On Another Note… Or Pitch?

Pitch Class CircleNicholas D. Lewis

So it turns out that music theorists often don’t make the distinction between the terms note and pitch.  If music theorists don’t make the distinction, then what motivation do students have to speak correctly?  Like father like son; like teacher like student.  Comment on the bottom of the page about whether or not you guys knew the difference.  It will serve as a case in point, and statistics are good.  And worry not, I promise I’m not being too much of a pedant.  It turns out that this difference is fundamental to the way that we talk about music theory, so it’s actually important.

pitch refers only to the frequency of a given sound.  That means it’s actually impossible to name a note based on listening to someone playing a piano… Theoretically at least.  More on that later. The idea of a note in Western culture was developed by the need to transmit sounds in a semiotic (symbolic) way.  A note is therefore the symbolic representation of a pitch on paper, and is defined by a system of rules that have no other function than to define tonality.  When speaking of pitch, it is therefore technically impossible to speak of tonality.  The two ideas are separate and incompatible.

Well, some interesting arguments can be derived from these definitions.  Most importantly, it turns out that the idea of perfect pitch inherently collapses upon itself.  The idea that a person can hear a pitch and tell you what “note” that pitch represents is rubbish.  Today I was in a room with someone playing piano, and a smart-aleck in the back stood up and proudly said “You’re playing a C”.  I hate to burst his bubble – and that may be an impressive bar trick – but that “pitch” actually doesn’t correspond to any note.  Why?  Let’s analyze this on three levels:

1.  Even if we forget the definitions of these terms, the “note” could have been a B# or a D-double-flat.  It depends on the tonality of the piece.  In rare cases, could it have also been an A-triple-sharp?  You bet!

2.  Taking the definitions into account, it turns out that pitches represent nothing other than a frequency.  You can sing the pitch that a note represents, but the converse is a fallacy.  You cannot write a pitch (without harmonic context… But even then, it’s still technically impossible).

3.  I know in western culture an A4?440 hertz.  That’s great.  Turns out that this is arbitrary and actually depends upon the culture and time periods. In Baroque tuning, an A4?415 hertz.  If we take a person with “perfect pitch” and blast at them an A4 in baroque tuning, they would probably say that the “note” is an A-flat or G-sharp, or something in that ballpark.  But they’d be wrong.

If a person can hear a note and tell me the frequency, then they may have “perfect pitch”.  But in terms of how perfect pitch is normally defined, the notion is just silly.  Notes are notes, and pitches are pitches.  As far as I can see – from a practical standpoint – they live in different worlds.  One in the air, one of the staff.

2 thoughts on “On Another Note… Or Pitch?

  1. Since we’re being pedantic, I’d like to contest that it is impossible to write a pitch. It is very possible, in physical terms, to write a pitch. A pure sine wave pitch can be easily written as sin( 2 pi f t ), with f being the frequency. A non-pure pitch (such as the one produced by a piano or violin) can be written as a set of Fourier coefficients. If writing (or representing) a pitch was impossible, the logical consequence would be that it would be impossible to record music (digitally or analogically).

  2. Thanks for commenting. I disagree with you for a couple of reasons. Firstly, it turns out that very few pitches – and especially pitches created by musical instruments or voices – are actually pure sine waves. You could represent frequencies with a set of Fourier coefficients, and a number of other ways. But differentiating between “frequency” and “pitch” is important in music theory. Remember that a ‘pitch’ is an auditory sensation that is ultimately a result of the tonal system. Frequencies, which can certainly be objectively described in physics as you explained, are independent phenomenon. A pitch has to be heard (processed by the brain), a frequency can exist independent of a person’s perception of it. Therefore, I argue that since perception is so important to the definition of a pitch, the idea of “perfect pitch” and being able to notate a pitch – which depends upon context as it relates to scales and modes – is misunderstood at best.

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