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#1297408 - 10/31/09 08:00 PM cycle of fourths
Overexposed Offline
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I have started taking jazz piano lessons and my teacher has me practicing chords using the cycle of fourths: C, F, Bb,Eb etc. It ends back with C. I've noticed there are no sharp chords. And as I look through a fake book "The Real Book" I see that they use no sharp keys either. Is it just understood that Gb is the same as F# (that each sharp chord is just an extra name for a flat chord)? I could also ask my teacher at next lesson, but I found it interesting so I thought I'd post about it.

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#1297420 - 10/31/09 08:16 PM Re: cycle of fourths [Re: Overexposed]
John v.d.Brook Online   content
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Ann, these are called enharmonic notes/chords. They are not really the same, but on a piano, they are. The chord progression, whether you go clockwise or counter-clockwise around the circle of fifths, gets you exactly the same keys/chords.

If you think about it for a minute, it has to work out this way. There are seven white keys only five black keys. Working through the circle of fifths clockwise takes you from C to G to D to A to E to B. That's 6 of the 12 possible tones. Going counter-clockwise, you begin on C, then to F, and from then on, you must use black keys, as there are no white keys left, and as you are flatting the 4th tone on each new iteration, you're adding flats to the key signature.

Most classical music uses C# and F# rather than Db and Gb out of convention more than pure logic.

John
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#1297588 - 11/01/09 07:23 AM Re: cycle of fourths [Re: John v.d.Brook]
Kreisler Offline


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Jazz tends to focus on flat keys because of the instruments used. Alto saxophone is an Eb instrument, and trumpets and bari saxes are Bb instruments.

On an alto saxophone, playing in the key of Eb means no sharps or flats, while playing in the key of D would mean 5 sharps!
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#1297592 - 11/01/09 07:36 AM Re: cycle of fourths [Re: John v.d.Brook]
Jim Frazee Offline
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Ann,

What you are referring to is called a "chord of the fourth", not a cycle of fourths. This is a sound character which is built on adding intervals of perfect fourths, usually three or more, on any key.

The Real Book uses mostly "flat" key signatures because that's what horn players (trumpets, saxes) find easier to read and improvise on (because that's how their instruments are built and name their concert pitches, a Bflat trumpet or an Eflat alto, for example).
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#1297596 - 11/01/09 07:51 AM Re: cycle of fourths [Re: Jim Frazee]
keystring Online   content
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Jim, when you say "sound character built on adding intervals of P4" do you mean one chord is built on fourths such as a chord that would go CFBb or CFBbEb (quartal chords)? Or do you mean a progression along intervals of perfect fourths?


Edited by keystring (11/01/09 08:09 AM)
Edit Reason: added "quartal chord"

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#1297605 - 11/01/09 08:29 AM Re: cycle of fourths [Re: keystring]
Jim Frazee Offline
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No, it's a chord consisting entirely of perfect fourths. Used in both classical and jazz writing and very useful in modal writing. Just play one and you'll recognize it immediately.
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#1297619 - 11/01/09 09:15 AM Re: cycle of fourths [Re: Jim Frazee]
keystring Online   content
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Thanks. I learned to call this "quartal chord" when I did rudiments and that might be the stuffy crowd's name for it. I have a feeling that Ann was dealing with chord progressions (ordinary triads) the way one does in the circle of fifths for sharps, but backward in fourths along the wheel so that one adds one flat at a time: doesn't jazz tend to use the wheel that way?

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#1297626 - 11/01/09 09:24 AM Re: cycle of fourths [Re: keystring]
Overexposed Offline
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Yes, I've been doing chord progressions, practicing major chords, then minor chords and now adding 7 chords. Yes, I see how whether you move in 4ths or 5ths you still end up covering all 12 tones. The idea is to move from chord to chord in tempo...not having to stop and think about it.

The explanation about jazz using flat keys because of the instruments used makes sense.

But, John, I don't see how enharmonic chords are different. You mentioned they are the same on piano. How are they different? Is it just another way of saying the same thing?

