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Extracts from Pitch, Pi, and other Musical Paradoxes (a practical guide to natural microtonality)
Chapter 3: Scales available in LucyTuning


Equal Temperament twelve notes per octave (12tET) assumes that there is only one interval on which all musical scales are based. This interval is the semitone (100 cents). Twelve equal semitones make one octave. Two semitones make one whole tone.


The naturals arranged in order of fifths gives: F-C-G-D-A-E-B 1 2 3 4 5 6 7 This is a chain of seven notes, an expanse of six steps. Hence the first digit in the code is 6/ None of these notes are missing, so the second digit is 6/0. Each scale begins on the notes in positions 1 through 7 as follows:

So for Scales Using All The Naturals.

Notice that each octave consists of 5 Large (L) and 2 small (s) intervals in the circular sequence LLsLLLs with each scale starting from a different position in the sequence.

1 2 3 4 5 6 7 8



Greek Name & Interval Pattern Indian Name
C D E F G A B C 6/0/2 Ionian LLsLLLs Bilaval
D E F G A B C D 6/0/4 Dorian LsLLLsL Kafi
E F G A B C D E 6/06 Phrygian sLLLsLL Bhairavi
F G A B C D E F 6/0/1 Lydian LLLsLLs Kalyan
G A B C D E F G 6/0/3 Mixolydian LLsLLsL Khamaj
A B C D E F G A 6/0/5 Aeolian LsLLsLL Asavari
B C D E F G A B 6/0/7 Locrian sLLsLLL -

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Related Pages
LucyTuned ScaleCoding
LucyTuned ScaleCoding analysis of 2333 unique scales - Nov 2008
Chapter 1 is this the Lost Music of the Spheres?
Chapter 2 Fourths and Fifths: Circles, Spirals, or Cylinders?
Chapter 4 Pitch and Colour Connections
Chapter 5 Scalemaking
Table of more than 60 scales