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Tuning SystemsTuning Systems
By Jamila SmartBy Jamila Smart
Just ScalesJust Scales
Made from integer ratiosMade from integer ratios
• PentatonicPentatonic
• PythagoreanPythagorean
• NaturalNatural
PythagoreanPythagorean
• DiatonicDiatonic– Addition of third and Addition of third and
seventhseventh– Different C4 frequencyDifferent C4 frequency– Syntonic commaSyntonic comma
• DodecaphonicDodecaphonic– Intervals created by Intervals created by
raising the fifth to a raising the fifth to a powerpower
– Creates circle of fifthsCreates circle of fifths– Different ratios for the Different ratios for the
tritonestritones
NaturalNatural
• ChromaticChromatic– Just and Pythagorean Just and Pythagorean
M3, m3, M6 and m6 offM3, m3, M6 and m6 off– Syntonic diatonic scaleSyntonic diatonic scale– Wolf tonesWolf tones
• MajorMajor– Uses integers 1-6Uses integers 1-6– Two different semitone Two different semitone
intervalsintervals
TemperedTempered
• Mean-tone – optimize thirds and Mean-tone – optimize thirds and fifths in certain keysfifths in certain keys
• Well-tempered – All keys usableWell-tempered – All keys usable
• Equal-tempered – make all keys Equal-tempered – make all keys sound the samesound the same
Mean-tone TemperedMean-tone Tempered
• Uses whole numbers as well as Uses whole numbers as well as irrational numbersirrational numbers
• Perfect M3Perfect M3
• Fifth not correctFifth not correct
MicrotoneMicrotone
• Small scale degreeSmall scale degree
• More chance that note will fall close More chance that note will fall close to a ratioto a ratio
• ff(k,v)(k,v) = f = fR R x 2x 2v+k/Nv+k/N
53 Tone53 Tone
• N = 53N = 53
• 3.615 cents apart3.615 cents apart
• Fifth still flatFifth still flat
Quarter ToneQuarter Tone
• N = 24N = 24
• 50 cent note interval50 cent note interval
• Three Quarter-tone pieces for Two Three Quarter-tone pieces for Two Pianos ii. Allegro - IvesPianos ii. Allegro - Ives
43 Tone43 Tone
• Invented by Harry Invented by Harry PartchPartch
• JustJust
• GG
• SymmetricSymmetric
Bohlen-PierceBohlen-Pierce
• 13 tones A-H, J13 tones A-H, J
• TritaveTritave
• B-P tenthB-P tenth
Wendy CarlosWendy Carlos
• Octaves must not Octaves must not contain whole contain whole number of notesnumber of notes
• More important to More important to get ratios correctget ratios correct
• AlphaAlpha
• BetaBeta
• GammaGamma