Scales

(We are now working in European Equal Temperament.)

A scale is any sequence of intervals (notice: not notes) that adds up to 12 semitones. Think of any bonkers combination, and someone somewhere will have a guitar tutorial explaining why it should be the very next thing you learn.

A key or mode is a scale plus a starting note (the "tonic") that then defines a sequence of notes. We say "the key of G-Major" scale or "the Major scale". (Musical speech is sloppy, so we also say "the Major key" or "the G-Major scale".) Two keys are equivalent if they have the same scale. “Scale” = intervals; key = notes.

There are a number of well-known seven-note scales:

Major / Ionian Mode: Tone-Tone-Semitone-Tone-Tone-Tone-Semitone
Natural Minor / Aeolian Mode: Tone-Semitone-Tone-Tone-Tone-Semitone-Tone
Harmonic Minor: Tone-Semitone-Tone-Tone-Tone-Tone-Semitone
Lydian Mode: Tone-Tone-Tone-Semitone-Tone-Tone-Semitone
Mixolydian Mode; Tone-Tone-Semitone-Tone-Tone-Semitone-Tone
Dorian Mode: Tone-Semitone-Tone-Tone-Tone-Semitone-Tone
Phrygian Mode: Semitone-Tone-Tone-Tone-Semitone-Tone-Tone

The Ionian, Aeolian, Lydian, Mixolydian, Dorian, Phrygian modes are often called Church Modes, as they were used in early choral singing.

There are two well-known five note (pentatonic) scales:

Major Pentatonic: Tone-Tone-Minor Third-Tone-Minor Third
Minor Pentatonic: Minor Third-Tone-Tone-Minor Third-Tone

Two well-known six note scales:

Major Blues: Tone-Tone-Semitone-Minor Third-Tone-Minor Third
Minor Blues: Minor Third-Tone-Tone-Semitone-Minor Third-Tone
(Minor Third = 3 semitones)

Exactly one scale of only tones: Whole-Tone: Tone-Tone-Tone-Tone-Tone-Tone (There are two keys: C and C♯. After that the notes repeat, so starting on D gives the same notes as starting on C.)

Exactly one scale of only semitones: Chromatic: Semitone (x12)

If you want to see something truly out of control, look at the eight-note diminished scale.