More stuff about the circle of 5ths

Subject: RE: More stuff about the circle of 5ths
From: GUEST,josepp
Date: 26 Mar 12 - 07:10 PM

So what does the circle do for us? It gives us a scheme by which we can be as musical as possible. For example, I was surprised to learn that many DJs at clubs use the circle when programming their sets. They learn the keys of all the songs they want to use and arrange them using the circle.

For example, if a song is in the key of C major, it can be followed up with one in G major or F major. What this does is allows one song to segue into another without a radical change in key. Not only does it sound superior to a DJ whose set is not arranged in keys, but it won't break the groove of the dancers. The DJ wants to keep them on a the floor as long as possible. He sets up a groove with a certain key and beat. He then segues into another song by matching the key and the beat but not in a boring way. Something in C major at 80 beats minute should not be followed up with something else in C major at 80 beats a minute. Maybe segue into something at 160 beats a minute in G major. The two beats are related (80 x 2 = 160) and so are the keys. Why? Because G major is a fifth away from C major and therefore has a relationship to it. This holds the dancers in the groove and keeps them dancing which keeps them in the club which keeps them buying drinks, etc. A DJ who breaks the spell with songs that are out of key with one another and/or with ill-matched beats causes dancers to leave the floor and possibly the club.

DJs say that you can even use the equivalent minors and get away with it--go from C to A, or C to D (the minor of F major) for example. Basically go around the circle link-by-link and program your set that way and you will became a sought-after DJ who knows how to get and keep people dancing. You don't want to jump from C to Eb for example because that might break the spell by changing key too radically. If the current tune is in Eb then go to Ab next or Db or B (B being the minor equivalent of Db).

Basically, if the seguing key is a fourth or fifth away from the current song and the beat is close, you can jump to it seamlessly and keep your crowd entertained.

Subject: RE: More stuff about the circle of 5ths
From: Jack Campin
Date: 26 Mar 12 - 07:31 PM

That's a useful and common stunt - it's also used in those modulating traditional dance tunes I mentioned, on a smaller scale but for the same effect, and is used in pretty near every ceilidh band set in Scottish or Irish dance.

But there is no circle involved. Just moving up and down from tonic to dominant or subdominant. You don't need to think about getting from G# to Eb in any disco set.

To introduce the matter of "pure temperament" into this thread is:
A. Off the subject; and
B. Needlessly confusing to a beginner.

And telling them they're using a tonal system that lets them modulate 12 times in the same direction and end up where they started is useful?

I introduced pure temperament simply because it is something your insistence on total chromaticism makes incomprehensible. And that incomprehension can be prevented by simply not talking about ET-specific tricks until they matter. Being able to modulate right round a circle is NOT a fundamental skill, and is absolutely useless for anything relating to any kind of music anyone would would describe as "folk" or "traditional". Developing fancy diagrammatic representations for it with millimetric accuracy by compass constructions (as in josepp's original post in this thread) is simply adding totally pointless graphical refinements to a not very useful concept.

Subject: RE: More stuff about the circle of 5ths
From: Don Firth
Date: 26 Mar 12 - 07:55 PM

"And telling them they're using a tonal system that lets them modulate 12 times in the same direction and end up where they started is useful?"

I don't know anyone who does that, Jack.

". . . totally pointless graphical refinements to a not very useful concept."

The only conclusion I can draw form that is that you haven't grasped what it is that Josepp is talking about. I found that Circle of Fifths gizmo that the salesman gave me early on to be a great help in learning the chord families of the keys.

I didn't use it to "go around the circle" with a program of songs. There are many other factors involved in setting up a good, enjoyable program of songs, such as variations in tempo, mood, subject, grouping under occupation, country of origin, and a number of other things.

Don Firth

Subject: RE: More stuff about the circle of 5ths
From: Tootler
Date: 26 Mar 12 - 07:58 PM

If they were tempering, then they were attempting, with at least some degree of success, 12-TET.

That's rubbish, I'm afraid, Josepp. There are many temperaments and all but one are most definitely not 12-TET, nor was 12-TET seen as an ideal in the past. It has been known about much longer than it has been used. Bach called his set of preludes and fugues "The Well Tempered Clavier" for a reason.

A common temperament (more correctly set of temperaments) in Bach's time were the various meantone temperaments. These basically aimed to produce pure major thirds at the expense of slightly out of tune fifths. Meantone worked well in closely related keys but the further you got from the "home key" the instrument was tuned to the more discordant some chords became until you ended up with a "wolf tone" (i.e. a horrible discord) somewhere round the other side of the circle. Well temperaments aimed to remove the wolf tones so that it was possible to play in any key. At the same time well temperaments aimed to preserve the varying character of different keys, (something that 12-TET fails to do) which was considered desirable in Bach's time. There has been controversy over exactly what temperament Bach used, but there is general agreement these days that it was not 12-TET.

That said, the circle of fifths is still a very useful tool for thinking about relationships between different keys and although traditional instrumental music uses very few keys, singers will sing in whatever key best suits their voice so a wide variety of keys are used in practice in traditional music.

Bach Prelude No. 1 in Cm played using three different temperaments. It's worth listening as the differences can be clearly heard, especially with the Lehmann which at first doesn't seem to sound "quite right" to our ears as we are accustomed to 12-TET.

Subject: RE: More stuff about the circle of 5ths
From: Artful Codger
Date: 26 Mar 12 - 08:28 PM

In terms of standard notation, the pattern of 5th relations is not really a circle but a spiral, and the points where one arc of the spiral parallels another are generally not interchangeable, but only correspond in pitch due to equal temperament. The extent of the spiral is from Fbb to Bx, though for common practical use one can generally get by with only the range spanned by single accidentals (Fb to B#). For most applications of the 5ths series, I agree with Jack--a "ladder" or set of strips shiftable in the manner of a slide rule comes in handier than a circle or even a set of nested wheels.

