Matrix Carillon progress

Dear Tuning Folk:

I have uploaded the tables referred to in this post to
www.acceleration.net/darren/matrix.html. Please take a moment to review
the file and let me know what y'all think. This post and the html file
contain my latest thoughts on the tuning for the microtonal carillon I am
building. The carillon will use steel bars driven by solenoids and
amplified through large outdoor PA speakers.

The first table in the file is the 15 limit tonality diamond, nothing new
-- included for reference.

The tuning I am considering for the carillon will use the 15 limit matrix
intervals as a scale (49 tones to the octave), ala Partch, but will be
arranged in such a way as to allow easy access to each harmonic and
subharmonic scale of the matrix. The tuning will comprise two complete
octaves of the scale. 1/1 will be 192 hertz, 4/1 will be 768. 99 bars
will be manufactured with the first three partials tuned to 1/1, 3/1, and
5/1. I have successfully developed a method for achieving this relationship
of partials to a great level of accuracy. It just so happens that the 4th
partial just about lands on an 8/1, although I have not been able to
measure it very accurately due to equipment problems. If anyone is
interested, I will post detailed tuning data and notes.

The second table in the file illustrates the keyboard layout. It features
128 keys in an 8 by 16 format. The keyboard can be either a matrix midi
controller or use simple analog swiches to drive the solenoids directly.

Each subharmonic scale from 16 to 9 is available on a diagonal, and each
harmonic series based on the subharmonics 16 to 9 of 1/1=384 extend from
the first diagonal line of subharmonics. I may arrange the keyboard as a
rhomboid so that the subharmonic scales are found in vertical or near
vertical lines.

Also note that I have "stolen" a few of the 2/1's to make them 4/1. This
will create some variations in the fingering of some of the scales, but
will allow for a complete 2nd octave to 4/1.

I believe this arrangement gives the best of both worlds. It allows for
playing of the 8x8 matrix in its pure form, and at the same time uses the
matrix resources as a scale allowing for voice leading, chord inversions
and melodic lines not possible with a strict matrix.

There are of course large gaps (esp. between 1/1 and 16/15, 15/8 and 2/1)
which could be filled in Partch-style with secondary intervals to yeild a
continuous 15 limit scale. I have played around with substituting some of
the duplicated intervals in the keyboard (ie 1/1, 2/1, 4/3, 3/2, 8/5, 5/3
and 6/5) and including the resourses that Partch added to his scale. I was
actually able to include all of his secondary intervals, although
substituting these intervals in for the repeated ones creates alot of
inconsistancy in the keyboard fingerings for some of the basic scales. Of
couse, the 13 and 15 limits suggest additional secondary resourses for
which there is simply not enough room to include them in the context of a 8
by 16 keyboard. If I go the route of an analog keyboard with switches
directly driving the solenoids, then I would consider adding a second small
bank of keys to play the bars tuned to the secondary intervals. A matrix
midi controller would require a second midi channel if secondary intervals
were added in a extra bank of keys.

Peace,
Darren Burgess
SEJIS
Gainesville FL

Dear Tuning Folk:

I have uploaded the tables referred to in this post to
www.acceleration.net/dburgess/matrix.html. Please take a moment to review
the file and let me know what y'all think. This post and the html file
contain my latest thoughts on the tuning for the microtonal carillon I am
building. The carillon will use steel bars driven by solenoids and
amplified through large outdoor PA speakers.

The first table in the file is the 15 limit tonality diamond, nothing new
-- included for reference.

The tuning I am considering for the carillon will use the 15 limit matrix
intervals as a scale (49 tones to the octave), ala Partch, but will be
arranged in such a way as to allow easy access to each harmonic and
subharmonic scale of the matrix. The tuning will comprise two complete
octaves of the scale. 1/1 will be 192 hertz, 4/1 will be 768. 99 bars
will be manufactured with the first three partials tuned to 1/1, 3/1, and
5/1. I have successfully developed a method for achieving this relationship
of partials to a great level of accuracy. It just so happens that the 4th
partial just about lands on an 8/1, although I have not been able to
measure it very accurately due to equipment problems. If anyone is
interested, I will post detailed tuning data and notes.

The second table in the file illustrates the keyboard layout. It features
128 keys in an 8 by 16 format. The keyboard can be either a matrix midi
controller or use simple analog swiches to drive the solenoids directly.

Each subharmonic scale from 16 to 9 is available on a diagonal, and each
harmonic series based on the subharmonics 16 to 9 of 1/1=384 extend from
the first diagonal line of subharmonics. I may arrange the keyboard as a
rhomboid so that the subharmonic scales are found in vertical or near
vertical lines.

Also note that I have "stolen" a few of the 2/1's to make them 4/1. This
will create some variations in the fingering of some of the scales, but
will allow for a complete 2nd octave to 4/1.

I believe this arrangement gives the best of both worlds. It allows for
playing of the 8x8 matrix in its pure form, and at the same time uses the
matrix resources as a scale allowing for voice leading, chord inversions
and melodic lines not possible with a strict matrix.

There are of course large gaps (esp. between 1/1 and 16/15, 15/8 and 2/1)
which could be filled in Partch-style with secondary intervals to yeild a
continuous 15 limit scale. I have played around with substituting some of
the duplicated intervals in the keyboard (ie 1/1, 2/1, 4/3, 3/2, 8/5, 5/3
and 6/5) and including the resourses that Partch added to his scale. I was
actually able to include all of his secondary intervals, although
substituting these intervals in for the repeated ones creates alot of
inconsistancy in the keyboard fingerings for some of the basic scales. Of
couse, the 13 and 15 limits suggest additional secondary resourses for
which there is simply not enough room to include them in the context of a 8
by 16 keyboard. If I go the route of an analog keyboard with switches
directly driving the solenoids, then I would consider adding a second small
bank of keys to play the bars tuned to the secondary intervals. A matrix
midi controller would require a second midi channel if secondary intervals
were added in a extra bank of keys.

Peace,
Darren Burgess
SEJIS
Gainesville FL