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

Working on The Wilson Archives

It is funny to think of one studying just the subject of tuning for over 20 years much less with one person, Erv Wilson. Such a subject while specialized is not inseparable from all the other aspects that go into music though. That is how it was possible and often the focus of discussion.
Much more than number games, once a scale is designed and what one understands what material is made available, one needs nothing more than ones ear to guide one into the territory one has developed.
Often I have been asked if I have been influenced by certain composers, but as in one case, I had not even heard their works until a little over a decade ago having absolutely no access to their work. Nor has much stuck since then either. Similarity can come about out of the nature of the material itself and what it enables one to do as well as what it wants to do. Say everyone in history had only done oils and a few pick up watercolor for the first time, different individuals are bound to discover and marvel at some of the things it can do. Possibly the real question is why one would want to use them like Oil since they already have the means to do so. Especially when using something as removed as glass.
Hopefully we can move on and see it as ‘sensitivity’ to the subject as opposed to an influence.
I have just returned from the US where the entire papers of this man were digitized. Myself organizing them into files of like subject while Terumi Narushima, my wife who is also working on a thesis on Erv’s Keyboard designs and strategies scanned the material. All this in the mere 17-day window we had to do it. Credit goes to Stephen Taylor also for prompting us to come to do this realizing that it needed to be done soon. Also he provided us with the workspace, even being our shuttle at times as well as diving in and putting in his full effort and advice. It would not have happened without him not to mention the others steps he has taken to help Erv’s well being. Jim French deserves much in this way too staying with him for extended stays beyond what anyone could be asked to do.
Others should be also mentioned as putting in their experience with the work in a few nighttime gatherings. These included Marcus Hobbs, Gary David, Jim French and Chuck Jonkey each who like Stephen and I and all of Erv’s students have developed their work in a singular and unique way that makes the idea of a Wilson “style” absurd. The visit also invoked Jose Garcia who I hadn’t seen in maybe 20 years as well as Marsha Mann telling Stephen what she remember of Erv.
Taylor requested, actually insisted I provide a proposed filing system in which all his could be organized and mapped. And after four goes at it, this is diagram is what I came up with (still in progress though). It reflects how the papers cross-reference themselves and not some personal preference on my part.
We ended up with over 355 files, some as many as a hundred pages and few less than a dozen. The files often were general and single documents scattered in different places. Fortunately only a few pieces that are a complete mystery yet these already are coming to light. So my work is still going on here and will take some time with the goal to make it available.
Erv stated that his work was like assembling a bird’s nest, finding the pieces and placing them in the right place when he found it. So maybe this is how his nest looks in the creative imaginative dimension he created it in and for.
He remains the one person in my life I must give the highest thanks to. I hope the finish product will be a testament to that thanks.

Harry Smith-"Early Abstractions" (1946-57), Pt. 3

No. 5: Circular Tensions, Homage to Oskar Fischinger (1950)
No. 7: Color Study (1952)

Pictures from the NowNow Festival

Thanks to Adrian for taking these. More wonderful shots of the festival can be seen herehttp://www.flickr.com/photos/ajebec/4302681073/
Performers were Kraig Grady
Terumi Narushima
Alex Masso (bottom pic)
and Finn Ryan who despite being the tallest is not seen.

The Chopi Timbila/Venancio Mbande

The Chopi were thankfully the interest over a half century ago of Hugh Tracy who collected extensive data about their tuning, music and practice. Its closest tuning relatives in the world seem to be Burma and Thailand more so than those in Indonesia as originally thought. These traditional instruments with their tunings has now been reduced to the skill of this one man. The Chopi has been a prominent investigation and exploration of mine for years and is the basis of the tuning used on my hammer dulcimer and an organ (Meta-Mavila) . I consider it the second most important tuning i am working with. Hopefully it will manage to become an orchestra of instruments like i have been able to with Meta-Slendro. It is more important that this work continues where it started and good to see what we see here.

An Aperiodic dispatch from the CENTRE FOR ALPHABETICAL SEQUENCING

TRANSCENDENTAL AND EMPIRICAL RESEARCH CENTER AND LIBRARY
OF ANAPHORIAN CRYPTOGRAPHY
418 HUGURU DRIVE
VEIVULANGIGI, ANAPHORIA


Rants the Applause

The vendor the crude country asset.

a mysterious expressway stirring underneath
the crowd presses a wary hope
a capable reminder that distances
the doubt in an abolition neighborhood.

