Definition and purpose of scales
A scale is a melodic structure which includes a group of notes, it is a set of their ascending and descending melodic intervals. In a scale, each note has its own function and plays an individual role. There is a great number of scales but diatonic is the most important for us. The diatonic scale is a heptatonic (seven-note) scale and consists of two half steps and five whole steps. The first note - the tonic is a tonal centre and a note of resolution. The second - the supertonic is just a step above the tonic. The third - the mediant is a midway between the tonic and the dominant. The fourth - the subdominant is the lower dominant. The fifth - the dominant is a note of second importance. The sixth - the submediant is the lower mediant. The seventh - the leading tone (in major and in harmonic or melodic minor), it leads us to the tonic; subtonic (in natural minor) is a whole step below the tonic. Diatonic scales are major and minor scales, all Gregorian modes.
If we will stack fifths from F we will get the next progression (circle of fifth): F-C-G-D-A-E-B-F. The last fifth in this circle will be diminished. This set of pitches forms seven musical modes: Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian.
Circle of fifth
Ionian mode starts with C and includes next intervals: P1, M2, M3, P4, P5, M6, M7, P8.
Pattern of Ionian mode: T-T-s-T-T-T-s
Dorian mode starts with D and includes: P1, M2, m3, P4, P5, M6, m7, P8.
Pattern of Dorian mode: T-s-T-T-T-s-T
Phrygian mode starts with E and includes: P1, m2, m3, P4, P5, m6, m7, P8.
Pattern of Phrygian mode: s-T-T-T-s-T-T
Lydian mode starts with F and includes: P1, M2, M3, A4, P5, M6, M7, P8.
Pattern of Lydian mode: T-T-T-s-T-T-s
Mixolydian mode starts with G, includes: P1, M2, M3, P4, P5, M6, m7, P8.
Pattern of Mixolydian mode: T-T-s-T-T-s-T
Aeolian mode starts with A, includes: P1, M2, m3, P4, P5, m6, m7, P8.
Pattern of Aeolian mode: T-s-T-T-s-T-T
Locrian mode starts with B and includes next intervals: P1, m2, m3, P4, d5, m6, m7, P8.
Pattern of Locrian mode: s-T-T-s-T-T-T
The major scale is the most used scale. Natural major is equal to Ionian mode. There are half steps between the third and fourth and between the seventh and eighth degrees, and whole steps between all other degrees. Sometimes composers use harmonic major with lowered sixth degree to get minor subdominant chord. There are half steps between the third and fourth and the fifth and sixth and the seventh and eighth degrees. Also, there are one and a half step between sixth and seventh degrees.
Pattern of Natural major scale: T-T-s-T-T-T-s
Pattern of Harmonic major scale: T-T-s-T-s-Ts-s
The minor scale is the second most useful scale. Natural minor is equal to Aeolian mode. There are half steps between the second and third and between the fifth and sixth degrees. Composers use harmonic minor with raised seventh degree to get the leading tone in dominant chords. There are half steps between the second and third, the fifth and sixth, and the seventh and eighth degrees. Also, there are one and a half step between the sixth and seventh degrees. Sometimes composers use melodic minor with raised sixth degree to avoid augmented interval between the sixth and seventh degree of harmonic minor. There are half steps between the second and third and the seventh and eighth degrees, and whole steps between all other degrees.
Pattern of Natural minor scale: T-s-T-T-s-T-T
Pattern of Harmonic minor scale: T-s-T-T-s-Ts-s
Pattern of Melodic minor scale: T-s-T-T-T-T-s
The chromatic scale is a duodecuple (twelve-note) scale and it contains all of the possible notes. Ascending chromatic scale notated in sharps and descending chromatic scales notated in flats. To get a regular circle of fifth musicians use alteration: F-C-G-D-A-E-B-F#-C#-G#-D#-A#/B♭-F. A# sharp is equal to B♭. These pitches form the chromatic scale.