Consider the following set of strips:

  Strip 1: The Base
   Fb  Cb  Gb  Db  Ab  Eb  Bb  F   C   G   D   A   E   B   F#  C#  G#  D#  A#  E#  B#
   E   B   F#  C#  G#  D#  A#  E#  B#              Fb  Cb  Gb  Db  Ab  Eb  Bb  F   C
  
  Strip 2: Transposition Map
   Fb  Cb  Gb  Db  Ab  Eb  Bb  F   C   G   D   A   E   B   F#  C#  G#  D#  A#  E#  B#
  
  Strip 3: Scale/chord degrees
   V   II  VI  III VII IV  I   V   II  VI  III VII IV
  
  Strip 4: Modes
       MAJ         MIN
  |Lyd Ion Mix Dor Aeo Phr Loc|
   Maj Maj Maj min min min dim 
  

The second line of notes on the Base strip are enharmonic equivalents. To avoid confusion, those notes should ideally be printed in smaller type and enclosed in parentheses, since they will be referred to relatively infrequently. This is one of the great failings of the wheel--that one too often sees enharmonic equivalents that are the improper choice for the desired context. The transposition map is merely a duplication of the top line of the Base, and in fact may be preferable to use in place of the Base when enharmonics are irrelevant. (Actually, orienting these strips vertically, in "ladders" and Jack suggests, is probably easier to read, and longer names can be used. But I'm limited by the medium of text.)

First, let's look at the Base. It's the sequence FCGDAEB repeated three times, first with flats, then naturals, then sharps. (Memorize this sequence forwards and backwards, since it pops up continually.) The enharmonics row just repeats the opposite end of the previous row, as if the ends were overlapped in a circle (as on a more complete spiral of fifths).

Now, place the Modes strip so that "MAJ" is positioned over a selected major key on the Base, like A, and place the Degrees strip between them with the "I" underneath "MAJ" as well:

                                              MAJ         MIN
                                         |Lyd Ion Mix Dor Aeo Phr Loc|
                                          Maj Maj Maj min min min dim 
                      V   II  VI  III VII IV  I   V   II  VI  III VII IV
   Fb  Cb  Gb  Db  Ab  Eb  Bb  F   C   G   D   A   E   B   F#  C#  G#  D#  A#  E#  B#
  

What does this tell us? First, the notes within the A major scale are those that fall between the vertical bars: D A E B F# C# G#; so we know the key signature is 3 sharps (and in fact, they're notated on the staff in the order given; flat signatures appear in reverse order: Bb, Eb, Ab...). Using a typical circle of fifths, you'd see Db and Ab instead of C# and G#; now maybe what Jack is saying becomes a bit clearer. Yes, in equal temperament, they have the same pitch, but in proper notation, they're entirely different beasts.

We find that the relative modes for A major (or Ionian)--those which share the same key signature and note set--are D Lydian, E Mixolydian, B Dorian, F# minor (or Aeolian), C# Phrygian, and G# Locrian. What about enharmonics like Db Phrygian? Ain't no such thing, because (checking the enharmonics row) there are no single-accidental equivalents for two notes in the scale--D and A--and standard key signatures don't use double-accidentals (Ebb and Bbb would be required). Is that readily apparent from the circle? Nope.

We find that the common chords of A major, per the third (Maj/min/dim) row, are: tonic (I) AMaj, subdominant (IV) DMaj, dominant (V) EMaj, supertonic (II) Bmin,
submediant (VI) F#min, mediant (III) C#min and subtonic (VII) G#dim. Note the degree order: it just interleaves I, II and III between IV, V, VI and VII. The primary chords for any major key can be read directly off the Base strip by itself: IV is to the left of the tonic, V to the right, and all three are major.

Now, let's shift our point of reference to F# minor, by the simple expedient of shifting the Degrees slip so the I is under "MIN". The same notes and common chords are used, but their interpretation relative to the tonic is now different: I, IV and V are now all minor chords (F#m, Bm and C#m), II is diminished (G#dim) and III, VI and VII are major (A, D and E). In fact, VII becomes a primary chord in minor mode.

The most common modulations are up/down a fourth/fifth. Up a fifth is down a fourth, and vice versa. On the ladder, this means shifting the tonic to a neighboring rung. The next most common modulations are up/down a third, typically between relative major and minor keys--we've already dealt with that, but as josepp described, major to minor is a shift clockwise (left) three steps and minor to major is a shift counterclockwise (right) three steps.

Now we come to one of the best advantages of the ladder over the circle: transposition. Slip the Transposition slip over the Base slip so the Base indicates the source key and the Transposition slip the destination key. Now you can read the proper transpositions directly, with no confusion regarding enharmonic equivalents. It may help to position the Modes slip over both, so that the range of notes in the scales, per the mode, is more apparent. Try it with keys not close together (say, transposing by a mere semitone) and compare the results with what you'd read from a standard circle of fifths.

Jack is right: even though the equal tempered scale may be circular in terms of pitches and enharmonic equivalents, much music is not equal tempered, and most tonal music is governed by theory and notational practice that does not treat enharmonic pitches as interchangeable. The harmonic applications of sequences of fifths never encompass the entire circle but rather, as Jack asserted, only operate within a subrange of what is better described as a linear continuum than a cycle. This is where the ladder shows its superiority over the circle, despite the ubiquity of the latter in common dedagogy. I believe the popularity of the circle lies more in its sexiness of presentation than in its practical utility.

Subject: RE: More stuff about the circle of 5ths
From: Don Firth
Date: 26 Mar 12 - 09:06 PM

God help the innocents!

I give up!!

Don Firth

Subject: RE: More stuff about the circle of 5ths
From: GUEST,josepp
Date: 26 Mar 12 - 09:06 PM

///That's rubbish, I'm afraid, Josepp.////

You're right. And that's because I have absolutely no idea what Jack Campin is talking about. Moreover, I don't care. I don't listen to this "traditional" music and I'm not going to ever listen to it. My interest in music simply doesn't go there. I can't comment intelligently on a subject of which I know absolutely nothing. But if you're going to insist on engaging me in conversation concerning it, then you can see the level of response you're going to get from me. I'm muddling along the best I can to try to accommodate. If that's inadequte (and it certainly is), you need to go somewhere else and talk with people who are on your wavelength because I'm not.

Subject: RE: More stuff about the circle of 5ths
From: GUEST,josepp
Date: 26 Mar 12 - 09:15 PM

Let's not talk about the Greek-designated modes. They are not necessary to understanding music. None of the jazz musicians I know use them and, consequently, I don't use them. We're talking about the circle of fifths. If you don't like the circle of fifths and think sliding sticks work better then you're on the wrong thread. If you believe the majority of music is not enharmonically tempered then you're on the wrong thread because that is exactly the music we ARE going to discuss here.