Behind the ambassadors a parade roars after each funniest coincidence
Example a fraud appeared beside the pool bending
Spoke frog the staggering
A master gutter riots into any garbage and overcomes appeal
The offending group questions why another quiet manifesto
How can the wasteful ploy chain the infallible autumn magic?

Why does Pope ascend above the voice
so new catholic can recycle a grief
likewise treads the other fundamentalist on its followers

How did the prophet breed such a stereotype?

Even my passive corn objects.
Heaven waits for an approach toward a humane diameter.

Bequeath the psychologist proceeds a genocide.
The silent mob conveys the sneaky doom of wallet
a soldier groans with his bigot toed officer
Huff the helicopter frowns
A military expires across the horrific bridge
strays a gun strays

A bankrupt search insults one killer
A terrified commentator can only yawn
a contemporary repertoire that lifts the conspicuous policeman
The flagging civilian quibbles next to the receiver
How the collective terminator is apologized
This mass understands unhappy censorships

The intervening sunrise revolts near another mechanism.
a diagonal mud changes across the earth
Will any geography succeed to wash aside an indigenous interference?

An interactive hardware dances inside this culture.

The evolutionary reward stirs
Around the yearly childhood
The newcomer flavors a lifetime
The toy licenses a charmed adult

A stone dances over a heart.
A temple dances behind a lecture.
The applause rants throughout a seventh

Addition to National Gallery/Of Threads and Bridges

What is believed to be the oldest depiction of Anaphoria by a foreigner arrived yesterday from Japan accompanied by the interim ambassador R. Tomasula. Carbon dating places it at over 3500 years old and in pristine condition for a woodcut of this age. There has been much speculation about the arc between Anaphoria's two highest peaks as it coincides with many myths of this time as a connection that existed between two famous holy men who while never meeting seemed to provide the people with almost instantaneous dual proclamations.
It was known as the time of the great thread or bridge depending on which peak one is able to trace as the source of the story. Much to do as also been made about the actual curve itself resembling the exact proportions of some of Japan's famous bridges.

notation/invention-Kris Tiner

http://kristiner.com/blog/category/compositions/
It is not very often that one gets to get a good look at those whose work lie within the boundaries of composition and improvisation. Kris seamlessly combines both. I have always gained both musically and conceptually from the way Kris puts things- down on a page and also how he threats it. Especially check out Ele(jg)y and Recourse to Unison. At least!

review and dream

Perhaps it is odd to repeat this review but i found it quite accurate which is rare and welcomed. He missed the instruments but that is minor as he quite understood what was going on in the music.
http://www.wonderfulwoodenreasons.co.uk/
" Anaphoria - Footpaths and Trade Routes
(ini.itu #0902)
LP
Kraig Grady has been making his beautifully rotund music for quite a while and it shows. The struck bell (or prayer bowl) like ringing tones upon which his music is established are an erratically gentle fall of sound, unpredictable and incandescent. It's form is reminiscent of John Cage's Music for Prepared Piano but of a more elegant and stately nature.
Grady has previously recorded for ensembles but the three pieces here are two solo and one edited amalgam. All are delicately poised with shifts in tension given sparingly as the music waxes and wanes. There is a moonlit quality that is hugely immersive and compulsive. The music has a pull and a call based on it's refusal to settle into one particular shape and as such I've found yourself losing hours of time as I relentlessly flip the album over replaying each side in turn.
( www.iniitu.net )"

As an aside i have a recent dream here which surely is a response to reading Jung's The Red Book. While his work has always increased my dreaming, not usually in this direction.
http://annandaledreamgazetteonline.blogspot.com/

Two Recent Sculptures

Our special Antenna to get Radio Free Anaphoria and our Guardian Kachina at the outpost

Prelude to a Whirlpool

Thanks to Mike Cooper for putting this up who work can be found linked to this video. A very early show of Chris Abrahams and I and early in the set. Perhaps turn down the volume a bit if it distorts. It is not easy to record such thing off the cuff. It has evolved quite a bit since here and even the instruments have changed color:)

Talaprastara

Anyone who has crossed paths with Erv Wilson will sooner or later will be given a copy of Meru Prastara. So when looking at South Indian meters and stumbling across the term above, I had to take notice. In South India they have a method to figure out all the combinations and permutations, but they do so in a very specific order which when listed in a row one can easily fail to see the pattern. In these two diagrams the subdivisions of 6 and 7 are arranged in a way that i think makes the pattern method clearer.

