extract from CHAPTER THREE of

Pitch, Pi, And Other Musical Paradoxes



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 Scale


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 -

Table of more than 60 scales For more information on LucyTuned ScaleCoding
conventional keyboard layout for modulation of pattern (.gif)

Pitch Pi,....|Chapter One| |Chapter Two|

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