We have no interest in anything else on this particular thread. So thank you all for your contributions, there are well-noted but it's time to say goodbye, sayonara, ciao. If you don't understand, please read the title of this thread, the topic of discussion is contained in it. THAT is what we ARE going to talk about--if I can ever get around to it. Would it be alright with you all if I got around to it?

Subject: RE: More stuff about the circle of 5ths
From: GUEST
Date: 26 Mar 12 - 09:30 PM

Here's a DJ mix that is pretty typical of what I hear in clubs Billboard Hits Party Mix.

Maybe I'm wrong, but I don't hear any "circle of 5ths" transitions between songs, and most of the cuts have a kind of drone-like quality,and don't seem to shift to shift to the dominant, even when it sounds like they should:-)

I am sure that the tempo is never 80bpm, though...

Subject: RE: More stuff about the circle of 5ths
From: GUEST,Chord Chucker
Date: 26 Mar 12 - 09:37 PM

WTF!!!

"I have absolutely no idea what Jack Campin is talking about. Moreover, I don't care. I don't listen to this "traditional" music and I'm not going to ever listen to it. My interest in music simply doesn't go there"

Tell me, please, josepp, what are you even doing at Mudcat, which has been a folk/traditional music forum since the last millenium?

Subject: RE: More stuff about the circle of 5ths
From: GUEST,josepp
Date: 26 Mar 12 - 10:35 PM

Gee, buddy, I'm sorry I don't have the same interests as you. I didn't know it was that important to you.

And for those who don't think DJs use the circle of fifths:

http://www.jeffvyduna.com/blog/archives/2005/02/djs_use_the_cir.html

Subject: RE: More stuff about the circle of 5ths
From: John P
Date: 26 Mar 12 - 11:14 PM

I guess I either know too much or too little. I don't see any usefulness in the circle of fifths. What's it do for the practical musician?

josepp, this is folk music forum. If you don't like folk music, why are you here? There are HUGE differences between many types of folk music an classical music, and many of the classical rules simply don't apply to folk.

Off topic, but it was mentioned earlier: The nyckelharpa players I play with don't use equal temperment. They carefully tune specific strings a certain number of cents flat or sharp in order to maximize the intonation for the common nyckelharpa keys. Somewhere in between equal temperment and just intonation.

Subject: RE: More stuff about the circle of 5ths
From: GUEST,Chord Chucker
Date: 26 Mar 12 - 11:36 PM

Mudcat is a folk/traditional music forum. That's why Jack, and the rest of us, are here. You are way off the mark telling him "you need to go somewhere else and talk with people who are on your wavelength" we are on his wavelength.

Maybe you should go somewhere else and talk with people on your wavelength.

Subject: RE: More stuff about the circle of 5ths
From: GUEST,Larry Saidman
Date: 27 Mar 12 - 02:16 AM

Come on, everybody. Play nice.

Subject: RE: More stuff about the circle of 5ths
From: GUEST,Gerry
Date: 27 Mar 12 - 02:48 AM

I published a paper: J Clough and G Myerson, Musical scales and the generalized circle of fifths, American Mathematical Monthly 93 (1986) 695-701.

I'm sure it wouldn't interest anybody outside of a small circle of fifths, er, friends.

Subject: RE: More stuff about the circle of 5ths
From: Will Fly
Date: 27 Mar 12 - 04:46 AM

There are quite a number of traditional melodies which make use of the same harmonic conventions as other forms of music such as jazz. As far as I'm concerned, anything which contributes to an understanding of the harmonic structure behind such music on this forum is to be welcomed, and I see no problem with Josepp or anyone else discussing it in a serious manner.

The only area where I would comment on Josepp's diagram drawing is that, after time, a diagrammatic representation of the harmonic progression as shown by the circle of 5ths won't be necessary. Experience of playing through chord sequences - particularly jazz and some blues sequences and sequences in traditional tunes - will reveal the underlying patterns both to the ear and to the instrument. Once the patterns are understood - and I personally think in patterns on the guitar - then matters like transposition become less mechanical and more organic and natural.

Playing jazz with other musicians is a wonderful way to haul yourself up by the musical bootstraps. In my jazz days, quite often a guest musician would drop in for a blow. The etiquette was to ask him to choose a number to play - and pick the key. Occasionally, there would be a number that I hadn't heard before; occasionally the musician would prefer a key that wasn't the norm... What better way to get to grips with the whole business of transposing quickly into a different key and/or getting to grips with an unfamiliar chord sequence?

This is where some early knowledge of the harmonic progression underlying the circle of 5th was useful to me. I very quickly discarded the diagram and just 'knew' the patterns in it.

Subject: RE: More stuff about the circle of 5ths
From: Will Fly
Date: 27 Mar 12 - 04:49 AM

And I forgot to say that, as well as playing jazz, I also play traditional tunes, blues, ragtime, early country music, popular songs from the 1920s, music hall, classical, etc. All music is music to my ears, and nothing is out of bounds.

Subject: RE: More stuff about the circle of 5ths
From: John P
Date: 27 Mar 12 - 09:51 AM

Thank you, Will. Yes, any understanding of music is good. I think it's possible that some of the flak that josepp is getting is because he's trying to dictate that there be no thread creep, and he's being sort of rude about it. Also, he lost me way up top when he drew a line across the circle and didn't know what chord went there, but did know the two on either side. Doesn't make a great deal of sense.

One thing I've noticed is that I can think about music as if it were equal tempered, making everything line up neatly, while also playing with instruments that aren't tuned that way. All the math doesn't really have anything to do with making music.

I am, however, still struggling to understand the utility of the circle of fifths. So far I've gathered that it's used to transpose. Seems like a complicated way to do it. Are there other uses?

Subject: RE: More stuff about the circle of 5ths
From: Will Fly
Date: 27 Mar 12 - 10:01 AM

Where it helped me, John, was with getting to grips with jazz 'standards', because the popular songs on which much of mainstream jazz was based, use the same progression patterns - utilising the harmonic progressions in the 5ths cycle. Once I understand that, I could follow and improvise on those tunes, and get to grips with them more easily.

