tuning systems by jamila smart. just scales made from integer ratios pentatonic pentatonic...

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