On 3/11/02 11:33 PM, "paulerlich" <paul@stretch-music.com> wrote:

> this is my understanding as regards the brun algorithm.

>

> historically, there have been many algorithms applied that do what the brun

> algorithm does, and they all give slightly different results.

>

> none of them is 'perfect' like the euclidean algorithm is for single dyads

> (ratios of two numbers).

>

Being twins, I know exactly what you're talking about, about Brun and dyads.

The Brun thing made a little more sense when we took note of when a

temperament didn't wind up on the top row after the operation, devaluing

them all into an "auxiliary" catalog. It started making more sense when we

applied rounding to the list of temperaments and saw the congealing of

discrete JI webs in each temperament.

At the point where we left computers on for days and printed out tens of

thousands of combinations of interval combinations pushed thru the

Brun-o-matic did we see this sort of elusive crystal structure; there is

sort of a "priority" awarded to the list of intervals in top to bottom order

- as you fold the intervals, the topmost have the most folds into them so

their harmonic composure is more figured into the later calculations, makes

sense:

{2:1, 3:2, 5:4, 7:6} seems to de-emphasize the 7th harmonic.

{2:1, 7:4, 3:2, 5:4} seems to over-emphasize it.

> most recently, the ferguson-forcade algorithm was developed and is 'perfect'.

>

I searched tuning AND tuning math and I didn't find either Ferguson or

Forcade. What exactly is this algorithm? I'm serious, I have to hear this.

I've been smacking Brun around for 12 years now. I've never heard of

anything similar or anything claiming to be more useful. So. Hit me.

A link would suffice as well. Web searches have turned up empty.

> but for these problems, for tunings with a reasonable number of notes, a

> brute-force approach seems best to me.

>

You know, when I sit with a temperament and ask myself how this note sounds

and what that dyad is like compared with this one etc, there doesn't seem to

be any kind of mathematical explanation more than a guess. Other than the

fact that I have my own recognizable sense of taste in terms of composing.

At which point, if you were me, which actually you are, you'd come up with

the same set of useful intervals and such that I would.

The math models form a sort of obsessive tension which, playing the actual

buffet choice notes forms a sort of rebellion against. The idea of the

"convergence webs", and everything leading up to them, all the way down to

the anything-goes, all-zeroes logic grid, past the point where any note can

pass to any other note, that provides the indeterminate hinge, out of the JI

convergences, into dimensions like umm just playing what you feel like.

To me, I think it's all just an analytical mantra to keep the other side of

the brain busy so I can be more creative.

> in other words, try out *all* the possibities, and come up with an error

> measure that will pick out the 'best' ones.

>

> there's been quite a bit of this on the tuning-math list, for equal

> temperaments, and even more so for linear temperaments.

I try following it once in awhile, but I haven't managed to translate all

the terms at any one point so. I'm never fully sure what's going on.

Moreso than last year but still a bit lost.

> i say this not to put you down or to question you but to encourage you to

> share your ideas more frequently on the tuning-math list, where they will much

> more often become 'seeds' around which mutual intelligibility, and mutual

> enlightenment, coalesce.

Yes thank you for clarifying the invitation. In less enlightened states of

mind I tend to take things the wrong way.

Marc

--- In tuning-math@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> I searched tuning AND tuning math and I didn't find either Ferguson or

> Forcade. What exactly is this algorithm?

It's an integer relation finding algorithm. There is even an integer relation finding web site now where you can email and get the relation (using PSLQ, I think.) Here's mathworld on it:

http://mathworld.wolfram.com/Ferguson-ForcadeAlgorithm.html

I've not found these useful for searches, but maybe I should consider the matter; however brute force seems to suffice.