Music Theory 101: Chromatic and Major Diatonic Scales
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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. Theory provides 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.

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 song’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. 

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)

Thumb via:  http://esd.cs.ucr.edu/labs/music/scale.gif  with my appreciation

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

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Comments (8)

I used to have a basic understanding of reading music. That's long gone, but your article reminded me of a few things.

excellent, I could never read music

Impressive work Sir. You have broaden my knowledge in this area specifically I am concerned and researching the relationship of music to architecture, as it is known that "Architecture is a Frozen Music".

Ranked #2 in Music

Excellent work! Diatonic scales became so common to me I have even forgotten they were diatonic.

Ranked #1 in Music

Happy to help, Abdel-moniem. Yes, music-as-architecture-as-music would certainly be a fascinating area to explore.

Ranked #1 in Music

Thanks Sandy and Carol. Carol, the thing about theory is that is provides anyone--even non-readers--a way to conceptualize what they hear. After so many years of not reading (the 70s when I was a studio musician), it's a tedius struggle for me to read sheet music. But knowing theory, I can still easily visualize music structure. Theory CAN lead to reading, but it is actually separate and apart.

A truly helpful article for anyone. I always noticed that my piano students would improve at ear tests (playing back a simple melody after hearing it), and even sight reading, when they finally grasped theory.

Ranked #1 in Music

Even in a non-formal setting, Sharla, theory can help even non-musicians gain insight into music they never thought possible. I've taught elements of basic theory to non-musical friends--just for fun--who were shocked at how well they could understand basic musical concepts like harmony despite the fact that they didn't play instruments.

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