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https://github.com/kennethreitz/pytheory.git
synced 2026-06-05 14:50:18 +00:00
Fix RST inline markup: remove bold wrapping around links
RST cannot nest inline markup — **`link <url>`_** renders the raw markup instead of a clickable link. Removed all 37 instances across 5 guide pages. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
This commit is contained in:
+10
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@@ -1,7 +1,7 @@
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Working with Chords
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===================
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A **`chord <https://en.wikipedia.org/wiki/Chord_(music)>`_** is two or more tones sounding simultaneously. Chords are the
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A `chord <https://en.wikipedia.org/wiki/Chord_(music)>`_ is two or more tones sounding simultaneously. Chords are the
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vertical dimension of music — while melody moves horizontally through
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time, harmony stacks tones on top of each other.
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@@ -9,7 +9,7 @@ Chord Construction
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------------------
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Chords are built by stacking **intervals** above a **root** note. The
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most common chord type is the **`triad <https://en.wikipedia.org/wiki/Triad_(music)>`_** — three notes built from
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most common chord type is the `triad <https://en.wikipedia.org/wiki/Triad_(music)>`_ — three notes built from
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alternating scale degrees (root, 3rd, 5th).
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The four triad types::
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@@ -19,7 +19,7 @@ The four triad types::
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Diminished root + minor 3rd (3) + diminished 5th (6) Tense, unstable
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Augmented root + major 3rd (4) + augmented 5th (8) Eerie, unresolved
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Adding a 7th creates a **`seventh chord <https://en.wikipedia.org/wiki/Seventh_chord>`_** — the foundation of jazz
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Adding a 7th creates a `seventh chord <https://en.wikipedia.org/wiki/Seventh_chord>`_ — the foundation of jazz
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harmony::
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Dominant 7th root + 4 + 7 + 10 Bluesy, wants to resolve (G7)
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@@ -31,7 +31,7 @@ Inversions
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----------
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A chord is in **root position** when the root is the lowest note.
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When a different chord tone is in the bass, the chord is **`inverted <https://en.wikipedia.org/wiki/Inversion_(music)>`_**:
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When a different chord tone is in the bass, the chord is `inverted <https://en.wikipedia.org/wiki/Inversion_(music)>`_:
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- **Root position**: C E G (root in bass)
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- **First inversion**: E G C (3rd in bass) — notated C/E
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@@ -61,7 +61,7 @@ For seventh chords, there's also **third inversion** (7th in bass):
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Extended Chords
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---------------
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Beyond seventh chords, jazz harmony builds **`extended chords <https://en.wikipedia.org/wiki/Extended_chord>`_** by
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Beyond seventh chords, jazz harmony builds `extended chords <https://en.wikipedia.org/wiki/Extended_chord>`_ by
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continuing to stack thirds:
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- **9th chord**: adds the 9th (= 2nd, one octave up)
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@@ -196,9 +196,9 @@ Tritone 45:32 Waves rarely align
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Dissonance Score
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~~~~~~~~~~~~~~~~
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The ``dissonance`` property uses the **Plomp-Levelt `roughness <https://en.wikipedia.org/wiki/Roughness_(psychoacoustics)>`_ model**
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The ``dissonance`` property uses the Plomp-Levelt `roughness <https://en.wikipedia.org/wiki/Roughness_(psychoacoustics)>`_ model
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(1965). When two frequencies are close together, their sound waves
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interfere and produce rapid amplitude fluctuations called **`beating <https://en.wikipedia.org/wiki/Beat_(acoustics)>`_**.
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interfere and produce rapid amplitude fluctuations called `beating <https://en.wikipedia.org/wiki/Beat_(acoustics)>`_.
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This beating is perceived as roughness — the physiological basis of
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dissonance.
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@@ -268,7 +268,7 @@ against 17 known chord types (triads, 7ths, 9ths, sus, power chords).
