Yahoo Tuning Groups Ultimate Backup tuning NOT Fourier Analysis!

Rick,

I just gave your article a quick skim and contrary to our prior
disagreements, I think it looks very good.

You're approaching this problem from a "time domain" perspective rather than
a "frequency domain" perspective; the former seems to be the direction that
a lot of the latest research on this is going. Furthermore, I think that if
you were to reformulate your ideas in a "frequency domain" perspective, I
think you'd find that you're saying a lot of the same things that many here
have been saying as well, but in a different way.

In general I think your ideas are pretty solid here, with a few things to
consider:

1) There are a few special cases in which I don't think the brain will
always tend to the "greatest" common denominator. It's possible for a single
isolated sinusoids to be heard as, say 3/1 with a "virtual" pitch being
produced at 1/1, even though no "interval" exists. Prior exposure and
context can influence this.
2) The phase of the sinusoids, for all intents and purposes, does not have
any bearing at all on the perception of the dyad. Two phase-shifted versions
of the same "5/4" dyad will NEVER seem to "sync up" visually, but it won't
matter.

-Mike

On Wed, Feb 17, 2010 at 12:04 AM, rick <rick_ballan@...> wrote:

>
>
> Hi everyone,
>
> I'd just like to state that the approx. GCD's in the article I posted
> produce harmonies that are NOT revealed by Fourier analysis. That is its
> whole point! Since they deconstruct the intervals between sine waves upon
> which FA is by definition based then we cannot cite the latter as 'proof'
> against them, not even in principle. So please stop sending me personal
> emails to that effect. Thanks,
>
> -Rick
>
>
>

🔗rick <rick_ballan@...>

Hi Mike,

Thanks, it means allot coming from you. I was worried about phase-shifts (you read my mind?) so it's good to know that the results are general. And yes I agree that we don't want too much from a music 'theory' because prior experience, context etc...is where the art must come in. I also figured that there still would be certain aspects of virtual pitch which are separate from what I'm talking about and the distinction would come out eventually.

Now I'm not sure how to proceed via the frequency domain yet quite simply because there seem to be other cycles in the wave which I don't understand. 16:19 for eg has 5:6 on either side and 6:7 in the middle with a phase shift of the average frequency?? Yet other intervals give other results. I'll just plod away as I always do and hope that something jumps out eventually. In the meantime, I don't feel so lonely now knowing that others are working along similar lines. Thanks for letting me know.

Rick

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Rick,
>
> I just gave your article a quick skim and contrary to our prior
> disagreements, I think it looks very good.
>
> You're approaching this problem from a "time domain" perspective rather than
> a "frequency domain" perspective; the former seems to be the direction that
> a lot of the latest research on this is going. Furthermore, I think that if
> you were to reformulate your ideas in a "frequency domain" perspective, I
> think you'd find that you're saying a lot of the same things that many here
> have been saying as well, but in a different way.
>
> In general I think your ideas are pretty solid here, with a few things to
> consider:
>
> 1) There are a few special cases in which I don't think the brain will
> always tend to the "greatest" common denominator. It's possible for a single
> isolated sinusoids to be heard as, say 3/1 with a "virtual" pitch being
> produced at 1/1, even though no "interval" exists. Prior exposure and
> context can influence this.
> 2) The phase of the sinusoids, for all intents and purposes, does not have
> any bearing at all on the perception of the dyad. Two phase-shifted versions
> of the same "5/4" dyad will NEVER seem to "sync up" visually, but it won't
> matter.
>
> -Mike
>
>
> On Wed, Feb 17, 2010 at 12:04 AM, rick <rick_ballan@...> wrote:
>
> >
> >
> > Hi everyone,
> >
> > I'd just like to state that the approx. GCD's in the article I posted
> > produce harmonies that are NOT revealed by Fourier analysis. That is its
> > whole point! Since they deconstruct the intervals between sine waves upon
> > which FA is by definition based then we cannot cite the latter as 'proof'
> > against them, not even in principle. So please stop sending me personal
> > emails to that effect. Thanks,
> >
> > -Rick
> >
> >
> >
>

🔗rick <rick_ballan@...>

I forgot to mention Mike that I did try a Fourier analysis of the first cycle but got nothing spectacular. Using Mathematica 7 I isolated the first cycle of 16:19, created a continuous period function from it and then took a Fourier series. It just punched out all the harmonics with a large amplitude at 16 and 19 as expected.