So, for example, many standards start on the tonic chord, drop down to somewhere on the circle and then work their way back round the circle to finish on the tonic. Once you 'get' this, it's immensely useful. "Sweet Georgia Brown" comes to mind - let's say it's in G...

Starts with a preliminary run down from G to E7, then goes to A7, then goes to D7 and back to G briefly - that's the first 8 bars, more or less. Well, that E7-A7-D7-G riff is right on the cycle and part of a cycle which goes:

G-C-F-Bb-Eb-Ab-Db-F#-B-E-A-D-G (choose whether you want chords written as sharps or flats). So, "Sweet G B" starts in G, drops down to E in the circle and works its way back through the succeeding chords to G. Et voila! Once that clicks, you're away and a jazzer (more or less)
:-)

Subject: RE: More stuff about the circle of 5ths
From: JohnInKansas
Date: 27 Mar 12 - 10:13 AM

Jack has made several references to ET being unavailable to early instrument makers. To the accuracy with which they (or anyone today) can build an instrument, the same geometric construction used by many current luthiers could have been used by ancient Greeks long before the argument over BC or BCE.

Since the pitch of a string is linearly dependent on the length, for constant tension, all that's required for an ET scale is that frets be placed so that each fret changes the string length by some same ratio relative to the adjacent fret. Placing a series of frets to meet that requirement is almost trivial geometry. Placing the frets so that you'll come out with exactly 12 spaces giving a preditermined pitch for the tonic note on a string of a preselected lenght is a little tricker, but if you layout 30 frets, picking any 12 that span a convenient length and making the string twice the length of that series gets an octave worth of frets, and you can change the string tension (or string weight) to put the note where you want it. The "ancients" were not able to know the angle A for which 1/(1-cosA) = 2^1/12, but that wasn't really all that necessary - just a modern convenience like having strings of uniform diameter.

The only reason early makers didn't make an ET scale instrument is because they didn't want to since the ancients established the "idea" that there was truth, beauty, and purity in having all the ratios be integer fractions. The "purity of tone" when notes at "harmonic ratios" are combined to play chords played a large part in resistance to "rationalizing" a standard interval, and many modern musicians still prefer to tune that way (within the limits of their instruments) - which is fine as long as it's appropriate for the genre in which they choose to perform. Any serious musician should know how to set up his/her own instrument to simulate either system within the accuracy required for the music chosen.

The "argument" need not be about one being better than the other. The point is "which is best for today in this place to do that."

John

Subject: RE: More stuff about the circle of 5ths
From: dick greenhaus
Date: 27 Mar 12 - 11:39 AM

There's really no problem in making an instrument that will play in any key and any temperament--the fidddle family does it jes' fine. The problem arises when you want niceties like frets or keyboards.
    The Circle of Fifths, I've found, is a convenient way of visualising chordal relationships if you limit yourself to an even-tempered scale.For most folk musicians, that's not a serious limitation.

Subject: RE: More stuff about the circle of 5ths
From: Jack Campin
Date: 27 Mar 12 - 11:58 AM

And telling them they're using a tonal system that lets them modulate 12 times in the same direction and end up where they started is useful?
I don't know anyone who does that, Jack.

That's the only capability a circle gives you that a ladder doesn't.

If you have a final cadence in G minor with an F sharp in in the melody, the usual explanation of what it's doing there is that it can be seen as part of a Dmaj or D7 chord. The circle of fifths says you could also see that note as a G flat. Does that create any additional understanding? Is it actually likely that any chord with a G flat in it would fit at that point?

Subject: RE: More stuff about the circle of 5ths
From: TheSnail
Date: 27 Mar 12 - 12:03 PM

John P

Also, he lost me way up top when he drew a line across the circle and didn't know what chord went there, but did know the two on either side.

Must say I thought he was making life unnecsarily difficult there. Why not just draw your circle with twelve points, Write C at the top and then write in the fifths in order clockwise? To work out what the next fifth is, write out the chromatic scale and count up seven semitones.

Subject: RE: More stuff about the circle of 5ths
From: GUEST
Date: 27 Mar 12 - 02:28 PM

Why use all that space explaining how to draw the circle, and no space explain what it's for?

Subject: RE: More stuff about the circle of 5ths
From: Artful Codger
Date: 27 Mar 12 - 02:54 PM

I think josepp was targetting the discussion to people who don't already know what the fifths progression is--that's one of the reasons to teach the circle of fifths. But the answer to that is pretty simple: first learn the FCGDAEB sequence, for which you can create a mnemonic, like (off the top of my head) Fast Cars Grimly Drive Around Every Body. I'm sure someone has a better one.

The problem is that, in drawing and labelling a circle using only the "ABC" sequence everyone knows, you have to skip points on the circle, so starting from C, you can only label six points: 12, 2, 4, 6, 8 and 10. How do you label the points in between? A simpler solution than what josepp describes (that jumping across the circle bit) is just to remember that to the left of C you have to put F, then continue the ABC sequence.

But this raises the second problem: how do you know when to start adding accidentals (if you're the sort of neophyte who doesn't already understand all the intervalic relationships)? First learning the FCGDAEB mnemonic solves the problem. When you get to the end of the sequence forward, you start adding sharps (and if you continue on, double sharps); when you reach the end going backwards, you add flats. So starting from C and labelling the points in turn, you get:

  12 1  2  3  4  5
  C  G  D  A  E  B
  

(The numbers here just indicate the clock points; you wouldn't write them down.) Contining with sharps you get:

  12 1  2  3  4  5  6  7  8  9  10 11
  C  G  D  A  E  B
  B#              \ F# C# G# D# A# E#
  

Continuing backward from C we get:

  12 1  2  3  4  5  6  7  8  9  10 11
              Fb Cb Gb Db Ab Eb Bb
  C  G  D  A  E  B                \F 
  B#              \ F# C# G# D# A# E#
  

We now have, essentially, a spiral in the form of a circle, with all the single-accidental harmonic equivalents shown. Moreover, it's now clearer (following the jogs indicated by the slashes) which spelling you should use when figuring out the notes in the scale, the accidentals in the key signature, the relative major/minor and so on. This is equivalent to the first strip in my message above, but in circular form (and with potentially confusing overlaps). By continuing the spiral this way beyond what is normally shown in typical circle-of-fifths diagrams, not only are all sharps/flats of the scale/signature duly represented, but the diagram works for minor scales (and other modes) as well as major ones.

