[Dixielandjazz] More on the Circle of Fifths

[Talegatorz at aol.com]

Well John, you've started a great thread.

In answer to your original question: The first tone is called # 1. Therefore 
C=1
D=2, E=3, F=4 and G=5. It is the fifth tone. Call G #1 and count to five 
again and we have D and so on.
 
I now quote from Ear Training and Sight Singing by George A. Wedge c.1921.
 
"A key is a family of tones. These are all derived from one tone, the head of 
the family, called a Key -Tone. If a vibrating string gives the pitch of C, 
and we wish to find a tone most nearly related in vibration, but differing in 
pitch, we would first divide the string into halves and set either half in 
vibration. Either segment vibrates twice as fast and gives the pitch of C, but one 
octave higher. Next try dividing the the string C into thirds and set the 
two-thirds length into vibration. This gives the pitch of G or the fifth tone 
above C. This fifth tone is the most nearly related tone, differing in pitch, to 
the fundamental."
"In the same way the next nearly related will be two thirds of G or a fifth 
above G, which is D, the next a fifth above D, which is A, the next a fifth 
above A, or E: next a fifth above E, or B." 
       "Conversely, if D is two thirds of G and G is two thirds of C, C must 
be two thirds of a tone a fifth below, or the tone of  F."
       "The most comprehensive arrangement of these key tones is shown upon a 
clock face, placing C at twelve o'clock, each new sharp key a hour to the 
right and each new flat key an hour to the left, The hour at which the key occurs 
gives the number of sharps and flats in the signature, A is at three o'clock 
(halfway), and has three sharps in its signature; Eb is halfway on the other 
side and has three flats..."

 That so many get along just fine without this bit of knowlege could be 
because it is based upon one of the core principle of a string's vibration and how 
its length detirmines the tone. 
I find that some stringed instruments are easily tunable with electronics and 
some are not. Disregarding poor set up, worn strings or a warped neck, could 
this be because loose manufacturing tolerences result in inconsistent 
distances between the fretting?
Tuning the open strings electronically does not always translate to tuned 
notes up the neck. Know your instrument.

So, everyone, get out your guitars, tuners and tape measures and have a ball. 
I hope this has added to our interest and confusion.

Gus Bloch