editing disabled

Division of a seventh (e. g. 9/5) into n equal parts


Division of e. g. the 9:5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence has not even been posed yet. The utility of 9:5 or another seventh as a base though, is apparent by being used at the base of so much modern tonal harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

Incidentally, one way to treat 9/5 as an equivalence is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 (tempering out the comma 2430/2401). So, doing this yields 5, 7, and 12 note MOS, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. "Microdiatonic" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely compressed. However, a just or very slightly flat 9/5 leads to the just 7/5 generator converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the harmonic entropy of a pelogic temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 cents of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously.

Where examples of this particular temperament in use are concerned, they are already everywhere, just with notes which are rather farther apart.