But let's focus on what's important: these representations aim to capture the usefulness of the fifths series: ...Bb FCGDAEB F#... It's good to know the (equal tempered) pitch equivalences, but that's something one picks up better from a semitone-oriented mapping rather than one organized in fifths. In practice, when moving about by fifths, you will rarely jump from the flats series to the sharps series, though once you modulate into five-accidentals territory, it may be easier to consider this a switch to the enharmonic key (for instance, Ab instead of G#).

So (you'll smugly observe) if you have to learn the fifths sequence to create the circle, why create the circle at all? Because it's a helpful visual aid when explaining things commonly related by fifths, like progressions, modulations, key sighatures, primary chords and relative modes. The fifths sequence, combined with the diatonic interval pattern derived from approximating the overtone series, could be considered the underpinning of our musical experience.

In presenting my ladder version, I mentioned transposition, which some have downplayed, saying that once you learn the patterns, transposition becomes a more organic matter of applying those patterns. I agree with that, except when you're trying to notate music. Then it helps a great deal to have an explicit note-to-note transposition map to reference.

Of course, many people these days use music-notation software which handles transpostion in a far easier manner. But if you're not so blessed, a tool like the strips can be a real boon. A pair of nested wheels would also answer the bill, as long as the wheel is large enough to contain the entire 35-note sequence (Fbb to Bx) without overlapping. In this case, a fifths organization is better than a semitone organization, because it just happens that the most common notes and chords--those corresponding to the diatonic scale--will be grouped together, whatever the key and mode.

Subject: RE: More stuff about the circle of 5ths
From: Jack Campin
Date: 27 Mar 12 - 03:13 PM

This is getting a bit like PowerPoint as Edward Tufte sees it:

every time you make a Power Point, Edward Tufte kills a kitten

Never mind the music, look at the presentation graphics.

Subject: RE: More stuff about the circle of 5ths
From: Artful Codger
Date: 27 Mar 12 - 03:28 PM

Did you learn "the music" without any technical explanations or diagrams? Many people have, especially before widespread literacy, but nowadays we tend to use a fuller set of tools, and that can shorten the learning curve. After all, in "the music" there are no note letters or staves at all. What's yer point?

Subject: RE: More stuff about the circle of 5ths
From: Don Firth
Date: 27 Mar 12 - 04:12 PM

What with people tripping over their own feet to display their extensive knowledge of music for the whole world to admire, Josepp's original, fairly straightforward purpose has gotten buried in a vast pile of egos.

The Circle of Fifths is a simple concept for learning what chords go with what keys.

PRESTO!!

Let us say that you are a raw beginner on the guitar. You know your chord diagrams, having learned them from a book entitled something like "Guitar Chords for the Intellectually Challenged." So no problem there. But you are learning a song from a songbook, and in the book, the song is in the key of C. The chords over the melody line are C, F, G7, and at one point it uses an Am. But—the melody is too high for your voice.

You did have some piano lessons when you were a kid and you can read music. Good. So you go to the piano and mess around a bit, and you discover that you can sing the song comfortably in the key of G.

So—knowing diddly-squat about chord relationships, you pick up your copy of "Guitar Chords for the Intellectually Challenged" and look at the helpful little chart in the back of the book. At the top of the page, it says, "Circle of Fifths," subtitled "How to Transpose." [Or you could try to draw a circle of fifths the way Josepp described it.] You look at the key of C at the top of the circle. And lo! There is the C chord at 12 o'clock. The F is at 11 o'clock. The G is at 1 o'clock. And the Am is inside the circle, just below the C.

You crank your head around to the G chord, which is at 1 o'clock, one step to the right on the Circle of Fifths. That's the key chord you want to use for the key of G. You replace the F with the C, the G7 with a D7, and the Am with an Em, and there are the chords you want to use for the song.

It's a helluva lot more complicated to explain than it is to just simply look at the circle, note the relative positions of the chords in the key you want to change from, then use the chords in the same relative positions in the key you want to change to.

Duck soup! If you don't get all tangled up in matters of how they may have done it in ancient Greece or in Count Esterhazy's salon three centuries ago.

As I say, it's a lot messier to explain than it is to just DO it.

And this, I am sure, is why Josepp didn't want people coming in and burying a simple aid for beginners under tons of stuff that is irrelevant to the needs of a beginner just so they can demonstrate what hot-shots they are!

Am I somewhere in the ballpark, Josepp?

Don Firth

P. S. Not a ladder, not a trapezoid, not a helix, not a spiral, not a tetrahedron, not a Mobius strip—you get the idea! A simple circle, like a clock face.

Subject: RE: More stuff about the circle of 5ths
From: GUEST
Date: 27 Mar 12 - 09:17 PM

Josepp has been gone for nearly a day--perhaps trying to reconcile his avowed distaste for traditional music with the fact that he's been rather seriously involved with a traditional music forum for several months now.

Good Luck, josepp. I know it's disturbing to discover this latent tendency, but come out of the closet and accept it. You'll never make any money, but it can be fulfilling in many other ways:-)

Subject: RE: More stuff about the circle of 5ths
From: GUEST,josepp
Date: 27 Mar 12 - 09:53 PM

Thanks, Don. Yes, that gave a good synopsis of one way to use the circle. The DJ thing was simply another way that I thought would be a very simple thing to introduce people in its use. Namely, that the notes next to each other on the circle share a close musical relationship. The further apart they are, less so.

As for "traditional" music from the Shetland Islands or whatever, I mean, give me a break, folks--I'm American. What could I possible learn about a music I know nothing of and have no teacher to learn it from? My teachers are jazz/classical. That's what I know.

