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