I thought this would be the best place to post this query. My teacher briefly explained these to me at my lesson on Monday and drew me two diagrams. However, I've slept since then and my old addled brain's struggling to remember how she explained it

Help?

Thanks (in anticipation of enlightenment)

Not an idiots guide, but it does explain it: http://en.wikipedia.org/wiki/Circle_of_fifths

Thanks Mad Tom ... I'm off to investigate the wonderful world of Wiki

I like to think of it as a clock face. Replace the '12' with a 'C'. Clockwise gives you major keys with sharps and anti gives you major keys with flats. So 'C' has no sharps or flats. Count up 5 notes (including C) C,D,E,F, 'G'. Gmajor has one sharp. Going back to our major scale construction of TTSTTTS, we know this sharp is an F#. Count up 5 again: G,A,B,C, 'D' So 'D' major is our next major key. We can see this has two sharps. One is F#, and the new sharp is 5 notes above the last sharp so it is a C#. The last sharp in the key signature always applies to the 7th degree of the scale too. The note before the key note. So in G major the last sharp is F#. In D major the last sharp will be C# etc.
Going anti clockwise, count backwards 5 notes. C, B, A, G, 'F' So our first major key with a flat is F major. Again using the construction of the major scale TTSTTTS we see the flat must be a Bb. 5 notes back from F is B. We know it is the key of Bb because F major already has a Bb in it's key signature. So Bb major has 2 flats: Bb and Eb ( the last flat is 5 notes below this time) B, A, G, F, 'E'

I hope this helps. I am learning my self so if any of this is incorrect I am sorry and most prepared to be corrected!

I find the clock analogy helpful too, but I prefer to think of the movement from a key to its subdominant as clockwise, because it's the way the music naturally "wants" to go. Modulation to the dominant is more like pushing against resistance.

Mnemonic for cycle of fifths:

Cats Go Down And Eat Beef For Choice (the last two need to be sharpened, of course) ... 4ths is the same, in reverse.

nick

I don't think that the standard learners diagram is written that way though is it?



I was taught something similar too! But to remember the order of sharps and flats in the keys - although they are just memory aids and don't teach us the why or how;
#s - Father Charles Goes Down And Ends Battle
bs - Battle Ends And Down Goes Charles' Father

OOOoooo, yes that's what my tutor said. It's starting to come back to me now. Thanks for all your helpful responses.

I think it varies, as you'd expect. Certainly C is sometimes at 6 o'clock rather than 12. Anyway the important thing is to find something that works for you because you understand it, rather than just accepting what someone else tells you.

Very true. I must admit I have only seen the diagram with C at the top. You learn something new as they say!

Just thought I'd let you know that the penny FINALLY dropped yesterday and I now understand how it works. Thanks to all who posted and for giving me a shove in the right direction

Any time! Glad if I could help in any way, as a studendent my selfit's nice to be able to help others as so many help me on here x

Anyone insecure on the traditional circle of 12 fifths should not read the rest of this post, which is irrelevant to ABRSM Grade Exams.





Closing the circle of fifths is possible only by assuming that several pairs of notes that are represented differently correspond to identical pitches. On fixed pitch instruments, the makers make that assumption, and nowadays its precise form is almost always that C# = Db, D# = Eb, F# = Gb, G# = Ab and A# = Bb. In the past, other assumptions were made. In particular, a few keyboard instruments (probably either harpsichords or organs) were made with 19 keys in each octave. In addition to the more common split of each of the black keys, so that flats and sharps could be differentiated, these instruments had a key between E and F, and another between B and C. On these instruments, the circle had 19 fifths in it, one such being notated:

C, G, D, A, E, B, F#, C#, G#, D#, A#, E#, B#, Fx = Gb, Db, Ab, Eb, Bb, F, C.

The extra keys played notes that were notated as E# = Fb and B# = Cb. Between other pairs of naturals, the sharp was equivalent to the double flat and the double sharp equivalent to the flat. If the tuning was equal tempered, the diatonic semitone was twice the size of the chromatic one.

Other tunings of the octave in equal temperament that improve on ET12 thirds and sixths are those into 31 and 53 steps. Enharmonic equivalences in ET31 can be found here. In this tuning, diatonic and chromatic semitones are in the ratio 3:2.

In ET53, it is possible to distinguish the major tone from the minor tone. In order to show its enharmonic equivalences, normal notation must be extended by triple and quadruple flats and sharps, so I shall leave that as an opportunity for someone who is even more geekish than I am.

If anyone is interested in being more geekish than kenm, the free program 'Scala' http://www.xs4all.nl/~huygensf/scala/ is a great one with which to play around. You can load literally hundreds of different temperaments, or put in your own, and hear the resulting available interval & chord tunings. Unfortunately, I haven't worked out how to get these temperaments into a MIDI synthesizer thingy, despite my mastery of technothingywotsits. I'd love to be able to play back Bach midis with different temperaments.

If you want an ungeekish demonstration of the mirage of the 'circle of fifths', find a keyboard tuned in just intonation, and try playing Ab major. It doesn't exist, as what you might think of a fifth on a normal (equally tempered tuned) keyboard (Ab-Eb), is actually G#-Eb, which, as any student of theory will know, is a diminished 6th ... or, in common parlance, in this case, the 'wolf fifth'. This is where the circle doesn't quite meet up. The not-meeting-upness sounds horrible, and makes Ab an unusable key on such keyboards. Just intonation was still sometimes used in the 17th century ... which is why you won't find any music from the Fitzwilliam Virginal Book in Ab major.

If I've got my facts wrong, please feel free to correct me, kenm!

I haven't checked any of your references, but it all sounds fine to me.

Re processing MIDI, I have just downloaded the demo version of MPL (MIDI Programming Language) from this site. At present I have a project to use the combination of a keyboard, a laptop and a Roland sound generator to simulate a double-action pedal harp and do the clever glissandi that harps can do so easily (e.g. A B# C D# Eb F# Gb for a diminished seventh). On the back burner is a harpsichord simulator with dynamic tuning depending on the chord. The language is a curious mixture of sophisticated built-in file and MIDI hardware interfaces, with five separable processes within the program, and sound but very basic programming control and arithmetic on two data types, string and integer. Built-in solution of the hardware interface problems saves weeks of work, so having to adopt programming techniques similar to those of my assembler programming experience (c. 1967) is a small price to pay. The working program will need the full version of MPL, but it costs only 25 US dollars.