Chords » A Dominant Eleventh

Using the scale degree formula, we first start with the A 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, 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 lowest note of the chord (A), then move our first interval (M3), which brings us to our second note in the chord (C#). 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:

On acoustic instruments (such as guitar or piano), a single played note will result in more than a single sounded frequency. There's a lot of complexity here, but at its simplest, the fundamental (eg: A4 = 440Hz) will sound, as well as a number of harmonies, which are multiples of that frequency.

The graph below presents a simplied representation of the sounds and relative amplitudes that are sounded when this chord is played. The exact instrument, and even how the chord is played, can vary things dramatically, but this can give you an understanding of certain sounds you may hear when playing a chord.

Each fundamental and its harmonies are given a different color. The height of the bar represents the amplitude (volume) of the frequency, and the position (left-to-right) represents the frequency of the sound (further to the right means higher). Finally, the grid-lines represent notes in 12-tone-equal-temperment (notes used in traditional western music).

From these frequencies, we can determine harmonics that sound when we play the notes of a chord. These harmonies are listed below, along with the frequencies contributing to each. It's worth noting that these frequencies won't all be the same for higher harmonies, and some harmonies will be flat, sharp (or both).