Pinetone: Difference between revisions

Consider instead the just scale: 10/9 6/5 4/3 3/2 5/3 9/5 2/1, a just Dorian scale. This scale has 1 large step of 9/8, 4 medium steps of 10/9, and 2 small steps of 27/25, with step pattern MsMLMsM (mode 0). It can be represented with step signature and step mapping 1L 4M 2s = (9/8, 10/9, 27/25). This is our just porcutone diatonic.If we temper out the difference between L and M, we get LsLLLsL, Meantone[7] mode 0: Dorian; if we temper out instead the difference between 10/9 and 27/25, we get sssLsss, Porcupine[7] mode 0, which is referred to as symmetric minor. In this way, the porcutone diatonic mode 0 is said to be the [[product word]] of Meantone[7] mode 0 and Porcupine[7] mode 0, i.e., LsLLLsL *sssLsss -> MsMLMsM, where L*L -> L, L*s -> M, and s*s -> s. So the porcutone diatonic is the product of Meantone[7] and Porcupine[7].

We see 11/8 as the 4th in Lydian dark major. In Meantone[7] this is an augmented fourth, so whereas 11/8 is represented by the major 4th in Porcupine (L+ 2s), it is represented by the augmented fourth of Meantone[7] (3L). The meantone extension representing 11/8 with an augmented fourth is call Meanenneadecal, referencing the fact that it is most at home in [[19edo]].