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Harmonic Analysis
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-----------------
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**`Roman numeral analysis <https://en.wikipedia.org/wiki/Roman_numeral_analysis>`_** labels each chord by its function within a
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`Roman numeral analysis <https://en.wikipedia.org/wiki/Roman_numeral_analysis>`_ labels each chord by its function within a
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key. This is how musicians describe chord progressions independent of
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key — "I-IV-V" means the same thing in C major (C-F-G) as in G major
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(G-C-D).
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@@ -320,7 +320,7 @@ quantifies this based on:
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Voice Leading
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-------------
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**`Voice leading <https://en.wikipedia.org/wiki/Voice_leading>`_** is the art of connecting chords smoothly. Instead of
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`Voice leading <https://en.wikipedia.org/wiki/Voice_leading>`_ is the art of connecting chords smoothly. Instead of
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jumping all voices to new positions, good voice leading moves each note
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the minimum distance to reach the next chord. Bach's chorales are the
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gold standard — every voice moves by step whenever possible.
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@@ -338,7 +338,7 @@ The Overtone Series
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-------------------
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Every musical tone is actually a stack of frequencies — the
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**fundamental** plus its **`overtones <https://en.wikipedia.org/wiki/Overtone>`_** (harmonics). The overtone series
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**fundamental** plus its `overtones <https://en.wikipedia.org/wiki/Overtone>`_ (harmonics). The overtone series
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is nature's chord: it contains the octave, perfect fifth, perfect
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fourth, major third, and more, in that order.
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@@ -37,19 +37,19 @@ Playing a Chord
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Waveform Types
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--------------
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The waveform shape determines the **`timbre <https://en.wikipedia.org/wiki/Timbre>`_** (tonal color) of the sound.
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The waveform shape determines the `timbre <https://en.wikipedia.org/wiki/Timbre>`_ (tonal color) of the sound.
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Different waveforms contain different combinations of **harmonics** —
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integer multiples of the fundamental frequency.
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- **`Sine wave <https://en.wikipedia.org/wiki/Sine_wave>`_** — the purest tone. Contains only the fundamental
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- `Sine wave <https://en.wikipedia.org/wiki/Sine_wave>`_ — the purest tone. Contains only the fundamental
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frequency with no harmonics. Sounds smooth, clear, and "electronic."
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This is the building block of all other waveforms (`Fourier's theorem <https://en.wikipedia.org/wiki/Fourier_series>`_).
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- **`Sawtooth wave <https://en.wikipedia.org/wiki/Sawtooth_wave>`_** — contains all harmonics (both odd and even),
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- `Sawtooth wave <https://en.wikipedia.org/wiki/Sawtooth_wave>`_ — contains all harmonics (both odd and even),
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each at amplitude 1/n. Sounds bright, buzzy, and aggressive.
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Named for its shape. Used extensively in `additive synthesis <https://en.wikipedia.org/wiki/Additive_synthesis>`_ and analog synthesizers.
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- **`Triangle wave <https://en.wikipedia.org/wiki/Triangle_wave>`_** — contains only odd harmonics, each at amplitude
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- `Triangle wave <https://en.wikipedia.org/wiki/Triangle_wave>`_ — contains only odd harmonics, each at amplitude
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1/n². Sounds softer and more mellow than sawtooth — somewhere between
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sine and sawtooth. Often described as "woody" or "hollow."
