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kennethreitz
9da3ac8b28
- circle_of_fifths.py — visualize keys around the circle - chord_identifier.py — identify chords from notes and fingerings - key_explorer.py — explore keys, signatures, progressions, borrowed chords - temperament_comparison.py — compare equal, Pythagorean, and meantone - chord_tension.py — analyze tension, consonance, and voice leading - world_scales.py — scales from 6 musical traditions - fretboard_explorer.py — instruments, tunings, capo transposition - midi_converter.py — MIDI ↔ note ↔ frequency reference - progression_writer.py — famous progressions, Nashville numbers, random generation - interval_trainer.py — interval names, songs, and consonance ranking - overtone_series.py — harmonics and why chords sound good - key_detection.py — detect keys from melodies and chord progressions Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
69 lines
2.5 KiB
Python
69 lines
2.5 KiB
Python
"""Explore the overtone series — nature's chord."""
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from pytheory import Tone, Chord
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a4 = Tone.from_string("A4", system="western")
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print("The Overtone Series")
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print("=" * 65)
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print()
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print("When you play a note, you're actually hearing many frequencies")
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print("at once. The fundamental plus its integer multiples:")
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print()
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print(f"{'Harmonic':>9s} {'Frequency':>10s} {'Nearest Note':>13s} {'Interval from Root'}")
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print(f"{'─' * 9} {'─' * 10} {'─' * 13} {'─' * 25}")
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overtones = a4.overtones(16)
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for i, hz in enumerate(overtones, 1):
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nearest = Tone.from_frequency(hz)
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if i == 1:
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interval = "Fundamental"
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else:
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interval = a4.interval_to(nearest)
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print(f"{i:>9d} {hz:>10.1f} {nearest.full_name:>13s} {interval}")
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# ── Why Chords Sound Good ───────────────────────────────────────────────
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print()
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print("Why the Major Triad Sounds 'Natural'")
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print("=" * 65)
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print()
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print("The first 6 harmonics contain: root, octave, 5th, 2nd octave, 3rd, 5th")
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print("That's a major triad! The major chord is literally embedded in physics.")
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print()
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c4 = Tone.from_string("C4", system="western")
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harmonics = c4.overtones(6)
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harmonic_names = [Tone.from_frequency(hz).name for hz in harmonics]
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unique = []
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for n in harmonic_names:
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if n not in unique:
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unique.append(n)
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print(f" First 6 harmonics of C: {', '.join(harmonic_names)}")
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print(f" Unique pitch classes: {', '.join(unique)}")
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print(f" C major triad: C, E, G")
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print()
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# ── Shared Overtones = Consonance ───────────────────────────────────────
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print("Shared Overtones Between Intervals")
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print("=" * 65)
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print()
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print("The more overtones two notes share, the more consonant they sound.")
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print()
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root = Tone.from_string("C4", system="western")
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root_overtones = set(round(h, 1) for h in root.overtones(12))
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for semitones, label in [(7, "Perfect 5th (C→G)"),
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(4, "Major 3rd (C→E)"),
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(5, "Perfect 4th (C→F)"),
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(3, "Minor 3rd (C→Eb)"),
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(6, "Tritone (C→F#)"),
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(1, "Minor 2nd (C→C#)")]:
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other = root + semitones
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other_overtones = set(round(h, 1) for h in other.overtones(12))
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shared = root_overtones & other_overtones
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print(f" {label:25s} {len(shared):2d} shared overtones (of first 12)")
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