vault backup: 2025-12-25 16:01:44

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+---
+id:
+aliases: []
+title: "2025-12-22"
+tags:
+  - authorship/original
+  - destiny/permanent
+  - status/draft
+  - type/daily
+---
+# 2025-12-22
+
+## 2025-12-22 08:51
+
+[[music-theory]]
@@ -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