows the artifice of the circle of 5ths.
These are not absolute truths but mere conveniences.
Every area of human endeavour needs within it a dunnie or two.

[fearfaoin]

Point is, the circle isn't a circle unless you make F#=Gb, as in the same note.

The artifice of equal temperament allows the artifice of the circle of 5ths.
These are not absolute truths but mere conveniences.
Every area of human endeavour needs within it a dunnie or two.

Well, that is a good point, chaps. It's like you have
to take a Mulligan to make it a circle. I guess there's
always the spiral version, which doesn't overlap.

[anniemcu]

Not the same, but related... Reminds me of how/why I made the Whistler's Little Circle of 5ths... http://www.angelfire.com/mo/sassafrassg ... ctions.pdf (The link is to the prototype version, not the final one)

And Fear, that spiral is one beautiful (in more ways than one) illustration!

[fearfaoin]

And Fear, that spiral is one beautiful (in more ways than one) illustration!

I was rather taken with it myself. Sometimes
wikipedia research can turn up unexpected things.