Flying through the expanded Magic Squares.

Etienne Deleflie is a composer working at the University of Wollongong on compositions dealing with the perception and simulation of spatial orientation of sound. He originally asked for help in how to map Patch’s Scale onto a matrix that lead to a deeper and deeper joint exploration of some other intonational possibilities.


It quickly became apparent that he envisioned a just intonational matrix in which one could 'fly' through, as a space where nearby harmonies would have some relation to each other yet still retain a special identity in the overall field to aid in the sense of movement. This reawakened my own interest in parallel ideas of unifying space and pitch.


Those familiar with lambdomas [of which Partch’s diamond is an example] would recognize this as a logical choice, but these result with everything higher on one end. Thus the results are rather unbalanced and also lack a harmonic variety we sought for.


The situation instead seemed ripe for other types of intonational possibilities and I thought that some of the simpler recurrent sequences would work well.


So with a bit of experimenting I found that 'magic squares' placed in the middle provided good seeds for making different series running in four directions . Nearby tones would retain various difference tone reinforcements yet over ‘space’ one would move away or toward where one started harmonically in a significant yet varied way. Yet there was something musically appealing to having certain harmonics stand out and even be repeated yet then diverge in different directions from there.


After going into the anechoic chamber where Deleflie has his speakers set up and listening to some of the results, we found it warranted pursuing an actual installation with small speakers in a space where people can walk through. We are working toward this at the moment.


While this idea continues to develop further, this diagram shows some of the ways I am constructing my matrices. This one serves as a good illustration in that it includes more than one series embedded into it. [Click to enlarge.]

The numbers refer to harmonics (that in turn have to be multiplied to get them in the hearing range). First I started with a magic square made of numbers 4-12 that one can see in the outlined box in the near middle. From here I construct recurrent sequences for each direction of two varieties.

I illustrate.

Take a number, say 5, in the box and call this A with B and C being the numbers above it. Now if we create a sequence such as A + C = D we take 5 + 9 =14 which is the number above 9. Now if we move the sequence up we add 10 + 14 = 24 and we continue this pattern. Next the same formula is applied moving to the right where 5 + 7 = 12 and 12 + 12 = 24 etc. For the other two directions I used a different recurrent sequence. This one is A + B = D. So in this case we add 7 + 12 = 19 and 12 + 5 = 17 in the case of the bottom row moving left or in the case of moving down 9 +10 = 19 and 10 + 5 =15 etc. These two sequences I learned from Erv Wilson who uses them to create his Meta-Pelog and Meta-Slendro scales. He might be the first to have found them embedded in Pascal's Triangle or Meru Prastara, as it was known centuries earlier . His papers on this can be seen here.

You will notice that being a magic square the number 24 comes out being the sum of the row or columns in the box, and if one follows any of the lines in either direction where one has three 24s in a row you might notice we get simple harmonics of this 24. Quickly each quadrant deverges in its own unique way on either side of these rows. The corners become the highest notes with the center the lowest, which is a useful balanced arc. Yet it is possible to treat this whole series as a subharmonic series where the corners become the lowest and the center the highest.

Etienne has realized this using SuperCollider. The piece is now available here https://anaphoria.bandcamp.com/album/second-flight-over-an-island-interior

A Reassignment for Banaphshu

In response to those inquiries regarding the omission of Banaphshu’s name as a contributor here in the last month, we apologize that we delayed in order to enable her to speak for herself.

“It has been touching to read the inquiries as to my whereabouts from even people I have never met and it brings joy to my heart as I remember all the wonderful people I have come across through my work acting as a guide and consultant for first the Embassy and later this Austronesian Outpost.

I pray that many of you will find the opportunity to visit me in my new position as the director at RNC (Radio Nabu Congul) and I want to let you know those doors will be open ones.

With this new position comes access to the facilities that will enable me to pursue my own artistic endeavors and to develop much of the electronic music that has taken a peripheral or back seat since my first musical collaborations. I expect to become more active than ever before, and I am sure that my long time partner, Kraig Grady, will keep you informed of these developments as we remain committed supporters of each others’ work.

It was originally amusing to allow inadvertently our identities to become confused. Often our collaborations were of a magical nature where neither of us cared to remember who did what, so our merging identities were less about deception and more about artistry. For the record, our long and deep connection was of a spiritual, cerebral nature, not a physical one. We had little choice.

The last few years, however, have seen those collaborations become less and less frequent, as we have become more familiar with the territory each provided for the other. We both feel that we will always carry these experiences with us into our musics.

To Kraig and all the supporters of Anaphoria, I thank you with my heart and my soul. May you always be nourished by the gifts of the imaginous spirit!

Banaphshu
24th November 2010
Nabu Congul”

"Chopsticks" in the style of Charles Ives

From Richard Grayson's 32nd (final) Annual Occidental College Concert, March 31, 2001. Improvisation on a theme from the audience.
Yearly he would improvise on a theme and style given from the audience.

Bagobo Agung Ensemble, Philippines 1960's

Hammer Dulcimer at Serial Space (excerpt)

from Serial Space- Sydney July 19.2010. NowNow series. excerpt near end of solo performance performed on Hammer Dulcimer tuned to Meta Mavila- a recurrent sequence that resembles a tuning found among the Chopi of Mozambique.
Flamenco music has always been a music that has quite informed my directions on this instrument

Why Just Intonation?

A summary~

Why Just Intonation?

1. Just Intonation is based on the harmonics relations one finds in nature and is a natural product of the sounds we hear.

2. Just Intonation represents the most consonant intervals. It likewise can create great dissonances thereby extending the range of tension between the two.

3. Just Intonation is tunable by ear due to its acoustical qualities that are unambiguous in nature. This in turn gives one a palette of limitless emotional depth and flexibility.

4. Just Intonation is a modular system. . It is infinitely expandable in terms of intervals at one disposal. Just intonation scales are also ‘open’ scales. While they can form self-contained consistent structures, they are always capable of being augmented in many different ways. This though does not require having to change or discard the pitches one already has, the array of building blocks are the same.

5. Just Intonation allows perceivable structural possibilities that cannot be realized effectively any other way. While ambiguousness has it place in all the arts , It should be by choice.

6. One can have many different intonation systems and scales yet still have common tones, intervals and even scales common between them that can act as bridges. These easily can exist side by side. In a free world of any pitch at any time one can move from one system to another freely by common tone scales or chords.

7. As Just Intonation produces scales with unequal size intervals, this gives one the possibility of more different size intervals with fewer notes.
For example there are Just Intonation pentatonics that give one more different intervals than 12-tone equal temperament. As another example one particular 7 limit 12 tone scale harmonic known as Centaur will give one 50 different intervals within the octave.

8. Just Intonation allows for the possibility of each key or area of the tuning having its own unique flavor and quality.

The Shadow Theatre Of Anaphoria

From The Follies of Dr. Placebo