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#1297636 - 11/01/09 09:39 AM Re: cycle of fourths [Re: Jim Frazee]
jazzwee Offline
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Originally Posted By: Jim Frazee
No, it's a chord consisting entirely of perfect fourths. Used in both classical and jazz writing and very useful in modal writing. Just play one and you'll recognize it immediately.


Jim, Ann is of course talking about the true Circle of Fifths which is the same thing as the Circle of fourths, just opposite directions. I saw nothing in her post that implied any discussion of Quartals, nor would it make sense.
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#1297639 - 11/01/09 09:51 AM Re: cycle of fourths [Re: jazzwee]
Studio Joe Offline
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Originally Posted By: jazzwee
Jim, Ann is of course talking about the true Circle of Fifths which is the same thing as the Circle of fourths, just opposite directions. I saw nothing in her post that implied any discussion of Quartals, nor would it make sense.



That's the way I read it too Jazzwee. Her teacher has her learning new keys and key signatuers by adding one flat at a time, which follows the circle counter clockwise.
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#1297703 - 11/01/09 12:38 PM Re: cycle of fourths [Re: Overexposed]
John v.d.Brook Online   content
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Ann, string instruments are tuned in perfect fifths, the piano is not. If you were to go up a perfect fifth from the G string until reaching G again, you wouldn't be playing G, but a much sharper tone (I think, my memory is foggy on this). Even if you tuned a violin to the piano's G pitch, the E string would be "out of tune" relative to the piano.

I prefaced this to explain that perfect intervals do not exist on the piano, we're always slightly out of tune. The piano is tuned, not exactly, but closely, to a logarithmic division of the octave into twelve equal intervals. Close enough to be listenable, but not pure. When you work your way around the circle of fifths using pure intervals, you do not arrive at the same point half way as going counter clockwise. The tones are off quite a bit and create a most unpleasant sound.

There are probably some web sites which explain this better and in more detail.
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#1297848 - 11/01/09 05:23 PM Re: cycle of fourths [Re: Studio Joe]
Jim Frazee Offline
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Perhaps I read it incorrectly but when I see a chord built of these notes "C,F,Bflat,Eflat", (assuming they are in ascending order), to quote Ann's original post, I think of Quartals, not a "Circle of Fourths". Had I seen "C, G, D, A" in ascending order or had I seen C, F, Bflat in descending order I would have assumed the Circle of Fifths, as you say. I do beg your pardon. And, for the record, neither Harvard nor Oxford or even Grove refer to a Circle of Fourths. I'm guessing that's not common parlance?
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#1297853 - 11/01/09 05:33 PM Re: cycle of fourths [Re: Jim Frazee]
keystring Online   content
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Jim, The OP says:
Quote:
... has me practicing chords using the cycle of fourths: C, F, Bb, Eb etc. It ends back with C.

The comma between notes, a teacher choosing the word "cycle", and "ending" with C, suggests that it's a series of chords. She doesn't say "build". Besides, Ann has confirmed it. There is an exercise for getting the chords "into your hands" which goes just like that, and the term "circle of fourths" is used.
Chart example - see top label

Ann: Re: enharmonics. Instrumentalists who can adjust pitch do often distinguish between G# and Ab, for example, one being a titch more sharp than the other. Pianos obviously can't do that. Theory books often refer to enharmonics by saying their pitch is the same "when played on the piano", mentioning the piano for that reason.


Edited by keystring (11/01/09 05:34 PM)

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#1297864 - 11/01/09 06:03 PM Re: cycle of fourths [Re: keystring]
Jim Frazee Offline
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Keystring, thanks.
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#1297868 - 11/01/09 06:24 PM Re: cycle of fourths [Re: Jim Frazee]
Overexposed Offline
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Oh, yes this is about "equal temperament"...I had read about it, but now it makes more sense.

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#1297874 - 11/01/09 06:33 PM Re: cycle of fourths [Re: Overexposed]
jazzwee Offline
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Jim, common usage is to refer to 'Circle of Fifths' but I hear it also referred to also as the Circle of Fourths. That's because the interval of going down a 4th is the same interval as going up a 5th. So it's just whether you approach it counterclockwise or clockwise.

