Music Theory 101: Chromatic and Major Diatonic Scales

Music “theory” is essentially a mathematical approach to explaining the principles behind the construction of music. Theory not only provides an understanding of musical composition, it provides a common language for communicating musical concepts.

Music “theory” is essentially a mathematical system designed to explain the principles behind the construction of music composed in the Western World.

Theory not only provides an understanding of musical composition, it serves as a common language for communicating musical concepts; a way to visualize harmony, chord construction, and scale usage.  And whether you’re new to music or a road-worn professional, music theory can open doors of comprehension and creativity nothing else can.

The Chromatic, 12-Tone Scale

All music of the Western World--from Classical to Country--is based on a progression of 12 notes called the Chromatic Scale. From this scale, all major and commonly used minor scales, intervals, and chords are derived.

A, A? (Bb), B, C, C? (Db), D, D? (Eb), E, F, F? (Gb), G, G? (Ab), A

This series of notes, which follows an ordered succession of what are termed “half-steps” or half tones, reflects the progression of white and black keys of the piano or the frets of a guitar.

Even a quick observation of this scale reveals a few very significant points.  For one thing, the notes basically follow the alphabet from A to G and then repeat themselves, with mid-point notes (accompanied by either a ? or b) interspersed throughout.  For another thing, while for every sharp sign (?) there is a corresponding flat sign (b), there is no B? (Cb) or E# (Fb).  And finally, this scale can easily be imagined as an endless continuum of notes--a “circle,” as it were.

A, A? (Bb), B, C, C? (Db), D, D? (Eb), E, F, F? (Gb), G, G? (Ab), A, A? (Bb), B, C . . .

But what may not be immediately apparent is that within this pattern is a "pattern-within-a-pattern" that emerges when we analyze the relationship between the notes minus the “accidentaled” notes (the ones with sharps and flats). This is best illustrated when we begin the continuum with the C note--although since it is a continuum, we can begin it anywhere:

C, C? (Db), D, D? (Eb), E, F, F? (Gb), G, G? (Ab), A, A? (Bb), B, C . . .

When examined closer, we see that between the C and D notes is an interval of 2 half steps (or 1 whole step); the D and E, 1 whole step; the E and F, 1 half step; the F and G, I whole step; the G and A, 1 whole step; the A and B, 1 whole step; and the B and C, 1 half step. Thus a pattern within the pattern surfaces:

Whole step (W), whole step (W), half step (H), whole step (W), whole step (W), whole step (W), half step (H)

And though it may not be obvious, this "pattern-within-a-pattern" is none other than the scale most kids know as do, re, mi, fa, sol, la, ti, do, but what is commonly known in music theory as the Major Diatonic Scale.

The Diatonic, 7-Tone Scale

Major Scales

While most kids and adults can sing the well-known song that begins, “Doe, a deer, a female deer, ray, a drop of golden sun . . .” few fully appreciate how significant the Diatonic Scale is to virtually every song composed in the Western World--regardless of the musical genre. And unless they read music, even most professional musicians do not fully appreciate the relationship between the Chromatic Scale, what we term “Major Diatonic Scales,” and the W, W, H, W, W, W, H pattern.

As every musician soon discovers, every song comes with its own “key. But what exactly is a “key”?

Fundamentally, a key reflects the particular scale used as a given song’s basis; the specific 7 notes derived from the total 12 available. But additionally, key also lets a musician know what notes will be used to form harmonies, and which chords will most likely be utilized in the son’s structure. Thus, if a musician says, “The key of F,” these four words convey succinctly which chords will most likely be used and which scale it will be based upon--which is handy info for the soloist or backup singer.

So, what exactly is the relationship between the Chromatic Scale, Major Diatonic Scales, and the W, W, H, W, W, W, H pattern?

By design, each letter name of the Chromatic Scale has a corresponding “key” assigned to it. Thus the 12 keys found in Western music correspond to the letter names of the Chromatic Scale, one for each in the succession:

A, A? (Bb), B, C, C? (Db), D, D? (Eb), E, F, F? (Gb), G, G? (Ab),

And by design, music theory provides a mathematical formula that allows musicians to ascertain the note pattern of any of the 12 keys--as derived from the Chromatic Scale. And that formula is the W, W, H, W, W, W, H pattern. And this is how it works.

