Wilson's Mapping of the Hypercube

 

For any composers interested in doing a followup to Xenakis' Nomos Alpha, here is a pitch based option. While Wilson had plotted out the cube, he also did one for the hypercube which i added some factors, a different rotation with dyads closer to the best fifth possible with 1 thru 15 to my own with pure fifths Since the only links are via dyads the piece is bound to be pretty dissonant but higher harmonics are possible of course. the latter one might be the most perceptible at least for present ears.

In the lower right version there isa repeat of the product of 3-5-9-21 and 1-7-15-27, but if i space the structure in this way 18-20-21-24-27-28-30-32 these two tones will be two octaves apart

Rethinking the Guitar as a cross-set.

 

While I am not a guitar player, I have nevertheless observed how the instrument is played and used as most of us who are non players. It has struck me that at one possibility has been over looked which i will explain here and provide one example, not to be definitive tuning but as an good example of  what i see as a fruitful direction for the instrument. 

The tuning of a guitar can be thought of as a cross-set between the open strings and the where the frets are placed. Traditionally this has resulted in the same notes of the scale but has been useful with exploring the spacing of chords as well as range. With JI or subsets of larger ETs interesting variations occur as a result. While this has been a concern those working with any type of inequality, it has advantages that open up musical possibilities. 

If we look at how the instrument is often used we see guitar players often using the upper fret area in points of  excitement. traditionally the timbre of the instrument becomes more inharmonic due to the shorter length of the string coupled with the side to side motion of the string.  and it seem that tuning systems could be designed to explore intervals that might have more of the nature of the music played. It is easier to conceive the guitar as a cross-set when we still preserve having frets that run all the way across. While it is possible to retune the open strings that have individual frets it potentially become complex .

 Conceptually this idea would be to have more restful intervals in the lower range with more bright or most even dissonant intervals above. Since it takes very few changes in a scale to change to over all character, It could be just the change in a few ratios ( or say scale steps if using an ET. A conservative example might be having more 5 limit ratios in the lower range with their pythagorean counterparts in the upper range.  For myself it would be useful also in my vacillation between my Centaur and Centaura tunings. Here is a diagram showing one fretting possibilities (not to scale) .

Hopefully this will provide some further ideas. Various high number ETs such a 31 and especially 41 could choose subsets that covered all the 41 tones just in different ranges for their different tension and expression.

Andreya Ek Frisk has been kind enough to forward this accurate fretting of the tuning discussed. 

My Introduction to the Music of Alan Hovhaness

Having to support myself while a music maker required other means.  I ended up working as a scenic artist in Hollywood. I started at the bottom which consisted of having to clean the the rollers, buckets, brushes, and what ever else needed to be cleaned up and only when then thing would i get out onto the floor.  While a noisy environment, i would still listen to the classical channel as a good contrast to the commotion.  One day a piece had just started a few minutes before when one of my co-workers, Dennis Mancini, who also worked as an actor, entered the room, stopped, and listened and then commented about how the music reminded him of his living on Mt. Shasta for months by himself. He described how he lived totally off the land and this was his way of self-healing from his time engaged in the Vietnam War. When the piece finally ended the announcer said that the piece was "Mysterious Mountain" by Alan Hovhaness and we both were quite taken back that the music had captured his experience. Something that music seems less inclined to do these days. 

Years later, the composer Los Harrison told me that the music that saved him from his breakdown was the music of Harry Partch and Alan Hovhaness. I have many recordings of both, but the later's output is so large i have much more.