Book recommendations on Microtonality

This blog post is basically a handy list of written resources for those interested in Just intonation and microtonality starting from the simplest to the more specialized and detailed. We suggest owning hard copies as all serve as important references.


The Just intonation Primer by David B. Doty
http://www.dbdoty.com/Words/Primer1.html

On The Sensations of Tone. Hermann Helmholtz
http://store.doverpublications.com/0486607534.html
   
Genesis of a Music by Harry Partch
https://monoskop.org/images/b/be/Partch_Harry_Genesis_of_a_Music_2nd_ed.pdf

Divisions of the Tetrachord by John Chalmers
http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/

Microtonality and the Tuning Systems of Erv Wilson by Terumi Narushima (available in Octotober 2017)
https://www.routledge.com/Microtonality-and-the-Tuning-Systems-of-Erv-Wilson/Narushima/p/book/9781138857568

Musical Mathematics by Cris Forster
https://www.amazon.com/Musical-Mathematics-Science-Acoustic-Instruments/dp/0811874079

Harmonic Experience by W. A. Mathieu
https://www.amazon.com/Harmonic-Experience-Harmony-Natural-Expression/dp/0892815604

'Temperament' and 'Temperament; or the Divisions of the Octave' R.H.M. Bosanquet
 http://anaphoria.com/library.html

Greek Musical Writings: Volume II, Harmonic and Acoustic Theory. Edited by Andrew Barker.
https://www.amazon.co.uk/Greek-Musical-Writings-Cambridge-Literature/dp/0521616972

Multiple Division of the Octave and the Tonal Resources of 19-Tone Temperament. Mayer Joel Mandelbaum. Thesis
http://anaphoria.com/mandelbaumthesis.pdf

The Greek Aulos by Kathleen Schlesinger
https://archive.org/details/KathleenSchlesingerTheGreekAulos

Augusto Novaro Musica Natural and approximation (Two editions) 1927-29 and 1951
http://anaphoria.com/novaro.html

Tuning and Temperament: a Historical Survey. Barbour, J.Murray 1951
https://archive.org/details/tuningtemperamen00barb

Bach and Tuning. Johnny Reinhard 2016.
https://www.amazon.com/Quellen-Studien-Musikgeschichte-Gegenwart-Antiquity/dp/3631672055?fbclid=IwAR3yAvoq3AzNXlG8zVEto7fjXDm-Yb-BPPp29VpCLjHQcsHdvZrnIbiIOTo

Harmonics and Spirals. Neil Haverstick. 2016 https://microstick.net/product/harmonics-spirals/

This list also covers much of a Just Intonation nature that best is seen there as opposed to copying.
http://sacredrealism.org/catlamb/tuninginformation/resources.html
I will be updating this as i am sure i am forgetting many

Diamonds, Lambdomas, and Mt. Meru: The Return of Sacred Objects to a Secular Landscape.

Wilson's Chart of the Mt. Meru/Lambdoma interface

Today, as never before,

we are witnessing an opposition

 not between art and life,

 but between sacral and secular spaces.

-Ilya Kabakov

In the process of my wife, Terumi Narushima working on her book on Erv Wilson's Tuning innovations, the subject of the Partch's Diamond and its origin have come up. What strikes myself is that how this structure seems to have been reawakened in not only Harry’s vision even if through Mayer, but the others to as close relatives. Spontaneously they appear in others such as Novaro (in the same year as Partch, 1927), but also Schlesinger too once one scratches the surface of her subharmonic scales sharing a common tone.  That all this rediscoverering would happen within a few brief years after 2000 years is uncanny and could be seen almost as if the structure had a life of its own. In its former context it was used to please the gods or to represent the celestial clockwork or even as a reflection of political structure.  This Lambdoma returns, but not in the context of an object to be worshipped, but as a something that nevertheless is once again in communication with our secular world. It is within this contact and communication that Partch deserves credit for placing his work and vision. His rituals do not worship these objects, but nevertheless places them within the conversation throughout his own aesthetic objects.

           Erv Wilson firmly explored many of the geometrical properties of various organisations and while publicly he would not attribute anything extraordinary about them, he would always point them out when he ran across them. One of the most common mathematical figures he would return to,  or maybe uncannily repeatedly returned to him was Pascal's triangle which was known in  India where it was discovered 1000 years before Pascal it was known as Meru Prastara.