Rick

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:
>
> Hi Mike,
>
> Thanks, it means allot coming from you. I was worried about phase-shifts (you read my mind?) so it's good to know that the results are general. And yes I agree that we don't want too much from a music 'theory' because prior experience, context etc...is where the art must come in. I also figured that there still would be certain aspects of virtual pitch which are separate from what I'm talking about and the distinction would come out eventually.
>
> Now I'm not sure how to proceed via the frequency domain yet quite simply because there seem to be other cycles in the wave which I don't understand. 16:19 for eg has 5:6 on either side and 6:7 in the middle with a phase shift of the average frequency?? Yet other intervals give other results. I'll just plod away as I always do and hope that something jumps out eventually. In the meantime, I don't feel so lonely now knowing that others are working along similar lines. Thanks for letting me know.
>
> Rick
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > Rick,
> >
> > I just gave your article a quick skim and contrary to our prior
> > disagreements, I think it looks very good.
> >
> > You're approaching this problem from a "time domain" perspective rather than
> > a "frequency domain" perspective; the former seems to be the direction that
> > a lot of the latest research on this is going. Furthermore, I think that if
> > you were to reformulate your ideas in a "frequency domain" perspective, I
> > think you'd find that you're saying a lot of the same things that many here
> > have been saying as well, but in a different way.
> >
> > In general I think your ideas are pretty solid here, with a few things to
> > consider:
> >
> > 1) There are a few special cases in which I don't think the brain will
> > always tend to the "greatest" common denominator. It's possible for a single
> > isolated sinusoids to be heard as, say 3/1 with a "virtual" pitch being
> > produced at 1/1, even though no "interval" exists. Prior exposure and
> > context can influence this.
> > 2) The phase of the sinusoids, for all intents and purposes, does not have
> > any bearing at all on the perception of the dyad. Two phase-shifted versions
> > of the same "5/4" dyad will NEVER seem to "sync up" visually, but it won't
> > matter.
> >
> > -Mike
> >
> >
> > On Wed, Feb 17, 2010 at 12:04 AM, rick <rick_ballan@> wrote:
> >
> > >
> > >
> > > Hi everyone,
> > >
> > > I'd just like to state that the approx. GCD's in the article I posted
> > > produce harmonies that are NOT revealed by Fourier analysis. That is its
> > > whole point! Since they deconstruct the intervals between sine waves upon
> > > which FA is by definition based then we cannot cite the latter as 'proof'
> > > against them, not even in principle. So please stop sending me personal
> > > emails to that effect. Thanks,
> > >
> > > -Rick
> > >
> > >
> > >
> >
>

🔗cameron <misterbobro@...>

Rick, there are some huge and glaring problems in your paper, sorry to say. Right off the bat, determining whether a third is "major or minor" is just wacky, as middle thirds are completely normal for many millions, probably easily a billion and more, people, and have been since time immemorial.

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:
>
> I forgot to mention Mike that I did try a Fourier analysis of the first cycle but got nothing spectacular. Using Mathematica 7 I isolated the first cycle of 16:19, created a continuous period function from it and then took a Fourier series. It just punched out all the harmonics with a large amplitude at 16 and 19 as expected.
>
> Rick
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> >
> > Hi Mike,
> >
> > Thanks, it means allot coming from you. I was worried about phase-shifts (you read my mind?) so it's good to know that the results are general. And yes I agree that we don't want too much from a music 'theory' because prior experience, context etc...is where the art must come in. I also figured that there still would be certain aspects of virtual pitch which are separate from what I'm talking about and the distinction would come out eventually.
> >
> > Now I'm not sure how to proceed via the frequency domain yet quite simply because there seem to be other cycles in the wave which I don't understand. 16:19 for eg has 5:6 on either side and 6:7 in the middle with a phase shift of the average frequency?? Yet other intervals give other results. I'll just plod away as I always do and hope that something jumps out eventually. In the meantime, I don't feel so lonely now knowing that others are working along similar lines. Thanks for letting me know.
> >
> > Rick
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > Rick,
> > >
> > > I just gave your article a quick skim and contrary to our prior
> > > disagreements, I think it looks very good.
> > >
> > > You're approaching this problem from a "time domain" perspective rather than
> > > a "frequency domain" perspective; the former seems to be the direction that
> > > a lot of the latest research on this is going. Furthermore, I think that if
> > > you were to reformulate your ideas in a "frequency domain" perspective, I
> > > think you'd find that you're saying a lot of the same things that many here
> > > have been saying as well, but in a different way.
> > >
> > > In general I think your ideas are pretty solid here, with a few things to
> > > consider:
> > >
> > > 1) There are a few special cases in which I don't think the brain will
> > > always tend to the "greatest" common denominator. It's possible for a single
> > > isolated sinusoids to be heard as, say 3/1 with a "virtual" pitch being
> > > produced at 1/1, even though no "interval" exists. Prior exposure and
> > > context can influence this.
> > > 2) The phase of the sinusoids, for all intents and purposes, does not have
> > > any bearing at all on the perception of the dyad. Two phase-shifted versions
> > > of the same "5/4" dyad will NEVER seem to "sync up" visually, but it won't
> > > matter.
> > >
> > > -Mike
> > >
> > >
> > > On Wed, Feb 17, 2010 at 12:04 AM, rick <rick_ballan@> wrote:
> > >
> > > >
> > > >
> > > > Hi everyone,
> > > >
> > > > I'd just like to state that the approx. GCD's in the article I posted
> > > > produce harmonies that are NOT revealed by Fourier analysis. That is its
> > > > whole point! Since they deconstruct the intervals between sine waves upon
> > > > which FA is by definition based then we cannot cite the latter as 'proof'
> > > > against them, not even in principle. So please stop sending me personal
> > > > emails to that effect. Thanks,
> > > >
> > > > -Rick
> > > >
> > > >
> > > >
> > >
> >
>

🔗rick <rick_ballan@...>

Thanks Cameron,

But these are just familiar examples used to introduce a mathematical model. You are quite welcome to choose any of these middle thirds as your initial 'a' and 'b'. The example of interval matching is just that, an example. The main game is that given any pair of sine waves then the mathematical solution between the time of the first maxima and the next will always be T = (a + b)/(p + q), where 'p' and 'q' are whole-numbers which need to be determined for each unique interval. I'm counting on the fact that people like you will take it to heights that I never imagined.

