Definitions and notation conventions. First, let's define some terms. An "interval" is the distance between two tones. There are five qualities of intervals; their names are perfect, major, minor, diminished, and augmented. These qualities of intervals are defined as follows: o Perfect interval: an interval which, when inverted, becomes another perfect interval (a self-referential definition if ever I heard one). E.g., C-F is a perfect 4th, F-C is a perfect 5th; C1-F2 is a perfect 11th (where the 1 and 2 mean that the C and F are in different octaves), C2-F2 is a perfect 4th, F2-C3 is a perfect 5th; and so on. o Major: an interval other than a perfect interval that appears in a major scale. o Minor: an interval that does not appear in a major scale. o Augmented: a raised perfect or major interval. o Diminished: a lowered perfect or minor interval. In defining major and minor scales, the intervals between adjacent notes in the scale are sometimes called "half step" and "whole step", or, equivalently, "semitone" and "whole tone". o Semitone: the interval between the notes of two adjacent keys on the piano, or two adjacent frets on the guitar. Also called a "minor 2nd" or "half step". Example: C-Db. [b is used to denote flat] o Whole tone: the interval between a key and the key next to the adjacent key on the piano [two keys away], or at two frets' apart on the guitar. Also called a "major 2nd" or "whole step". Example: C-D. I will use the following conventions in my notation: o M: major interval, scale, or chord o m: minor interval, scale, or chord o b: the "flat" symbol, i.e., the specified note is lowered by one semitone. Example: Bb is a semitone lower than B. o #: the "sharp" symbol, i.e., the specified note is raised by one semitone. Example: G# is a semitone higher than G. o nat: used to indicate that a note is neither sharped nor flatted (usual music notation uses a sort of L7 symbol that I can't reproduce at the computer keyboard). o upper case Roman numeral: a major-, dominant-, or augmented- family chord. The number refers to the degree of the scale on which a chord is built. Example: I indicates the major chord built on the first degree of a scale (e.g., C in the key of C). o lower case Roman numeral: a minor-, half-diminished-, or diminished-family chord. The number refers to the degree of the scale on which a chord is built. Example: vi indicates the minor chord built on the sixth degree of a scale (e.g., Am in the key of C). The Major and Minor Scales 1.2.1. The Major Scale. The major scale is defined as an 8-tone scale comprising the set of intervals (in terms of whole- and half-steps). The intervals are: whole whole half whole whole whole half The C Major scale is: C D E F G A B C 1.2.2. The Natural Minor Scale. The natural minor scale is defined as an 8-tone scale containing the same notes as its relative major scale, but starting on the 6th scale degree of its relative major scale; also known as the Aeolian mode. The relative minor of C Major is A Minor, and its intervals are: whole half whole whole half whole whole The A natural minor scale is: A B C D E F G A 1.2.3. The Harmonic Minor Scale. Similar to the natural minor scale but with a raised 7th scale degree. The component intervals are: whole half whole whole half m3 half The A harmonic minor scale is: A B C D E F G# A 1.2.4. The Melodic Minor Scale. Similar to the natural minor scale but with a raised 6th and a raised 7th when ascending; identical to the natural minor scale when played descending. The component intervals are: whole half whole whole whole whole half The ascending A melodic minor scale is: A B C D E F# G# A Other definitions and conventions will be introduced as needed. Elementary Chord Construction From Tertiary Harmony. One can develop a useful set of chords by stacking notes from the scale. For the purposes of this set of lessons I will stack thirds. I will start with, say, a C major scale; over that I will place the same scale but starting with the 3rd scale degree (E); over that I will place the same scale starting with the 5th scale degree (G). The harmony deriving from stacking alternate scale tones is called "tertiary harmony". The harmonized scales in C and its relative minors are: C major: G A B C D E F G - fifth above root E F G A B C D E - third above root C D E F G A B C - root of chord A natural minor: E F G A B C D E - fifth above root C D E F G A B C - third above root A B C D E F G A - root of chord A harmonic minor: E F G# A B C D E - fifth above root C D E F G# A B C - third above root A B C D E F G# A - root of chord A melodic minor: E F# G# A B C D E - fifth above root C D E F# G# A B C - third above root A B C D E F# G# A - root of chord If we examine the intervals contained in these stacks of notes, we'll discover that there are only a few distinct sets of relationships. Listed with the bottommost interval first, these are: o M3 m3 - defined as a "major" chord, e.g., C-E-G. It's called a "major" chord because the chord built upon the tonic of the major scale is of this type. (Warning - another kind of chord containing the intervals M3 m3 on the bottom is called a "dominant" chord. Dominant chords are not distinguishable from major chords in three-note chords, but are distinguishable in chords having four or more notes. See part 2 for more information.) o m3 M3 - defined as a "minor" chord, e.g., A-C-E. It's called a "minor" chord because the chord built upon the tonic of the minor scale is of this type. o m3 m3 - ambiguous, either diminished or half-diminished, e.g., B-D-F. This chord will divide in unambiguous ways starting with 4-note chords in Part 2. o M3 M3 - defined as an "augmented" chord, e.g., C-E-G#. These interval patterns, along with one or two others, will serve as the basis for a chord classification system to be introduced in Part 2.