In brief
Frequency is a physical rate measured in cycles per second. Pitch is the perceptual attribute by which sounds can be heard as higher or lower.
What you’ll learn
- Distinguish pitch from frequency and loudness.
- Use frequency ratios to compare octaves.
- Read a pitch name with a register and an explicit tuning reference.
Useful first: Sound and vibration
A measurement and an experience
A steady pure tone with a higher frequency generally produces a higher perceived pitch. But a musical note is rarely just one pure tone. It may contain many frequency components, changing attacks and noise. A pitch description tells us how a listener organises that sound, while a frequency measurement describes a physical or recorded signal. The two are strongly related without being identical.
Try humming a comfortable note, then hum it more softly without intentionally changing its height. You are attempting to vary loudness while holding pitch. Next glide upward while keeping the effort comfortable. This separates two listening questions that beginners sometimes mix together. Words such as high, loud, bright and thin may overlap in everyday speech; in a rehearsal, clarify which feature you want to change.
References: [1]
Octaves are ratios, not fixed differences
Under the usual octave model, doubling a frequency moves up one octave; halving it moves down one. Thus 150 to 300 Hz and 300 to 600 Hz are both octave relationships even though their differences are 150 and 300 Hz. Equal musical steps in a tuning system therefore cannot generally be obtained by adding the same number of hertz each time.
An octave relationship often lets us recognise pitches as belonging to a similar named family while still hearing a difference of register. A low C and a high C are not the same physical sound. They can share a pitch class in Western naming while occupying different positions in a melody. Other musical questions may require more precision than a pitch-class label provides.
References: [2]
Names need registers and references
In common scientific pitch notation, a letter with an accidental identifies a pitch class, and a number identifies its octave register. C4 is middle C in this convention. With A4 set to 440 Hz and twelve equal divisions of the octave, a note n semitones above A4 has frequency 440 × 2^(n/12). State the reference and system rather than assuming that every performance uses them.
For instance, the name A does not tell an instrumentalist whether you mean a low or high register. Nor does the syllable Sa assign a universally fixed frequency: a performer establishes the tonic for the musical setting. When exchanging a recording, include an audible reference, a tuning note or a clear written specification. Relative musical identity and an absolute laboratory measurement solve different coordination problems.
References: [2]
Use a tuner as evidence
A tuner estimates pitch from a microphone signal and displays a note name or deviation from a reference. Give it a clear, sustained sound and watch whether the estimate settles. The first instant of a pluck, surrounding noise or several simultaneous notes can make the reading unstable. Before adjusting an instrument, check that the device is analysing the sound you intend.
Compare a hummed reference with a second note, then use the display to check your prediction. This order keeps your ear involved. If the tuner names a different octave, listen again and consider whether a strong upper component has influenced its estimate. Accurate musical intonation also depends on context, instrument and tradition; matching a single screen value is not the whole of playing in tune.
References: [1]
A worked example
A ladder built by multiplication
Start with an imagined 150 Hz tone. Build a ladder in which every step is an octave. Then compare it with a ladder built by adding 150 Hz at each step.
- The octave ladder is 150, 300, 600 and 1,200 Hz. Each adjacent pair has a frequency ratio of 2:1.
- The addition ladder is 150, 300, 450 and 600 Hz. Its adjacent ratios are 2:1, 3:2 and 4:3.
- Although the second ladder has equal numerical gaps, its musical intervals become smaller.
- Read the same result downward: 600 to 300 and 300 to 150 Hz each divide frequency by two and descend an octave.
Notice: Pitch comparisons commonly depend on proportion. This explains why a keyboard's equal semitone spacing corresponds to multiplying by a constant ratio rather than adding a constant frequency.
Try it / Listening experiment
Hear a relationship.
Two short, pure tones: a starting pitch followed by a higher pitch. This model uses twelve-tone equal temperament. It does not model a raga’s intonation or ornamentation.
Frequency ratio: 27/12 ≈ 1.4983
Choose an interval, then listen to the two tones.
Start with a comfortable device volume. Audio plays only when you press Listen.
Try it yourself
Describe three pitches without confusing class, register and ratio.
- Take a tone at 220 Hz under the A4 = 440 Hz reference.
- Find the frequencies one octave above and below it.
- Name the three notes in scientific pitch notation, then explain what they share.
Compare your thinking
The notes are A2 at 110 Hz, A3 at 220 Hz and A4 at 440 Hz under this reference. They share the pitch-class name A and are separated by octaves. They differ in frequency and register; saying only “play A” does not specify which of the three is required.
What to remember
- Pitch is perceived; frequency is measured.
- An octave corresponds to a doubling or halving of frequency.
- A precise pitch specification includes register and tuning context.
References & further study
Use these sources to check terminology and continue studying. The worked examples and exercises are written for this collection.
- Pitch
Robert Hutchinson, University of Puget Sound
Introduces pitch as musical highness and lowness and connects it to the rate of vibration.
- Note names, MIDI numbers and frequencies
Joe Wolfe, UNSW Music Acoustics
Supplies pitch-frequency conventions, octave relationships and the equal-tempered frequency formula.
Educational writing by Burnt Chapati. Send a correction or suggest a source.