How music works: waves, harmonics and why octaves sound the same
Why do two notes an octave apart sound like the same note? Why does a clarinet sound hollow? Why is a piano tuned slightly wrong on purpose? Most questions show a waveform, a spectrum or a vibrating string and ask what you'll hear. It's for curious listeners and musicians. You don't need music theory, and the math stops at ratios. You can check several answers by humming or with a free tuner app.
Questions
- Not answered. Two notes an octave apart sound like the same note, only higher. What do their waves have in common?
- Not answered. A plucked string vibrates in all of these shapes at once. Shape 1 is at 100 Hz. What frequencies does the string produce?
- Not answered. An open guitar string plays a note. How much of the string must vibrate to play the perfect fifth above it, a 3:2 frequency ratio?
- Not answered. A guitarist rests a fingertip lightly on the exact middle of an open string, without pressing it down, and plucks. What do you hear?
- Not answered. A guitarist plucks the same open string first near its middle, then right next to the bridge. Which statements about the second pluck are true?
- Not answered. Among the first six harmonics of one note, which intervals appear between two neighboring harmonics?
- Not answered. One spectrum is a clarinet in its low register, the other is a flute. Which one is the clarinet?
- Not answered. A pipe closed at one end resonates lowest at 100 Hz. What is the next resonance frequency above that, in hertz?
- Not answered. Overblow a flute and its note jumps up an octave. When a clarinetist presses the register key, how far up does the note jump?
- Not answered. Waves A and B contain the same six harmonics at the same strengths. Only the timing of each harmonic differs. How do they sound as steady tones?
- Not answered. After breathing in helium, a person's voice sounds squeaky and high. What actually changed?
- Not answered. Which of these sounds have overtones at, or very close to, whole-number multiples of their lowest frequency?
- Not answered. Why does a struck drumhead give a vaguer pitch than a plucked string?
- Not answered. Two flutes hold steady notes at 440 Hz and 442 Hz. What do you hear?
- Not answered. You tune a guitar string against a 440 Hz reference and hear 3 beats per second. You tighten the string a little, and the beats speed up to 5 per second. What was the string's frequency before you tightened it, in hertz?
- Not answered. Played on a violin, a perfect fifth sounds smooth and a tritone sounds rough and tense. What is one physical reason?
- Not answered. Stack twelve pure 3:2 fifths up from C, and you'd expect to land on C again, seven octaves higher. Instead you overshoot. By how much, and what do modern keyboards do about it?
- Not answered. On an equal-tempered keyboard, how are the frequencies of the twelve notes in one octave spaced?
- Not answered. Which statements about equal temperament, the tuning of nearly every modern piano and fretted guitar, are true?
- Not answered. A phone's tiny speaker can't produce 60 Hz, yet you still hear a bass line play a 60 Hz note. Why?
- Not answered. This sound contains only the frequencies shown. What pitch do listeners hear, in hertz?
- Not answered. A piano tuner deliberately tunes the highest notes sharp and the lowest notes flat compared with exact equal temperament. Why?