![]() This interval is less than a unison (2 0 = 1) but greater than one octave down (2 -1 = 1/2), so multiply by 2 once to get 9/5. Subtracting a just perfect fourth ( 4/3) from a classic minor third 6/5 corresponds to 6/5 divided by 4/3, thus 9/10 (or 0.9).Adding 4 just perfect fifths ( 3/2) corresponds to (3/2) 4, thus 81/16 (or 5.0625), which is greater than 2 octaves (2 2 = 4), but less than 3 octaves (2 3 = 8), so divide by 2 twice to get 81/64.4/1 is greater than 2, so divide by 2 to get 2/1, which is equal to 2, so divide by 2 to get 1/1.7/2 is greater than 2, so divide by 2 to get 7/4.3/4 is less than 1, so multiply by 2 to get 3/2.Repeat until the resulting interval is less than 2. If the starting interval is greater than 2, divide it by 2.Repeat until the resulting interval is greater than 1. If the starting interval is less than 1, multiply it by 2.If the starting interval is greater or equal to the unison (1) and less than the octave (2), it is already in reduced form.For instance, going up an octave means multiplying by 2, while going down an octave means dividing by 2. Stacking intervals expressed as ratios corresponds to multiplying those ratios. ![]() frequency ratios), or logarithmic measures (e.g. The choice of an appropriate method depends on the interval size measure being used: linear measures (e.g. There are also several methods that can be followed. This is especially useful when working with very complex ratios. An easy way to find the reduced form of an interval is to use a specialized calculator such as xen-calc.
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