# Woodshed Wallpaper ™

# Scales and Modes

These charts give the scale degrees — both the quality, and the relative construction — and the chord qualities, for all the modes of various common scales.

For each scale, the chart has a row for each mode, and is numbered for that mode — and so the numbers also correspond to the scale degree on which the mode is built. The chart's first column gives the diatonic chord built on each degree, including tensions — i.e. the root chord for that mode; or also, the chord built on that scale degree. So, the first column also gives all of the diatonic chords in the scale. These diatonic chords are color-coded.

[Key: Δ Major ‒ Minor ø Half-Diminished ○ Diminished + Augmented (no symbol) Dominant]

For each mode of the scale (each numbered row), the chart shows the quality of each degree (from the Diatonic); and the interval construction, by half-step interval; based on the column for each degree. Each degree is cross-referenced by color; which gives the quality of the chord built on that degree, in each mode.

For example: looking at the the Diatonic chart, and the Ionian mode (the first row), the chart gives the following:

Mode number (1), and name (Ionian).

That mode's diatonic chord (the chord built from the first scale degree — Major 7, 9, 11, 13).

The quality of each scale degree (all natural notes).

By color also, the quality of each chord built on each scale degree.

The first cell, giving the diatonic chord, is colored red on this mode; and in all the modes for this scale, on each degree colored red, that chord will be the same (Major 7, 9, 11, 13) — e.g. in the Dorian mode, the 7th degree is colored red, and the chord built on that degree is a Major 7, 9, 11, 13. The colors are there to allow you to locate the quality of the chord built on any given degree of any given mode: by tracing the color back to the full chord with the same color.

The colors do also simply follow the scale degrees. I.E, it's simply the same as the root note for each chord. Therefore, every cell colored red will be the same note as the root note from the root scale — and every note with a given color is always the same note in all modes.

The chart also gives the scale's ordered pitch class set for reference; and it's interval vector. For these, we have dispensed with hex or proprietary notation ("A" or "t" for ten, etc.) and we 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 here. If you are not familiar with pitch class sets or interval vectors, here is a brief explanation:

## Pitch Class Set

This is notated in parenthesis. You can simply read the given ordered set by half-step intervals. E.g. in Diatonic, the root note is zero; then the Ⅱ is two steps up (the number 2 appears); and the Ⅲ is another two steps (the number 4 appears); and the Ⅳ is one step from there (the number 5); and etc. The vices and virtues won't be discussed: classes eliminate enharmonics for one, but you can see Wikipedia's article on Musical Set Theory for more.

So with the pitch class set: 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, there are 12 pitch classes – C, C♯/D♭, D, D♯/E♭, E, F, etc. In a set, 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 is 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.)

## Interval Vector

This is notated in angle brackets. The interval vector is another set of numbers: this time, always 6 numbers, each one representing how many instances of each 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 (they are: m2/M7, M2/m7, m3/M6, M3/m6, P4/P5, A4/d5 — Tritone). The six classes are always listed in this order. So for example, 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). This vector would be notated as <0 0 1 1 1 0>. Again, Wikipedia has an article for more.

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