Yahoo Tuning Groups Ultimate Backup tuning sound mandalas

Hallo Tuners,
thanks very much to Jacky Ligon for the suggestion to speak about sound
mandalas:

> From: ligonj@northstate.net
>Subject: Question for Lawrence Ball: Harmonic Mandala
> Date: Mon, 12 Feb 2001 02:03:12 -0000
>Lawrence,
>Hello!
>I have recently came to learn a little about your music through a
>friend, and I would like to kindly ask if you could speak about your
>Harmonic Mandala work.
>From what I gather, this would be something of great interest to many
>members and kind lurkers on the list.

SOUND MANDALAS:
The term was suggested by Terry Riley, although earlier the (not sure what
to call them) were called UFO tones and later "Shapetapes".
Apologies if any of this is hard to understand, I will attempt any angle,
depth or aspect of clarification, don't hesitate to ask.
Apologies also for the slightly "pig's breakfast" order of these notes.
This work dates from 1983, and I'm still trying to evolve an understanding
of this.
Please be aware its for me a bit like trying to describe a huge magic cave
of possibilities that goes a long way into the hillside. If any of you can
understand it, it would be really great to get some thoughts on where to
build the roads from here.

>How did you develop your ideas?
>What inspired your creative work into this area?
>Do you derive any influence from Indian music for this - perhaps from
the use of the tanpura in this music?

ORIGINS/INSPIRATIONS/OVERVIEW:

LaMonte Young's work particularly with long held continuous pitches has
always inspired me; the late John Whitney (Sr)'s films and moreover his
principle of
"differential dynamics" led me to apply an extension of such techniques to
timbrally-varying drones, (the tamboura also was certainly present as muse),
although later its been applied to scores and midi. So initially it began
life as a 128 harmonics'-modulating drone/graphics audio-visual sequence
where one sees the magical transforms one hears.

WHITNEY'S DIFFERENTIAL DYNAMICS:

(see Whitney's out of print book 'Digital Harmony' McGraw Hill (1980?))
A Hundred point "radius":
Imagine 100 points (or more, or less) forming the radial line of an
invisible circle. Imagine each point, prepared to set off on a circular
motion at a distance from the circle's centre which is equal to its initial
distance from it. If moving at the same angular velocity, the points would
move in rotation like a stick connected to the circle centre. But- now start
off again with each of the 100 points moving with an angular velocity
proportional to an index number from 1 to 100 assigned to each point,
numbered from one end to the other (it matters not from which end - each
option has interesting and beautiful outcomes). This is best timed to last
between 10 and 30 minutes (I feel). At first, a winding spiral dominates,
but winds itself to 'break-up' point at which stage crystallisations and
dissolutions of order begin to occur.(These are really good).
At the end of the cycle, point 1 ('speed 1 also) will have done one
complete circle orbit, point 2 - 2 circles, point 3 - 3 circles etc. up to
100 orbits for point 100. So the cycle at this point would begin again from
a line identical to the position of the start. At the 'halfway' stage, all
the odd numbered points will have covered n/2 (n divided by 2) laps (where n
is the point's index number), which will be 'an integer plus one half'
orbits, forming a line halfway around the circle from the start position.
The even numbered index points will all be at their start position.
In fact, any fraction up to a denominator of about a fifth or a sixth of
the number of points plotted will yield a figure like this halfway shape-
but having a number of projecting radial arms equal to the fraction's
denominator.
This results in a quite breathtaking display of simple forms emerging from
and dissolving into the teeming of moving points.

Another elementary way in which the principle can be demonstrated:
A line of points may be drawn along the leftmost (say), column of a
screen. 256 points (say), are each assigned a row of of the screen to move
along to the right .Upon reaching the far end of the screen, the points may
either reappear at the opposite edge to move again from the left, or , as an
alternative system, each one could 'BOUNCE' , i.e. travel backwards, and
then eventually forwards again.
Making the points move at speeds proportional to their respective index
number, as described earlier gives rise to comparable effects to the circle
system, only with vertical instead of radial alignments at the
crystallization points.

Maybe this is how an ant would perceive a 128-harmonic tone or a JI chord
if it were a)
musical and b) its time sense was slowed sufficiently??

>What are some of the technical aspects of this work?

