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
Just Intonation Explained By Kyle Gann
On The Sensations of Tone. Hermann Helmholtz
Genesis of a Music by Harry Partch
Divisions of the Tetrachord by John Chalmers
Microtonality and the Tuning Systems of Erv Wilson by Terumi Narushima (available in Octotober 2017)
Musical Mathematics by Cris Forster
Greek Musical Writings: Volume II, Harmonic and Acoustic Theory. Edited by Andrew Barker.
Multiple Division of the Octave and the Tonal Resources of 19-Tone Temperament. Mayer Joel Mandelbaum. Thesis
The Greek Aulos by Kathleen Schlesinger
Augusto Novaro Musica Natural and approximation (Two editions) 1927-29 and 1951
Tuning and Temperament: a Historical Survey. Barbour, J.Murray 1951
I will be updating this as i am sure i am forgetting many
Monday, March 28, 2016
|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.
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.
- Mount Meru, the abode of the gods at the center of the universe in Hindu, Jain, and Buddhist traditions
|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.
Wednesday, March 23, 2016
|DETAIL SHOWING DAMAGE CAUSED BY THE HRZ 432 VIRUS|
Tuesday, February 16, 2016
|Riley's 5 limit tuning for "Harp of New Albion"|
Tuesday, January 19, 2016
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
Saturday, February 28, 2015
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.
Sunday, October 12, 2014
|Meru Set 1 - Back of Screen 1|
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|
|Meru Set 3 -Front of Screen 2|
|Meru Set 3 - Front of Screen 3|
|Meru Set 3 - Front of Screen 4|
|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|
|Meru Set 4 -View of The Tree|
|The Tree - Front of Screen 5|
|The Tree - Back of Screen 4|
|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.