But I can understand the confusion if you've never heard it referred like that.

Here in Wiki, they show both references...
http://en.wikipedia.org/wiki/Circle_of_fifths

now "Cycle" is not common usage as far as I know...
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#1297876 - 11/01/09 06:38 PM Re: cycle of fourths [Re: jazzwee]
Overexposed Offline
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No, I'm not moving down a 4th. Start with major chords and move along in this pattern: C, F, Bb, Eb, Ab, Db, Gb, (F#), B, E, A, D, G, C. It's presented as cycle of fourths in a jazz book in addition to my jazz teacher's instruction.

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#1297880 - 11/01/09 06:49 PM Re: cycle of fourths [Re: Overexposed]
jazzwee Offline
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Originally Posted By: Ann in Kentucky
No, I'm not moving down a 4th. Start with major chords and move along in this pattern: C, F, Bb, Eb, Ab, Db, Gb, (F#), B, E, A, D, G, C. It's presented as cycle of fourths in a jazz book in addition to my jazz teacher's instruction.


That's fine Ann. As you can see in Wiki, it's more traditionally referred to as a Circle because of the appearance (regular music theory). I should have said moving left in the circle (not down). In any case, it's all the same stuff and all good. You're on the right track. thumb
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#1297924 - 11/01/09 08:16 PM Re: cycle of fourths [Re: jazzwee]
John v.d.Brook Online   content
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I just going to nitpick here a minute. In the circle of 5th, we go from the tonic to the dominant, which is going up a fifth. In reversing the order, you go down a 5th, to the 4th tone. That's called the sub-dominant, because it's a fifth tone under (down).
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#1298052 - 11/02/09 05:01 AM Re: cycle of fourths [Re: John v.d.Brook]
jazzwee Offline
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With all due respect John, that is not the relationship in the Circle of Fifths. One would think think that if you actually execute the Circle of Fifths in purely ascending or descending order which is not case. You will quickly run out of keyboard and of course be in too wide a register range. In reality it is executed in an alternating pattern on the keyboard (up/down/up/down).

The real relationship in a Circle of Fifths is ii-V-I.

(going counter-clockwise in the circle)
C F Bb
ii V I
Bb Eb Ab
ii V I
Ab Db Gb
ii V I
Gb B E
ii V I
E A D
ii V I
D G C
ii V I
(translate enharmonically as needed)

So it is actually not appropriate to refer to a subdominant relationship.

The reason it is often taught going counter-clockwise is that this is the typical flow in diatonic music.

IV-vii-iii-vi-ii-V-I (extremely common cadence in music) where the intervals are all ii-V's.

Thus although it is called the Circle of Fifths, in application it is the Fourths movement counter-clockwise which is more often used because of its tension-release sequence and that is how it is often taught.


SECOND POINT

The same notes in the circle can be approached UP or DOWN.

F....C...F
G...C....G

So the same chords in the circle have a dual relationship. So where there is a subdominant relationship, there is always a reverse DOMINANT relationship. C to F vs. F to C. This cannot be resolved just by looking at the circle so the relationship has to made clear by chord quality itself.

CMaj7 to FMaj7 is subdominant relationship but
C7 to Fmaj7 is a dominant relationship, yet they appear in the circle the same way. So the circle itself does not define this.

Can of worms you see?
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#1298059 - 11/02/09 05:47 AM Re: cycle of fourths [Re: jazzwee]
keystring Online   content
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Can this be untangled? There may be several languages going here. I thought about this last night.

The simplest thing that was being discussed yesterday was what intervals were involved, without the context of degrees or music (which jazz musicians must keep in their heads at all times, so there is no separation for you guys as I understand it.)

If you go clockwise up the circle of fifths, you go:
from C4 to G4 = P5
from G4 to D5 = P5
etc.

If you go down a fourth you go:
from C4 to G3.
That's where the confusion is occurring. You still have a C and a G like before. But let's compare the C4 - G4 of the first, and C4 - G3 of the 2nd. In the key of C, both of them are the Dominant and Tonic. So functionally they are the same thing.

