FROM: mclaren

TO: New Alternative Wanking List

SUBJECT: dubious invention

Jeff Scott appears to have credited me with the

invention of something involved with dynamic lattice

programs for navigating ratio space. This seems highly

unlikely for several reasons.

First, Carter Scholz wrote a routine for JICalc

which sounds pitches when the user clicks on specific

points in the ratio-space representation of a tuning.

This upgrade to JICalc appeared, if memory serves,

someime around 1993.

However, shortly thereafter Carter Scholz wrote

a much more comlex HMSL program which he used to realize

his composition LATTICE 3327. Carter's program uses real-

time calculations and multiple MIDI channels to send

out pitch-ebnd messages which retune successive notes

of a DX7II equipped witht he E! board to any desired

point in a 7-dimensional ratio space.

Moreover, Carter's HMSL program not only generates

pitches corresponding to those ratio-space coordinates in

7 dimensions, it also uses a variety of different metrics

to evaluate so-called "harmonic complexity" in 7-D ratio space.

The user can choose which metric is used by hitting keys

on the computer keyboard.

Lastly, Carter's HMSL program navigated 7-D ratio

space according to gradients which pointed in the direction

of "more complexity" (using the current measure) or "less

complexity" and also by specifying the general algorithm.

If memory serves, drunakrd's walk and Levy flight and several

others were the choices available.

-----

Doubtless others prior to Carter Scholz in late 1993

did these sorts of things. My vague suspicion is that the

League of Automated Composers did something like this on

their KIM-1s back the late 1970s, but an early computer composer

at a university in British Columbia did something similar even

earlier using real-time FM on a PDP-11.

------

The important point, however, remains that whomever

invented this particular wheel, the wheel itself has 4 sides

and is made out of marshmallow. This wheel don't work, kiddies.

My own experience with using Csound to realize various

precompositional studies in ratio space around 1994 gave rise

to the dark suspicion that ratio space metrics bore no audible

relationship to anything the human ear can hear.

Subsequent double-blind listening tests, using a Turbo Pascal

program which renamed and scrambeld audio files and wrote a record

of the new names to a text file which could be examined later,

clinched my suspicion that ratio space involves mathematical

chimerai which do not relate to anything the human ear can hear.

Consequently, manipulations of departed mathematical ghosts

in ratio space prove musically meaningless. Ratio space itself

constitutes an ignis fatuus as far as actual music is concerned --

a delusion with no discernible relation to either the roughness

of intervals, pitch height, logarithmic interval width, or any

other known property of msuical intervals or individual musical

pitches.

NOTA BENE: Representations of TUNINGS in ratio space can

exhibit some useful info -- for instance, you can see quickly whether

the JI tuning is subharmonic or harmonic or symmetrical (viz., has as

many utonal as otonal pitches), etc.

However, in terms of extracting useful musical info via

mathematical operations in ratio space, this is not possible, any

more than it is possible to turn lead into gold by chanting various

incantations, or to detect the luminferous ether with the proper

arrangement of interferometers and mirrors.

Fokker's introduction of 3-D ratio space followed the much

earlier use of 2-D ratio space by Hugo Riemann and other German

theorists even earlier in the 19th century. As far as illustrating

abstract properties of musical *SCALES*, these diagrams had some

limited use and served some very limited purporse.

When people unwisely moved on from diagramming scales to

trying to use ratio space to compose music or extract information

about actual musical properties of intervals, the whole enterprise

headed into the ditch and wound up spinning its wheels in the mud.

Some people periodically claim "Oh, no, I create music using

ratio space lattices..." Experience has shown that ratio space

diagrams and/or lattices represent a debilitating hurdle, rather than

a facilitating tool which helps people compose music. The proof is

clear and straightforward -- all the people who avoid using ratio

space compose much more music than the people who try to use ratio

space to compose music. This is no coincidence. Ratio space

represents a roadblock, a pothole on the road to composition, as much

of a conceptual barrier to composing music as the notion of

phlogiston was to creating a valid science of thermodynamics.

---------

--mclaren

> The important point, however, remains that whomever

> invented this particular wheel, the wheel itself has 4 sides

> and is made out of marshmallow. This wheel don't work, kiddies.

> My own experience with using Csound to realize various

> precompositional studies in ratio space around 1994 gave rise

> to the dark suspicion that ratio space metrics bore no audible

> relationship to anything the human ear can hear.

Absolutely correct. Distance in the lattice doesn't reflect

perception, at least for triangular lattices. Tenney complexity

is the only simple metric for JI that seems to work well enough

to mean anything, and its visualization as a lattice metric

would require... thinking about volumes in an octave-specific

rectangular lattice, I guess... or city block distance on an

octave-specific rectangular lattice whose rungs are scaled by

the log of their vector class ('zthat right, Paul?)?

> Consequently, manipulations of departed mathematical ghosts

> in ratio space prove musically meaningless. Ratio space itself

> constitutes an ignis fatuus as far as actual music is concerned --

...as far as *acoustics* is concerned, since:

> NOTA BENE: Representations of TUNINGS in ratio space can

> exhibit some useful info -- for instance, you can see quickly

>whether the JI tuning is subharmonic or harmonic or symmetrical

>(viz., has as many utonal as otonal pitches), etc.

Correctamundo. And that's what we use 'em for, over on the

big list, and tuning-math.

-Carl Lumma

instrument builder

--- In crazy_music@y..., Carl Lumma <carl@l...> wrote:

> or city block distance on an

> octave-specific rectangular lattice whose rungs are scaled by

> the log of their vector class ('zthat right, Paul?)?

That's right! It's the Tenney lattice.