Shorthand Notation
Common jazz parlance refers to upper structures by way of the interval between the root of the bottom chord and the root of the triad juxtaposed above it. For instance, in example one above (C7♯9) the triad of E-flat major is a (compound) minor 3rd away from C (root of the bottom chord). Thus, this upper structure can be called upper structure flat three, or US♭III for short.
Example two (C13♭9♯11) is called upper structure sharp minor four, and can be written shorthand as US♯iv.
Other possible upper structures are:
USII - e.g. D major over C7, resulting in C13♯11 9
US♭V - e.g. G♭ major over C7, resulting in C7♭9♯11
US♭VI - e.g. A♭ major over C7, resulting in C7♯9♭13
USVI - e.g. A major over C7, resulting in C13♭9
USi - e.g. C minor over C7, resulting in C7♯9
US♭ii - e.g. D♭ minor over C7, resulting in C7♭9 ♭13
US♭iii - e.g. E♭ minor over C7, resulting in C7♯9♯11
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