Scales systematics

Theory - Definitions

Scale
Trivial name
Systematic name
Texture
Interval row
Tone-row

The word scale comes from Italian and means “ladder“ which denotes that you somehow play notes in an order of increasing tone frequencies. A scale that goes from one octave to next octave is called an octave-scale. In the tempered tone-system there are 2048 possible scales. Some of these have particular names, the so-called trivial names. In Sds you can amongst others find the most common standard scales major, different minor scales, the diminished scale, whole-tone scale and the chromatic scale. The pentatonic standard scale is a major scale where the leading notes have been omitted. Most scales are part of a pattern with several scales, a so called texture or scale texture.

A scale is by definition a texture in a certain position.

If you have opened the SCALES dictionary you can work with many trivial names of scales-
Trivial names of scales are non-systematical names like major, pure minor, dorian, chromatic, arabian, synthetic..
In Sds you can quickly show and play the common standard scales
Major,
Pentatonic,
Eolian minor,
Harmonic minor,
melodic minor ascending,
melodic minor descending (same as eolian),
diminished scale,
Wholetone scale and Chromatic scale
by simply clicking Standard Scales on the Main menue or right-click at an empty spot in the main window and choose from the popup menue (well, there are not much empty space but you'll learn if you try...). The Chromatic scale is always available by the keyboard shortcut CTRL-K since it is used when you want to create a 12 notes tone-row.
You can search for trivial names or part of trivial names using the command Edit-Find or scroll through available scales in the combo box down to the right in the graphics window. You can obtain all the standard scales on the history stack by opening the STANDARDS.STX scale from the File menue.

In the Sds data base there are currently over 350 trivial names.

Scroll through all the trivial names in the combo-box down to the right in the graphics window, click on a name and it will be loaded on top of the stack immediately.

A systematic name is derived from the item itself strictly following certain rules. In Sds the intervals are assigned code names to build a row of intervals. The row is put in the best lexical order and so the name falls out by itself.
Example: The common major scale is buildt from 7 intervals when played from one octave to next. This makes it an octave scale. The interval codes build the interval row AABAAAB, the row is rotated to the best lexical order: AAABAAB and that is the name of a unique texture of intervals in the tempered tone system i.e. where all the smallest intervals are halt tone-steps (HS). The interval row can be played into next octaves below or above so there are seven possibilities to start with when you want to play an octave scale in this texture. Several consequtive intervals of the same kind may be notated as an interval name and a number e.g. BBBBB may be written B5 etc. The systematical name of the texture AAABAAB therefore could be written A3BA2B and it has seven scales all of which have trivial names as well.The scales are A3BA2B(1), A3BA2B(2) and so on. The common major scale is number 5 in this texture thus the systematic name of this scale is A3BA2B(5).

A texture (or scale texture) is a unique one-dimensional interval row that has an interval sum of 12 HS (halftone steps), repeats in every octave and has been rotated into the best possible alphabetical order. A texture that is composed of different intervals contains several scales. You see the different scales in a texture when you rotate it. If a texture contains more than one period which is repeated inside the octave this is indicated by surrounding parentheses and index.

If the period comprises the entire octave this is not indicated e.g. it is written A3BA2B not (A3BA2B)1. The number of intervals in the period = the number of scales in the texture.
The size of the period expressed in HS shows how many times the scale can be transposed.

Example:

The texture A3BA2B has the period A3BA2B (= the entire octave) and contains the scales
A3BA2B(5) Major, A3BA2B(6) Dorian, A3BA2B(7) Phrygian, A3BA2B(1) Lydian, A3BA2B(2) Mixolydian, A3BA2B(3) Pure Minor and A3BA2B(4) Locrian. Each scale transpose 11 times.

The texture (A)6 has the period “A“ that repeats 6 times inside the octave and contains only one scale, the Whole Tone Scale. This scale transpose once, i.e., there exist only 2 Whole Tone Scales on a musical instrument. You can flip through all possible textures using the slider next to the interval row textbox. Click in the textbox and the texture is displayed immediatelly in its first position. Then rotate the texture to see which scales it contains.

Look at this well-known example of a scale texture rotation. Move one interval at the end of the texture to the other end. You get another scale but all the intervals are the same. On an musical instrument it is like if you played a scale over some octaves and started on different positions, so technically, in this example, the lydian and mixolydian scales are the same, you just start the common major scale from another tone.

An interval row is any sequence of intervals expressed in Interval Codes. When the sum of all interval codes equals 12, the interval row becomes a scale.
Example: AAB is an interval row of two major and one minor second, i.e. the sum is 5 HS (chromatic half tone steps). DDD is an interval row of three major thirds which forms a complete scale (DDD is mostly known as an augmented chord).

Tone-row, definition

Tone-rows are also called series or tone series. The most common application of tone-rows is in twelve tone music writing, where you use all the twelve notes of the chromatic scale. A tone-row, however, may be derived from any scale thus forming melodies that merely use the notes of the scale. Once created, the tone-row is often used in some strictly rule-following ways:
Inversion. The original row is played as a virtual mirror placed perpendicularly below the original row.

Retrograde. The original row is played backwards.
Retrograde inversion (or inversion retrograde). This is a combination of the two modifications inversion and retrograde.
The easiest way to understand these features is to create a little tone-row in Sds and try it:

2) Switch to TONEROW mode by pressing CTRL-T or click the button labeled Tone row (see picture above).
2) Enter an interval row of a few intervals e.g. AB in the interval row window and press Enter (or enter a few notes in the graphics window).

3) Randomly create a tone-row by clicking the Random button.
4) Start playing if you want to.
5) Click the buttons Orig, Invrs, Retr and Retr Inv, watch and listen!.

If you wish to create a twelve tone row you will first fetch the chromatic scale. You can do this through the short-cut key CTRL-K.
NOTE: All the variations original, inversion etc are always positioned so that the lowest note is c1 (middle c) unless any transposition is active.

NOTE: In Sds all series use all the notes of the scale i.e. also the octave tone will be a member of the row. If you want to use only unique tones, you first have to delete the octave note.