Keys

[Paul Graupp]

Listening to Georgia Public Radio this afternoon, the announcer said this classical composer had: "Written 24 Preludes; one for each key."

The wheels started to grind as I ran the circle of 5ths through my head and I came up with 15. I must have missed something...perhaps the related minors ?? But that gave me 30 so I was still wrong.

Then I remembered something we had learned from Bob Hoffnar a few years back. Enharmonic Equivalents !

B is the equivalent of Cb; Db is the equivalent of C# and F# is the equivalent of Gb. So there are only twelve actual keys plus their 12 related minors and we have the 24 keys he composed in.

It took a little time and a lot of thought but my learning here on the Forum came to good use !!

Regards, Paul

[Richard Sinkler]

Technically, wouldn't there only be 11 keys (the 12th is an octave of the 1st), assuming only major keys at this point.

So there are only twelve actual keys plus their 12 related minors and we have the 24 keys he composed in

Corrected statement below

[Paul Graupp]

Good point Richard. I was only thinking about the circle of 5ths but the fretboard reference is a valid one. Where did I put my thinking cap ?? I won't have the answer for a few days because I'm having eye surgery in the morning.

Truth be known, I may not have it then but perhaps Bob Hoffnar will catch this and solve the puzzle...

Regards, Paul

[Blake Hawkins]

If you start the list on "A" wouldn't the 12th key
be Ab?

[Paul Graupp]

Blake: When you work in the circle, the rotation is based on the 5th step or dominant note. Sharp scales are built until the scale become C# with all steps (7 each ) adding one sharp note for each new scale.

The Dom in C is a G and the next scale, with one sharp note, is GM. This repeats using the 5th of G, a D with two sharped notes. Then an A with 3 sharps and so on.

Flat scales use the 5th below or sub-dominant which in C is an F note. Building a major scale on F requires the B step to be flatted to fit the major scale intervals.

This Bb is now the new sub-dom and building a scale on it requires two flatted notes. This process repeats until you get a Cb scale with all flatted signs. The circle then reads:

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

15 steps and remove the Enharmonics and you get 12.

But you cannot correlate this 5th Circle to the fret board and therein lies my puzzle. It may well be just a terminology thing but I'm on medication and cannot solve it.

Regards, Paul

[David Doggett]

Forget about the cycle of 5ths and enharmonics. Blake has the answer. I prefer to count starting on C, but the chromatic diatonic scale has 12 tones, not counting the octave (Richard, you must have miscounted). So there are 12 unique keys, and counting the relative minors, that's 24. Theoretically each one could be either a sharp key or a flat key, but the notes would be the same. By convention, the key name for any given note that has the fewest sharps or flats in the signature is the one commonly used, and the other is ignored. Gb and F# have the same number of flats or sharps, so take your pick.

Oh wait, I see your problem. You must have thought that since the octave is at the 12th fret, there must be only 11 notes not counting the octave. But that's because the nut is called the 0 fret rather than the 1st fret. When you count up a scale, the root note is counted as one, not zero.

[Richard Sinkler]

Dave, I think you're right about my miscounting. If I write out the notes as below, there are 12 distinct notes, not counting the octave. I guess I need an enema so my brain will work.

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

[Dave Boothroyd]

Assuming you are referring to Johann Sebastian Bach, his set of demonstration pieces for his well-tempered scale is actually the 48 Preludes and Fugues.
24 Preludes and 24 Fugues. The whole set were published in a book called "The Well Tempered Clavier" (only in German!)
The scale he used was not quite the same as modern "twelfth root of two" equal temperament, but unlike the traditional just tunings, it did allow the use of all twelve major and minor keys, and avoided the offensive "wolf notes" when playing in keys remote from the reference note from which the JI intervals had been calculated.
As we often see on here, some people still find the pitch inaccuracies of even temperament offensive.
Cheers
Dave

[John Cipriano]

Edit: Dave beat me to it, apparently I can't read.

Well-Tempered Clavier is notable for being supposedly the first book written with pieces for all keys, as well as just a really popular collection of "educational" baroque keyboard pieces.

http://en.wikipedia.org/wiki/Well-Tempered_Clavier
(harpsichord recordings of the pieces)

http://en.wikipedia.org/wiki/List_of_co ... 0.93893.29
(you can count all of the keys here)

Regarding keys, frets, and the circle of fifths...you keep adding 7, which is the number of half steps in a fifth. When you get a number that's 12 or larger you subtract 12 (that is, move down an octave). Just as there are 12 keys, there are 12 unique frets...0/E to 11/D#.

C: 8th fret
G: 3rd fret (15 - 12)
D: 10th fret
A: 5th fret (17 - 12)
E: open (12 - 12)
B: 7th fret
F#: 2nd fret (14 - 12)
C#: 9th fret
G#: 4th fret (16 - 12)
D#: 11th fret
A#: 6th fret (18 - 12)
F: 1st fret (13 - 12)

and so on.

What I always found really crazy in music class was the way that the keys progress in the number of sharps and flats, and the actual sharps and flats follow the circle of fifths. Like Key of G has one sharp, F#. Key of D has two sharps, F# and C#. It's probably just a side effect of the way piano keys are laid out but it's a neat symmetry.

[Paul Graupp]

John: In the Testing Forum, I have made two charts titled Keys and you can see how the scales work themselves out. Notice that while maintaining the intervals of a major scale, each note that is sharped or flatted retains that sign in each succeeding scale and hence the accumulation.

Regards, Paul