I once went to see a writer lecture when I was a boy. I believe it was the guy that wrote "Gentle Ben" about the bear--it used to be a TV series. After his lecture, he did a Q&A with the audience, which was mostly kids. One kid asked him what he would suggest someone who wants to write fiction should keep in mind as an aid. The one thing he said that has stuck with me all these years is--WRITE WHAT YOU KNOW ABOUT. Don't put the setting in London if you've never been there. Try putting it in your hometown or a fictional town modeled on your hometown so that when are describing something, you actually have something in mind rather than making up vapid descriptions trying to make the reader see a place you've never seen yourself. That's my approach to music. I play what I know. Why should I play something from another culture across the ocean of people whom I have no contact with and no knowledge of? Especially when the greatest, richest treasure trove folk music to be found anywhere in the world comes from America. No other place comes close--certainly not the UK. America is where it's at and it is what I know.

Subject: RE: More stuff about the circle of 5ths
From: GUEST
Date: 27 Mar 12 - 10:19 PM

You're still not with the program, josepp--lots of that that "richest treasure trove" that's found here came from there, and let's not even talk about the slightly embarrassing fact that a lot of Americans first learned about "The Blues" by listening to British Blues bands.

And, besides, about 2/3rds of Mudcatters seem to be from "across the pond" these days.

Subject: RE: More stuff about the circle of 5ths
From: GUEST,josepp
Date: 27 Mar 12 - 11:21 PM

Now that I have explained myself concerning "traditional" music, let's get back to the circle of 5ths.

We generally associate I-IV-V with blues but we find it in classical. Jazz has a number of progressions, one of the simplest and most prevalent is ii-V7. It is also found in other styles of music including folk just as the folk root-5th bass line is found and taught in jazz. ii is in lower case because it is minor while the V is major and so is upper case. What does it refer to?

If we lay out the notes of a scale--say, F major--on a staff in order 1-8, it is F G A Bb C D E F. Now we can make chords of each of these notes simply by stacking 3rds, 5ths and 7ths on top of these "roots." So, the F would have stacked on it ACE and FACE is the F major 7th chord. The G would have BbDF stacked on it and GBbDF is G minor 7th. The A would have CEG and that is an A minor 7th. The Bb would bhave DFA and would be a Bb major 7th. The C would have EGBb and CEGBb is the C7th. The D as a chord becomes a D minor 7th and the E becomes an E minor 7th half-diminished. Right now, it's not important how we determine these chords. Just buy it for now.

So F is I, G is ii, A is iii, Bb is IV, C is V, D is vi and E is vii. It works out that way for any scale--I, ii, iii, IV, V, vi, vii. So in ii-V7, we are interested in G minor 7th and C7th. The ii and the V7 form a very musical relationship. Many songs are written in ii-V7 such as "Satin Doll" and "Getting Some Fun Out of Life."

There are 24 keys to run through and they are arranged in order: D minor 7, G major 7, C minor 7, F major 7, Bb minor 7, Eb major 7, Ab minor 7, Db major 7, F# minor 7, B major 7, E minor 7, A major 7, Eb minor 7, Ab major 7, C# minor 7, F# major 7, B minor 7, E major 7, A minor 7, D major 7, G minor 7, C major 7, F minor 7, Bb major 7 and then ends on Eb.

Now if you look at a circle of 5ths, you'll see that we are following counterclockwise (in 4ths). We skip around a bit after A major 7, we go back to Eb rather than continuing to D but from there we follow the circle all the way until the end. These are all the possible ii-V7s to choose from.

I'll explain a little more about it in a bit but right now I'm dog-tired and need to crash and burn.

Subject: RE: More stuff about the circle of 5ths
From: Don Firth
Date: 28 Mar 12 - 12:34 AM

Oh, wow, Josepp, your comments about "America's where it's at when it comes to music" is going to get up a few noses across the pond! And I would say, justifiably so. While you rest and recuperate, I'll stick in my 2¢ worth.

I do agree about "write what you know," which is what my high school Creative Writing class teacher kept saying (except, of course, if you're writing science fiction and your story is set on Alpha Centauri Two).

But I can't agree about music. The vast majority of American folk songs and ballads have British Island roots, having been brought to this county and kept alive by the many early settlers and their descendants, largely Scots-Irish. Acquaint yourself with the work of English folk song collector Cecil J. Sharp, who collected many songs and ballads in England, then came to the United States and did the monumental collection of English Folk Songs in the Southern Appalacians (two volumes of really great stuff!). Even some cowboy songs collected by the Lomaxes have British Island roots!

As to classical music, Europe in general dominates there. A number of very good American composers, writing "serious music" (European tradition) have arisen (Aaron Copeland, Leonard Bernstein, others), but the major European composers whose names almost everyone knows predominate in the concert halls and opera houses.

Jazz, primarily American. Actually, African-American, at least originally. As to the blues, I have to disagree with GUEST there. Most of the younger blues singers and enthusiast I know learned their blues from people like Lightnin' Hopkins and Mississippi John Hurt.

Don Firth

Subject: RE: More stuff about the circle of 5ths
From: JohnInKansas
Date: 28 Mar 12 - 02:10 AM

We seem to have a number of people participating here with an excess of learnedness who have neglected the acquisition of understanding. Much of what is being ARGUED is in defense of things that don't need defending, and for the most part are not germain to the intended purpose of the thread.

Since we have some who wish to argue about historical trivia, a minor (off topic) response is required for:

what are you even doing at Mudcat, which has been a folk/traditional music forum since the last millenium?

Mudcat was intended to be about BLUES.
Max, in spasm of generosity, made a home for the DT, when they were booted out of their previous home.
(Un?)fortunately, the DT attracted a couple of Brits, and for some unknown reason(s) they were allowed to come back.
It's been a downhill slide in the Mud since, which is one way of rationalizing (tempering) the predominance of "Folkishness" at MUD-cat.

A little closer to the subject:

While the frets on your guitar are spaced according to 12-ET you are free to tune the strings relative to each other in any way you choose. Since it's impossible (mostly) to simultaneously play two notes on the same string, its the relationship between strings that determines what scale you're using, and within normal ranges of most individual pieces of music it doesn't really matter much where the frets are. If you "tune by ear" you will likely be close to "harmonic tuning." If you tune with an electronic (or stroboscopic) tuner, you'll likely to be closer to an ET tuning, although neither ears nor instruments are precise enough to make all that much difference - you're still probably out of tune somewhere in the range where you play. and lots of people seem happy with being a little off everywhere - certainly far enough to obliterate much of the difference between choices of scale tunings.

