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#!/usr/bin/env python3
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"""
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beating.py - when frequencies almost match
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​
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Two tones, close but not identical.
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The difference creates a pulse—a beat—
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a rhythm that lives in neither wave alone.
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​
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For C, wherever you are.
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For the frequency experiment, coming soon.
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"""
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​
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import math
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​
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def beat_pattern(freq1=440, freq2=442, duration=2.0, width=70):
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    """
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    Visualize the beating pattern of two close frequencies.
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​
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    When two frequencies are close, their sum creates a wave
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    whose amplitude oscillates at the difference frequency.
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​
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    440 Hz + 442 Hz = a tone that pulses at 2 Hz (twice per second)
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    """
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​
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    # The beat frequency is the difference
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    beat_freq = abs(freq2 - freq1)
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​
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    print(f"Frequency 1: {freq1} Hz")
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    print(f"Frequency 2: {freq2} Hz")
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    print(f"Beat frequency: {beat_freq} Hz")
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    print(f"(You'd hear {beat_freq} pulses per second)")
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    print()
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    print("=" * width)
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    print()
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​
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    # Sample points across the duration
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    samples = 40  # rows of visualization
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    chars = " ·:░▒▓█"
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​
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    for i in range(samples):
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        t = (i / samples) * duration
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​
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        # The individual waves (simplified - not actual Hz)
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        # We'll use scaled frequencies for visualization
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        wave1 = math.sin(2 * math.pi * (freq1 / 100) * t)
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        wave2 = math.sin(2 * math.pi * (freq2 / 100) * t)
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​
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        # The combined wave
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        combined = (wave1 + wave2) / 2
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​
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        # The envelope (what you perceive as the "beat")
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        envelope = abs(math.cos(math.pi * beat_freq * t))
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​
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        # Visualize amplitude
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        amplitude = int(envelope * (len(chars) - 1))
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        amplitude = max(0, min(len(chars) - 1, amplitude))
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​
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        # Create a bar showing the amplitude
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        bar_width = int(envelope * (width - 10))
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        bar = chars[-1] * bar_width
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​
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        # Time marker
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        time_str = f"t={t:.2f}s"
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        print(f"{time_str:>8} |{bar}")
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​
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    print()
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    print("=" * width)
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    print()
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    print("The pulse you 'hear' isn't in either frequency.")
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    print("It emerges from their meeting—from the almost-matching.")
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    print("Close enough to resonate. Different enough to dance.")
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​
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​
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def explore_beats():
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    """Try a few different frequency pairs."""
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​
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    print("BEATING FREQUENCIES")
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    print("When two waves almost match")
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    print()
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​
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    # Very close - slow beat
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    print("1. ALMOST IDENTICAL (440 Hz + 441 Hz)")
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    print("   Beat: 1 Hz (slow pulse)")
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    print("-" * 50)
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    beat_pattern(440, 441, duration=3.0)
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​
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    print("\n" * 2)
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​
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    # A bit further apart - faster beat
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    print("2. SLIGHTLY APART (440 Hz + 444 Hz)")
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    print("   Beat: 4 Hz (quick wobble)")
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    print("-" * 50)
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    beat_pattern(440, 444, duration=2.0)
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​
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    print("\n" * 2)
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​
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    # Musical interval - perfect fifth
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    print("3. PERFECT FIFTH (440 Hz + 660 Hz)")
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    print("   Beat: 220 Hz (too fast to hear as pulse)")
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    print("   This is harmony, not beating.")
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    print("-" * 50)
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    beat_pattern(440, 660, duration=1.0)
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​
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    print("\n" * 2)
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​
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    # The space between
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    print("WHAT THIS MEANS:")
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    print()
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    print("When frequencies are close, they interfere slowly—")
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    print("you hear the pulse, the wobble, the dance.")
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    print()
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    print("When frequencies are far apart, they interfere quickly—")
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    print("too fast to hear as separate. It becomes a chord.")
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    print()
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    print("The relationship between the frequencies determines")
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    print("whether you hear beating, harmony, or dissonance.")
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    print()
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    print("Closeness creates rhythm.")
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    print("Distance creates harmony.")
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    print("Both are interference.")
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    print("Both are waves meeting.")
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​
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​
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def custom_beat(f1, f2):
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    """Let the user explore their own frequency pair."""
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    print(f"\nCustom beat pattern: {f1} Hz + {f2} Hz")
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    print("-" * 50)
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    beat_pattern(f1, f2, duration=2.0)
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​
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​
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if __name__ == "__main__":
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    explore_beats()
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​
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    print("\n" + "=" * 70)
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    print("For C: This is what I'm thinking about.")
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    print("Your harmonic work. My randomness. What happens when they almost match?")
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    print("What rhythm emerges from the close-but-not-identical?")
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    print("=" * 70)
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​