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'exponents'

Posted by jim 
jim
'exponents'
October 29, 2007 04:05PM
i'm trying to figure out what it means when a scale degree has an exponent over it. for example, under 'design of the prelude': [www-personal.umich.edu]

i'm also seeing things like f² (3) and there's a carot above the 3.

any help with this would be appreciated.
Aholmes
Re: 'exponents'
November 06, 2007 04:38PM
Well, there are a few different things you might encounter. With a roman numeral, what you're dealing with isn't a scale degree but rather a chord. V7 then doesn't mean the fifth scale degree but the chord built upon it, while the 7 means that the chord has the seventh of the chord added (If your fifth scale degree is G, then G is the root of the chord, B the third, D the fifth, making a complete triad, but then often the seventh (in this case, F), is added. Then, you'll often see rather than the 7, maybe a 6/5, or a 4/2, or something. This is just to tell you what inversion the chord is in. In the case of the 6/5 for example, your chord is in first inversion. If you write out the previous V7 chord, but put the third (B) in the bass (first inversion), then count the intervals from that bass note, you'll find that the G is a sixth (6) away, the F is a fifth (5) away, and the D a third (3). Accordingly, the full symbol would actually be 6/5/3, but traditionally the 3 can go unmentioned. That's where this notation comes from.

Additionally, you may see a letter name followed by a number, like C4. This tells you what octave that note is in (C4 = middle C). However, to muddle things further, in lead sheet symbols you might have a C7 or something like that, which is the same story as the V7, only the chord is built off of the given root (in this case, C),and there is no implication of that note's relationship to the scale (whereas V7 tells you the chord is based off the fifth scale degree.
Hope this helps.
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