Gustav Holst
(1874-1934)

Musical  Intervals

Musical  Intervals

Musical  Intervals

Musical  Intervals

Musical  Intervals

Musical  Intervals

Musical  Intervals

Pythagorean Scale

Pythagorean Scale

Pythagoras’s  Rule

Pythagoras’s  Rule

Pythagoras’s  Rule
Step #1

Pythagoras’s  Rule
Step #2

Pythagoras’s  Rule
Step #3

Pythagoras’s  Rule
Step #4

Pentatonic Scale

Pythagoras’s  Rule
Step #5

Pythagoras’s  Rule
Step #6

Pythagoras’s  Rule
Step #7

Musical  Intervals

Dorian  Mode

Modes

Ionian Mode or
 Major Scale

Aoelian Mode or
 Minor Scale

Major and
Minor Scales

 Seven Modes

Phrygian Mode

Mathematical Basis
for Scales

Mathematical Basis
for Scales

Mathematical Basis
for Scales

Aesthetic Basis
for Scales

Equal-Tempered Scale

Equal-Tempered Scale

Equal-Tempered Chromatic Scale

Major Scales
C Major

Major Scales

Major Scales Quality

Minor Scales
 A Minor

Minor Scales

Minor Scales Quality

Diatonic vs. Chromatic

Equal Tempered
vs. Pythagorean

Equal Tempered vs. Pythagorean