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+12
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@@ -48,7 +48,7 @@ Major and Minor
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The **major scale** (`Ionian <https://en.wikipedia.org/wiki/Ionian_mode>`_ mode) is the foundation of Western tonal
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music. Its pattern of whole and half steps creates a bright, resolved
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sound. Every major key has a **`relative minor <https://en.wikipedia.org/wiki/Relative_key>`_** that shares the same
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sound. Every major key has a `relative minor <https://en.wikipedia.org/wiki/Relative_key>`_ that shares the same
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notes but starts from the 6th degree:
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- C major → A minor (both use only white keys)
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@@ -63,7 +63,7 @@ notes but starts from the 6th degree:
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# Same notes, different starting point
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set(c_major.note_names) == set(a_minor.note_names) # True
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The **`harmonic minor <https://en.wikipedia.org/wiki/Harmonic_minor_scale>`_** raises the 7th degree of the natural minor,
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The `harmonic minor <https://en.wikipedia.org/wiki/Harmonic_minor_scale>`_ raises the 7th degree of the natural minor,
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creating an augmented 2nd interval (3 semitones) between the 6th and
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7th degrees. This gives it a distinctive "Middle Eastern" or "classical"
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sound and provides the leading tone needed for dominant harmony::
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@@ -75,7 +75,7 @@ sound and provides the leading tone needed for dominant harmony::
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Modes
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-----
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The seven **`modes <https://en.wikipedia.org/wiki/Mode_(music)>`_** of the major scale are rotations of the same interval
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The seven `modes <https://en.wikipedia.org/wiki/Mode_(music)>`_ of the major scale are rotations of the same interval
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pattern, each starting from a different degree. Each mode has a distinct
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emotional character:
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@@ -87,32 +87,32 @@ emotional character:
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c["ionian"] # C D E F G A B C
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**`Dorian <https://en.wikipedia.org/wiki/Dorian_mode>`_** (ii) — minor with a raised 6th. Jazzy, soulful (So What,
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`Dorian <https://en.wikipedia.org/wiki/Dorian_mode>`_ (ii) — minor with a raised 6th. Jazzy, soulful (So What,
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Scarborough Fair)::
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c["dorian"] # C D Eb F G A Bb C
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**`Phrygian <https://en.wikipedia.org/wiki/Phrygian_mode>`_** (iii) — minor with a flat 2nd. Spanish, flamenco, dark
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`Phrygian <https://en.wikipedia.org/wiki/Phrygian_mode>`_ (iii) — minor with a flat 2nd. Spanish, flamenco, dark
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(White Rabbit)::
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c["phrygian"] # C Db Eb F G Ab Bb C
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**`Lydian <https://en.wikipedia.org/wiki/Lydian_mode>`_** (IV) — major with a raised 4th. Dreamy, floating, ethereal
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`Lydian <https://en.wikipedia.org/wiki/Lydian_mode>`_ (IV) — major with a raised 4th. Dreamy, floating, ethereal
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(The Simpsons theme, Flying by ET)::
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c["lydian"] # C D E F# G A B C
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**`Mixolydian <https://en.wikipedia.org/wiki/Mixolydian_mode>`_** (V) — major with a flat 7th. Bluesy, rock, dominant
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`Mixolydian <https://en.wikipedia.org/wiki/Mixolydian_mode>`_ (V) — major with a flat 7th. Bluesy, rock, dominant
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(Norwegian Wood, Sweet Home Alabama)::
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c["mixolydian"] # C D E F G A Bb C
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**`Aeolian <https://en.wikipedia.org/wiki/Aeolian_mode>`_** (vi) — the natural minor scale. Sad, dark, introspective
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`Aeolian <https://en.wikipedia.org/wiki/Aeolian_mode>`_ (vi) — the natural minor scale. Sad, dark, introspective
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(Stairway to Heaven, Losing My Religion)::
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c["aeolian"] # C D Eb F G Ab Bb C
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**`Locrian <https://en.wikipedia.org/wiki/Locrian_mode>`_** (vii) — minor with flat 2nd and flat 5th. Unstable,
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`Locrian <https://en.wikipedia.org/wiki/Locrian_mode>`_ (vii) — minor with flat 2nd and flat 5th. Unstable,
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rarely used as a home key (used in metal and jazz over diminished
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chords)::
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@@ -167,7 +167,7 @@ Scales are iterable and support ``len()`` and ``in``:
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Building Chords from Scales
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----------------------------
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**`Diatonic <https://en.wikipedia.org/wiki/Diatonic_and_chromatic>`_ harmony** builds chords by stacking every other note of the
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`Diatonic <https://en.wikipedia.org/wiki/Diatonic_and_chromatic>`_ harmony builds chords by stacking every other note of the
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scale. A **triad** takes the 1st, 3rd, and 5th; a **seventh chord** adds
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the 7th.
