Searching for the best val for a mapping

Is the best way to do this to just do a brute force search of all vals
that lie at most some number of alterations away from the patent val?

For example, if I'm looking for the best val in the 2.3.5 subgroup for
11-EDO, I'd set some cutoff for the number of alterations (let's say
at 2) and then look at 11p, 11b, 11c, 11bc, 11bb, 11cc, 11bbc, 11bcc,
and 11bbcc, and pick the best?

Or is there some more elegant way I don't know of?

-Mike

Mike wrote:

>Is the best way to do this to just do a brute force search of all vals
>that lie at most some number of alterations away from the patent val?

I found that testing the patent vals based on octaves
+/-0.5 cents from pure essentially never misses the best val.
In fact it beats a monte carlo sampling of val space near the
patent val until you do a truly ridiculous number of trials.
And that's only with the octaves in 0.1 cent steps. You can
use 0.01 cent resolution and you'll definitely get the goose
with only 50 tests. The reason this works, at least in the
case of TOP damage, is no doubt due to the existence of TOP-FP
octaves.

Graham has a method proven to find the best val within given
error bounds. See his source code.

-Carl

That's a simple way but not an efficient one. It has exponential complexity.
What I do is predict the range of mappings for each prime recursively given the mappings of smaller primes. That converges faster on good mappings if you set a strict target. It's all in the code.

Graham

------Original message------
From: Mike Battaglia <battaglia01@gmail.com>
To: <tuning-math@yahoogroups.com>
Date: Wednesday, January 11, 2012 3:28:05 PM GMT-0500
Subject: [tuning-math] Searching for the best val for a mapping

Is the best way to do this to just do a brute force search of all vals
that lie at most some number of alterations away from the patent val?

For example, if I'm looking for the best val in the 2.3.5 subgroup for
11-EDO, I'd set some cutoff for the number of alterations (let's say
at 2) and then look at 11p, 11b, 11c, 11bc, 11bb, 11cc, 11bbc, 11bcc,
and 11bbcc, and pick the best?

Or is there some more elegant way I don't know of?

-Mike

------------------------------------

Yahoo! Groups Links

My method has O(1) complexity. You can't beat that!
I can't guarantee it'll work for TE error like it does
for TOP, but I think it's highly likely.

-Carl

At 12:49 PM 1/11/2012, you wrote:
>Content-Transfer-Encoding: 7bit
>
>That's a simple way but not an efficient one. It has exponential complexity.
>What I do is predict the range of mappings for each prime recursively
>given the mappings of smaller primes. That converges faster on good
>mappings if you set a strict target. It's all in the code.
>
> Graham
>
>------Original message------
>From: Mike Battaglia <battaglia01@gmail.com>
>To: <tuning-math@yahoogroups.com>
>Date: Wednesday, January 11, 2012 3:28:05 PM GMT-0500
>Subject: [tuning-math] Searching for the best val for a mapping
>
>Is the best way to do this to just do a brute force search of all vals
>that lie at most some number of alterations away from the patent val?
>
>For example, if I'm looking for the best val in the 2.3.5 subgroup for
>11-EDO, I'd set some cutoff for the number of alterations (let's say
>at 2) and then look at 11p, 11b, 11c, 11bc, 11bb, 11cc, 11bbc, 11bcc,
>and 11bbcc, and pick the best?
>
>Or is there some more elegant way I don't know of?
>
>-Mike
>

But will it work out for ridiculous wacked out subgroups?

Sent from my iPhone

On Jan 11, 2012, at 3:55 PM, Carl Lumma <carl@lumma.org> wrote:

My method has O(1) complexity. You can't beat that!
I can't guarantee it'll work for TE error like it does
for TOP, but I think it's highly likely.

-Carl

At 12:49 PM 1/11/2012, you wrote:
>Content-Transfer-Encoding: 7bit
>
>That's a simple way but not an efficient one. It has exponential
complexity.
>What I do is predict the range of mappings for each prime recursively
>given the mappings of smaller primes. That converges faster on good
>mappings if you set a strict target. It's all in the code.
>
> Graham
>
>------Original message------
>From: Mike Battaglia <battaglia01@gmail.com>
>To: <tuning-math@yahoogroups.com>
>Date: Wednesday, January 11, 2012 3:28:05 PM GMT-0500
>Subject: [tuning-math] Searching for the best val for a mapping
>
>Is the best way to do this to just do a brute force search of all vals
>that lie at most some number of alterations away from the patent val?
>
>For example, if I'm looking for the best val in the 2.3.5 subgroup for
>11-EDO, I'd set some cutoff for the number of alterations (let's say
>at 2) and then look at 11p, 11b, 11c, 11bc, 11bb, 11cc, 11bbc, 11bcc,
>and 11bbcc, and pick the best?
>
>Or is there some more elegant way I don't know of?
>
>-Mike
>

At 02:07 PM 1/11/2012, Mike wrote:

>But will it work out for ridiculous wacked out subgroups?

Should do. You can always compare it to Graham's method
and see what happens. -C.

>On Jan 11, 2012, at 3:55 PM, Carl Lumma <<mailto:carl@lumma.org>carl@lumma.org> wrote:
>
>>
>>My method has O(1) complexity. You can't beat that!
>>I can't guarantee it'll work for TE error like it does
>>for TOP, but I think it's highly likely.
>>
>>-Carl

It's at least linear time because you have to loop through the primes. It may be that you have to increase the resolution as you add more primes and complexity gets hidden that way.

Graham

------Original message------
From: Carl Lumma <carl@lumma.org>
To: <tuning-math@yahoogroups.com>
Date: Wednesday, January 11, 2012 12:55:23 PM GMT-0800
Subject: Re: [tuning-math] Searching for the best val for a mapping

My method has O(1) complexity. You can't beat that!
I can't guarantee it'll work for TE error like it does
for TOP, but I think it's highly likely.

-Carl

At 12:49 PM 1/11/2012, you wrote:
>Content-Transfer-Encoding: 7bit
>
>That's a simple way but not an efficient one. It has exponential complexity.
>What I do is predict the range of mappings for each prime recursively
>given the mappings of smaller primes. That converges faster on good
>mappings if you set a strict target. It's all in the code.
>
> Graham
>
>------Original message------
>From: Mike Battaglia <battaglia01@gmail.com>
>To: <tuning-math@yahoogroups.com>
>Date: Wednesday, January 11, 2012 3:28:05 PM GMT-0500
>Subject: [tuning-math] Searching for the best val for a mapping
>
>Is the best way to do this to just do a brute force search of all vals
>that lie at most some number of alterations away from the patent val?
>
>For example, if I'm looking for the best val in the 2.3.5 subgroup for
>11-EDO, I'd set some cutoff for the number of alterations (let's say
>at 2) and then look at 11p, 11b, 11c, 11bc, 11bb, 11cc, 11bbc, 11bcc,
>and 11bbcc, and pick the best?
>
>Or is there some more elegant way I don't know of?
>
>-Mike
>

------------------------------------

Yahoo! Groups Links

I assumed we were thinking of the scaling with ET number... -C.

At 11:28 PM 1/11/2012, you wrote:
>Content-Transfer-Encoding: 7bit
>
>It's at least linear time because you have to loop through the primes.
>It may be that you have to increase the resolution as you add more
>primes and complexity gets hidden that way.
>
> Graham