An Akashic Torus

The title An Akashic Torus refers first to the Akashic records, that library found in the ether that contains all knowledge. The Torus is a donut shaped structure that somehow is a common representational mapping in our mind of many multi-dimensional patterns. Along with the intonation employed we have a looking back but not to some ‘Golden Age’ that never was, but as a door to view what been discarded as musical possibilities or even what have been spoiled.  The piece centers solely on pentatonics, an interest resurrected by my contact with Lou Harrison, who I envision as the present caretaker of pentatonic scales in the previously mentioned library. It is not unlike the room he had in his house of similar purpose.  Of much interest also is in the effect of long meters as a resistance to the short time thinking we all are subject to. Although the meter of this piece contracts or expands it remains centered on a meter of 101 beats long, making each bar about 55.5 seconds long. The striking of a Meru Bar most often marks this meter, but not always so I advise not counting.  The piece has only 11 bars to show yet it makes the piece exactly 1111 beats long.

For those interested and familiar with Moments of Symmetry patterns, here is also the final rhythmic breakdown of the piece based on secondary Moment of Symmetry patterns. The basic 101 was both subdivided by a 64 beat generator which was cycled around or another generator which resulted in 64 different subdivisions. from there the 101 pattern was both expanded  to a 138 beat pattern and contracted to both a 64 and 37 beat ones.

It was a quite difficult piece to write in that the Clarinis were limited to a range of a ninth and this coincided with only the lowest octave of the vibraphone. They also were only capable of playing diatonic scales of 7 notes each and two different ones were necessary for getting all 12 tones of the scale. I worried much about the whole concert sounding too high in pitch lacking bass instruments so this is one of the reasons i added the Meru bars. You need headphones to really hear it though. Care had to be taken also to cue the Pitches for the violin like Tahru as often the lines were melodically more than harmonically conceived making it a bit harder for any string player, much less one also being handed a new instrument.  Fortunately it was all recorded in the studio a few days later which should appear with the other fine works on the program which you can access the links from the youtube video.

"Prepared" Intonation as opposed to "Tempered" Intonation

     Maybe the most common way tuning is thought of is to enable a series of harmonies or scales to be performed in as many different ways or in related ways depending on quite a varieties of approaches. Intonation regardless of the ‘school’ has given both melody and harmony new options as well as different stresses and pull even in sometimes the most familiar of material.

     These explorations have lead to sometime unforeseen musical situations that result in acoustical phenomenon not sought for but compelling when it appears sometimes out of nowhere. More than a few have sought these events exclusively by means that can be as simple as close pitches creating beat and beat patterns, or proportional triads or larger units as well as difference tones. It we pursue this path and construct tunings to do so, might the term ‘tempering” not be the best term we might use.

I think what is happening in many of these cases in pursuit of both sound and noise is closer to what Cage described and did with the term “prepared” in the case of the piano .

 The prepared piano was changed so that specific notes would be changed into specific sounds. In the field of intonation this shift goes from the noun of a singular pitch to the verb of the interaction of two or more, by interval. Being tied to ‘interval’ instead of a single atom of sound allows each individual tone to act potentially in a variety of roles that might be unique in its relationship and situations to the whole matrix of others. This places an overarching "political " framework by the roles each plays within its structure. It becomes capable of personality as well as identity. This approach calls for more investigation along these specific lines as these goals and desired will lead to new forms to have them realized. While we have new melodies and harmonies, we also have new sounds and even new noises and it is these four elements that promises much to the modern sound alchemist even via just  the one parameter of tone.

Another 14 tone scale [from a 2-3-7-11-13 Dekany]

As a prelude let me say not to worry. I will tell you what a Dekany is , and yes somehow I have come up with quite a few 14 tone scales, in fact more than any other number.

The harmonics 2-3-7-11-13 as a set have raised some interest. George Secor and Margo Schulter, are just two important microtonal theorist who have seen interesting possibilities in them. While the former sees it as a bedrock for harmonic development and is interested in scales that can accommodate them as in this paper of his. The latter, Margo Schulter is interested in this set as the basis to explore her neo-renaissance/neo-gothic approach to music since these harmonics are the basis of the Persian scales of the time.