1. Mount Meru, the abode of the gods at the center of the universe in Hindu, Jain, and Buddhist traditions

 His first notice of it was in its relationship with his combination product sets. Later he appears to be the first to investigate the additions of the diagonals of Mt. Meru beyond the one known to produce the Fibonacci series. Here he found scales that reflected the practices of various indigenous music that some now found a way to appear in their own rituals.

Wilson's scale tree within the tetrachord showing
 both the super-particular ratios between the notes as well as the two sums of the diagonals.

Later I was fortunate enough to catch and point out to Wilson that Novaro’s series coincided with a reseeded triangle. From this he saw how Mt. Meru was tied to both the Lambdoma and the Farey series. The latter is imbedded in his scale tree, his reinvention of the Stern-Brocot tree. All this represented in the chart shown.

This series starts with the numbers 0/1 and 1/0 from which he described as possibly divine numbers but would not say or define further. One might wonder like myself if they are the infinitely small and large respectfully.  Then is the 1/1 like the "mesocosm" between these infinities. Hence why I have preferred to call my music Mesotonal.

Our relationship though is not in worshipping these structures even though they are probably worthy. They indeed act as forces often universal and beyond our control, even more so to surpass. Attempts to play these megastructures have proven less satisfactory than the material that rest upon them. Thus here they communicate and inform us at a distance  and there is good reason to listen.

First "Frequency" Virus Hits Anaphoria. HRZ-432

DETAIL SHOWING DAMAGE CAUSED BY THE HRZ 432 VIRUS

It didn't take long for a non fatal but extremely debilitating virus  to sweep and fan wide spread panic. " I was just filled with nausea and feelings of vision of no future. I felt stuck with no motivation could no longer eat, especially any food that hadn't been tried before" reported one citizen hit with one of  the worse cases . Without any clear cause, rumors was that finally the island was under attack by hostile forces. Finally it was found that the source lie in an old abandoned mission  recently occupied by followers of La Roche  who seemed to have entered the country illegally. Within the make shift headquarters lie handouts as well as material belonging to a Schiller Institute with plans to launch a variety of other regressive virus. It was found in fact that the sounding of 432hz was having effects of nausea and since the closing of the institute under its strong anti-missionary laws and the removal of the devices sounding 432, Health and progress have returned to the Island. Still the mere mention of the frequency has caused almost instant relapses of nausea.

Riley's 5 limit tuning for "Harp of New Albion"

Riley's 5 limit tuning for "Harp of New Albion"

I had recently replaced my missing copy of Harp of New Albion by Terry Riley and decided to lattice out the tuning which i guess many might have already done. It is interesting in how La monte uses 7 limit intervals to approximate 5 and here we have Riley doing the opposite with the 16/15 over the 15/8 7 cents shy of an 8/7. Riley's use of the tuning is interesting also in that he never uses the 1/1 of his tuning for the tonic, albeit the D of 16/15 could have been also a good choice for the 1/1. Anyway in the context of the pieces it shows how far one can go into new territory with a relative simple 5 limit. I like the choice of the 64/45 giving him two just major scales which he seems to avoid using more than using. If you tuned the row with 5/3 , 5/4 and 15/8, and decided keep it in the same relationship wit h3/2 and 9/8 by lowering thise too, the scale would coincide with the Centaur Scale.

THE DOWSING POLES- New instrument member of the Meta-Slendro Ensemble

The Dowsing Poles This instrument grew out of a desire to have something like Tubular Bells to add to my ensemble of Meta-Slendro instruments. This tuning is anything but a conventional Slendro encompassing instruments using 12, 17 and 22 unequally spaced pitches in the octave informed by both traditional sources and recurrent sequence mathematics. 

In order to realize such a Tubular Bell instrument and after much experimentation, I decided to explore the possibilities of suspending the tubes in the middle instead of the conventional nodes used on all my other instruments. This produces a somewhat similar sound to the desired orchestral instrument but with even more pitch, making the use of small distances between some pitches in the tuning much more practical and realistic.

