Easy Scales by Interpolating between Harmonic Series: Difference between revisions

A very easy way to construct a scale that's instantly recognizable, even without repeated listening/priming in the absence of listening the music in 12EDO, is to interpolate between harmonic series.

The '''x/12 and x/9''' harmonic series become particularly stressed in the '''(Maqam) Rast''', also known as the '''"Blues" scale''', of

Feel free to add comments or find/punch loopholes in this theory, but this is what I'd consider an idea '''"extended diatonic"''' scale in that it stresses likely the most important harmonic series in the diatonic scale while adding an extra (x/7) into the mix, giving the scale a wider range of tonal color.

Above calculations such as the interpolation of (11/7)/(14/9) can also be expressed as commas e.g. 99/98, which can be plugged into Graham Breed's Temperament Finder on [http://x31eq.com/temper/uv.html http://x31eq.com/temper/uv.html] to reveal temperaments and ultimately scales likely to contain the above harmonic series segments.

. However, most of the more advanced scales on my method would require tempering out several different commas and, presumably, also countless related commas indirectly. I am afraid this would often result in huge and much more challenging to play in (think: well over 15 notes) scales needed to contain, say, the x/7,x/8,x/9,and x/12 harmonic series from the root tone with reasonable accuracy in regular temperament theory.

If any '''experts on Xenharmonic math''', including related lists, can find a way to related the input of harmonic series segments to, say, MOS scales guaranteed to have them I would really appreciate it.