Tuning Systems
By Jamila Smart
Just Scales
Made from integer ratios
• Pentatonic
• Pythagorean
• Natural
Pythagorean
• Diatonic
– Addition of third and
seventh
– Different C4 frequency
– Syntonic comma
• Dodecaphonic
– Intervals created by raising
the fifth to a power
– Creates circle of fifths
– Different ratios for the
tritones
Natural
• Chromatic
– Just and Pythagorean M3,
m3, M6 and m6 off
– Syntonic diatonic scale
– Wolf tones
• Major
– Uses integers 1-6
– Two different semitone
intervals
Tempered
• Mean-tone – optimize thirds and fifths in
certain keys
• Well-tempered – All keys usable
• Equal-tempered – make all keys sound the
same
Mean-tone Tempered
• Uses whole numbers as well as irrational
numbers
• Perfect M3
• Fifth not correct
Microtone
• Small scale degree
• More chance that note will fall close to a
ratio
• f(k,v) = fR x 2v+k/N
53 Tone
• N = 53
• 3.615 cents apart
• Fifth still flat
Quarter Tone
• N = 24
• 50 cent note interval
• Three Quarter-tone pieces for Two Pianos
ii. Allegro - Ives
43 Tone
• Invented by Harry
•
•
•
Partch
Just
G
Symmetric
Bohlen-Pierce
• 13 tones A-H, J
• Tritave
• B-P tenth
Wendy Carlos
• Octaves must not
•
•
•
•
contain whole number
of notes
More important to get
ratios correct
Alpha
Beta
Gamma