Circle of fifths and key change information

Hi all

If I start an improvisation in say C Minor - how do I follow the circle of fifths to make sure that I transition naturally from the starting key to other keys?

Also in the Wedge Fugue by Bach (BWV 548) can anyone tell me the key changes used in the entire fugue for my understanding of it?

thanks!

Bach>Meer said:

Hi all

If I start an improvisation in say C Minor - how do I follow the circle of fifths to make sure that I transition naturally from the starting key to other keys?

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With regard to your first point, I would not necessarily do this. Consider modulating to keys a third apart, or by chromatically altering one or two notes of a chord successively, in order to move to a new key.

By sticking only to tonic -> dominant -> secondary dominant (etc) keys, one can limit the aural structure of a piece. You could modulate to the relative major, of course. However, one must try to strike a balance between changing too quickly from one key to another and, on the other hand, not allowing time for the new key to be established. However, simply adhering to a cycle of fifths can result in a hackneyed effect, the result being somewhat predicatble. Try to use common notes between chords and keys and experiment with slipping from one key to another. This can be made to work even with 'remote' keys.

One (true) story might help, here:

For a number of years, Pierre Cochereau taught a summer school in improvisation. (Bear in mind that Cochereau's own harmonic idiom was both rich and constantly varied - he did not stay in one key for long, yet there was rarely and sense of 'harmonic bewilderment'.) One year, there was a female student of mature years who was, shall we say, unadventurous in her harmonic language. She would tend to stay in one key for a long stretch - often for an entire piece. This naturally drove Cochereau crazy. One day, wishing for a little light relief, he brought a pistol to the lesson (it was not loaded) and, after saying tersely "Modulate - modulate!", he pulled the gun from his pocket, placed it against the unfortunate woman's temple and said sharply "Modulate - NOW!" Apparently, she saw the gun, shrieked loudly, threw her arms in the air - and ran from the room exclaiming "Mon Dieu! Mon Dieu! Il est un fou furieux!"

She was never seen again....

That's an echo (albeit with an extra twist) of an old story, when Debussy was a pupil in Franck's organ class. Franck told him, not without irritation: “You must modulate. Come on, modulate! Why on earth don't you modulate?"

Debussy calmly replied: “But why? I'm perfectly happy where I am now.”

I'll heartily second pcnd's comments as I'm a big fan of modulating a 3rd away (major or minor, up or down) from the starting key. One of the reasons I like it is because it's not a hugely unexpected surprise, but it's certainly enough to maintain attention and have casual listeners think "that was interesting" (IMO of course, but I have had people say exactly that).

One of my favourite chord progressions moves in alternating major and minor thirds (descending). You can move through all 12 major and all 12 minor triads and it can create quite a sense of tension as you're never sure just where it's going to end. So for example, starting at C major, down to a minor, then down to F maj, --> d min --> Bb maj --> g min --> Eb maj --> etc etc etc. You can essentially stop anywhere and it doesn't really sound "wrong"

As for the circle of 5ths, as a general rule, the most common thing to do is to introduce the leading note of the new key (ie, dominant of the dominant as it's called), so if you were moving from c minor to g minor, introduce the f# in a D major chord (the dominant of G).

Personally if I choose to use the circle of 5ths through which to modulate, I tend to use diminshed chords rather than a straight dominant 7th - it's adds to the expectation that you're going somewhere else. Again sticking with c minor, my choice to go to g minor would be to go from c minor root position, move the g up to a (natural not a-flat), then add the f# to that and there you have a nice diminished 6th with which to slide over to g minor.

All of the above also presupposes that I'm staying relatively tonal in my improvisations. 9 times out of 10, I'm usually in some strange mode (easier to cover up "wrong" notes )

Soubasse said:

I'll heartily second pcnd's comments as I'm a big fan of modulating a 3rd away (major or minor, up or down) from the starting key. One of the reasons I like it is because it's not a hugely unexpected surprise, but it's certainly enough to maintain attention and have casual listeners think "that was interesting" (IMO of course, but I have had people say exactly that).

One of my favourite chord progressions moves in alternating major and minor thirds (descending). You can move through all 12 major and all 12 minor triads and it can create quite a sense of tension as you're never sure just where it's going to end. So for example, starting at C major, down to a minor, then down to F maj, --> d min --> Bb maj --> g min --> Eb maj --> etc etc etc. You can essentially stop anywhere and it doesn't really sound "wrong"

As for the circle of 5ths, as a general rule, the most common thing to do is to introduce the leading note of the new key (ie, dominant of the dominant as it's called), so if you were moving from c minor to g minor, introduce the f# in a D major chord (the dominant of G).

