Pitch · Theory

What Is a Musical Sound Note Name Octave Harmonic Series Concert Pitch

Pitch is the hearing of frequency. That sentence is easy to say, but two things have to be pulled apart: frequency is a physical quantity, pitch is a perceptual one, and the ear does not hear frequency linearly.

Frequency and pitch

Frequency is the number of cycles per second. Double it and the pitch rises by one octave — the first brick of the whole theoretical building.

Then notice the next step. Going from 100 Hz to 200 Hz is one octave. Going from 200 Hz to 400 Hz is also one octave. The two jumps differ completely in hertz (100 versus 200) yet sound the same distance apart. The ear is counting ratios, not hertz.

Frequency	Relation to A4	Perceived position
110 Hz	two octaves below	low register
220 Hz	one octave below	low-middle register
440 Hz	the reference A4	middle register
880 Hz	one octave above	high register

Every distance concept in music — intervals, scales, keys — is built on this ratio scale. That is why pitch appears as evenly spaced steps on paper but as a doubling sequence in frequency. The two pictures are not the same picture, and mixing them up causes real errors.

Pitch is continuous, note names are discrete

The ear can distinguish differences far smaller than a semitone. Note names cut that continuous line into fixed points, like driving posts into a slope. What players call "out of tune" is simply a landing point that falls too far from its post.

This explains two things at once:

Why string instruments are hard — there are no frets, so every note has to find its own landing point;
Why the piano looks easy — the landing points are manufactured. Press the key and the pitch is correct.

And there is a third case that is neither: glissandi, vibrato, and vocal slides do not sit on posts at all. They are the slope between two posts. Notation has almost no dedicated symbol for them, so they are conveyed by performance instructions or simply by listening to a recording.

Diagram: the same octave, drawn two ways

Listen: pitch is continuous

Play the twelve semitones in a row and you hear a smooth rising slope, not twelve unrelated points. The sense that "there is space between two notes" is exactly why intonation can be heard at all.

Common misconceptions

"Higher frequency, so it is a straight line." Perceptually it is not. Equal frequency steps sound

increasingly crowded, which is why the frequency axis has to be drawn geometric to match hearing.

"Pitch is objective, intonation is subjective." The reverse. Pitch is the perception; frequency is the

objective quantity. A tuner's hertz reading is objective, but it is only a tool for approximating pitch.

"Every key on a piano has one fixed frequency." That holds only in twelve-tone equal temperament.

Retune the same keyboard to just intonation and every hertz value shifts. :::

Listen in the library

Piano Sonata No. 14 in C-Sharp Minor, Op. 27 No. 2 "Moonlight": I. Adagio sostenutoC16:10A triplet arpeggio figure held for the whole movement — any drift in pitch is immediately audibleDetailsInvention 1C11:03Bach's first two-part invention — two voices state the same subject at different pitches, easy to compareDetailsAmazing GraceC11:09A single-line hymn tune — every note is held steadily and can be repeated exactly, the clearest case of pitch as a perceptionDetails

All tracks from midicn-lib — inline badge is the license tier (C1 commercial / C2 non-commercial / C3 study only).

Sources

频率与音高的对应关系、听觉的对数特性、A4 = 440 Hz 的近代标准，属音乐声学通则
本文行文为原创，未采用任何参考源句式

Used for fact-checking only; all prose is original.

Related