Pixabay

By starting with any given note of the Chromatic Scale (which then becomes designated the “keynote”) and then following the W, W, H, W, W, W, H pattern, the 7 notes of any given key can be derived.  For example, if we begin with C as our keynote and apply the pattern, we end up with:

A, A? (Bb), B, C, C? (Db), D, D? (Eb), E, F, F? (Gb), G, G? (Ab), A, A? (Bb), B, C . . .

> C, D, E, F, G, A, B, C

Similarly, if we begin with G as our keynote and apply the W, W, H, W, W, W, H pattern we get:

A, A? (Bb), B, C, C? (Db), D, D? (Eb), E, F, F? (Gb), G, G? (Ab), A, A? (Bb), B, C, C? (Db), D, D? (Eb), E, F, F? (Gb) . . .

> G, A, B, C, D, E, F# (Gb), G

And by continuing this pattern, we get all the major keys used in Western music:

C, D, E, F, G, A, B, C

C? (Db), D? (Eb), F, F? (Gb), G? (Ab), A? (Bb), C, C? (Db)

D, E, F? (Gb), G, A, B, C? (Db), D

D? (Eb), F, G, G? (Ab), A? (Bb), C, D, D? (Eb)

E, F? (Gb), G? (Ab), A, B, C?, D? (Eb), E

F, G, A, A? (Bb), C, D, E, F

F? (Gb), G? (Ab), A? (Bb), B, C? (Db), D? (Eb), F, F? (Gb)

G, A, B, C, D, E, F? (Gb), G 

G? (Ab), A? (Bb), C, C? (Db), D? (Eb), F, G, G? (Ab)

A, B, C? (Db), D, E, F? (Gb), G? (Ab), A

A? (Bb), C, D, D? (Eb), F, G, A, A? (Bb),

B, C? (Db), D? (Eb), E, F? (Gb), G? (Ab), A? (Bb), B

Interestingly, when we analyze this list more closely, we see a new pattern-within-a-pattern emerge.

With the exception of the key of C Major (which has no sharps or flats), all the remaining 11 keys follow a pattern of increasing numbers of accidentals. And when we factor in the commonly accepted method of key signature notation we find in Western music manuscript (preferences for either flats or sharps), we find these familiar patterns emerge:

Sharps Pattern:

G, A, B, C, D, E, F?, G  (1 sharp)

D, E, F?, G, A, B, C?, D (2 sharps)

A, B, C?, D, E, F?, G?, A (3 sharps)

E, F?, G?, A, B, C?, D?, E (4 sharps)

B, C?, D?, E, F?, G?, A?, B (5 sharps)

F?, G?, A?, B, C?, D?, F, F? (6 sharps)

Flats Pattern:

F, G, A, Bb, C, D, E, F  (1 flat)

Bb, C, D, Eb, F, G, A, Bb (2 flats)

Eb, F, G, Ab, Bb, C, D, Eb (3 flats)

Ab, Bb, C, Db, Eb, F, G, Ab (4 flats)

Db, Eb, F, Gb, Ab, Bb, C, Db (5 flats)

And since modern music theory is based on principles dating back centuries--with many Classical composers opting to establish their own signature preferences (some effectively composing in B# or Fb)--these keys also exist:

Gb, Ab, Bb, B (Cb), Db, Eb, F, Gb (6 flats)

Cb, Db, Eb, Fb, Gb, Ab, Bb, Cb (7 flats)

C?, D?, E?, F?, G?, A?, B?, C? (7 sharps)

But in any regard, we can easily see how Major Diatonic Scales and their related keys are derived from the Chromatic Scale.

References:

Forty years as a professional guitarist (during which I have studied music theory at the university level and taught many theory classes)

Visit JAMES R COFFEY WRITING SERVICES AND RESOURCE CENTER for more information

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