Inverting Cage's Sqare Root Form/Wilson's Geometries

It has taking me a while to figure this out. The answer finally came when I was working on another problem. My brain is just not that linear.

Some time back while looking at Takemitsu’s application of Cage’s square root idea to Pitch, I stumbled upon its relationship to certain geometric structures of Erv Wilson. Pitch or duration doesn’t matter in that the structure is the same. I posted this to the Silence list that I was on at the time. I repeat the jest of that below.

This is the simplest example using only 4 durations. This gives us a good visual representation as to what happens with more complex examples. Here is the resulting square using A B C D to be what ever you want.

AA AB AC AD

BA BB BC BD

CA CB CC CD

DA DB DC DD

Now compare this with this excerpt from one of Wilson’s letters to John Chalmers found here
http://anaphoria.com/CPStoC-pt1.PDF shown above

One has only to replace the number by the letters.
What interests me though is the second diagram on this page.
Which shows a possible variation of Cage’s square root idea in reverse with each successive element having the reverse relationship above. To make this square, one uses the complementary elements not included in the original. This is what i had missed despite being right there in front of me.

BCD CD BD BC

DC ACD AD AC

DB DA ABD AB

BC CA BA ABC

It is interesting to observe where the two intersect which he does on the next page.






















More often than not such a form is used with more elements. With 6 elements [here using the first 6 odd numbers] we can see below what happens as a like wise inter structure and its complements.




The thing about the set made by the intersection forms a cycle and makes it easy to proceed to the next element in a smooth fashion. same with the other ones i mention later.
There is no reason at this point no to consider the combinations of 3 out of 6 and if we look at those points where it interests with it complement we get the Eikosany. One of Erv’s Favorite structures. Which you can find it the article linked above.

I had a dream two nights ago where i had my Meru bars in a pentagram which i post next. Perhaps my mind is more linear than i thought.

Ethiopian Ortodox Tewahdo Song

Thanks to Albert Ortega for finding this

A Scale Develops: Rod Poole's Tuning

It is often easier to talk about someone else’s work than one‘s own. Here I can do a bit of both. Rod Poole and I ended up sharing an interest in microtonality that moved from my introducing him to the field to him as a friendship as a shared partner of similar concerns, questions, and often difficulties. We hadn’t known each other very long when I lent him a 12-tone guitar tuned to my centaur tuning (pictured in red). It was this tuning that became his point of departure, which is illustrated in this picture.

Later Rod shared living in the house with Erv Wilson. Something I had also done twice. It has to be one of the most highly concentrated learning environments one can find one self in. I provided both the knowledge and tools he needed to find what suited him to create his own palette. This is one of the great gifts of working with a teacher like Erv Wilson.

The process I find interesting mainly in that it has a contour that resembles my own, possibly it is universal. Rarely does anyone build directly on previous paths. Often one backs up to some point first and venture in a different direction.

In our case we both worked with larger number of tones and found our self pulling back to less. Rod in turn took what he would always tell me as ‘the best 7 limit 12 scale for the guitar, period’, (something he was more sure of than me) but dropped all the 5 limit intervals. [These are the hollowed red dots in the diagram]. La Monte’s tuning brought his attention to the possibility of dropping 5s for higher limit possibilities. He preferred to add 11 and 13 over 7s though. He was not one to waste time on over explored territory. Originally he added a 17 and a 19 harmonic, I think to try them out. He felt though how the instrument felt under his hand was a prime concern, and these added more problems than he gained for musically). His tuning is the solid red and black notes together. He had 19 tones originally after toying with 22 I believe, but pulled back to 17. All after taking my 12 and keeping only 8 of 3 and 7 limit intervals. I myself ventured out to 31 tones before pulling back to 22.

