vault backup: 2026-01-20 17:02:44
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-18
@@ -54,9 +54,11 @@ In equal temperament tuning, all pitch classes are---
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according to human perception---equally spaced.
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There is no missing half between E and F or B and C,
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because there are no halves at all.
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C# is as legitimate a pitch class as C,
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and in some disciplines, accidentals are marked on every note,
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even "redundantly", in acknowledgement of this fact.
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C# is as legitimate a pitch class as C.
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> [!info]
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> In some disciplines, accidentals are marked on every note,
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> even "redundantly", in acknowledgement of this fact.
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What is meant by the poor terminology is this:
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@@ -86,7 +88,7 @@ which is a [[ambiguity#Category Mistake|category mistake]].
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| ----- | ------- | -------- | ------------ |
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| bb | 𝄫 | eses | double flat |
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| b | ♭ | es | flat |
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| | ♮ | | natural |
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| | ♮ | ! | natural |
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| # | ♯ | is | sharp |
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| x | 𝄪 | isis | double sharp |
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@@ -146,7 +148,7 @@ The common intervals
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| 6 | 11 | M7 | Major seventh |
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| 7 | 12 | P8 | Perfect octave |
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[^1]: difference in staff position (interval number)
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[^1]: difference in staff position (interval number - 1)
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[^2]: difference in semitones
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#### Augmented and Diminished Intervals
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@@ -178,22 +180,22 @@ A **key** is a [[set-theory|set]] of pitch classes
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created by modifying a starting pitch class (the **tonic**)
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according to some sequence of intervals.
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| Key | Interval Sequence |
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| ------------- |:-----------------:|
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| Major | W--W--H--W--W--W--H |
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| Natural Minor | W--H--W--W--H--W--W |
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| Key | Interval Sequence |
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| ------------- |:-------------------:|
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| Major | W--W--H--W--W--W--H |
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| Natural Minor | W--H--W--W--H--W--W |
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### Modes
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| Mode | Interval Sequence |
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| ---------- |:-----------------:|
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| Ionian | W--W--H--W--W--W--H |
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| Dorian | W--H--W--W--W--H--W |
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| Phrygian | H--W--W--W--H--W--W |
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| Lydian | W--W--W--H--W--W--H |
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| Mixolydian | W--W--H--W--W--H--W |
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| Aeolian | W--H--W--W--H--W--W |
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| Locrian | H--W--W--H--W--W--W |
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| Mode | Interval Sequence |
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| ---------- |:-------------------:|
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| Ionian | W--W--H--W--W--W--H |
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| Dorian | W--H--W--W--W--H--W |
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| Phrygian | H--W--W--W--H--W--W |
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| Lydian | W--W--W--H--W--W--H |
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| Mixolydian | W--W--H--W--W--H--W |
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| Aeolian | W--H--W--W--H--W--W |
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| Locrian | H--W--W--H--W--W--W |
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### Scale
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