binary-scale

A (western well tempered) scale implemented with binary numbers.

IMPORTANT: This is a low-level library. Probably you'll use music-scale

You can see a demo here: http://danigb.github.io/scales

Usage

Install the module: npm install binary-scale --save and use it:

var Scale = require('binary-scale')
var major = Scale(2773)
major.binary // => '101011010101'
major.length // => 7 (7 note scale)
major.steps // => [2, 2, 1, 2, 2, 2, 1] (the distance in semitones between notes)

API: Scale(number)

The method receives an integer and returns an object with the following attributes:

• decimal: the scale decimal equivalent to the binary representation
• binary: a string with the binary representation
• length: the number of notes of this scale
• steps: an array with the distance in semitones between the notes of the scale
• leap: the maximum distance between notes of the scale
• modes: an array of binary strings with all the possible modes of this scale
• rootMode: a binary string representing the root mode that generates the rest of the modes. The rootMode of all the modes of the same scale is the same

If the number is below Scale.MIN or bigger than Scale.MAX an exception is thrown.

Theory and inspiration

binary-scale is inspired by the works of Rich Cochrane, Walter Zettel and William Zeitler

Binary representations of scales

This is a implementation of binary scales as presented in the awesome book Arpeggio & Scale Resources by Rich Cochrane, chapter 18.

The following explanation is extracted from the book. (The book has a Creative Commons Usage Attribution-Noncommercial-No Derivative Works 3.0... thanks a lot Rich!)

The major scale is 1 0 1 0 1 1 0 1 0 1 0 1. This number (2773 in decimal, see previous example) uniquely represents the Major scale. The method of representation is simple: each position, reading left to right, represents a note: 1, b2, 2 and so on. A 1 in that position means the note is included in the scale and a 0 means it is not included. So we have:

1   0   1   0   1   1    0   1   0   1   0   1
1  b2   2  b3   3   4   b5   5  b6   6  b7   7

Why 2048 scales?

All the scales have root, so the smallest scale is '100000000000' (2048) and the biggest is '111111111111' (4095), so the total number is 2048 (4096 - 2048)

Most of they are not interesting enough to be used in music. For example, in the allthescales.org site they limit all the possibilities to those with leap < 5 (1490)

Scale modes

Note that modes of a scale are obtained by the technique known as 'bit rotation'. We would normally eliminate all those rows that begin with a zero, since they don't contain a root note:

101011010101 // ionian
010110101011
101101010110 // dorian
011010101101
110101011010 // phrygian
101010110101 // lydian
010101101011
101011010110 // mixolydian
010110101101
101101011010 // aeolian
011010110101
110101101010 // locrian

License

MIT License