A quick review of scales and chords
Music has vertical harmonic structure and horizontal, melodic, moving lines.
Chords are vertical stacks of notes. The basic idea of harmony is to play scale triads below the melody. Chord progressions follow a musical syntax. In the triadic version, the chords conform to scale notes. Classical music is based on tonality that follows rules of scales and key changes. Jazz is an evolving, improvisatory form of music that continues to depend on chords, scales , tonality and progressions that players and listeners recognize. Jazz adds the option of individual expression, novel and sometimes surprising improvisations that wander away from and back to the melody of a song and the tonality that feels like home. The best jazz musicians combine the talents of virtuoso performance and skilled composition. Some innovations in jazz involved modal scales beyond major and minor sequences and atonal improvisations that ignored the rules of tonal music (following chord progressions and melody with brief passing notes.)
You can understand all scale structures on the piano by starting with the root note, middle C.
If you play all the white keys on a piano C, D, E, F, G, A, B, C you have a C major scale. The sequence of semitones is 2,2,1,2,2,2,1.
Each note in a scale can be named with a roman numeral I, II, III, IV, V, VI, VII. The same notation is used to describe chords based on the scale notes.
The C minor sequence is C,D,Eb,F,G,Ab,Bb,C. As semitones, the minor sequence is 2,1,2,2,1,2,2.
Scale sequences are also described as modes. If you stay with the white keys on the piano, you can play all the modes by starting with different tonic notes.
Modes are described by names from ancient Greece: The Ionian mode starts on C and is the C major scale. The Dorian mode is all the white notes between two Ds. The Phrygian mode starts on E; the Lydian mode on F; the Mixolydian on G; the Aeolian is the natural minor scale that begins on A; and the Locrian on B.
The tonality of each mode is declared by emphasizing the tonic note, the root triad, and using cadences such as V, I. The sequences of each mode are distinctive enough to create different musical " flavors or moods."
The root C major chord, I, is a triad C,E,G. Beginning triads on different notes of the scale, you get chord progressions described with roman numerals: I, IV, V, I means triads starting on C,F,G, returning to C.
Each triad has a root position and two inversions: C,E,G; EGC; GCE.
Different descriptions of chords, harmony and melody can be confusing. The most important idea is that music consists of stacks and sequences of intervals. A composition that uses only the notes of one scale or mode is diatonic. Popular tunes are often diatonic. The scale becomes the "key" of the piece. In classical music, pieces are often described by the key --- Concerto in D major, for example. Bach and Mozart stayed mostly with diatonic composition. Their music is easy to understand and like. As a piece develops, you can move from one scale to another usually with some preparation for the key change, but return to the original scale (key) before the piece completes. A sense of closure is achieved with a perfect cadence, a V to I ending. Notes that are foreign to the tonic scale are played briefly as passing notes or as chromatic sequences that ascend and descend by semitones.
Chord progressions tend to follow basic patters with variations. I, IV, V is the first to learn. This is played as triads: C major (I), F Major (IV) and G Major (V).
A II-V-I chord progression in the key of C major is played as D minor (II), G major (V), and C major (I).
A III-VI-II-V-I chord progression in the key of C major is played as E minor (III), A minor (VI), D minor (II), G major (V), and C major (I).
Circle of 5ths
Another method of designing chord progression is to move by jumps of 5ths.
Adding extra notes to triads adds interest to basic cord progressions.
Diatonic triads are consonant, creating harmonies that are familiar and pleasing. Dissonance is created by non triadic intervals that create tensions that want to be resolved to consonance. "Squashed" chords involve adjacent semitone and single tone intervals. C7 in the root position involves C and B and octave apart. The semitone interval is not dissonant until the B and C are played together in the first and second inversion.
Harmony implies the harmonious feel of consonance, but melody is more interesting when it interacts with both dissonance and consonance, moving from tension to resolution. Moving lines in music consist of combinations of major, minor, modal and chromatic scales and arpeggios. A chromatic scale is a sequence of semitones only. You play all the white and black notes from C to C.
Arpeggios are chord notes played as moving lines. Piano students learn to play ascending and descending arpeggios that span several octaves in each key. More about Arpeggios. Jazz improvisation often involves episodes of several moving elements combined in a novel manner.
There are two whole tone scales with six notes beginning at C: C, D, E, F#, G#, Bb". On the keyboard this scale is obvious, you play three white note and three black notes. Or you can begin at Db, and play Eb, F, G, A, B – two black keys followed by 4 white keys.
Pentatonic Scales are five note scales. The C major pentatonic scale is C, D, E, G, A; minor pentatonic scale "C, Eb, F, G, Bb". The C tonic pentatonic scale can be used over Cmaj7 and Cm7 over the 5 minor scale.
E, F, A, B, D is the Japanese 5 note scale.
The sequence of intervals of any scale is a formula that avoids the
complexities of naming scales and chords.