Divisions of the 4/1 Double Octave [read description]

The 4/1 double octave is a frequency between two pitches in which one his four times higher than the other. This interval is very consonant. In this video, the double octave is arithmetically divided into equal parts. Arithmetic division by 3, for example, divides 4/1 like this: 1 (1/1) 2 (2/1) 3 (3/1) 4 (4/1) And by 4: 1 (1/1) (7/4) 2.5 (5/2) (13/4) 4 (4/1) What I do to find this is I subtract the higher frequency from the base (4 - 1 = 3) and then divide it by the divisor (e.g. 4, so 3 / 4 = ) and then I keep adding until I get to 4. This results in the set of frequencies shown above Equal division divides intervals logarithmically (octave / 2 = √octave or 12-tet tritone), whereas arithmetic division divides them linearly (octave / 2 = perfect fifth) #microtonal #tuning #intonation #edo #musictheory