Ed4/3: Difference between revisions

One of the key advantages of dividing the perfect fifth (3/2) into equal parts is that it creates scales where the interval between the unison (1/1) and the mapped minor third (6/5) is the same as the interval between the mapped major third (5/4) and the perfect fifth (3/2). This symmetry arises because the product of (6/5) and (5/4) equals (3/2). Consequently, the errors in approximating the minor third and the major third are of equal magnitude but in opposite directions. Similarly, when dividing the perfect fourth (4/3) into equal parts, the interval between the unison (1/1) and the mapped septimal major second (8/7) matches the interval between the mapped septimal minor third (7/6) and the perfect fourth (4/3), as (8/7) multiplied by (7/6) equals (4/3). Thus, the errors in approximating the septimal major second and the septimal minor third are also equal in size but opposite in direction. In essence, equal divisions of the perfect fourth (4/3) relate to 7-limit intervals in the same way that equal divisions of the perfect fifth (3/2) relate to 5-limit intervals.

In this sense, [[13ed4/3]], [[15ed4/3]], and [[28ed4/3]] are to the division of the fourth what [[9edf|9ed3/2]], [[11edf|11ed3/2,]] and [[20edf|20ed3/2]] are to the division of the fifth.