But in ordinary theory rudiments, divorced from function, the second one, C4 to G3, will be classified as a P4 and not P5 because you always start with the lower note when classifying an interval.

There seem to be two ways of looking at the notes going on.

I'd like to extrapolate from something:
Quote:

The real relationship in a Circle of Fifths is ii-V-I....
... C F Bb
... ii V I
the typical flow in diatonic music. IV-vii-iii-vi-ii-V-I


What I'm seeing is that in jazz, where you are improvising with others, maybe you have that that flow going on in the bass line, and this then governs your chords and the notes that fit inside it. It's in real time. If you get that motion going along fourths, then you will end up with that sequence which will also get you IV-vii-iii-vi-ii-V-I in an automatic way. The result of going along these fourths will create this. And that is why the OP is being given that particular exercise. Would that be so?

But working classically in composition and harmony theory, the thinking and approach is along different lines. It's sort of like fish and monkeys trying to discuss the nature of the environment. The only reason your description made sense to me is that I was hammering out differences with someone a few months ago where I first felt like a space alien. We were both talking music and supposedly about familiar things, yet I couldn't relate to anything. I'm still not there.








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#1298061 - 11/02/09 05:55 AM Re: cycle of fourths [Re: jazzwee]
Studio Joe Offline
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I think the confusion arises from the fact that some are thinking scale degrees, and others are thinking intervals.

When you go counter clockwise, C to F is an interval of a 5th, and yet if you are thinking of C as the tonic, F is the 4th scale degree (ascending) of the C scale.

Jazwee, since we are not in the jazz thread here, I will contest you on your view that "The real relationship in a Circle of Fifths is ii-V-I".

The II doesn't have to be a minor chord in a circle of fifths. In fact, I know some songs that use an extended circle of fifths like (for example) III, VI, II, V, I, all major chords.
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#1298076 - 11/02/09 06:40 AM Re: cycle of fourths [Re: Studio Joe]
keystring Online   content
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Quote:
I think the confusion arises from the fact that some are thinking scale degrees, and others are thinking intervals.

Did we just say the same thing?
--

Can we define "circle of fifths"? I understand it to mean a representation of how key signatures relate to each other in P5's. It happens to include the important Dominant, which is often where modulations happen in classical music, and the sharps or flats increase/decrease sequentially. That's what it shows.

But S.Joe and Jazzwee, you seem to be using "circle of fifths" to refer to something in c music - as though music always travelled along that circle. But at least in classical it does not always do that. The main shape is I-V-I and the in between things can be a number of choices. It seems this is a second meaning to circle of fifths. Is it?



Edited by keystring (11/02/09 06:41 AM)

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#1298119 - 11/02/09 08:35 AM Re: cycle of fourths [Re: keystring]
Studio Joe Offline
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Originally Posted By: keystring
But S.Joe and Jazzwee, you seem to be using "circle of fifths" to refer to something in c music - as though music always travelled along that circle. But at least in classical it does not always do that. The main shape is I-V-I and the in between things can be a number of choices. It seems this is a second meaning to circle of fifths. Is it?


I wasn't saying that music always progresses along a circle of fifths, but that it sometimes does, not through all 12 keys, but a portion of the circle. And this is often referred to by musicians as a circle of fifths.

Academy musician types who who feel it necessary to analylize the functioin of each chord would call the inner chords within the circle secondary dominants. For example, in Roman numeral analasis, II would be labeled as V/V, meaning dominant of the dominant.
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#1298150 - 11/02/09 09:28 AM Re: cycle of fourths [Re: Studio Joe]
jazzwee Offline
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There's two elements here. There's a mathematical relationship to the keys that's demonstrated in the Circle of Fifths. To the left, it's in intervals of fourths. To the right it's in intervals of fifths. I could have ended it at that.

Many teachers use the Circle just as a way to hit all the keys in some order other than chromatic. For that usage, the Circle is quite meaningless other than to demonstrate a mathematical reality.

