# Scales and modes

## Building a scale

A seven-note scale uses each letter name exactly once. Derive the letters from
the tonic first, then apply the accidentals the pattern requires. Never mix
sharps and flats in a standard key signature, and never repeat a letter.

This forces some spellings that look wrong and are not: F# major is
F# G# A# B C# D# E#, with E# rather than F, because the seventh letter must be
E.

## Major and minor

Intervals in semitones from the tonic:

| Scale | Degrees | Semitones |
|---|---|---|
| Major (Ionian) | 1 2 3 4 5 6 7 | 0 2 4 5 7 9 11 |
| Natural minor (Aeolian) | 1 2 b3 4 5 b6 b7 | 0 2 3 5 7 8 10 |
| Harmonic minor | 1 2 b3 4 5 b6 7 | 0 2 3 5 7 8 11 |
| Melodic minor (ascending) | 1 2 b3 4 5 6 7 | 0 2 3 5 7 9 11 |

Every major scale has a relative minor starting on its sixth degree, sharing the
key signature: C major and A minor, G major and E minor.

## The modes

Same seven notes as a major scale, different tonic. But teach them by their
*own* interval pattern, not as "start on the fifth degree" - the rotation trick
explains where modes come from and is useless for actually using one.

| Mode | Degrees | Character |
|---|---|---|
| Ionian | 1 2 3 4 5 6 7 | major |
| Dorian | 1 2 b3 4 5 6 b7 | minor with a raised 6th |
| Phrygian | 1 b2 b3 4 5 b6 b7 | minor with a flat 2nd |
| Lydian | 1 2 3 #4 5 6 7 | major with a raised 4th |
| Mixolydian | 1 2 3 4 5 6 b7 | major with a flat 7th |
| Aeolian | 1 2 b3 4 5 b6 b7 | natural minor |
| Locrian | 1 b2 b3 4 b5 b6 b7 | diminished |

The fastest way to hear a mode is its one distinguishing note against the
parallel major or minor: Dorian is minor but with a major sixth; Lydian is major
but with a sharp fourth; Mixolydian is major but with a flat seventh.

## Pentatonic and blues

| Scale | Degrees |
|---|---|
| Major pentatonic | 1 2 3 5 6 |
| Minor pentatonic | 1 b3 4 5 b7 |
| Blues | 1 b3 4 b5 5 b7 |

The blues scale is the minor pentatonic with a chromatic passing b5 added. Major
and minor pentatonic are rotations of one another, three semitones apart: C major
pentatonic and A minor pentatonic contain the same five notes.

## Key signatures

Sharps appear in the order **F C G D A E B**; flats in the reverse, **B E A D G
C F**.

| Sharps | Major | Minor |
|---|---|---|
| 0 | C | A |
| 1 | G | E |
| 2 | D | B |
| 3 | A | F# |
| 4 | E | C# |
| 5 | B | G# |
| 6 | F# | D# |
| 7 | C# | A# |

| Flats | Major | Minor |
|---|---|---|
| 1 | F | D |
| 2 | Bb | G |
| 3 | Eb | C |
| 4 | Ab | F |
| 5 | Db | Bb |
| 6 | Gb | Eb |
| 7 | Cb | Ab |

Two shortcuts worth teaching, once they can already do it the slow way: the
major key is a semitone above the last sharp, and with two or more flats the
major key is the second-to-last flat. One flat is the exception you have to
remember - that is F major.

## Grading

Check the letters before the accidentals. A scale answer with the right pitches
and a repeated or skipped letter is a spelling error - name it as such, and go
back to the one-letter-each rule rather than re-listing the scale.

For modes, check what the learner used as tonic. Answering "D Dorian" with the
notes of C major is right; answering it as though the tonic were C is the
mistake that rotation-based teaching produces, and is worth catching early.