Music is organized sound
All sounds come from vibrations. Noise is a jumble of random vibrations. A musical note is a sound with a steady, definite pitch, produced when something vibrates regularly.
Naming notes
Western music uses seven letter names: A, B, C, D, E, F, G. After G, the pattern starts over at A. Adding sharps (♯) and flats (♭) gives 12 different notes in each octave.
Frequency and pitch
Each note has a specific frequency. Orchestras around the world tune to A = 440 Hz.
| Note | Frequency (Hz) |
|---|---|
| Middle C (C4) | 262 |
| D4 | 294 |
| E4 | 330 |
| F4 | 349 |
| G4 | 392 |
| A4 | 440 |
| B4 | 494 |
| C5 | 523 |
The octave
When you double a note’s frequency, you get the same note one octave higher.
- A3 = 220 Hz
- A4 = 440 Hz
- A5 = 880 Hz
Notes an octave apart sound so similar that we give them the same name. A piano covers just over seven octaves, from about 27.5 Hz to 4186 Hz.
How instruments make notes
Standing waves
When you pluck a guitar string, waves travel along it, reflect off both ends, and overlap. The result is a standing wave, a pattern that seems to stay in place, with points that don’t move (nodes) and points that vibrate the most (antinodes).
The longest standing wave that fits on the string is half a wavelength long. It produces the fundamental frequency, the lowest note the string can play, which sets the pitch we hear.
Changing the note
| Instrument type | Vibrating part | How players change pitch |
|---|---|---|
| Strings (guitar, violin, piano) | Strings | Shorter, tighter or thinner strings give higher notes |
| Woodwinds (flute, clarinet) | Column of air | Covering holes changes the length of the air column |
| Brass (trumpet, trombone) | Air column, started by buzzing lips | Valves or slides change tube length; lip tension changes harmonics |
| Percussion (drums, xylophone) | Skins, bars or plates | Size and tightness; smaller bars give higher notes |
| Voice | Vocal cords | Muscles tighten or loosen the cords |
Harmonics and timbre
A vibrating string doesn’t only vibrate at its fundamental. It also vibrates in halves, thirds, quarters and so on at the same time, producing higher frequencies called harmonics (or overtones).
| Harmonic | Frequency (for A2 at 110 Hz) |
|---|---|
| 1st (fundamental) | 110 Hz |
| 2nd | 220 Hz |
| 3rd | 330 Hz |
| 4th | 440 Hz |
| 5th | 550 Hz |
Each instrument emphasizes different harmonics. This mix creates its timbre, the "colour" of its sound. That’s why a trumpet, a violin and a voice all sound different even on exactly the same note.
Scales and harmony
A scale is a set of notes in order. The C major scale uses the white keys on a piano: C, D, E, F, G, A, B, C.
Notes whose frequencies form simple ratios sound pleasant together (consonant).
| Interval | Frequency ratio | Example |
|---|---|---|
| Octave | 2 : 1 | C4 and C5 |
| Perfect fifth | 3 : 2 | C and G |
| Perfect fourth | 4 : 3 | C and F |
| Major third | 5 : 4 | C and E |
The ancient Greek thinker Pythagoras noticed these ratios on a vibrating string more than 2500 years ago.
Modern instruments use equal temperament: each of the 12 notes in an octave is spaced so the frequency goes up by the same factor (about 1.059) each step. This lets music be played in any key.
Resonance in instruments
The body of a guitar or violin is hollow. It resonates, vibrating along with the strings and making the sound much louder. Without its body, an electric guitar string is very quiet, which is why it needs an amplifier.
Common mistakes
- Thinking a note is a single frequency. Real instruments produce many harmonics.
- Thinking higher notes are louder. Pitch and loudness are separate.
- Thinking octave means eight times the frequency. It means double; "oct" refers to eight notes in the scale.
Try it yourself
- Use a tuner app to find the frequency of each string on a guitar or ukulele.
- Fill eight glasses with different amounts of water and tune them to a scale.
- Find the frequency of A6, two octaves above A4.
(Answer to 3: 1760 Hz)
Quick recap
- Musical notes have steady, definite pitches.
- Pitch depends on frequency; A4 is 440 Hz.
- An octave doubles the frequency.
- Instruments make standing waves; harmonics give each its timbre.
- Pleasant harmonies come from simple frequency ratios.