Pitch: What a Note Is
A note is a vibration counted per second. Double the count and you get the same note again, one octave up — that one fact shapes everything that follows.
Vibrations you can count
Pluck a guitar string and it swings back and forth hundreds of times a second. Each swing pushes the air, the air pushes your eardrum, and your brain reports a pitch: high if the swings are fast, low if they are slow. The number of swings per second is the frequency, measured in hertz (Hz). The A that orchestras tune to swings 440 times a second — 440 Hz. A bass guitar’s lowest string is about 41 Hz; a piccolo’s top note is near 4000 Hz. Human hearing runs from roughly 20 Hz to 20 000 Hz, but almost all the notes in music live between 30 and 4000.
The octave: the same note, twice as fast
Here is the most important fact in all of music theory. Take a note and double its frequency — 220 Hz to 440 Hz, 440 to 880 — and the new note sounds so much like the old one that we give it the same name. Both are called A. The distance between them is an octave, and every instrument, every scale and every chord is organised around it. Halve the frequency and you go one octave down; keep doubling and you climb A1, A2, A3, A4, A5… the number counts which octave you are in.
Why does doubling sound like “the same”? Because a vibrating string does not only swing as a whole: it also swings in halves, thirds, quarters — all at once, more quietly. Those extra vibrations are the overtones, and the second one is exactly the octave. A note already contains its octave, so the two blend almost perfectly. (Overtones also decide why a flute and a violin playing the same A sound different — but that is a story for later.)
Length, tension and thickness
What sets a string’s frequency? Three things. Shorter strings vibrate faster (press a guitar string against a fret and the pitch rises). Tighter strings vibrate faster (that is what tuning pegs do). Thicker strings vibrate slower (the low strings on a guitar are wound fat). The Greeks noticed 2500 years ago that halving a string’s length doubles its frequency — the octave — and that stopping it at two thirds gives another sweet, stable interval, the fifth. Music theory began as string arithmetic.
From A3 (220 Hz) to A4 (440 Hz) is 220 Hz. From A4 to A5 (880 Hz) is 440 Hz — twice as many hertz for the same musical distance. Our ears hear ratios, not differences: every octave multiplies by two, no matter where you start. Keep that in mind whenever a formula multiplies where you expected it to add.
In the lab below you own a single string. Shorten it, pluck it, and watch the frequency and the note name follow. Find the two lengths that give the same note name — they are your first octave.
🎼 Lab — The String
A string tuned to A3 (220 Hz). Slide the bridge to shorten the vibrating part, then pluck it.
- Set the length to exactly one half: the frequency doubles and the name stays A — an octave.
- Try two thirds: 330 Hz, an E. That interval, the fifth, will return in every unit of this course.
- Watch the waveform panel: shorter string, more wiggles in the same 20 milliseconds.
🎼 Lab — The Octave Ladder
Six A notes, each twice the frequency of the one below. Play them in order and listen for the family resemblance.
- Jump from A1 straight to A6: five octaves, 32 times the frequency, still the same note name.
- Compare the waveforms: every row fits twice as many periods into the same window.
Work it by hand — 0 / 3
No multiple choice here: compute the value and type it. Suffixes like 2.5k or 20m are understood; answers within ±2% count.