Chart of Transposition Ratios

Transposition Ratios Down/Up for 24 Semitones
Semitones Down Transposition Ratio Semitones Up Transposition Ratio Name of Interval
-1 0.94387431 1 1.05946309 Semitone [ (-)m2 ]
-2 0.89089872 2 1.12246205 Whole Tone [ (-)2 ]
-3 0.84089642 3 1.18920712 Minor Third [ (-)m3 ]
-4 0.79380053 4 1.25992105 Major Third [ (-)3 ]
-5 0.74915354 5 1.33483985 Perfect Fourth [ (-)4 ]
-6 0.70710678 6 1.41421356 Tritone [ (-)#4 ]
-7 0.66741993 7 1.49830708 Perfect Fifth [5]
-8 0.629996052 8 1.58740105 Minor Sixth [ (-)m6 ]
-9 0.59460356 9 1.68179283 Major Sixth [ (-)6 ]
-10 0.56123102 10 1.78179744 Minor Seventh [ (-)m7 ]
-11 0.52973155 11 1.88774863 Major Seventh [ (-)7 ]
-12 0.50000000 12 2.0 Octave [ (-)8 ]
-13 0.47193716 13 2.11892619 Minor Ninth [ (-)m9 ]
-14 0.44544936 14 2.24492410 Ninth [ (-)9 ]
-15 0.42044821 15 2.37841423 Minor Tenth [ (-)m10 ]
-16 0.39685026 16 2.51984210 Tenth [ (-)10 ]
-17 0.37457677 17 2.66968971 Eleventh [ (-)11 ]
-18 0.35355339 18 2.82842712 Octave + Tritone [ (-)#11 ]
-19 0.33370996 19 2.99661415 (3.0) Twelfth [ (-)12 ]
-20 0.31498026 20 3.17480210 Minor Thirteenth [ (-)m13 ]
-21 0.29730178 21 3.36358566 Thirteenth [ (-)13 ]
-22 0.28061551 22 3.56359487 Minor Fourteenth [ (-)m14 ]
-23 0.26486577 23 3.77549725 Fourteenth [ (-)14 ]
-24 0.25 24 4.0 Fifteenth (2 Octaves) [ (-)15 ]


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  Last Updated: 2 January 2007
  Layout revised: 31 July 2015; links revised 13 Nov '21