vault backup: 2025-12-25 16:01:44
This commit is contained in:
+221
@@ -0,0 +1,221 @@
|
||||
---
|
||||
id:
|
||||
aliases: []
|
||||
title: Music Theory
|
||||
tags: []
|
||||
---
|
||||
# Music Theory
|
||||
|
||||
```mermaid
|
||||
classDiagram
|
||||
class PitchSpelling {
|
||||
PitchLetter letter
|
||||
Accidental acc
|
||||
Octave octave
|
||||
}
|
||||
```
|
||||
|
||||
## 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](https://en.wikipedia.org/wiki/Modular_arithmetic)
|
||||
|
||||
> [!important]
|
||||
> Adjacent sharps and flats (e.g. C♯ and D♭)
|
||||
> only represent the _same_ pitch in [equal temperament tuning](https://en.wikipedia.org/wiki/Equal_temperament),
|
||||
> 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,
|
||||
and 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".
|
||||
|
||||
```lily
|
||||
\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](https://en.wikipedia.org/wiki/Minor_second)
|
||||
and [major second](https://en.wikipedia.org/wiki/Major_second) respectively,
|
||||
which is a [[ambiguity#Category Mistake|category mistake]].
|
||||
|
||||
|
||||
5 in 12 1 semitone increments result in augmented unisons.
|
||||
2 in 12 2 semitone increments result in diminished thirds.
|
||||
|
||||
#### Accidentals
|
||||
|
||||
| ascii | unicode | lilypond | Name |
|
||||
| ----- | ------- | -------- | ------------ |
|
||||
| bb | N/A | eses | double flat |
|
||||
| b | ♭ | es | flat |
|
||||
| | ♮ | | natural |
|
||||
| # | ♯ | is | sharp |
|
||||
| x | N/A | isis | double sharp |
|
||||
|
||||
#### Octave
|
||||
|
||||
### 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
|
||||
|
||||
|
||||
|
||||
| dP[^1] | dS[^2] | 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 |
|
||||
|
||||
[^1]: difference in staff position (interval number)
|
||||
[^2]: difference in semitones
|
||||
|
||||
#### Augmented and Diminished Intervals
|
||||
|
||||
| dP[^1] | dS[^2] | 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|set]] 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
|
||||
Reference in New Issue
Block a user