You can, in fact, "tweak" a note on almost any instrument, and on a guitar just "rolling your finger" on the fret can change the pitch about enough to bring your note into "harmonic agreement" with other players, or with the other notes of your chord. This is not an easy thing to do, but it's an observed technique in a few "masters," some of whom may not even be aware of doing it. This also means that a sloppy finger can put you "out of tune" by far more than the difference between the theoretical pitchs of the harmonic vs ET scales you might think you're using.

The complaint that the "Circle" only applies to ET tunings is BULLSHIT in the context of this thread and its purpose. (As are arguments about enharmonicity.) If you feel you must complain, it suggests you just don't know how to apply the circle (and/or when to ignore it when you exceed the limits of it's applicability in your own peculiar context).

The circle is a graphical method of illustrating that there is a certain sequence in which the "key" changes when sharps or flats are added or removed. The particular sharp or flat added or removed is in the same sequence but with a different starting point. The sequence of changes for minor keys is the same as for major keys, but with a different starting point in the sequence. The principal notes in chords are in the same sequence, each with an additional different starting point in the sequence. It's an aid to knowing how to change the key signature, and to picking the right notes for a chord when you change keys regardless of what tuning you use, within any reasonable range where a given scale structure is appropriate (without retuning). If you add enough foxtails and fuzzy dice (and a chrome stripe or two) it can be extended to "remind" you of quite a few other things, but the wheels won't spin any faster, and the wheel doesn't go much farther.

John

Subject: RE: More stuff about the circle of 5ths
From: Artful Codger
Date: 28 Mar 12 - 02:40 AM

The standard circle has few sharps on it, despite that the sharp keys are the most common (at least for fretted string instruments, which tend to predominate in this forum). If you only care about chord roots, that may not be a great hindrance to you. My experience, however, is that the standard circle is just too incomplete, so I use fuller representations that are more flexible--either grids or strips.

P.S. Not a circle, but a series that only "loops" enharmonically (a seldom useful relationship for proper notation). You seldom go across the circle (the most discordant intervals), so there's no real advantage of a circle over just counting forwards and backwards from your relative reference point. Simple, and no enharmonic ambiguities. Most people find it easier to apply pattern/distance relationships in the same orientation than to rotate their frame of reference mentally, so why use a circular representation unnecessarily?

Subject: RE: More stuff about the circle of 5ths
From: Trevor Thomas
Date: 28 Mar 12 - 10:37 AM

"Especially when the greatest, richest treasure trove folk music to be found anywhere in the world comes from America. No other place comes close--certainly not the UK. America is where it's at and it is what I know."

Of course, dear boy. America is The Greatest Country In the World, after all, so it follws that it's music must also be the Greatest Music In The World. All music that is any good was invented in the good old U S of Good Ol A. There's certainly no need for you to know anything about music from anywhere else to be convinced you're right. It's so obvious, it doesn't need anything like facts or evidence.

But you must expect that some of us will disagree with you about this.

Subject: RE: More stuff about the circle of 5ths
From: GUEST,josepp
Date: 28 Mar 12 - 12:15 PM

The music of America has taken over the world. There is no other music that has done that unless you want to count British bands who all--without exception--copied American music.

///The vast majority of American folk songs and ballads have British Island roots////

I'm not in agreement with that. The BEST KNOWN American folk has roots in the UK because white Americans had a tendency to only listen to the white man's music (remember, play what you know). But America has a huge French infusion that gave us Creole and Cajun music and, ultimately, jazz. Stuff like Zydeco has a multitude of influences--probably none of them from the UK. There's American Indian music, there's Mexican music. Norteno polka alone probably outnumbers all the UK-influenced stuff in America. You just don't hear about it as much. Then there's bossa nova and MPB that certainly has a huge influence (remember America isn't limited to the U.S. but Latin music even within the US is a huge business). And I won't even bring up ragtime, blues and gospel. Nowhere else on earth does such a diverse mixture of cultures exist. Too bad the music of Asia hasn't been assimilated to any real depth but I have hopes that this will happen because Asians are the fast growing populating in America. American folk is rich and it is deep. Nothing else can match it.

Subject: RE: More stuff about the circle of 5ths
From: Tootler
Date: 28 Mar 12 - 02:05 PM

I'm glad to see that jingoism is alive and well and not confined just to England.

Subject: RE: More stuff about the circle of 5ths
From: Don Firth
Date: 28 Mar 12 - 04:29 PM

Josepp, I was with you in suggesting the Circle of Fifths (unembellished with extraneous information) as a good learning tool for beginners, but I'm forced to abandon you on this idea of yours that "The music of America has taken over the world."

When it comes to folk music, most American folk music has British Island roots. I think a whole army of American folklorists would say that strongly in chorus.

And what I said about the predominance of European influences in "serious music," i.e., symphonic and operatic music is patently obvious if you glance through a list of works to be played during a symphony orchestra's season, whether that orchestra happens to be in Boston, San Francisco, London, Oslo, or Tokyo.

Even Broadway musicals by American composers, which many Americans assume are an American invention, are a legacy from people like Franz Lehar [Austro-Hungarian], Rudolf Friml [Czechoslovakian], and other European composers of operettas ("light operas"). A few American composers have written full operas recently, such as George Gershwin's "Porgy and Bess" (yes, most opera experts are now saying that that IS a genuine opera) or Leonard Bernstein's "Candide" (actually closer to an operetta than a genuine opera). Nevertheless, Italians (Verdi, Puccini, etc.), French (Gounod, Bizet, etc.), Germans (Wagner, Richard Strauss), and English (Benjamin Britten, and for comic opera, Gilbert and Sullivan) totally dominate the field of opera.

As to the list of folk musics that you advance, it IS true that America is a country of immigrants (contrary to the beliefs of some history-challenged American conservatives), and each of these groups has brought their music with them, making for a rich mix.

But that is hardly a solid basis for your Chauvinistic comments.

Don Firth

P. S. Jazz is assumed by most people to be an American invention. Yet, three of the finest, most innovative jazz musicians in the world were not Americans. Stéfane Grappelli (who practically invented jazz violin) and Claude Bolling (piano) were French, and Django Reinhardt, one of the most innovative guitarists around, despite two non-functioning fingers on his left hand, was born in Belgium. And the three of them did their thing in Paris.

