![]() The fraction or ratio 5/4 gives us what musicians call a "major third," that is, E in the key of C. The ratio 3/2 simply means that one pitch vibrates 3/2 as fast (three halves as fast) as the other. This is what musicians commonly call a "perfect fifth": C to G. If one pitch vibrates at 200 cycles per second and another at 300 cycles per second, we have a 3/2 ratio. That is,īecause those fractions are equivalent by multiplication by 2,Īnd the latter pair are between 1/1 and 2/1.įor many people, this is the hardest aspect of tuning theory: getting used to the idea that Fractions in tuning are usually written in such a way as to bring them between 1/1 and 2/1, multiplying or dividing by 2 when necessary. In just intonation, that's the way it is. We're used to eight different keys on the piano all being called by the same letter - C - but we're not used to fractions behaving this way: 1/1 = 2/1 = 4/1. That is, 1/1 is the same pitch as 2/1, and also the same pitch as 4/1. The confusing thing for most people is that fractions denoting octaves are equivalent. ![]() (An interval is simply the distance between any two pitches in perceived pitch-space.) We can call the first, lower pitch 1/1, and the second, higher pitch 2/1. Then the two pitches make an octave, the most basic of musical intervals. If one pitch vibrates at 200 cycles per second,Īnd another pitch vibrates at 400 cycles per second, These ratios are always ratios between the rate of vibration of two tones. E-flat can be 1/1, or F-sharp, or A-flat - it doesn't matter. In order to define pitches by fractions, some arbitrary pitch needs to be defined as 1/1. Or, the C an octave above a particular C can be denoted as 2/1, since a 2-to-1 ratio between frequencies is an octave. For example, if C is the reference pitch (if we're in the "key of C"), thenĪny C in the scale can then be denoted as 1/1. In the notation of just-intonation (pure) tuning, pitches are given as fractions, which are actually ratios between the named pitch and a constant fundamental. What Does Music in Pure Intervals Sound Like? How Is This Different from Our Normal Tuning?Ĥ.
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