ORIGINAL EXPERIMENTS:
Initially, the question arose- "What happens if I apply Whitney's
differential dynamics to the points in a wave table?"
Imagine a sine wave, composed (8 bits- this is 1983!) point 1 moves from its
initial position, incredibly slowly, when it reaches the maximum value, its
starts downwards again, and bounces back up again when reaching the lowest
possible value. It completes a cycle in say 44 minutes. Point 2 completes 2
cycles of movement, and arrives back at the start point in the same 44mins.
Point 3 will do 3 cycles &c &c.........and point 256 will have completed 256
cycles.
The sine waveform had index numbers assigned to each point (for speed
assignments) from 0 (!) at the left (say) end, to 255 at the right, I found
that a sonic journey (through 400,000 timbres) was produced, easily
fascinating enough - even on one pitch, which journeyed through complex
timbral 'states' formed from many combinations and amplitudes, gradually
changing, of 128 harmonics. An 'orchestral', 7-octave sheet of tone-anchored
from one, low fundamental.
I ran this timbre-itself-harmonically-transforming on a low B with the 2
speakers fractionally detuned to create a mobile phase loop.
Its like applying the laws of sound and harmonics of Helmhlotz's
"atmospheric ocean" to the shape itself of the sound waves on that ocean.
It quickly became known as "the tone",and "the UFO tone".

The sounds resulting are smoothly varying modulations of timbre that can be
very satisfying or stimulating or both, to listen to. I prefer the changes
on the slower side.

TIMBRAL ANALYSIS:
A very thin ripple of amplitudes (1 or sometimes 2) harmonics wide runs
slowly up and then down the harmonic axis (from 1 to 128 and then back the
same way) forming a difference tone at the fundamental resulting from the
ascending (ie n+1th) and descending (ie nth) harmonics.

BOUNCE MK 2 - MODIFIER SHAPES:
A modification of the assignment system of speeds to points was then
developed. Rather than always having the linear array of points moving at
speeds proportional to their "index number" , it became desirable to assign
the speeds in different ways. Such as having the middle points in the
sequence travelling fastest, and those at each end slowest. Or vice versa.
This gave rise to the concept of a MODIFIER shape. In the elementary system
described before, a graphical shape of position in sequence plotted against
speed was a ramp form (either ascending or descending). If fastest (or
slowest) speeds are assigned to the middle, this can be called a VEE
(because of its shape) or TRIANGLE modifier.
In another variant, fastest (or slowest) speeds are assigned to the 1/4 and
3/4 positions along the sequence of movable points.
The most successful sound/visual combination (on the video/Sound mandala
piece called
'Triangles') was a triangle wave starting point (this now referred to as the
SEED form, with 'two triangles' as a modifier. (Two 'mountains' with maximum
speed at 1/4 and 3/4 points. The two halves of the image were set to move in
different directions at the start. Many interesting forms arise, which
suggest Inca designs. The timbral and graphic sequences are each
characteristic of a particular quality, right through the whole cycle.

TIMBRAL ANALYSIS:
These sound sequences (or tones as they have been called) create on the
palette of 128 (or more of course) harmonics constellations or virtual
harmonics, gathering, scattering and reforming eg a ripple of amplitude
running up and then down the axis of harmonic numbers.
If I start with a sine wave and modify it with two humps (like the modulus
of a sine wave- values without a minus sign), and starting by moving the
left half up and the right down I get a strange bundle (looking at a dynamic
FFT) of harmonics 4 or so harmonics wide, travelling up and down.

EDIT or PREDESIGN?:
We (my then students Michael Tusch, James Larsson and other friends in the
80s, and now Dave Snowdon in the 90s and 00s) decided we like/d to listen to
an unedited algorithm, rather than edit fragments a la Shakespeare with
portions, we have gone for designing the action into the spec. (in the
envisioning of the characteristics and the ramifications) rather than
cutting up bits. This I feel is an interesting paradigm approach for all
kinds of computer-generated art. More organic? What do you think?
John Whitney Sr had a bad reaction to this approach at first, but when I
later met him, and discussed/elaborated it, he seemed much more open to what
I had been doing.

