Pinetone: Difference between revisions

If you have a [[Lumatone]], you can use the standard Bosanquet mapping for 12edo. The white keys are the porcutone diatonic, a cross between the meantone diatonic scale and Porcupine[7], and then black keys give the porcutone pentatonic, which approximates the just intonation pentatonic scale 9/8 5/4 3/2 5/3 2/1. I've chosen to colour the G♯/Ab key pink, and the other chromatic keys blue, because I'm a proud trans woman and a big nerd. You can use any colours, but I find it helps to colour the G♯/A♭ key a different colour since that's the one chromatic key used along with the diatonic keys to make the porcutone octatonic.  

The diatonic scale has a step signature of [[5L 2s]], meaning it has 5 large steps and 2 small step arranged in the step pattern LsLLLsL (represent in mode 0, Dorian mode). In Meantone[7], the large step represents both 9/8 and 10/9, the major and minor tones (''tempering out'' the [[81/80]] that separates them) hence the name "Meantone". The small step represents 16/15 and 27/25 (which differ again by [[81/80]]). We write this as [[5L 2s]] = (9/8~10/9, 16/15~27/25). Porcupine[7] instead has step step signature and step mapping [[1L 6s]] = (~9/8, 10/9~27/25), hence the difference between 10/9 and 27/25, [[250/243]], is tempered out. In mode 0 it has step pattern sssLsss. [[81/80]] is called the Meantone comma, and [[250/243]] is called the Porcupine comma.