# Diatonic Harmony

These charts list the scale degrees and chord qualities for all the modes of various common scales.

For each scale, the chart shows the diatonic chords built on each degree, including tensions; and these are color-coded. Then for each mode of the scale, the chart shows the quality of each degree; and, cross-referenced by color, the quality of each chord built on each degree. For example: looking at the the Diatonic chart and the Ionian mode, the chart shows the following: the mode number (1) and name (Ionian), that mode's diatonic chord (the chord built from the first scale degree) (Major 7, 9, 11, 13), and the quality of each scale degree (all natural notes). The cells showing the diatonic chord & tensions are colored red on this mode; and in all the other modes, on each degree colored red, that chord will be the same (Major 7, 9, 11, 13) — so in other words, in the Dorian mode, the chord built on it's 7th degree (colored red) is a Major 7, 9, 11, 13. (That's just a consequence of how the modes are built; each of the same seven diatonic chords are shifted around in the various modes.) The colors are there to identify the quality of the chord built on any given degree of any given mode.

The chart also shows the scale's ordered pitch class set for reference; and it's interval vector. For these, I have dispensed with hex or proprietary notation ("A" or "t" for ten, etc.) and I just use integers, even if they are 2 digits. This notation is just simpler, and there is no restriction that requires a single character for each item in the list or set, and little confusion is possible. If you are not familiar with pitch class sets or interval vectors, here is a brief explanation:

First, by virtue of the reason we perceive all notes "A" in any octave to be of the same kind (the periodicity causes us to name an "A" in any octave as the same note), we say that pitches are classified by "pitch class": So in 12-tone music, as there are 12 notes, there are 12 pitch classes – C, C♯/D♭, D, D♯/E♭, E, F, etc. The pitch classes are notated with 0-based numbers: 0-11 (and as mentioned, some people will use "t" and "e" for ten and eleven, or as in hexadecimal notation, "A" and "B"). A pitch class set is just a collection of some pitch classes. For example, the C-Major triad in root position — C E G — which has pitch classes 0, 4, and 7, would be notated as the ordered pitch class set (0 4 7). (There are more details: the set may be unordered, and then notated with curly braces usually; microtones can be represented with decimal numbers; there is no requirement that pitch class 0 is always C; and short scales like a pentatonic may use 0-4 for the scale degrees even though there are skips between some degrees. You should just be sure of the convention used for any given set.) The vices and virtues won't be discussed: classes eliminate enharmonics for one; but see Wikipedia's article on Musical Set Theory for more.

The interval vector is another set of numbers, this time, always 6 numbers, each one representing how many instances of each given interval class is present in the scale. An interval class is an identity given to each interval type along with it's inversion, again represented with numbers. You can see my chart of Interval Classes for identification of the 6 classes. So for example, again take the C-Major triad: it contains one Major 3rd, one Minor 3rd, and one Perfect 5th (and by inversion, it contains one Minor 6th, one Major 6th, and one Perfect 4th). The vector would be notated as <0 0 1 1 1 0>. Again, Wikipedia has an article for more.

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Diatonic Harmony