FROM BOUNCE to SEQUENCE:
DIFFERENTIAL DYNAMICS TO HARMONIC MATHEMATICS: We quickly generalised
Whitney's principle to not only governing motion (controlled by a large 1D
array of integers) but also the movement through a table of values (instead
of just travelling at constant rate, points would sweep through eg a timbre
wave table's values, each at a different integer rate).
I wanted then to make the motions do better than simply go up and down and
back to where they started. I conceived of a sequence of values (i.e.
positions) through which each point moves, but, again, at speeds related to
assigned integer values, which are in turn in whole number ratio (and hence
harmonic) to each other. Hitherto, each point moved up, bounced, moved down,
bounced, and moved back to starting point.
A harmonically constructed complex timbre form, (eg a timbre with
harmonics 1,2,3,4,6,12 with amplitudes gradually decreasing) is used instead
to control the movement sequence of each point. This 6-harmonic timbre gives
rise to a sequence of intricate, smooth bobbing motions, each point
gradually rolling in and out of alignment with others.
The points' motion in this more complex way I call SEQUENCE technique. The
crystallization points are spectacular in different ways, the way in which
they are approached are also, being not simply an 'overtaking' process, but
also having unrolling and twirling motions, implying a 3-dimensional
interpretation. Also one gets "magic carpet" effects where layers of points
waver and hover.
'Helix' uses a timbre, comprised of those harmonics 1,2,3,4,6 and12, as a
sequence. The points start off as a horizontal line (silence), and each
point moves through the sequence at a rate proportional to its distance from
the left hand end. (i.e. a ramp modifier).
The timbral journey resulting consists of the 6 harmonics "themselves
going on a journey" up and down the 7-octave spectrum of that synthesizer,
at a speed proportional to the no. of the harmonic.(ie at speeds
1,2,3,4,6,12). This I gleaned from FFTs I ran in the 80s.
Why these particular timbral/harmonic motions ? I don't know, and would
like to know,
so I can find interesting variant animations of these harmonics' ripples.
Doing an FFT is one thing, predicting how to get interesting results is
another. Help!
The maths of how and why specific harmonic processes result from the
seed and modifier shapes (in BOUNCE technique) and from the modifier and
sequence tables (in SEQUENCE technique) still evades me.

SOFTWARE PACKAGES/2001:
I currently am working to evolve this further using MAX/MSP on a Macintosh.
Super Collider needs for someone to write ugens in order to do calculations
on the fly in absolutely precise integers, which is not possible yet!
CSound seems to me currently (on the mac anyhow) to not permit dynamic
repeated cyclic update of in-use wave table entries- I couldn't see a way on
a PC version.

Thanks if you got this far.

Let me know any feedback
if anyone finds this useful or inspiring I'd be glad to know about it.
Yours mathematically, musically and spiritually
Lawrence Ball

LAWRENCE BALL-
composer
math tutor
director, Planet Tree Music Festival http://www.planettree.org

--- In tuning@y..., "Lawrence Ball" <Lawrenceball@p...> wrote:
> thanks very much to Jacky Ligon for the suggestion to speak about
sound
> mandalas:
> ORIGINS/INSPIRATIONS/OVERVIEW:
>
> LaMonte Young's work particularly with long held continuous pitches
has
> always inspired me; the late John Whitney (Sr)'s films and moreover
his
> principle of
> "differential dynamics" led me to apply an extension of such
techniques to
> timbrally-varying drones, (the tamboura also was certainly present
as muse),
> although later its been applied to scores and midi. So initially it
began
> life as a 128 harmonics'-modulating drone/graphics audio-visual
sequence
> where one sees the magical transforms one hears.

Lawrence,

Hello! And thanks for the wonderful description of your work here.

As someone who greatly enjoys using harmonic drones in their music, I
find this all particularly interesting!

I do have a few questions for you though.

>
> ORIGINAL EXPERIMENTS:
> Initially, the question arose- "What happens if I apply Whitney's
> differential dynamics to the points in a wave table?"
> Imagine a sine wave, composed (8 bits- this is 1983!) point 1 moves
from its
> initial position, incredibly slowly, when it reaches the maximum
value, its
> starts downwards again, and bounces back up again when reaching the
lowest
> possible value. It completes a cycle in say 44 minutes. Point 2
completes 2
> cycles of movement, and arrives back at the start point in the same
44mins.
> Point 3 will do 3 cycles &c &c.........and point 256 will have
completed 256
> cycles.

Let me ask if the movements here are incremental, or is it a smooth
slow glissandi between points? For instance, when you move from the
fundamental to the second harmonic, it is a single step?

I'm imagining that it would seem as a gliss at this slow of movement
in the higher harmonics.

> The sine waveform had index numbers assigned to each point (for
speed
> assignments) from 0 (!) at the left (say) end, to 255 at the right,
I found
> that a sonic journey (through 400,000 timbres) was produced, easily
> fascinating enough - even on one pitch, which journeyed through
complex
> timbral 'states' formed from many combinations and amplitudes,
gradually
> changing, of 128 harmonics. An 'orchestral', 7-octave sheet of tone-
anchored
> from one, low fundamental.

Ah, I was wondering about this. So the fundamental is present at all
times, while the harmonics above slowly move to other points?

Something like the sound of a giant tamboura? Amazing!

