zmVault/music-theory.md

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Music Theory	topic/hobbies/music type/encyclopedia

Music Theory

Note

Pitch

Refers to the human perception of frequency. It is usually only appropriate to prefer "pitch" over "note" when one is specifically referring to frequency.

Notes are enharmonic (or enharmonically equivalent) if they represent the same pitch.

Pitch Class

mod 12	name
0	C
1	C♯/D♭
2	D
3	D♯/E♭
4	E
5	F
6	F♯/G♭
7	G
8	G♯/A♭
9	A
10	A♯/B♭
11	B

Modular arithmetic

Important

Adjacent sharps and flats (e.g. C♯ and D♭) only represent the same pitch in equal temperament tuning, but they are still considered enharmonic in others.

Note: Semitones and Steps

It is common to speak of whole or half steps between pitches, but I find this confusing in a way music educators ought to better anticipate. In equal temperament tuning, all pitch classes are--- according to human perception---equally spaced. There is no missing half between E and F or B and C, because there are no halves at all. C# is as legitimate a pitch class as C.

[!info] In some disciplines, accidentals are marked on every note, even "redundantly", in acknowledgement of this fact.

What is meant by the poor terminology is this:

• "half step" = 1 semitone
• "whole step" = 2 semitones

There is no more nuance, E--F is also a "half step".

\score{
    a~ ais
    b~ c
    \layout {}
}

This is an unhelpful convention. Inexcusable, though, is conflating semitone increments with intervals. Wikipedia music theory articles frequently link "half step" and "whole step" to minor second and major second respectively, which is a category-mistake.

Accidentals

ascii	unicode	lilypond	Name
bb	𝄫	eses	double flat
b	♭	es	flat
	♮	!	natural
#	♯	is	sharp
x	𝄪	isis	double sharp

Octave

Octave is a property of staff position, not pitch. B♯³ is enharmonic with C⁴

Duration

• beats
• speed

Intensity

• pianissimo
• piano
• forte
• fortissimo

Interval

Refers to the difference between two pitches. Intervals are notated with an en dash (C♯--E).

Interval Number

Equal to the difference in staff position plus one.

Important

The number of an interval is not related to the difference in pitch. F♯ and G♭ are enharmonic, but F♯--G♭ is a second. F and F♯ are a semitone apart, but F--F♯ is a first.

Interval Quality

An interval of unspecified quality is called "generic".

difference in semitones

Perfect, Major, and Minor Intervals

The common intervals

dP1	dS2	Short	Name
0	0	P1	Perfect unison
1	1	m2	Minor second
1	2	M2	Major second
2	3	m3	Minor third
2	4	M3	Major third
3	5	P4	Perfect fourth
4	7	P5	Perfect fifth
5	8	m6	Minor sixth
5	9	M6	Major sixth
6	10	m7	Minor seventh
6	11	M7	Major seventh
7	12	P8	Perfect octave

Augmented and Diminished Intervals

dP1	dS2	Short	Name
0	1	A1	Augmented unison
1	3	A2	Augmented second
2	5	A3	Augmented third
3	6	A4	Augmented fourth
4	8	A5	Augmented fifth
5	10	A6	Augmented sixth
6	12	A7	Augmented seventh
1	0	d2	Diminished second
2	2	d3	Diminished third
3	4	d4	Diminished fourth
4	6	d5	Diminished fifth
5	7	d6	Diminished sixth
6	9	d7	Diminished seventh
7	11	d8	Diminished octave

Compound Interval

A compound interval is one greater than number 8.

Key

A key is a set-theory of pitch classes created by modifying a starting pitch class (the tonic) according to some sequence of intervals.

Key	Interval Sequence
Major	W--W--H--W--W--W--H
Natural Minor	W--H--W--W--H--W--W

Modes

Mode	Interval Sequence
Ionian	W--W--H--W--W--W--H
Dorian	W--H--W--W--W--H--W
Phrygian	H--W--W--W--H--W--W
Lydian	W--W--W--H--W--W--H
Mixolydian	W--W--H--W--W--H--W
Aeolian	W--H--W--W--H--W--W
Locrian	H--W--W--H--W--W--W

Scale

A scale is a progression of the elements of a key in ascending or descending order.

Scale Degrees

• degree 1: tonic
• degree 2: supertonic
• degree 3: mediant
• degree 4: subdominant
• degree 5: dominant
• degree 6: submediant
• degree 7: called the subtonic if it is 2 semitones/"a whole step"/a major second below the tonic or the leading tone if it is 1 semitone/"a half step"/a minor second below the tonic
• degree 8: tonic

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1. difference in staff position (interval number - 1) ↩︎

2. difference in semitones ↩︎