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I am new to learning piano and most of the notes I see in scores are in the length of a quarter note, and the time signatures I see are in 4/4. My question is if the quarter note is used so often, wouldn't it make more sense to call it the whole note and have the lengths of other notes relative to that?

I say this because, for instance, if there is a watch on my table and I wouldn't say there is a quarter of a watch on my table, that would just be unnecessarily complicated and silly.

Now let's bring the logic back to music. When you are first taught to read notation, you are told to play quarter notes. So the fundamental unit of counting is in quarters. How strange is that?

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    The most common duration is not the longest common duration. Therefore using it as the basis of notation would lead to lots of unreadable multi-tied notes. – Kilian Foth Jun 6 at 8:58
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    In addition to the given answer's: there might be an observational bias here - you are looking at music sheets for beginners at the moment which are meant to be simple in some ways for teaching purposes. Looking at more advanced music scores, you'll find pieces in other time signatures and another distribution of note length. Search the web for images of some well known pieces, like Mozart's Turkish March (Rondo "alla turca") to get an idea... - Though I'm really curious now, whether anyone had done note length and time signature statistics across a wide variety of pieces already :) – Arsak Jun 8 at 16:21
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Go back in history, and you'll discover the breve. The word means short, but it's actually worth eight crotchets (quarter notes).

Most music has a pulse to it - the part that one taps one's foot to, the heartbeat. The most common note to write for this amount of time has become the crotchet. In the most common time signature - 4/4 - that means there are four of them per bar. So, to put it into your way of thinking, one watch equals one bar.

That then makes it simple to divide up - or extend. These days one note in one bar of 4/4 is called a semibreve - all four beats - a whole note, taking up a whole bar. That bar could have two minims (half notes), or eight quavers (eighth notes). It all works smoothly.

By the time we get to sixteenth notes (semis), we see dots with stems that have two tails. Using your idea would add another tail, and start to get unwieldy. And since minims and semibreves work well, they would then be redundant. If it ain't broke...

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In a measure of 4/4 time there are four beats. A whole note in that same measure calls for a count of four beats. A half note calls for a count of two beats, half the number of beats called for in a whole note. A quarter note calls for one beat, 1/4 the number of beats that are called for in a whole note. If a quarter note were to be renamed a whole note, we would have to find another name for the note that represents 4 beats and 2 beats wouldn't we.

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The whole note is officially a "semi-breve", half of a short note. It was a unit melodies were written in, and then people found that for shorter notes, they needed subdivisions, and they used stems, filled in noteheads and started adding flags in order to manage successively smaller subdivisions.

Then at some point of time, musicians figured out that those further means of indicating subdivisions were actually faster to grasp and easier to read than the old divisions were and stuff tended to be written in shorter durations.

Triplet passages in older baroque times were written in 3/1 and were performed fast. In newer notation of the same music, this tends to have moved to 3/4 instead. It is hard to quantify, but those differences in notation tend to feel different also, making it somewhat more natural for me to sing from scores using the old durations. How much of a duration change makes the music feel "most natural" to modern performers may differ according to the musician.

But while usage of note lengths changed, the names stayed mostly the same after the initial transition from latin names (1 = semibreve, 2 = breve, 4 = longa) to fractions of a "whole" note (semibreve).

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