> I ran this timbre-itself-harmonically-transforming on a low B with
the 2
> speakers fractionally detuned to create a mobile phase loop.
> Its like applying the laws of sound and harmonics of Helmhlotz's
> "atmospheric ocean" to the shape itself of the sound waves on that
ocean.
> It quickly became known as "the tone",and "the UFO tone".

I'm not sure if I understand this part about the fractionally detuned
speakers. How did you do this? Couldn't you achieve this with
software these days, by changing the phase relationships between the
left and right channels?

What was the frequency of the "B" - the fundamental?

>
> The sounds resulting are smoothly varying modulations of timbre
that can be
> very satisfying or stimulating or both, to listen to. I prefer the
changes
> on the slower side.
>
> TIMBRAL ANALYSIS:
> A very thin ripple of amplitudes (1 or sometimes 2) harmonics wide
runs
> slowly up and then down the harmonic axis (from 1 to 128 and then
back the
> same way) forming a difference tone at the fundamental resulting
from the
> ascending (ie n+1th) and descending (ie nth) harmonics.

This is interesting. So was the pitch of B was high enough to allow
the perception of the difference tone below what would be the
fundamental pitch?

What I like about this is how you have taken this phenomenon produced
in the ear and have made it into a functional part of this work. Very
good!

>
> BOUNCE MK 2 - MODIFIER SHAPES:
> A modification of the assignment system of speeds to points was
then
> developed. Rather than always having the linear array of points
moving at
> speeds proportional to their "index number" , it became desirable
to assign
> the speeds in different ways. Such as having the middle points in
the
> sequence traveling fastest, and those at each end slowest. Or vice
versa.
> This gave rise to the concept of a MODIFIER shape. In the
elementary system
> described before, a graphical shape of position in sequence plotted
against
> speed was a ramp form (either ascending or descending). If fastest
(or
> slowest) speeds are assigned to the middle, this can be called a VEE
> (because of its shape) or TRIANGLE modifier.
> In another variant, fastest (or slowest) speeds are assigned to the
1/4 and
> 3/4 positions along the sequence of movable points.
> The most successful sound/visual combination (on the video/Sound
mandala
> piece called
> 'Triangles') was a triangle wave starting point (this now referred
to as the
> SEED form, with 'two triangles' as a modifier. (Two 'mountains'
with maximum
> speed at 1/4 and 3/4 points. The two halves of the image were set
to move in
> different directions at the start. Many interesting forms arise,
which
> suggest Inca designs. The timbral and graphic sequences are each
> characteristic of a particular quality, right through the whole
cycle.

It sounds very visually interesting as well as sonically. This would
make for an interesting union of visual and audio. Have you attempted
to create a video of this?

>
> TIMBRAL ANALYSIS:
> These sound sequences (or tones as they have been called) create on
the
> palette of 128 (or more of course) harmonics constellations or
virtual
> harmonics, gathering, scattering and reforming eg a ripple of
amplitude
> running up and then down the axis of harmonic numbers.
> If I start with a sine wave and modify it with two humps (like the
modulus
> of a sine wave- values without a minus sign), and starting by
moving the
> left half up and the right down I get a strange bundle (looking at
a dynamic
> FFT) of harmonics 4 or so harmonics wide, travelling up and down.
>
> EDIT or PREDESIGN?:
> We (my then students Michael Tusch, James Larsson and other friends
in the
> 80s, and now Dave Snowdon in the 90s and 00s) decided we like/d to
listen to
> an unedited algorithm, rather than edit fragments a la Shakespeare
with
> portions, we have gone for designing the action into the spec. (in
the
> envisioning of the characteristics and the ramifications) rather
than
> cutting up bits. This I feel is an interesting paradigm approach
for all
> kinds of computer-generated art. More organic? What do you think?

So basically you programmed all of the possibilities, to where one
didn't have the ability to edit it?

> John Whitney Sr had a bad reaction to this approach at first, but
when I
> later met him, and discussed/elaborated it, he seemed much more
open to what
> I had been doing.

What was the difference between his approach then and yours?

>
> Let me know any feedback
> if anyone finds this useful or inspiring I'd be glad to know about
it.
> Yours mathematically, musically and spiritually
> Lawrence Ball

It really does indeed sound interesting! I like the idea of a
continuously evolving timbre. I hope you'll keep us up to date about
the developments of this concept and music coming from it.

Too bad I'm on a PC, heard good things about MAX/MSP.

Thanks!

Jacky Ligon

sound mandalas

🔗Lawrence Ball <Lawrenceball@planettree.demon.co.uk>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗ligonj@northstate.net

🔗Lawrence Ball <Lawrenceball@planettree.demon.co.uk>