Those who know tuning might say is quite a distance from where Rod started to where he ended but he preserved the consistencies in the tuning. When I saw his notes, I smiled recognizing him being a student of Erv, there is no doubt of this.

There is more though. His frets ran straight across and he did much to explore different open strings tunings, as this is something he saw as the guitars strong point. Besides tetrachords he liked finding those close intervals such overlapping of tunings can provide. Likewise the harmonic spacings natural to the guitar molded by such overlaps. We have nothing on what he did with open string tuning in detail for his own playing outside the bowed guitar work. I know that he would tune strings 7 limit intervals away from personal statements he made.
What other push and pulls happened on this level before and after we might never know.

Both are music are scale based. Presently I pulled back to a 12 tone tuning that pushes the nature of what a scale of this number can be can be and remain so. This tuning, a Meta-Slendro based on Wilson’s, I have tune out to 22 on a different instrument, but I find that it loses something by having this many tones. For contrast I have another 9 tone ( which I had taken out to 16 tones) that uses many of the intervals that I the other lacks. It kind of plays ‘Pelog’ to my Slendro. Less tones need be no less adventuresome. One can explore all the ways a particular pitch can interact with all the others. While there are those venturing forth by just simple harmonic relations, letting harmony lead the way, melody and scale can also lead . In this situation harmony can develops more on the lines of ‘pandiatonic thinking’. By this, the free use of tones within a scale as opposed to the free scale developed out of harmony. One need not have to go back the way one came, there is no problem jumping from one point to the next. These were also concerns of Rod’s.

Yang Jing and Pierre Favre: Magic Moments from Unique Duo

Thanks to Phillip Gelb for this

Kadri Gopalnath

Thanks to Warren Burt for this

Anaphoria: Footpaths and Trade Routes

The people of Anaphoria are pleased that both some of their oldest and newest music appears on this first piece of vinyl made available in a limited edition from ini.itu We are grateful for their extreme effort and care in making this possible. Two excerpts available here. Complete press release available from this page.

The Quiet Erow/The Premiere Shadow Play from Anaphoria

The Shadow Theatre of Anaphoria in association with Playscript presents their first Australian performances

THE QUIET EROW
[new and improved]
Fri and Sat. 8pm
Oct 9 &10,16 &17
at the Bushland Chapel 94 Parkes Street Helenburgh
The Story of an Anaphorian Prenatal "Robin Hood"
starring Kraig Grady [director], Seth Harris, Mark Kennedy, Hamish Lane, Terumi Narushima, Friederike Krishnabhakdi-Vasilakis, and others
Bookings 4294 1695
more information 61 2 4271 4397

more images

Ainu Mukkuri

"RANAD-EK" Thailand Traditional Instrument

Phin Pia, A romantic plucked instrument

"Changsaton" Northern Thai new world music

Categories

Today I wish one could break out of categories. What opens a door on inception quickly becomes cemented into a partisan camp. Kandinsky was quite articulate at how the fertilizing ray transforms into the obstructing hand. The period in which this happens has quickened. An open door quickly locks those in it rooms into a state on what they will not venture beyond or worthy of being open to.
Sound exist in space only till it ends when it is no longer present in one, yet our lingering perception of it fills the total space dimension we are taking in at that moment. Hence it becomes a ‘totality’ and universal. It fades but fades into everything as an inseparable quality now dormant but eternal. It is this space/non-space I want to deal with directly beyond the prisons of style and categories.

Rod Poole- Voice of the Bowed Guitar

After Rod Poole's passing, I assembled a concert of shorten selections of some of Rods pieces from his works for three bowed guitars. I felt it was better to represent his variety on the subject and inspire maybe others to perform them as well as to allow people to hear how differently they were. Something the months in between his performances did not us able to do. In his notes we could find only 4 versions of which we realized three. It was quite enlightening what he had done.
Not only were none of the guitars tuned the same way in a single composition, instead much care was directed to the spacing of chords and doublings for resonance in what must have required much experimentation on his part. Rod did not tune to any reference pitch but worked with the sound and timbre of his guitar to start building a piece yet one version did require a capo around where the sharp 4 would be on an open string. While one might acknowledge that this began where he could get the intervals he wanted but also i imagine he also wanted to investigate that shorter string timbres as well as the difference the strings would react under the string tension.
Each of these versions represented a different way of approaching the limitation of a single chord. Each of the four versions he left couldn’t be more different in construction; the utilization of harmonics 13-14-17, an unusual Tetrachord, a 7-tone scale, or a 5-tone scale taken predominantly from the subharmonic series. On Sept 12 in Los Angeles SASSAS will be presenting a tribute to Rod taking these as it foundation. David Beardsley is also planning on presenting one in the future. I myself would like to bring this work to Australia but i also hope to write my own at some point in tribute to him and allowing the idea to continue to grow which is what Rod's approach was all about.

