The World of Scales, Intervals, The Circle of Fifths, and Diatonic Chords

Firstly, the majority of popular music is diatonic. This means it was composed within a major or minor key signature and does not modulate. Furthermore, a key signature determines the set of pitches that "agree" with each other harmonically. There are usually 7 different pitches in a key signature, and a specific formula generates them. The formulas are easy. Choose a note to call 1 ("do"), choose major or minor, and follow the respected pattern of half and whole steps to find the following 6 diatonic pitches.

• A half-step, or "semitone," is a distance of one note on a piano or one fret on a guitar.
• A whole step, or "whole tone," is a distance of two notes on a piano or two frets on a guitar.

Major Formula

whole - whole - half - whole - whole - whole - half

Mnemonics: "What Would Harry Wear When Weighing Himself?"

Examples: G, A, B, C, D, E,  F♯, (G) C, D, E, F, G, A, B, (C)

Solfege: do, re, mi, fa, sol, la, ti, do  

Natural Minor Formula

whole - half - whole - whole - half - whole - whole

Mnemonics: "We Had Waited While Harry Was Walking."

Examples: G, A, B♭, C,  D, E♭, F♮, (G) A, B, C, D, E, F, G, (A)

Solfege: do, re, me, fa, sol, le, te, do

*Several types (modes) of minors follow different interval formulas. Furthermore, I chose to explain natural minor in this introduction because it is the simplest minor mode. Notice its Formula is the same as that of major, except it starts on the 6th step.

An interval is a distance between notes. It can be measured in half-steps or by scale degree (1 through 7) and is often given a name based on sound quality. The most basic interval is called an octave. It describes a doubling in frequency and is the first interval in the Harmonic Series. Here are some other intervals….

• Perfect 5th: 7 half-steps
• Perfect 4th: 5 half-steps
• Major 3rd: 4 half-steps
• Minor 3rd: 3 half-steps
• Major 2nd: 2 half-steps
• Minor 2nd: 1 half-step
• Augmented 4th: 6 half-steps**
• Diminished 5th: 6 half-steps**

The Circle of Fifths

If you were to generate the scale for each major and natural minor key signature (24 scales total), you would notice that each scale is distinguished by the number of "flats" or "sharps" it contains. This diagram from Frank Jargstorff's blog is called The Circle of Fifths. Consequently, it shows that keys separated by 5ths are differentiated by one "flat" or "sharp" in the signature. Additionally, it is a persuasive tool when planning to modulate the tonal center.

**The "Enharmonic Spelling" of a note or interval is like a pseudonym for it. It describes the same sound in a different context. However, only one spelling is correct based on the context. The rule of thumb is to use "sharps" when there are sharps in the key and "flats" when there are flats in the key, except for ascending/descending accidentals and advanced chord alterations.
For example….

• F♯ and G♭ sound the same and look the same on an instrument. Each has its correct usage, depending on the key signature. You should never call F♯ "G♭" in the key of G, D, A, E, or B major because F♯ exists. 
• You should never call G♭ "F♯" in the key of Gb or Db because G♭ exists in those keys.
• An augmented 4th sounds like a diminished 5th but cannot exist in the same system. Either can be the correct name, depending on the context. 

Diatonic Chords

A chord is a simultaneous performance of two or more notes. On the other hand, a diatonic chord is simply a chord whose components exist within the key signature.

A triad is a chord consisting of 3 notes, separated by thirds. The function (major, minor, diminished, augmented, etc…) is determined by the quality of the interval between the notes in the triads.

Major Triad = root note + major 3rd above + perfect 5th above

Minor Triad = root note + minor 3rd above + perfect 5th above

Diminished Triad = root note + minor 3rd above + diminished 5th above

Augmented Triad = root note + major 3rd above + augmented 5th above. Finally, here are the diatonic triads that occur in major using the key of C major as an example.

A capital Roman numeral represents major, a lower-case Roman numeral represents minor, and the degree symbol represents a diminished quality.

CONTINUE TO PART 2: Using Modal Interchange Chords