NOW - when someone starts to imply some other relationship like SUBDOMINANT, then we have to shift to the other function of the Circle of Fifths and that relates to SCALE DEGREES which uses the relationship (counter-clockwise) of IV-vii-iii-vi-ii-V-I (4-7-3-6-2-5-1).

This is actually the DIATONIC relationship in the Circle of Fifths.

So Counter-Clockwise it goes at intervals of ii-V,ii-V,ii-V... (which creates that distinctive pattern ending in 6-2-5-1 - very correct Joe).

Going to the right it it is I-V,I-V,I-V.

All I'm saying is that subdominant is not part of this picture (at least in the Diatonic Scale Degrees explanation).

This is not some Jazz thing. It's just regular music theory. We jazzers just know it well because it is integral to what we do.

(Joe I didn't find anything we disagree on...)






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#1298155 - 11/02/09 09:40 AM Re: cycle of fourths [Re: Studio Joe]
jazzwee Offline
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Originally Posted By: Studio Joe

Jazwee, since we are not in the jazz thread here, I will contest you on your view that "The real relationship in a Circle of Fifths is ii-V-I".

The II doesn't have to be a minor chord in a circle of fifths. In fact, I know some songs that use an extended circle of fifths like (for example) III, VI, II, V, I, all major chords.



Hi Joe, I think we see eye to eye here. The interval is of a ii-V (implied). The actual chords actually, as you know change from ii-V-i (minor) to II-V-I (major). But I'm just pointing out the intervals.
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#1298171 - 11/02/09 10:09 AM Re: cycle of fourths [Re: jazzwee]
Studio Joe Offline
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Originally Posted By: jazzwee
To the left, it's in intervals of fourths.


C DOWN to F is an interval of a fifth. If you play a descending C scale, F will be the 5th note, however in the key of C it still functions as the subdominant because it is the 4th degree of the (ascending) C scale.

The other thing is that when you show Roman numerals you always show ii, iii, and vi in lower case as if they are always minor chords. My contention is that it depends on the context of the music. They are in many cases major chords.
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#1298181 - 11/02/09 10:19 AM Re: cycle of fourths [Re: jazzwee]
John v.d.Brook Online   content
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Originally Posted By: jazzwee
With all due respect John, that is not the relationship in the Circle of Fifths. One would think think that if you actually execute the Circle of Fifths in purely ascending or descending order which is not case.


What? F is down a fifth from C, Bb is down a fifth from F, etc. The circle of fifths works which ever way you go, clockwise or counter-clockwise.

I have my students practice scales going through the circle of fifths clockwise the first day, counter-clockwise the second day, and chromatically the third day, then repeat the cycle.
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#1298206 - 11/02/09 11:05 AM Re: cycle of fourths [Re: Studio Joe]
jazzwee Offline
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Originally Posted By: Studio Joe
Originally Posted By: jazzwee
To the left, it's in intervals of fourths.


C DOWN to F is an interval of a fifth. If you play a descending C scale, F will be the 5th note, however in the key of C it still functions as the subdominant because it is the 4th degree of the (ascending) C scale.

The other thing is that when you show Roman numerals you always show ii, iii, and vi in lower case as if they are always minor chords. My contention is that it depends on the context of the music. They are in many cases major chords.


What quality of chords you use is clearly your choice, but it would not necessarily be the "diatonic" circle of fifths. I move with fourths and fifth intervals all the time, but I'm not in the same key. I'm modulating.

My entire point is that the Circle of Fifths can be thought of as NOTHING MORE than a mathematical sequence. And in that use, it can serve any purpose pedagogically. And it does, like you say John, your students and even I purposely go around the Circle of Fifths sequence because it is nice and orderly and you hit all the keys.

If we stay along those lines and not connect "functional cadences" into the picture, there's absolutely no issue. All I was saying is that a SUBDOMINANT relationship is not to be inferred from the Circle of Fifths. SUBDOMINANT is a Scale Degree relationship that does not fit here since the true Diatonic (Scale Degree) relationship is ii-V.
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Original method for harmonic hearing development
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10/21/14 03:19 AM
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