Forming Tetrachordal Scales from the Subharmonic Series

Here is a page of a document  added to The Journal of Anaphorian Music Theory. The document looks at one simple way one can derive tetrachordal scales from a subharmonic series. Such scales have been observed on equally spaced holes on flutes as well possibly the Greek Aulos.  Regardless of the case,  the scales manage to touch upon some well known ancient Greek ones as well as presenting  a method to finding others. Such a method could be easily tuned with only an ability to tune fourths and fifths above a given note.
A direct link to the PDF is also Here.

Sand,Dust,Relics

C. Forster’s Musical Mathematics which I reviewed in my last post reminded me of how much subharmonic material is in the musical past from places as far removed as Greece to China. While I have been working for quite a few years with various recurrent sequences (of which the Fibonacci series is just one), this exploration has been almost exclusively in the harmonic direction.

Having brought back my Marion Prosynth from the US, I remembered what a good tool it was to try out a tuning as one can use the LFOs to trigger notes in different ways so one can place weights on keys which will bring them up and down at different times. I often will let something like this run for quite some period periodically moving as I pass by or not satisfied with what I am hearing. One of my favorite series is Wilson’s Meta-Meantone though I haven’t used it as much. The CD Beyond the Windows Perhaps among the Podcorn is the big exception. If one seeds it right one can have a triad using the ol’ 27/20 wolf with a third that beat equally giving it a more ‘consonant’ sound. Playing through a few recurrent sequences in their subharmonic version I found that indeed Meta-Meantone had much to offer.

So here is a mere sampling I call Sand, Dust, Relics. That eventually moves into the triad mentioned in its minor version.