The most common scales used in Western music are constructed using 7 notes. Modes are constructed by starting on a different note of the original scale each time. For example, if you took the C major scale, C D E F G A B, but started on the D instead of the C, you would have the second mode of the major scale. This would be D E F G A B C, which makes up the Dorian mode. Phrygian would begin on E; Lydian would begin on F; Mixolydian would being on G; Aeolian (natural minor) would begin on A; Locrian would begin on B. This means that whilst improvising over a C major chord, any of these modes can be used and fitted together to create more unusual melodies.
Major Modes
Ionian (Major) - 1, 2, 3, 4, 5, 6, 7
Dorian - 1, 2, b3, 4, 5, 6, b7
Phrygian - 1, b2, b3, 4, 5, b6, b7
Lydian - 1, 2, 3, #4, 5, 6, 7
Mixolydian - 1, 2, 3, 4, 5, 6, b7
Aeolian (Minor) - 1, 2, b3, 4, 5, b6, b7
Locrian - 1, b2, b3, 4, b5, b6, b7
Much like dominant chords, any scale that includes a major 3rd and a minor 7th can be referred to as some sort of "dominant" scale e.g Phrygian Dominant, Lydian Dominant. Similarly, any scale with a sharp 5th may be referred to as augmented.
Harmonic Minor Modes
Harmonic Minor - 1, 2, b3, 4, 5, b6, 7
Locrian #6 - 1, b2, b3, 4, b5, 6, b7
Ionian Augmented - 1, 2, 3, 4, #5, 6, 7
Dorian #4 - 1, 2, b3, #4, 5, 6, b7
Phrygian Dominant - 1, b2, 3, 4, 5, b6, b7
Lydian #2 - 1, #2, 3, #4, 5, 6, 7
Mixolydian #1 - 1, b2, b3, b4, b5, b6, bb7
Melodic Minor Modes
Melodic Minor - 1, 2, b3, 4, 5, 6, 7
Dorian b2 - 1, b2, b3, 4, 5, 6, b7
Lydian #5 - 1, 2, 3, #4, #5, 6, 7
Lydian Dominant - 1, 2, 3, #4, 5, 6, b7
Mixolydian b6 - 1, 2, 3, 4, 5, b6, b7
Aeolian b5 - 1, 2, b3, 4, b5, b6, b7
Altered scale (Locrian b4) - 1, b2, b3, b4, b5, b6, b7
Other 7-note Scales
Harmonic Major - 1, 2, 3, 4, 5, b6, 7
Hungarian Minor - 1, 2, b3, #4, 5, b6, 7
Persian - 1, b2, 3, 4, b5, b6, 7
Byzantine - 1, b2, 3, 4, 5, b6, 7
Romanian - 1, 2, b3, #4, 5, 6, b7
5-note Scales (Pentatonics)
Some scales are created using five notes; these are called pentatonics. For example the most common scale in rock music is the minor pentatonic, which has a definitive "rock" position on the fretboard. Although used in a variety of genres, this position is commonly associated with rock music.
The "Xs" represent the other notes within the natural minor scale to show how the pentatonic is built within it:
Here are some examples of pentatonic scales and how they are constructed intervallically:
Minor (Aeolian) Pentatonic - 1, b3, 4, 5, b7
Major (Ionian) Pentatonic - 1, 2, 3, 5, 6
Dorian Pentatonic - 1, b3, 4, 5, 6
Phrygian Pentatonic - 1, b2, 4, 5, b7
Lydian Pentatonic - 1, 3, #4, 5, 7
Mixolydian Pentatonic - 1, 3, 4, 5, b7
Locrian Pentatonic - 1, b3, 4, b5, b7
Harmonic Minor Pentatonic - 1, b3, 4, 5, 7
Hirajoshi - 1, 2, b3, 5, b6
Japanese - 1, 2, 4, 5, b6
Indian - 1, b2, 4, 5, b6
8-note Scales (Octatonics)
Arabian - 1, 2, b3, 4, #4, #5, 6, 7
Symmetrical Diminished (Half-Whole) - 1, b2, b3, b4, b5, 5, b6, b7
Symmetrical Diminished (Whole-Half) - 1, 2, b3, 4, b5, b6, 6, 7
6-note Scales (Hexatonics)
Blues Scale - 1, b3, 4, b5, 5, b7
Whole-Tone Scale - 1, 2, 3, #4, #5, b7
Prometheus Scale - 1, 2, 3, b5, 6, b7
There are some hexatonic scales that are constructed with interlocking triads:
Tritone Scale - This scale is made up of the intervals: 1, b2, 3, b5, 5, b7. It combines the notes of a major triad with the notes of another major triad that is a tritone interval away. For example, the notes from a C major triad (C E G) may be combined with the notes from a Gb triad (Gb Bb Db) to create this scale. However, they are rearranged to fit within one octave.
Augmented Scale - This scale (1, b3, 3, 5, #5, 7) combines two separate augmented triads that are a minor 3rd apart. If you took the notes from a C augmented triad (C E G#) and combined them with the notes from an Eb augmented triad (Eb G B) and arranged them ascending within one octave you would construct this scale.
Arpeggios
Arpeggios are basically the notes from a chord played consecutively rather than simultaneously with the additional octave note (for arpeggios limited to one octave). For example, the corresponding ascending arpeggio for a C major chord (1, 3, 5) would be C, E, G, C.
Below are some examples of arpeggios, composed of the same notes as the chords of the same names:
Major - 1, 3, 5, 8
Minor - 1, b3, 5, 8
Major 7th - 1, 3, 5, 7, 8
Minor 7th - 1, b3, 5, b7, 8
Dominant 7th - 1, 3, 5, b7, 8
Suspended 4th - 1, 4, 5, 8
Suspended 2nd - 1, 2, 5, 8
Major 6th - 1, 3, 5, 6, 8
Minor 6th - 1 b3, 5, 6, 8
Augmented - 1, 3, #5, 8
Diminished - 1, 3, b5, 8
Augmented Major 7th - 1, 3, #5, 7, 8
Diminished 7th - 1, b3, b5, bb7, 8
Major 9th - 1, 3, 5, 7, 9
Minor 9th - 1, b3, 5, b7, 9
Dominant 9th - 1, 3, 5, b7, 9
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