CATcerto

Michael Tenzer posted this on a list:)

Cheb Zahouani-Rai

Cheb Zahouani has always been one of my favorite Rai Artist. I have always loved the scales as well as the Synth sounds which in most other context just wouldn't work. Here they do. I am amazed how it doesn't bother me that it takes over two and a half minutes for him to even start the song.

Recent Correspondance

Assist
Dear Sir/Madam,

AM King Joe and i want to know if you can assist me to make an order for scales. I would need to know the types you have in stock,let me know the prices and also the types of credit cards you do accept for payment,i also don't need shipping cost because i will be coming to your shop for pickup or recommend a shipping company for the pickup when the scales are ready. Please Advise ASAP So that the project of the scales will be fast.

Regards,
King.

Is it safe?

For those of you interested in Just Intonation, i have started a yahoo discussion group here.
http://launch.groups.yahoo.com/group/JustIntonation/?yguid=42458

Here is a safe haven to discuss the practice without having to justify itself. Something it seems it has to spend too much time doing. It is the music that matters and even though I can come up with many advantages of JI over other systems, i don't feel like putting any more energy into that. It gives us useful and rewarding possibilities, what more can one ask for. It is small group but the quality of those involved is high and most of all positive. It is more than open to those who are just getting their feet wet or want to hear what people are doing with it.

Another Yahoo Tuning Group

An Eastern Western for Koto

A short little composition for Koto. The scale is derived from Meta-Mavila. This scale was inspired by the Chopi tuning in the village of this name. The mode chosen was which most resembled a Japanese scale so we might have added some S.E. African reference in the title too. It is dedicated to my lovely wife, Terumi Narushima who supplied the photo of her Koto

Uroborean Mirrors-Excerpt of Audio Installation

There is an excerpt of a piece now up in Newcastle, NSW, Australia. for headphone only listening on this page.
It takes my Meta Slendro splitting into two scales that produce beats only in the brain as the wave never touch. It starts unbelievably soft but does get louder. More so beyond the limit of the excerpt.
More later!

Ali Akbar Khan

A soul who will be missed. but not his soul work which stays with us.

Two from India

I have Mark Kennedy to thank for the first and Warren Burt for the second. Both send my way today.

http://www.emusic.com/album/Pandit-Kamalesh-Maitra-The-World-s-Musical-Traditions-Vol-10-Tabla-Tar-MP3-Download/10865021.html

Dimi Mint Abba

Ooleya Mint Amartichitt

THE FIRST PUPPET IN A NEW LAND

Is anyone surprised that it would be Ned Kelly? Here he is, almost Kachina like, an outsider who preserves it at all cost.
For the last 10 years I have been making my own puppets for the Shadow Theatre of Anaphoria. My first was a fish. Almost all the human ones I have made have been based on traditional models in a desire to fully understand what goes on in every detail before undertaking the task myself. Even here choices have been made. Often I will survey as many variants of a puppet I could find, selecting what spoke to me most and what harmonized together. Traditional puppets are multilayered enigmas carrying an extensive history with past remnants hidden and informing the present ones. Often a stylistic code is used throughout all of them. They can consider the nature of flame, or the need to represent humans and gods where such images are not allowed. It does not say I haven’t kept ones eyes on more modern designs. Often one finds two common ones, the oversimplified puppets or realistic ones. These counterparts have often failed to hold me. What was missing? The director Eugenio Barba talks about how even a still actor on stage has to remain energized in their posture. In the case of a puppet this is even more necessary as one cannot rely on gesture or motion as easily. The puppet has to be ready and attentive at every moment. It is a new concern for puppet design and opens the door to furthering this art is general. So this puppet was a result of this direction.