Mounting the bars in this fashion was extremely difficult as it a point of balance, but wanted the tubes to be vertical in order to take up less space and easier to play. The present method of tying elastic cord seems to work well but am still not cutting the cords quite yet in order to see how it works after at least a few weeks. Hence why they can still be seen for the time being. This instrument is also quite modular being usable in any or all of the three sections and it allows the tubes to be placed in any order of which is shown here. The sections themselves are also flexible in being placed in a chain of any configuration here conforming to the only flat section on the Anaphorian Embassy grounds. This instrument will get it premiere at the Now Now Festival this Thursday night at 107 Projects

A Near Flatland with a Bastard Lattice- An Addition to The Journal of Anaphorian Music Theory

This paper is an addition to the Journal of Anaphorian Music Theory that looks at one set of progressions that occur  within the normal 12 tone scale.  The overall idea is that analogous structures can be constructed in other systems but worth sharing with a broader music community for those interested in what can be done with pitch.
http://anaphoria.com/flatlandbastard.pdf

Installation as an Immersive Score

Meru Set 1 - Back of Screen 1

 Before I write about my final installation presented at UOW, on this blog, i wish to focus on the musical aspect of the installation separately as a mirror from the way it was realised.

For the moment I resist classifying this as sound art for reason which I will explain. Usually from that perspective,  sound is an added element to a visual display. In this particular case i am entertaining the idea to look at in an complementary way.  Here the concept is to having the totality of an immersive space replace or act a the musical score.As I am not imposing sound into the space, I am inviting the participants to explore
 what is presented as options. This to me is more like a score.

Meru Set 2 - Back of Screen 2

This allows new possibilities not possible with conventional scores regardless of their format.  The idea is to immerse the performer in the score as opposed it being an object presented in front of one where the other surroundings are suppressed or ignored. It also omits the role of the score of something that is projected outward into the space since one is already inside of it. In this installation a participant is open to explore the totality of everything that is presented to them. It thus represents a totality in which the visual elements provide the stimulus for the sound.

Meru Set 3 -Front of Screen 2

Such a composition opens up new possibilities in terms of being open ended, without a fixed perceptible beginning and ending,  for varied number of players, and of  changing  players who might only participate in part of the total duration. The nature of the participants moving through the space thus liberates the concept of one person one instrument or set of instruments. In this sense it works toward a composition without an author or an anonymous one. The players though unlike in traditional western music do not bring instruments, something closer to how gamelan ensembles are fixed and thus a centre where people congregate. The corporeal experience and presence becomes the determination of how the work unfolds in the space which will be unique to each participant.

Meru Set 3 - Front of Screen 3

A composition nevertheless can be quite specific yet allows for each participant to take an active part in the create act. There is no separation between performer and audience. In this case, the instruments are predetermined and where they sound in the room is fixed. How they are arrange influences what a person might play next as well as providing self contained units even if the overall movement of the space is not. It is the unique structural possibilities of a certain class of microtonal instruments that allow for this type of interaction where strong acoustical realities can go from one end of the room to the other while still providing a local identity.

Meru Set 3 - Front of Screen 4

The installation incorporates a few of my instruments being used both in for their visual presence and as the sounds they produce.

Meru Set 3 - Shadows on Wall

9 of my Meru bars are used which are arranged in 4 sets of closely related pitches that cause beating. 

Meru Set 4- Back of Screen 3

 In the space, there is an over all placement starting from the entrance from low to high to correspond to the general character of the visual screens in which in turn is based on the space itself.

Meru Set 4 - Front of Screen 4

 What happens is that each visual elements such as the screen ( not that the score is limited to them) might be viewed from more than one perspective.

Meru Set 4 - Front of Screen 5

Also each instrument set will be a local point of perspective of the whole installation which will interpret even the same screen and frame and the shadows in a different way.

Meru Set 4 -View of The Tree

Each set will have available multiple direction to draw upon and even what is placed in back of the head  can continue to inform the participant.

The Tree - Front of Screen 5

 The sound of other instruments in the space extends ones vision and interaction around the corners of the space as well as invoking the memories from their location.

The Tree - Back of Screen 4

The instruments themselves can form apart of the score.

The Tree - Overall 

 The space or score in this case thus reflects a totality, a universe that one finds one is within. All elements one witnesses in the space becomes part of the score thereby increasing the means in which the score can interact.