... All of the above also presupposes that I'm staying relatively tonal in my improvisations. 9 times out of 10, I'm usually in some strange mode (easier to cover up "wrong" notes )

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Thank you, Soubasse. I would be interested to hear some of your improvisations some time.

Not long ago, I read of somebody who claimed (he/she) could transpose from any key to any key in three chords. Maybe, but I'll bet some of them sounded a bit raunchy.

Oh, but I can do it in one chord. Depending on the interval between keys, it's just not going to sound nice. :grin:

:lol::lol: Thanks acc - have one on me! :cheers:

Not long ago, I read of somebody who claimed (he/she) could transpose from any key to any key in three chords. Maybe, but I'll bet some of them sounded a bit raunchy.

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Well, the ubiquitous diminshed 6th can really take you practically anywhere (it worked for Franck!)

Franck also seems to have been fond of modulating up by a minor 3rd. There's a very beautiful example towards the end of the 2nd Choral where the two themes are combined. But it was in the "Final" that he went farthest, producing some truly breath-taking modulations - he had a "raunchy" side too!

Soubasse said:

:lol::lol: Thanks acc - have one on me! :cheers:



Well, the ubiquitous diminshed 6th can really take you practically anywhere (it worked for Franck!)

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Loved your "bit raunchy" comment as, often, sudden harmonic shifts can sound sleazy or oily. Here are some one step solutions involving a pivot chord. I've put them in C major and C minor for the sake of easy (just transpose as required).

From Major Keys

1.1 C major to D flat major (or C sharp minor)
Interval - semitone up
Method

(a) German 6th becomes V7 of new key (note: enharmonic change)

(b) bVI becomes V of new key (where the "b" should be a flat symbol)
(Note: enharmonic change if a chormatic semitone up)

1.2 C major to A major
Interval - Minor 3rd down
Method
Transition from original I to new V7

From Minor Keys

2.1 C minor to E flat minor
Interval - Minor 3rd up
Method

Move straight from I to new V7

2.2 C minor to G sharp minor
Interval dimished 4th down
Method

Move straight from I to new V7
(note: enharmonic change)

More on chormatic harmony and raunchyness

Tonic Chormatic Seventh and Ninth

These chords are fairly useless as they are very oily (raunchy) but they can help you cope with a sudden alien note in a melodic line: (see attachment)

I'm so sad, really adored harmony, counterpoint and fugue in my youth! Still have my texts and still read them!

I like 1.1 there - haven't used that before but I just tried it and it sounds rather nice. All the other ones I know well (although sometimes I'll just go straight to them without even using a dominant 7th which I know for some people is a bit :scold::scold::scold: but the improvisations of Durufle, Dupre, Tournemire, Cochereau et al still manage to raise eyebrows down here, so conservativeness (if there is such a word) is alive and well :grin: )

Actually, the whole issue of whether something sounds raunchy or not is a good one as it is A MATTER OF PERSONAL TASTE. I happen to like the greasy/oily/raunchy use of chromatic harmony ... after all ... Ravel and Debussy used these devices as part of their harmonic palate .. .

I don't know if the circle of fifth is needed for key changes. I have a number of "tricks" for changing keys. One of these tricks is that if your in C minor you can easily take any chord that has a C in it and it won't be too much of a surprise if you make that chord a dominant to the following chord.

For instance
C minor - D7 - G minor,
C minor - F7 - B,
C minor - A flat 7 - D flat

Notice in the last example that the new key isn't fully established yet, If I follow with a G flat chord then it's clear the new key is D flat major, If I instead take a E flat 7 chord then suddenly it's evident that the new key is A flat major. This ambiguety can be useful. You can also give another function than dominant to the newly introduced chord:

C minor - C minor/Bb - Amin7 - D7 - G major/minor

Another useful trick is to make a major chord into a minor chord. Especially useful on the dominant as it so clearly gives it another function. A function depending upon the chords that follows it. For example:
C minor - G minor - C7 - F
C minor - G minor - D7 - G minor
C minor - G minor - F7 - B flat

There are so many other tricks and you learn them by spending countless of hours improvising on the instrument. Good luck and have fun.

Contratrombone64 said:

Loved your "bit raunchy" comment as, often, sudden harmonic shifts can sound sleazy or oily. Here are some one step solutions involving a pivot chord. I've put them in C major and C minor for the sake of easy (just transpose as required).

