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If an eighth note is half the duration of a quarter note, would the duration of an eighth note played at 60bpm be equal to the duration of a quarter note at 120bpm? If yes, why was the concept of different notes, like half, quarter, eighth, formed?

Wouldn't it be easier to have just one base/reference note and vary the tempo of the song whenever necessary?

Because if the first para is true, then having an 8th/16th note would be the same as changing the tempo of a quarter note to make it twice or 4 times as fast

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  • It works just like that. Depending on the majority of notes (short or long), the writer will make the decision. Too many long or too many short notes makes a piece more difficult to read.
    – Tim
    Commented Dec 16, 2018 at 19:30
  • Are asking about only the tempo indications in a score like đť…ź=120? But, if all the notes in a composition were written as one type of note - like đť…ź - and then you changed tempo to get eighths, sixteenths, triples, dotted durations a score would be hard to read.
    – Michael Curtis
    Commented Dec 17, 2018 at 17:44

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I'm sure other reasons exist, but to give you a quick answer, I'll extract it right from your question:

If yes, why was the concept of different notes, like half, quarter, eighth, formed?

Wouldn't it be easier to have just one base/reference note and vary the tempo of the song whenever necessary?

The notation system sets a particular duration per note, tempo is per song. Try to apply your idea to something like this (i.e. different notes played at the same time)

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It won't work.

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  • you would have to have different tempo changes for each staff and the voices would line up.
    – Michael Curtis
    Commented Dec 17, 2018 at 17:45
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Your math is correct and we do that type of thing all the time. But one fixed reference note or tempo would not allow us to express all the subtle variability of time, and syncopation. This could be partly an historical issue (a lot of musical definitions and conventions can be thought of as obsolete in modern times).

As the other answer points out, with one note type how could you tell one player to hold a long note while the other player plays a melody? Would you have them count at different speed? It makes more sense to have everyone counting together and direct musician to play different delta(T) by the current convention. Your idea may make sense for a programing trying to indicate note duration by number of clock cycles in a computer.

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Notation is useful in simple uncomplicated arrangements of a given song, however sometimes a song is arranged in a manner so that it contains several parts all performed in synchronization with each other. A tempo is selected and each player uses it as a reference as they play their individual parts. Where a bass player may be playing half notes according to the chosen tempo, a lead guitar or horn part may be calling for any combination of whole, half, quarter, eighth, notes all referenced back to the chosen tempo of the song. It's a system that allows several parts to be played together, all at the same tempo.

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