Tuning-Math Archive Section 1: 150

Message: 150 - Contents - Hide Contents Date: Wed, 06 Jun 2001 22:19:55 Subject: Re: True nature of tuning-math (was: True nature of the Blackjack scale) From: Dave Keenan --- In tuning-math@y..., graham@m... wrote:

> How about insisting that, as the list already exists, an absolute majority > of the Tuning List is required to vote it away? Then, the overwhelming > number of people who don't bother to vote are sure to carry the day!

How about recognising that there's nothing democratic about it. If Paul wants to post to it he will. If Paul refuses to discuss certain topics with me on the main list, I am forced to post here too. Cest la vie. But I'd still like it combined with Harmonic Entropy. Regards, -- Dave Keenan

Message: 151 - Contents - Hide Contents Date: Thu, 07 Jun 2001 00:08:56 Subject: Re: True nature of tuning-math From: carl@l...

> How about recognising that there's nothing democratic about it. Right! > If Paul wants to post to it he will. If Paul refuses to discuss > certain topics with me on the main list, I am forced to post here > too. Cest la vie. But I'd still like it combined with Harmonic > Entropy.

I agree about the fusion (I did suggest it, after all). But also, Dave, I'd ask you to consider the general issue of seperation again. I used to be opposed to it -- in fact I was quite opposed to the creation of the harmonic entropy list. But that was back in the good old days of merely 1000 posts/month. The volume on the main list now supports a seperation, in my opinion. Math is a logical seperation. It frees up the main list for things like info on synthesizers, instrument building, album reviews, and concert information. This is something we need, and after all the complaining about the math it is something we should get. -Carl

Message: 154 - Contents - Hide Contents Date: Thu, 07 Jun 2001 19:11:51 Subject: Re: Refinement (?) of "true 5-limit" adaptive tuning From: Paul Erlich --- In tuning-math@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> > Ohmigosh, it's FAQ editor all over again! ;-> What are the duties?

None. But perhaps someone else will volunteer.

Message: 155 - Contents - Hide Contents Date: Thu, 07 Jun 2001 19:14:01 Subject: Re: linear approximation From: Paul Erlich --- In tuning-math@y..., <manuel.op.de.coul@e...> wrote:

>> The best LS generator . . . Manuel, there are several _strange_ >> features in this calculation. First of all, you're including _both_ >> the 1/1 _and_ the 2/1, while every other pitch class appears only >> once. >

> It's only an example. The user can decide which intervals he wants > to approximate. > Whether or not calculations are strange is also something I want to > leave the user to decide. If some calculation may be useful to > someone I consider adding it. I'm not trying to impose a set of > values whether features are good or bad onto users.

Can you explain to me a situation in which this calculation, as it appears in the tutorial, is in a form that tells something useful to someone?

>> Second, you're forcing the fit line to pass through the 1/1. >

> That's because the points are equidistant horizontally. If that's > not done, the line would pass through the x-axis at a non-integer > coordinate in most cases.

What's wrong with that?

Message: 156 - Contents - Hide Contents Date: Thu, 07 Jun 2001 20:56:49 Subject: Re: Refinement (?) of "true 5-limit" adaptive tuning From: jpehrson@r... --- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote: Yahoo groups: /tuning-math/message/154 * [with cont.]

> --- In tuning-math@y..., "John A. deLaubenfels" <jdl@a...> wrote: >>

>> Ohmigosh, it's FAQ editor all over again! ;-> What are the duties? >

> None. But perhaps someone else will volunteer.

In my opinion, the best "moderator" is somebody that does ABSOLUTELY NOTHING, like Nowitsky on the "fat" Tuning List...! __________ ________ ________ Joseph Pehrson

Message: 157 - Contents - Hide Contents Date: Fri, 08 Jun 2001 00:45:58 Subject: Re: Math models (about Hypothesis) From: Pierre Lamothe Hi Paul, I will comment here very shortly so I forget << perhaps future responses should be directed to the Tuning list? >> for this time. I would like mainly to express that these quotes << the scale LssssLssss has only one size of class 0 _and_ only one size of class 5. >> << if there are N tones, there are N modes, since each tone can be taken as the 'tonic' >> indicate to me there exist a common ground on which a math discussion may be fertile. As I understood that, your term _scale_ here is tightly related to terms _step_ and _class_ obtained by rotation (I will discuss later about class, partition and equivalence relation) and the last term refers implicitely to the space of intervals subtended by a scale S and the matrix S\S showing the interval interconnection. All that implies what I name _macrotonal_ properties, qualifying so properties that could'nt be applied to an isolated interval for it is related to the specific configuration of an interval set. When I saw how so much terms were used to qualify intervals (mathematically defined) but so few to qualify structured interval sets, and when I saw the same term scale used to qualify tausends of interval sets having almost nothing (mathematically) in common, I was not highly motivated to face that. Your answers give me a better motivation. It remains only to find time. It will happen. Pierre

Message: 159 - Contents - Hide Contents Date: Thu, 7 Jun 2001 23:07:51 Subject: Re: True nature of tuning-math From: monz

> ----- Original Message ----- > From: Dave Keenan <D.KEENAN@U...> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Thursday, June 07, 2001 10:16 PM > Subject: [tuning-math] Re: True nature of tuning-math > > The blackjack guitar design on the tuning list is getting pretty > heavily mathematical. Should I move it to the tuning-math list now and > split the thread over two archives?

