modes, scales, & key signatures

introduction

I wanted to understand the concept of key in music - as, for example, where a piece of music is 'in' the key of E-flat Major. By looking up musical terms in the Oxford English Dictionary (OED), I came to understand that I could see and hear the twelve major scales as follows: Begin at any of the twelve keys (on the keyboard) from C to the next B inclusive, and use the interval sequence -T-T-s-T-T-T-s- where the dashes stand for the keys you press, 'T' stands for 'full Tone', and 's' stands for 'semi (or half) Tone'. That is 's' means press the next key (to the right if you are reading from left to right), and 'T' means leap frog over the next key to the following one.

At this point, I was able to play the German national anthem with my right hand, and I had copied the score from the internet. It was obvious that I was using the major scale that begins on E-flat, and it was tempting to say 'this music is in the key of E-flat Major' but I refrained. From the OED, I knew that the major scales have a major third, while the minor ones have a minor third. But the OED definitions were a bit circular - major being bigger than minor and minor being smaller than major. In order to understand both key and minor scale, I turned to the Wikipedia encyclopedia.

natural minors

I found: "The natural minor scale is the 6th (or Aeolian) mode of the major scale."

And I found the chart which I copied and photagraphed below. Given that the Ionian interval sequence is the one which generated the major scales, I applied the Aeolian interval sequence in the same way that produced the major scales. The result was a set of scales that agreed exactly with a chart in Wikipedia under the heading 'minor scales'. Using blocks and a camera on the rest of this page, the major scalses are shown with their natural minors.

the circle of fifths and the signature keys

Also in Wikipedia, I found a diagram labelled 'circle of fifths'. It shows the signature keys for the major and natural minor scales. I will not attempt to reproduce the pictures. Suffice it to look under the first picture below to see the description of the signature key for the c-minor scale. See how the blocks move to show you the signature key.

Major scale:    (yellow upper) C             &             its natural minor:    (red lower) c

Signature key for C Major:   blank

Signature key for c minor:   flatten E,A,B

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Major scale:    (yellow upper) D-flat             &             its natural minor:    (red lower) c-sharp

Signature key for D-flat Major:       flatten D,E,G,A,B    or    sharpen C,D,E,F,G,A,B

Signature key for c-sharp minor:       sharpen C,D,F,G

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Major scale:    (yellow upper) D             &             its natural minor:    (red lower) d

Signature key for D Major:   sharpen F,C

Signature key for d minor:   flatten B

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Major scale:    (yellow upper) E-flat             &             its natural minor:    (red lower) e-flat    or    d-sharp

Signature key for E-flat Major:   flatten E,A,B

Signature key for e-flat minor:   flatten E,G,A,B,C,D             Signature key for d-sharp minor:   sharpen E,F,G,A,C,D
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Major scale:    (yellow upper) E             &             its natural minor:    (red lower) e

Signature key for E Major:   sharpen F,G,C,D

Signature key for e minor:   sharpen F

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Major scale:    (yellow upper) F             &             its natural minor:    (red lower) f

Signature key for F Major:   flatten B

Signature key for f minor:   flatten A,B,D,E

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Major scale:    (yellow upper) G-flat / F-sharp             &             its natural minor:    (red lower) f-sharp

Signature key for G-flat Major:   flatten G,A,B,C,D,E       Signature key for F-sharp Major:   sharpen F,G,A,C,D,E

Signature key for f-sharp minor:   sharpen F,G,C

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Major scale:    (yellow upper) G             &             its natural minor:    (red lower) g

Signature key for G Major:   sharpen F

Signature key for g minor:   flatten B,E

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Major scale:    (yellow upper) A-flat             &             its natural minor:    (red lower) g-sharp

Signature key for A-flat Major:   flatten A,B,D,E

Signature key for g-sharp minor:   flatten A,B,C,D,E,F,G    or    sharpen G,A,C,D,F

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Major scale:    (yellow upper) A             &             its natural minor:    (red lower) a

Signature key for A Major:   sharpen C,F,G

Signature key for a minor:   blank

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Major scale:    (yellow upper) B-flat             &             its natural minor:    (red lower) b-flat

Signature key for B-flat Major:   flatten B,E

Signature key for b-flat minor:       flatten D,E,G,A,B    or    sharpen C,D,E,F,G,A,B

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Major scale:    (yellow upper) B             &             its natural minor:    (red lower) b

Signature key for B Major:   sharpen C,D,F,G,A    or    flatten C,D,E,F,G,A,B

Signature key for b minor:   sharpen F,C
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key and scale

In Wikipedia, I found the following statement - which vindicates my caution about using the word key:

Again in Wikipedia, I found the following statement - which vindicates, within the limits of simple music, my temptation to say that the version of the German national anthem that I found on the internet is written in the key of E-flat Major. I type the quote because it is too long to photograph.

BEGIN QUOTE FROM WIKIPEDIA
"
In music theory, the term key is used in many different and sometimes contradictory ways. A common use is to speak of music as being 'in' a certain key, such as 'in the key of C' or 'in the key of F-sharp'. Sometimes the terms major or minor are appended, as 'in the key of A minor' or 'in the key of B flat major', and so on. Although the concept of musical key can be a complicated subject when examined closely, broadly speaking the phrase 'in the key of C' means that C is the music's harmonic center or tonic. Note that the letter 'C' does not indicate a single specific pitch but rather all pitches with the letter name C (sometimes called a pitch class). The terms 'major' and 'minor' further imply the use of a major scale or a minor scale. Thus the phrase in the key of E major implies a piece of music harmonically centered on the note E and making use of a major scale whose first note, or tonic, is E. Although the term 'key' is commonly used this way, actual music can rarely be described so simply. This overview of the term also makes many assumptions and my not hold true for all forms of music.
"
END QUOTE FROM WIKIPEDIA