The Butterfly Constellation

The people of Anaphoria are perplexed at how some places in the world see a hunter [Orion] where they have only seen a Butterfly [Marpessa].

This photo has been updated here
http://anaphoria.com/mintime.html

A family of 9 tone Scales with some 14 ones on the side.

We have to thank John Chalmers for his Tritriadic Scales. It causes us to keep focus on the material generated by the combination of tonic, dominant and subdominant and how wide those parameters can be extended. It seems to be an idea that has been in the air recently. Warren Burt used in an installation, which you can listen to a bit here 3 11-limit harmonic series fifths apart. Such a structure while embedded in a Partch diamond (harmonic hexads on 1/1, 3/2, and 9/8) seems to stand on its own with it own life. The piece I am working on now for solo vibraphone that I will be playing in Brisbane and in Helenburgh explores these relationships within 7 tone scales much in the way Indonesians will use pentatonic within their 7 tone pelog. I mention some ideas about this here in relation to the idea of tempering to accommodate these three scales.
It appears it a similar idea caught the interest of Steve Grainger who took a classic 7-limit Pentatonic and extended it likewise up and down. This he mailed to me.
I made a mistake right off and assumed it was not a “constant structure”, that is a scale that where each occurrence of a ratio is always subtended by the same number of steps. It is a quality that gives a good melodic flow that otherwise only has harmonic relationships holding it together. Having both is worthwhile to pursue.
But I moved ahead and found 2 solutions right off for 14 tone scales. It is an unusual number to have as a scale and I seem to have come up with quite a few over the years. I am not sure why. These are illustrated and one could pick out of either set of alternatives depending on what one might like.

There is an important feature here though of Grainger’s 9-tone scale that as far as I know has been overlooked. It appears that there is a whole family of pentatonic based on 3 fifths plus 2 notes in between the fourths that will all produce 9 tone constant structures. These tones have to be larger than a 9/8 but smaller than a 32/27, most of your smaller minor thirds.

This scale would have been of interest to Rod Poole and note sure if La Monte Young has toyed with the idea, since it develops in the direction of 3 and 7s. It is in that territory

The Grounds of The Future Embassy of Anaphoria Island

Pictures from Canberra on our recent trip to inspect the final grounds chosen for the future Embassy of Anaphoria Island and witness the hoisting of the flag~

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.

Cris Forster's 'Musical Mathematics'

[C.Forster's Bass Marimba-Photo by Will Gullette]

Musical Mathematics by Cris Forster is a rigorous and highly organized book that deals with the construction and tuning of acoustic instruments. In a clear and graspable way, the book first tackles the physics of instruments, a subject that is often the greatest stumbling block for readers interested in building instruments of their own design. After a detailed examination of the subject of mass, Forster guides us through his knowledge of strings, which includes their physical properties and different usages on musical instruments. Only in retrospect does one realize what a careful choice as a starting point this is because it easily leads us to a more complex study of bars, rods, and tubes. Resonators follow, with thematic connections that reach back to earlier chapters and forward to air columns and flutes. A chapter on geometric progressions, logarithms, and cents concludes the first part of the book, and at the same time acts as a bridge to the study of tunings. The second part presents the reader with a strong foundation of the history of tuning in Western civilization and throughout the world, and the methods employed to realize these tunings. The book ends with an examination of Forster’s own instruments, which are extremely beautiful in both design and sound. He remains one of the greatest practitioners among instrument builders.

Although I have spent many years in the field, I discovered in Musical Mathematics a fresh and above all generous presentation of knowledge both with regard to acoustics and the history of scales. For example, the chapter on Chinese music discusses an approach to string tuning that I have never encountered in any other sources. Because of his own translations from other languages, Forster’s research is not limited to English texts; for this reason, his book is filled with many new sources that provide fresh perspectives of the historical record. The subjects of Indonesian, Indian, Arabian, Persian, and Turkish tunings are likewise treated with much care and depth. Perhaps the book might be compared to Harry Partch’s Genesis of a Music, but there are marked differences. The latter was written to explain Partch’s music and instruments, and only secondarily to help others build their own unique instruments. Musical Mathematics, on the other hand, focuses more on the needs of creative individuals; it encourages musicians to discover and explore aspects that are most useful and fruitful to their own work. It is toward this goal that Forster shares the benefit of his knowledge and experience.

Yes, here is a book I surely wish I would have had 30 years ago when I first started out as a just-intonation composer and instrument builder. Musical Mathematics is truly as useful to the beginner as to the most accomplished expert in the field; both will find much value in this book. Also, it is obvious from his thoroughness and practical insights that Cris is an authority who has actually worked with the materials — an important aspect that sets this publication apart. This is a work of depth and breadth written in a spirit of sharing and helpfulness for those interested in the subject. Musical Mathematics is a watershed book that will, without doubt, change acoustic instrument building for the better, and change many of our views on the history of mankind’s intonational practices.

I can't help to mention that it is

Available Here

http://www.amazon.com/Musical-Mathematics-Science-Acoustic-Instruments/dp/0811874079/ref=sr_1_1/181-1266760-1225831?ie=UTF8&s=books&qid=1269533071&sr=8-1