From Major Keys

1.1 C major to D flat major (or C sharp minor)
Interval - semitone up
Method

(a) German 6th becomes V7 of new key (note: enharmonic change)

(b) bVI becomes V of new key (where the "b" should be a flat symbol)
(Note: enharmonic change if a chormatic semitone up)

1.2 C major to A major
Interval - Minor 3rd down
Method
Transition from original I to new V7

From Minor Keys

2.1 C minor to E flat minor
Interval - Minor 3rd up
Method

Move straight from I to new V7

2.2 C minor to G sharp minor
Interval dimished 4th down
Method

Move straight from I to new V7
(note: enharmonic change)

More on chormatic harmony and raunchyness

Tonic Chormatic Seventh and Ninth

These chords are fairly useless as they are very oily (raunchy) but they can help you cope with a sudden alien note in a melodic line: (see attachment)

I'm so sad, really adored harmony, counterpoint and fugue in my youth! Still have my texts and still read them!

Click to expand...

Contra would you be prepared to post some of the texts? i'm especially interested in fugues!

Just noticed that there hasn't been a response to Bach>Meer's query about the key changes in the Wedge fugue. There are a number of web sites with detailed analysis of some of Bach's organ pieces but alas, I've been unable to find one on the Wedge. Whilst I'd be happy to do one of my own, it's time I don't have right at the moment, however, it would make for a good analytical exercise (maybe I'll inflict it on one of my classes!:devil

One of the things that retains interest in that fugue is the chromaticism of the subject itself and the implied harmony therein. My take on that has been: I (upbeat) | V , I(sharp 3, flat 7) | IV(sharp 3) , II(sharp 3, flat 5, flat 7, 3rd inversion) | I(2nd inversion) | V | I |
or for those who prefer chord names: Em | B , E7 | A , F#7(b5)/A# | Em/B | B | Em
which I find is an intriguing number of chords to move through in such a short space of time

That's probably another thing about some of the tips that have come up so far. An inversion can really add interest to a harmonic progression. I for one am fond of using the 7th of a V7 chord in the pedal, especially in last verse alternate harmonies of hymns. For example, if I see that I could use I - IV - V - I, I'll often go Ib7(3rd inv) - IV(1st inv) - V - I. I've had some very favourable comments about that one.

Soubasse

I think there is little point in analysing the theme for the Wedge Fugue (or any subject of any fugue for that matter) as it's never harmonised vertically ...

what do you think?

I probably should have clarified that it was my interpretation of the implied harmony for the very first statement of the "wedge" subject. You are quite right of course, because once we get past the exposition of all four voices, JSB utilises many alternate harmonisations of the subject (not to mention a few appearances of the counter-subject with alternating harmonisations as well) as any master fugal writer should ... well, let's face it, there really was only one master fugal writer wasn't there?!:grin:

I've often felt that he wrote that theme specifically for that reason - aside from its interesting shape on the page (and the ear), that much chromaticism is open to numerous harmonisations, particularly in his gifted hands.

As for other fugue themes, I'm inclined to think it depends on the subject, as there are some for which the harmony is not so much implied as it is painfully obvious. The "little" g minor subject for example fairly well shrieks of: I - V - I - V - I - V etc etc etc (one of the things that makes it just right for classes ). Later on of course, after exposition, there are some noteworthy harmonic alterations (amidst a substantial number of sequences for such a short piece).

Aloha Soubasse,

And here I thought you liked Shostakovich's 24 preludes and fugues - they are also masterful gems :angel::banana::nut::ut:

Cheerio,

CD :tiphat::tiphat::tiphat:

Ah yes, the Shostakovich. I've only heard a few of those, but yes, they did impress.:up:

Personally, I find that fugal writing tends to be relative to the era and sometimes even the country, rather than relative to the form in itself. For example, I don't believe that one can compare or analyse a Bach fugue the same way you would a fugue from one of the Mendelssohn sonatas (which frankly I think are awful, but that's just IMO). Nor could you really apply the same measure with a Bach fugue to a fugue by Handel or Boyce or anyone else across the pond. Let's face it, what the English called a fugue differed notably from the German version, specifically JSB. I still think that JSB took the form itself to its absolute zenith (and possibly even past it), and I'm not sure that too many have equalled or bettered it since. However, as I said, I think it's all relative, and 'tis a curly one to be sure. Happy to debate it with anyone far more knowledgable :grin:

Do you like this piece? I find it just amazing!

http://www.youtube.com/watch?v=5s4TKOaUZ7c

Glenn Gould talks about his work "And So You Want To Write A Fugue" on Canadian TV - this a bit satirical work was written and recorded 1n 1964 for the TV show Anatomy Of Fugue.

....For a canon in inversion is a dangerous diversion,
And a bit of augmentation is a serious temptation,
While a stretto diminution is an obvious allusion.... )

Here the lyrics and short analysis:

http://aix1.uottawa.ca/~weinberg/fugue.html

Man, Bach was THE polyphonist of all times, and Glenn Gould was THE musician who let this music speak!