# Key Signatures



## millionrainbows (Jun 23, 2012)

We'll start on C, project a minor third from that, yielding an Eb, then another minor third from there, giving us Gb. From Gb, up a minor 3rd is Bbb, or enharmonically, an A, giving us the familiar 'diminished seventh' chord. As you can see by the 'Bbb/A,' the glitch in our diatonic 7-letter-name scale system is revealed by this. A scale must consist of seven different letter-names. This is a good time to discuss this in more detail.
On a keyboard, Gb and F# are the same note, physically.

If one starts building fifths from a starting point of C, then going "forward" or clockwise around the "circle of fifths" would yield C-G-D-A-E-B-F#(C#-no need for D#).

If, on the other hand, you go in reverse (counter-clockwise), you travel the "circle of fourths", which yields C-F-Bb-Eb-Ab-Db-Gb (Cb).

As you can see, there are three keys which "overlap" under two different names: B (Cb), F# (Gb), and C# (Db). The reason it goes no further has to do with the physical layout of the keyboard itself (there are two semitone steps in the letter sequence), and the subsequent "letter-naming" of notes which results. To be a diatonic scale, you must have seven different letter names. 

For example, there is no key of "Fb" because this is E, a sharp key; but if we named it anyway, we would get Fb-Gb-Ab-Bbb (you can't repeat A - there must be seven different letter names with no repeats), Cb-Db-Eb-Fb. This "repeating letter or double-flat" dilemma does not arise on the three "repeat" keys of B (Cb), F# (Gb), and C# (Db), because this is the "seven-letter limit".

In equal tempered tuning, both end points (F# and Gb) are identical, because all the "fifths" have been adjusted flat by 2 cents, to keep from "overshooting" the mark. Otherwise, instead of a closed circle which repeats from octave to octave, we would have an endless spiral, and an infinite number of different notes.

In other tuning systems, which I am just now beginning to understand & study, the physical layout of the keyboard must remain as 12 notes (7 white and 5 black), regardless of what tuning we use.
We don't want to have a separate "F#" and "Gb" black key, although this has been tried.

In either mean-tone or Bach's tuning, what remains consistent in a "key signature" is the RELATIONSHIPS or intervals produced in that octave or key, all in relation to the "key" note.

For instance, in mean-tone tuning, starting from C and building our fifths, we have C-G, G-D, D-A, and A-E. The fifths are adjusted in mean-tone, made smaller, in order to create a good-sounding major third of C-E, which without adjustment would have been too sharp. This was a limited tuning, since going in fifths clockwise yields C-G-D-A-E-B-F#-G#(Ab), or counter-clockwise yields C-F-Bb-Eb. This sequence produces in G#- Eb (or Ab-Eb, or G#-D#) a "wolf" fifth. So there is the limit of mean-tone tuning.

Bach's tuning was not "equal", but it was "well" tempered, meaning that, unlike mean-tone tuning, he could get a decent sound in all twelve keys.

In mean-tone tuning, there IS no "Gb", only F#.

In the Bach tuning, the difference in F# and Gb would show up as the OTHER keys those notes are in; for example, in the key of D (a sharp key), the F# is the major third. This would be a different-sounding major third than the C-E in the key of C, it might be a wider or narrower interval span. 

Similarly, F# could be the fifth in the key of B (also a sharp key). This B-F# fifth is unique to this key.

Gb could be the fifth of the key of Cb, because a fifth below Gb (keeping our letter rule) would be Cb. This would be a unique fifth for that key, maybe more "perfect" and restful, or "sharper" and restless.

Gb can't be the major third in any key; there is no key of "Ebb". This is really D, in which case we must call it "F#", not Gb.

In Bach tuning, the keys of F# and Gb would also be identical.


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