C# Dominant Thirteenth

Construction

Using the scale degree formula, we first start with the C# major scale, and number each note in the scale starting from 1 - these are the scale degrees. Next, we use the scale degree formula, in this case 1-3-5-♭7-9-11-13, to select notes from our enumerated scale. When a chord requires notes that are not in the scale, this is indicated with a flat (♭) or a sharp (#) along with the scale degree; a ♭3, for instance, would be one half-step down from the 3rd scale degree.

Alternatively, we can use the interval stack to construct our chord. With this approach, we first start with the root of the chord (C#), then move our first interval (M3), which brings us to our second note in the chord (F). We repeatedly apply each of the remaining intervals in the stack to get the full list of notes for our chord.

The diagram below shows how both the scale degree formula and interval stack methods result in the same selection of notes: