Let’s take the octave from A 440Hz to A’ 880Hz and look at it as a ratio. 2/1 1/12 = 1.05946309436 (approx).Ĭonstructing the scale is done by starting from 440 Hz and then multiplying this value by the step size 1.05946309436 twelve times until we reach 880 Hz: 440Hz To divide 2/1 into 12 logarithmically equal steps we need to find the step size. These steps don’t look equal in terms of frequency – the Hz values get larger with every step. Maybe by now you have noticed one way in which the steps are equal… Each step is an equal ratio difference from the next. Comparing these two ways of dividing an octave equally To hear what it sounds like (I mean it’s just 12edo at A440Hz), you can follow this Scale Workshop link – it will open a page where you can press qwerty keys to play in this tuning. In an equal temperament, you can modulate between keys and every key will sound equally in-tune.
Which of these two methods sound equal to the ear? Whereas arithmetic divisions will only give you perfectly-tuned harmonics of a single fundamental with no concept of tonal modulation. It’s the logarithmic version – also known as equal temperament or EDO (equal division of the octave).
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