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Degree Names and Numbers

Why do you need a name for a degree? Why can't we just stick with numbers (FIRST, SECOND, THIRD, etc)?

First of all, a name, like TONIC or DOMINANT, communicates the function of the degree. TONIC is always going to be the "home base" of the key. DOMINANT will always be its counterpart "that pulls attention away from TONIC" etc.

Numbers can be seen as equivalent, e.g., FIRST=TONIC, FIFTH=DOMINANT, SEVENTH=...but wait.

...there can be keys with less than 7 degrees.

Pentatonic "key" only has 5 different degrees (for example, black notes on the piano).
(Occasionally, used in "Western Tonal music", though, it is most common in folk music around the world).

In this case TONIC=FIRST (always), but DOMINANT=FOURTH.

Can you figure out how it is that DOMINANT still sounds the same in relation to the TONIC, whether it is the FIFTH degree of a standard seven-degree key, or the FOURTH degree in the pentatonic "key"?

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