Pitch or frequency?
There seems to be confusion (certainly with me!) about the relationship between pitch and frequency. Trying to clear it up finds contrasting ideas. Obviously, when a note has a higher frequency than another, it is a 'higher' ( further to the right on a piano) note. Would it be correct to say the pitch of a note is, say, C, without specifying whether it's C4 or C5, for instance?
I'm not referencing the 'same note played on different instruments', but perhaps it's as simple as we call the frequency 440Hz as pitch 'A' (not always, I know), but there are other frequencies also called 'A' - like 220Hz, and 880Hz.
The other question is related (and my answer accepted), but that's all, I think.
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Frequency refers to the measurable number of cycles per second (Hz) of a periodic sound wave.
Pitch refers to (subjectively) how low or high that wave sounds to us as a note. The way I see it, pitch is the log-scale way that humans subjectively perceive frequency.
An unfortunate medical condition that highlights the difference between frequency and pitch is Diplacusis - people hearing the same frequency as different pitches in each ear.
Would it be correct to say the pitch of a note is, say, C, without specifying whether it's C4 or C5, for instance?
Out of context, it would be confusing, because C4 and C5 are not the same pitch - one sounds subjectively higher than the other. (It might be OK if it were obvious from context which C you were talking about).
In our musical system, I think it's OK in some contexts to say that C4 and C5 are the same note, as long as we're talking in a context where the idea of octave equivalence is understood.
To combine it all in one simple answer - No, C4 and C5 are different pitches. They are the same 'pitch class', which might be loosely described in some circumstances as the same 'note'. But they are different pitches.
Frequency is the scientific description of pitch.
Would it be correct to say the pitch of a note is, say, C, without specifying whether it's C4 or C5, for instance?
It might be helpful to consider the distinction between a pitch and a pitch class. A pitch is a specific location on a keyboard: A4, for instance, is a pitch.
But a pitch class is a collection of all pitches related by octave equivalence. In other words, every single A on the keyboard (and every other A out there) belong to the pitch-class A.
Such a distinction is really helpful when understanding post-tonal music that operates on the notion of octave equivalency. Stravinsky's arrangement of Happy Birthday, for instance, is best understood from a standpoint of pitch classes.
In my way of understanding, pitch in musical terms refers to the frequencies associated with musical notes, where as frequency might be associated with tones that are in between notes and not musical in nature at all. Pitch seems to be musical and frequency seems to be associated with Physics. Another way to look at it is pitches are things we can hear and frequencies can include pitches but can extend well below or above the capability of the human ear to perceive.
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