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@@ -218,7 +218,7 @@ Some of the most-used chord progressions in Western music:
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The 12-Bar Blues
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~~~~~~~~~~~~~~~~
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The **`12-bar blues <https://en.wikipedia.org/wiki/Twelve-bar_blues>`_** is the most influential chord progression in
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The `12-bar blues <https://en.wikipedia.org/wiki/Twelve-bar_blues>`_ is the most influential chord progression in
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American music. It's 12 measures long and uses only three chords
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(I, IV, V)::
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@@ -249,7 +249,7 @@ Parallel Major and Minor
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~~~~~~~~~~~~~~~~~~~~~~~~~
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Two scales are **relative** if they share the same notes (C major and
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A minor). Two scales are **`parallel <https://en.wikipedia.org/wiki/Parallel_key>`_** if they share the same tonic but
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A minor). Two scales are `parallel <https://en.wikipedia.org/wiki/Parallel_key>`_ if they share the same tonic but
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have different notes (C major and C minor).
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Mixing parallel major and minor is a powerful compositional tool —
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@@ -28,7 +28,7 @@ Indian Classical (Hindustani)
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-----------------------------
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The Hindustani system uses **swaras** (Sa, Re, Ga, Ma, Pa, Dha, Ni) and
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organizes scales into **`thaats <https://en.wikipedia.org/wiki/Thaat>`_** — the 10 parent scales from which `ragas <https://en.wikipedia.org/wiki/Raga>`_
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organizes scales into `thaats <https://en.wikipedia.org/wiki/Thaat>`_ — the 10 parent scales from which `ragas <https://en.wikipedia.org/wiki/Raga>`_
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are derived.
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.. code-block:: python
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@@ -124,7 +124,7 @@ and folk music worldwide. `Pentatonic scales <https://en.wikipedia.org/wiki/Pent
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known musical scales, found independently in cultures across every
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continent.
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The **`blues scale <https://en.wikipedia.org/wiki/Blues_scale>`_** adds the "`blue note <https://en.wikipedia.org/wiki/Blue_note>`_" (flat 5th / sharp 4th) to the
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The `blues scale <https://en.wikipedia.org/wiki/Blues_scale>`_ adds the "`blue note <https://en.wikipedia.org/wiki/Blue_note>`_" (flat 5th / sharp 4th) to the
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minor pentatonic — this chromatic passing tone is the defining sound
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of the blues.
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@@ -163,8 +163,8 @@ gamelan orchestra in 12-tone equal temperament. True gamelan tuning is
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unique to each ensemble and does not conform to Western intonation —
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these are the closest 12-TET approximations.
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**`Slendro <https://en.wikipedia.org/wiki/Slendro>`_** is a roughly equal 5-tone division of the octave, producing
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an ethereal, floating quality. **`Pelog <https://en.wikipedia.org/wiki/Pelog>`_** is a 7-tone scale with unequal
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`Slendro <https://en.wikipedia.org/wiki/Slendro>`_ is a roughly equal 5-tone division of the octave, producing
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an ethereal, floating quality. `Pelog <https://en.wikipedia.org/wiki/Pelog>`_ is a 7-tone scale with unequal
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intervals, typically performed using 5-note subsets called *pathet*.
