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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>
50 lines
1.7 KiB
Python
50 lines
1.7 KiB
Python
"""Compare equal, Pythagorean, and meantone temperaments."""
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import math
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from pytheory import Tone
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a4 = Tone.from_string("A4", system="western")
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print("Temperament Comparison")
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print("=" * 75)
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print()
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print(f"{'Note':>5s} {'Equal (Hz)':>12s} {'Pythag (Hz)':>12s} {'Meantone (Hz)':>14s} {'P diff':>8s} {'M diff':>8s}")
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print(f"{'─' * 5} {'─' * 12} {'─' * 12} {'─' * 14} {'─' * 8} {'─' * 8}")
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for semitones in range(13):
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tone = a4 + semitones
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equal = tone.pitch(temperament="equal")
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pyth = tone.pitch(temperament="pythagorean")
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mean = tone.pitch(temperament="meantone")
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# Difference in cents (1 cent = 1/100 of a semitone)
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pyth_cents = 1200 * math.log2(pyth / equal) if pyth > 0 else 0
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mean_cents = 1200 * math.log2(mean / equal) if mean > 0 else 0
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print(
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f"{tone.name:>5s} {equal:>12.3f} {pyth:>12.3f} {mean:>14.3f}"
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f" {pyth_cents:>+7.1f}¢ {mean_cents:>+7.1f}¢"
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)
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print()
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print("Key intervals to listen for:")
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print()
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intervals = [
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(4, "Major 3rd", "Meantone is pure (5:4), equal is sharp, Pythagorean sharper still"),
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(7, "Perfect 5th", "Pythagorean is pure (3:2), equal is slightly flat, meantone flatter"),
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(6, "Tritone", "The 'devil's interval' — all three temperaments handle it differently"),
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]
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for semitones, name, note in intervals:
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tone = a4 + semitones
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equal = tone.pitch(temperament="equal")
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pyth = tone.pitch(temperament="pythagorean")
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mean = tone.pitch(temperament="meantone")
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print(f" {name} ({a4.name}→{tone.name}):")
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print(f" Equal: {equal:.3f} Hz | Pythagorean: {pyth:.3f} Hz | Meantone: {mean:.3f} Hz")
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print(f" {note}")
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print()
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