P. P. S. Seattle, where I live, has a very large Scandinavian population. Ballard, in the northwest portion of the city has a Bergen Square and a large Nordic Museum. For years, until he passed away, Gordon Tracie taught hundreds of people two or three evenings a week at the Scandia Folk Dance Club, and there is a thriving Skandia Kapel Band. Stan Boreson, local musician and comedian had his own television show for years, on which he sang parodies of many popular and folk songs, using a thick Swedish or Norwegian accent (hard to tell the difference).

I'm still searching for the words to his hilarious parody of "The Streets of Laredo," entitled "The Streets of Stavanger." A dying fisherman, all wrapped up in oilskins, dying of—sea sickness.

Subject: RE: More stuff about the circle of 5ths
From: dick greenhaus
Date: 28 Mar 12 - 05:13 PM

A tsunami in a teacup.Look, the circle of fifths is a useful learning tool with inherent limitations(as most learning tools have) It assumes an even-tempered scale. It assumes that octaves have simple arithmetic frequency ratios.
    Take if for what it is---or reject it if it doesn't apply to the music you're interested in. I've always found it useful in teaching transposition. A point that confuses most students...if, for instamce,F# is the same note as Gb, why not just pick one? The answer of course, is that accidentals (and things like double sharps and double flats) let you write scales in which each letter appears once---a great help if you're using conventional notation.

Subject: RE: More stuff about the circle of 5ths
From: Don Firth
Date: 28 Mar 12 - 05:29 PM

Bingo! I think dick greenhaus just put a period to this sentence.

Subject: RE: More stuff about the circle of 5ths
From: GUEST,josepp
Date: 28 Mar 12 - 05:54 PM

ii-V can also be played without the 7th. One can play D F A D / G B D G instead of D F A C / G B D F. One can play in 4ths--D A / G D where D and A are called lower 5th and upper 5th respectively. Those notes are all lined up next each other on the circle--ii-vi-V-ii.

ii is a chord in its own right as is V. But are also part of another scale. D G C F, for example. D is ii and G is V of the scale of C major. Notice C is the next note in the sequence I listed. Like wise, you can look at G and C and the note to the right is F and so that is the scale that G and C are ii and V of. And so through all 24 arrangements.

Sometimes we play a pattern of the ii minor as 1 2 3 5 8 7 6 5. The 2 is called a "passing note." So using D G as an example, the pattern would be D E F A / G F E D. What the passing note tells us is what scale both D and G are ii and V of respectively. It will always be the major 3rd of that scale. In this case it is C since E is the major 3rd of C major.

If you look at a circle of 5ths, you'll that D and G are ii and V of C major. And E is the major 3rd. C, G and D are lined up in sequence clockwise while the passing note skips one more note over. The following circle of 5ths is wonderfully done and shows the relationships of the notes. You can turn the pointer to any note of the wheel and relationships hold true. I would copy this one if I were you. An excellent reference:

http://www.jmstaehli.com/images/music/Circle_of_Fifths.jpg

The following chart shows from left to right, the root, passing note, minor 3rd, major 3rd, 5th and 7th of all the possible chords in 12-TET. Look at the root D. It's passing note is E. Now look for E in the major 3rd column (4th one over from the left) and notice the root is C. The 5th of root D is A which is the passing note of the next note on the circle of 5ths after D going counterclockwise which is G. Notice the 5th of G is the root of the D scale.

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

Subject: RE: More stuff about the circle of 5ths
From: GUEST,josepp
Date: 28 Mar 12 - 06:00 PM

////When it comes to folk music, most American folk music has British Island roots. I think a whole army of American folklorists would say that strongly in chorus.////

If you're so Eurocentric in your views that the only American folk music that matters is white people's, if you can so blatantly ignore the huge contributions of Latins, Indians, and blacks that you even think Django Reinhardt invented jazz, it is you who is chauvinistic and probably a racist as well.

Subject: RE: More stuff about the circle of 5ths
From: Don Firth
Date: 28 Mar 12 - 07:11 PM

Josepp, don't be an ass.

I am fully aware of the rich musical heritage that this country has--inherited from its immigrant population.

And you are attributing meanings to what I said that are beyond what I actually said.

This whole thread started out being promising, and then it went all pear-shaped. Not your fault initially, but with your current jingoistic attitude, you're not helping NOW. Give it a rest!

Don Firth

Subject: RE: More stuff about the circle of 5ths
From: GUEST
Date: 29 Mar 12 - 12:22 AM

He started out with "Yeah, more stuff about the goddamn circle of 5ths so shut yer bloody, fookin' pieholes!" which wasn't that promising.

Subject: RE: More stuff about the circle of 5ths
From: Don Firth
Date: 29 Mar 12 - 12:50 AM

Now that you mention it, GUEST, you're right. The Circle of Fifths is a good learning tool for beginners, as I keep saying, and in that sense it was promising.

But certainly not in Josepp's means of expression. I should have seen it coming.

Don Firth

Subject: RE: More stuff about the circle of 5ths
From: GUEST,Guest from Sanity
Date: 29 Mar 12 - 02:13 AM

The 'circle of 5ths' is a GREAT tool...and should not only be utilized, but memorized! Invaluable to composers who wish to play beyond puerile simplistic pieces, that lazy musicians get stuck in a rut with!
Think of it a a tow chain, to get you unstuck! Those who 'poo-poo' it are just lazy and unimaginative, boring and proud of it! Ignore them!!
Besides, their 'music' is usually very ignorable, anyway!

GfS

Subject: RE: More stuff about the circle of 5ths
From: Big Al Whittle
Date: 29 Mar 12 - 02:30 AM

Yes indeed, these days there's too little ignoring going on. In an iage of great tools, ignorance is the only viable option.

Just because someone whips out a great tool, it doesn't mean I'll go out with him. In fact I think that's out of place in many relationships.

Subject: RE: More stuff about the circle of 5ths
From: GUEST
Date: 29 Mar 12 - 02:50 AM

I think the circle of 5ths divides people who are serious about writing,arranging, and playing music from people who are just playing around with it.

Subject: RE: More stuff about the circle of 5ths
From: GUEST
Date: 29 Mar 12 - 03:11 AM

Jack Campin not withstanding.