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.. code-block:: python
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@@ -16,7 +16,7 @@ The 12 chromatic tones are::
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C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B
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Notes with two names (like C# and Db) are **`enharmonic equivalents <https://en.wikipedia.org/wiki/Enharmonic>`_** —
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Notes with two names (like C# and Db) are `enharmonic equivalents <https://en.wikipedia.org/wiki/Enharmonic>`_ —
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different names for the same pitch. Whether you call it C# or Db depends
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on the musical context (key signature, harmonic function).
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@@ -32,7 +32,7 @@ pitch notation**, where the octave number increments at C::
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Key reference points:
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- **`A4 = 440 Hz <https://en.wikipedia.org/wiki/A440_(pitch_standard)>`_** — the international tuning standard (ISO 16)
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- `A4 = 440 Hz <https://en.wikipedia.org/wiki/A440_(pitch_standard)>`_ — the international tuning standard (ISO 16)
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- **C4 = 261.63 Hz** — middle C on the piano
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- **A0 = 27.5 Hz** — the lowest A on a standard piano
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- **C8 = 4186 Hz** — the highest C on a standard piano
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@@ -96,17 +96,17 @@ Temperament
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Different temperaments produce slightly different frequencies for the
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same note name:
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- **`Equal temperament <https://en.wikipedia.org/wiki/Equal_temperament>`_** (default): Every semitone has an identical
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- `Equal temperament <https://en.wikipedia.org/wiki/Equal_temperament>`_ (default): Every semitone has an identical
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frequency ratio of 2^(1/12). This is the modern standard — it allows
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free modulation between all keys but no interval is acoustically
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"pure" except the octave.
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- **`Pythagorean temperament <https://en.wikipedia.org/wiki/Pythagorean_tuning>`_**: Built entirely from pure perfect fifths
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- `Pythagorean temperament <https://en.wikipedia.org/wiki/Pythagorean_tuning>`_: Built entirely from pure perfect fifths
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(3:2 ratio). Produces beatless fifths but introduces the "Pythagorean
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comma" — a small discrepancy when 12 fifths don't quite equal 7
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octaves. Used in medieval European music.
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- **`Quarter-comma meantone <https://en.wikipedia.org/wiki/Quarter-comma_meantone>`_**: Tunes major thirds to the pure ratio of
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- `Quarter-comma meantone <https://en.wikipedia.org/wiki/Quarter-comma_meantone>`_: Tunes major thirds to the pure ratio of
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5:4, distributing the resulting error across the fifths. Dominant in
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Renaissance and Baroque music (15th–18th century). Sounds beautiful
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in closely related keys but "wolf intervals" make distant keys
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@@ -204,7 +204,7 @@ The Overtone Series
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Every tone you hear is actually a composite of many frequencies. When
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a string vibrates, it doesn't just vibrate as a whole — it also vibrates
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in halves, thirds, quarters, and so on, producing the **`harmonic series <https://en.wikipedia.org/wiki/Harmonic_series_(music)>`_**:
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in halves, thirds, quarters, and so on, producing the `harmonic series <https://en.wikipedia.org/wiki/Harmonic_series_(music)>`_:
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.. code-block:: python
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@@ -231,7 +231,7 @@ It's also why the major triad (root, major 3rd, perfect 5th) feels
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Different instruments emphasize different harmonics, which is why a
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violin and a flute playing the same note sound different. This quality
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is called **`timbre <https://en.wikipedia.org/wiki/Timbre>`_**.
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is called `timbre <https://en.wikipedia.org/wiki/Timbre>`_.
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Enharmonic Equivalents
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----------------------
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@@ -258,7 +258,7 @@ tones carry their enharmonic equivalents:
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The Circle of Fifths
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--------------------
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The **`circle of fifths <https://en.wikipedia.org/wiki/Circle_of_fifths>`_** is the most important diagram in Western music
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The `circle of fifths <https://en.wikipedia.org/wiki/Circle_of_fifths>`_ is the most important diagram in Western music
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theory. Starting from any note and ascending by perfect fifths (7
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semitones), you pass through all 12 chromatic tones before returning
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to the starting note:
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