Margo had recently posed the question about how these harmonics might also be developed into scales that include the non-tonal centered harmonics structures of Erv Wilson's called Combination Product sets, or CPS for short. These structures provide a gateway into a somewhat 'atonal' or perhaps 'pantonal' environment while retaining relatively simple consonances. The interest is in adding to the language of this period before tonality would take such a strong hold.

The simplest CPS we can form of these is the 2 out of 5 Dekany. The Dekany is a 10 tone structure that takes the combination 2 out of 5 elements at a time and multiplies these together. [2*3, 2*7, 2*11, 2*13, 3*7, 3*11, 3*13, 7*11, 7*13, 11*13]. You can download the chart above or a larger one here to see how one can map it out on a lattice. Now while this give us a wonderful harmonic set, there is a great advantage in going one step further and trying to find what is called a Constant Structure. This is a structure where each times ratio occurs in such a scale, it will be have the same number of notes in between. [We find this property in the pentatonic scale on the black notes, in the diatonic and in the 12 tone scale for instance] Now this Dekany does not have this property on its own and the chart shows how I solved the problem and ended up with a 14 tone scale.

I preserved on the left half shows the steps it took to solve [in case one wishes to do so with any set that might interest one.]

First one arranges the main intervals from smallest to largest possible with the harmonics one is working with.  This coincides with the series one sees running down the right hand side in the left half of the chart.

While 14/13 were all one unit the 13/12  we can observe that one of the three occurrences  are two units to the other two being only one. Hence we need to add tones so that all the 13/12 are 2 units in size. This is designated with a circle with an arrow from side to side which is carried down and counted in determining the other intervals.

A rather odd thing happen though as when we reach down to 11/8, we can see that the 12 notes up to that point do form a constant structure,  but the 11/8 is only 4 units is much too small as the smaller 4/3 is 6 units. While one can have a bit of an overlap on range, we instead fix this oddity by adding two tones in the large gap to make it at least the same number of units as the 4/3. Since the idea was to have possible repeated tetrachords the pitches chosen to be added were ones that were a 3/2 above or below tones we had. There are other solutions one could pick.

Viggo Brun's Algorithm Applied to Rhythm and Long Meters

http://anaphoria.com/ViggoRhythm.pdf Here is a short paper about to be added to The Journal of Anaphorian Music theory on how Viggo Brun's Algorithm can be used to generate long meters or metric patterns. These produce different variations than the ones i have worked out with Horogram Rhythms found in that journal.

The Pentatonic Family pt. 1

This is a very elementary paper that i thought i would share.
It touches upon the use of Bi-level Moments of symmetry as well as chains with slight variations.
All is discussed in terms of an undefined 12 but the principle can be applied to any tuning. hope it is helpful. http://anaphoria.com/pentatonics.pdf

It is like a third world application of Xenakis sieve method. but then again we might prefer to apply complex ideas in simple ways than simple ideas to complex ones.

The Death of [blank] Music

It is not the death of new music, of contemporary music, of avant-garde music, of experimental music, of new music, of classical music, of rock music, of jazz music, of punk music, of free improv music, of indigenous music, of folk and traditional music, of electronic music, of conceptual music, of silent music, of professional music, of amateur music, of music on CDs or vinyl, of live music, or even anti-music, but it is the only the death of music that should concerns us. The healthy whole is made of many organs

Music and Evolution

I keep not posting cause i don't have extended things to say , sometime only a line of two.
please forgive. But people talk about all musical innovation as being evolutionary,yet if we are basing this on nature, possibly we might be stricter and point out in nature there are all types of variations produced that don't always result in a forward progression of the species.
Many of these are sterile, so what really constitutes what is evolutionary is the ability of something to produce fertile offspring as opposed to sterile hybrids. Let history define where musical evolution is or what might be like the parallel to Monsanto. What good is it to go somewhere if once you get there there is no where to go but the way one comes in. Perhaps there are more Cul-de-Sacs than ever before, but perhaps history knows them as the commonest of lots.