*There's* the drawback of having separate lists. Here's the policy I've been following: if a thread on the big tuning list (or actually, on any of the others) suddenly starts showing signs of math, I post any response to it which contains more math to this list. In other words, one post with lightweight math is the limit on any other list. If it requires any further math, it goes here. That way as soon as the discussion turns mathematical, it stays on this list and all one needs to have to follow it is a single quote of the original post containing the math... and the other tuning lists are spared all but the most elementary math. I really think this procedure will keep the largest number of people the happiest. -monz Yahoo! GeoCities * [with cont.] (Wayb.) "All roads lead to n^0" _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)

Message: 160 - Contents - Hide Contents Date: Fri, 08 Jun 2001 09:18:43 Subject: CS From: carl@l... Really, Dave? No comment the CS alternative I fashioned at your request? I'm surprised. -Carl

Message: 164 - Contents - Hide Contents Date: Fri, 08 Jun 2001 17:38:03 Subject: Re: uniqueness From: carl@l...

> I've changed the routine, hoping the results are right. > Do you have a means to check them? > I have to change the file consist_limits.txt too.

What prompted the change? Did you find a bug? -Carl

Message: 165 - Contents - Hide Contents Date: Fri, 08 Jun 2001 17:40:59 Subject: big "mean" math question From: jpehrson@r... Well, my big "mean" math question has to do with the idea of the "root mean square" (RMS) method of finding averages that Graham Breed was talking about on the "fat" list... I'm actually intrigued by this, since I'm not understanding why squaring everything, adding it all together and then taking the SQUARE ROOT of the sum is going to lead to an accurate average... Why is this done this way again?? This is pretty interesting, actually... _________ ________ _______ Joseph Pehrson

Message: 167 - Contents - Hide Contents Date: Fri, 08 Jun 2001 20:48:58 Subject: Re: linear approximation From: Paul Erlich --- In tuning-math@y..., <manuel.op.de.coul@e...> wrote:

>> What's wrong with that? >

> It's assumed that 1/1 is on degree 0. If you'd create an ET with > the step size given by the slope of the line it wouldn't be the > best approximation anymore because the whole line would shift.

It seems to me the opposite would be true. Allowing the whole line to shift would allow, in general, a better approximation to the step sizes, wouldn't it?

Message: 169 - Contents - Hide Contents Date: Fri, 08 Jun 2001 21:01:49 Subject: Re: big "mean" math question From: Paul Erlich --- In tuning-math@y..., jpehrson@r... wrote:

> Well, my big "mean" math question has to do with the idea of > the "root mean square" (RMS) method of finding averages that Graham > Breed was talking about on the "fat" list... > > I'm actually intrigued by this, since I'm not understanding why > squaring everything, adding it all together and then taking the > SQUARE ROOT of the sum is going to lead to an accurate average... > > Why is this done this way again?? This is pretty interesting, > actually...

You don't want to take the _straight_ average because it might be zero just from positives and negative signs canceling out. The two simplest alternatives are to take the _maximum_ error, or to take the average of the absolute values of the errors (called MAD, for Mean Absolute Deviation). The RMS is known as the Standard Deviation in statistics. It's the standard measure of error in science and engineering. There are several reasons for this. Let me give you a rough idea of why it makes some sense in this context. Look at the dips in the harmonic entropy curve. Notice how they are "rounded" at the bottom. Any curve with a round minimum like this (not getting too technical) approximates a parabola more and more closely the more you zoom in on the minimum. A parabola is just the curve representing squared error. So if you sum the squared errors, you're summing the dissonances, in a sense. And then you have to take the square root at the end so that the result is comparable with the units for a _single_ error. For example, in the 3-limit there's only one interval to evaluate. Let's say it has a 2-cent error. So any sort of _average_ over this one interval would have to be 2 cents. It wouldn't make much sense to say the average was 4 cents when there's only a single 2 cent error, would it? So that's why you have to take the square root after summing. If you want to get more technical, check out a statistics book.

Message: 171 - Contents - Hide Contents Date: Fri, 08 Jun 2001 21:38:23 Subject: Re: big "mean" math question From: jpehrson@r... --- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote: Yahoo groups: /tuning-math/message/169 * [with cont.] Thanks, Paul... this gives me a good overview on this one! It's pretty interesting... ________ _______ ______ Joseph Pehrson

Message: 172 - Contents - Hide Contents Date: Fri, 08 Jun 2001 21:40:38 Subject: Re: big "mean" math question From: Paul Erlich --- In tuning-math@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> On 6/8/01 5:01 PM, "Paul Erlich" <paul@s...> wrote: >

>> The RMS is known as the Standard Deviation in statistics. It's the >> standard measure of error in science and engineering. >

> THAT'S what standard deviation IS? Ahh.. > > Thank you Paul. I don't think I ever knew that. > Or if I did, I managed to not retain it...

Sorry, I was wrong about that. The Standard Deviation is something different. It's actually the RMS deviation of a set of measurements from their collective mean. The RMS we're talking about here, rather, is the RMS deviation from a pre-determined standard, namely the JI interval. SO it's somewhat different.