second lesson - part 1

There are 5 variations to each of the full musical notes (C, D, E, F, G, A, B) based on a semi-tone seperation on the lower and higher ends. These are called Accidentals of a note. They are :
1) Double-flat (♭♭) 2) Flat (♭) 3) Natural (♮) 4) Sharp (♯) 5) Double Sharp (×)
♭♭is being used here for want of a symbol that looks can represent double-flat. Originally, it must look like the 2 flat symbols are stuck together instead of the gap. I must constantly be on the look out for a better utf8 symbol
When we refer to a note, say A, we generally mean A♮ - which is A-natural. With semitone separation between notes, there are 12 notes. C, C^♯, D, D^♯, E, F, F^♯, G, G^♯, A, A^♯, B.
Logically, then, there will be multiple ways to refer to a note. So, C can be referred to as D^♭♭ or B^♯. So, for the first time after I started learning guitar, I heard the term B^♯ ... or even E^♯, for that matter. Naturally, I got skeptical and curious and asked Deepak, what was this all about .. there is no such thing as B^♯ and so on. He said that is not true. Then I asked him, why accidentals, when we have clear cut representations for the 12 notes. Why even bother to represent them in multiple ways and create ambiguity ? As an answer he started me off on Circle of Fifths:

Circle of fifths:
The idea is to start of with a scale (major or minor) and write down the scale of the with the fifth note (from beginning or end of the scale) of current scale as the key. While doing this, we must make sure that all 7 notes C, D, E, F, G, A, B are mentioned with the appropriate accidentals. This is to avoid having to mention the accidentals of the same note again and again within a scale. For example, if we needed to mention A and A^♯, we rather mention A and B^♭.

Here goes the circle of fifths with C note as the first key. Both ascending (fifth from beginning of each scale) and descending (fifth from end of a scale).

Ascending Circle of Fifths:

C	D	E	F	G	A	B	C
G	A	B	C	D	E	F♯	G
D	E	F♯	G	A	B	C♯	D
A	B	C♯	D	E	F♯	G♯	A
E	F♯	G♯	A	B	C♯	D♯	E
B	C♯	D♯	E	F♯	G♯	A♯	B
F♯	G♯	A♯	B	C♯	D♯	E♯	F♯
C♯	D♯	E♯	F♯	G♯	A♯	B♯	C♯
G♯	A♯	B♯	C♯	D♯	E♯	F×	G♯
D♯	E♯	F×	G♯	A♯	B♯	C×	D♯
A♯	B♯	C×	D♯	E♯	F×	G×	A♯
E♯	F×	G×	A♯	B♯	C×	D×	E♯

Descending Circle of Fifths:

C	D	E	F	G	A	B	C
F	G	A	B♭	C	D	E	F
B♭	C	D	E♭	F	G	A	B♭
E♭	F	G	A♭	B♭	C	D	E♭
A♭	B♭	C	D♭	E♭	F	G	A♭
D♭	E♭	F	G♭	A♭	B♭	C	D♭
G♭	A♭	B♭	C♭	D♭	E♭	F	G♭
C♭	D♭	E♭	F♭	G♭	A♭	B♭	C♭
F♭	G♭	A♭	B♭♭	C♭	D♭	E♭	F♭
B♭♭	C♭	D♭	E♭♭	F♭	G♭	A♭	B♭♭
E♭♭	F♭	G♭	A♭♭	B♭♭	C♭	D♭	E♭♭
A♭♭	B♭♭	C♭	D♭♭	E♭♭	F♭	G♭	A♭♭

When a major scale, such as a C major scale, is being worked upon, it is interesting to observe how the ionion mode of another scale would sound like, if the scale started off from the fifth note of the current scale. When writing these scales, to avoid ambiguity of having to use the same note in its natural and sharp format, the accidentals of a previous or a next note are used, so that all the notes have a representation within a given scale.