-Rick

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
> Rick, there are some huge and glaring problems in your paper, sorry to say. Right off the bat, determining whether a third is "major or minor" is just wacky, as middle thirds are completely normal for many millions, probably easily a billion and more, people, and have been since time immemorial.
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> >
> > I forgot to mention Mike that I did try a Fourier analysis of the first cycle but got nothing spectacular. Using Mathematica 7 I isolated the first cycle of 16:19, created a continuous period function from it and then took a Fourier series. It just punched out all the harmonics with a large amplitude at 16 and 19 as expected.
> >
> > Rick
> >
> > --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> > >
> > > Hi Mike,
> > >
> > > Thanks, it means allot coming from you. I was worried about phase-shifts (you read my mind?) so it's good to know that the results are general. And yes I agree that we don't want too much from a music 'theory' because prior experience, context etc...is where the art must come in. I also figured that there still would be certain aspects of virtual pitch which are separate from what I'm talking about and the distinction would come out eventually.
> > >
> > > Now I'm not sure how to proceed via the frequency domain yet quite simply because there seem to be other cycles in the wave which I don't understand. 16:19 for eg has 5:6 on either side and 6:7 in the middle with a phase shift of the average frequency?? Yet other intervals give other results. I'll just plod away as I always do and hope that something jumps out eventually. In the meantime, I don't feel so lonely now knowing that others are working along similar lines. Thanks for letting me know.
> > >
> > > Rick
> > >
> > > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > > >
> > > > Rick,
> > > >
> > > > I just gave your article a quick skim and contrary to our prior
> > > > disagreements, I think it looks very good.
> > > >
> > > > You're approaching this problem from a "time domain" perspective rather than
> > > > a "frequency domain" perspective; the former seems to be the direction that
> > > > a lot of the latest research on this is going. Furthermore, I think that if
> > > > you were to reformulate your ideas in a "frequency domain" perspective, I
> > > > think you'd find that you're saying a lot of the same things that many here
> > > > have been saying as well, but in a different way.
> > > >
> > > > In general I think your ideas are pretty solid here, with a few things to
> > > > consider:
> > > >
> > > > 1) There are a few special cases in which I don't think the brain will
> > > > always tend to the "greatest" common denominator. It's possible for a single
> > > > isolated sinusoids to be heard as, say 3/1 with a "virtual" pitch being
> > > > produced at 1/1, even though no "interval" exists. Prior exposure and
> > > > context can influence this.
> > > > 2) The phase of the sinusoids, for all intents and purposes, does not have
> > > > any bearing at all on the perception of the dyad. Two phase-shifted versions
> > > > of the same "5/4" dyad will NEVER seem to "sync up" visually, but it won't
> > > > matter.
> > > >
> > > > -Mike
> > > >
> > > >
> > > > On Wed, Feb 17, 2010 at 12:04 AM, rick <rick_ballan@> wrote:
> > > >
> > > > >
> > > > >
> > > > > Hi everyone,
> > > > >
> > > > > I'd just like to state that the approx. GCD's in the article I posted
> > > > > produce harmonies that are NOT revealed by Fourier analysis. That is its
> > > > > whole point! Since they deconstruct the intervals between sine waves upon
> > > > > which FA is by definition based then we cannot cite the latter as 'proof'
> > > > > against them, not even in principle. So please stop sending me personal
> > > > > emails to that effect. Thanks,
> > > > >
> > > > > -Rick
> > > > >
> > > > >
> > > > >
> > > >
> > >
> >
>

🔗rick <rick_ballan@...>

Actually Cam there is one other possibility that you're missing about the paper. It's that the frequency spectrum becomes more continuous and less discernible the higher we go. No-one would mistake a fifth as 2:3 with a fourth as 3:4. But what about 100:101 against 101:102 etc...? So there are certain advantages in having a mathematically rigorous method of 'mapping' non-sequential large numbered ratios to the lower ones. And given that there are an infinite amount of possible ratios we need at least some guidelines. And why go only SO far? There is in principle an uncountably infinite number of these "middle thirds". Is it 'closed-minded' of us to select some and not others? Of course not. Hardly "batty" of me.

-Rick.

NOT Fourier Analysis!

🔗rick <rick_ballan@...>

🔗Michael <djtrancendance@...>

🔗rick <rick_ballan@...>

🔗Mike Battaglia <battaglia01@...>

🔗rick <rick_ballan@...>

🔗rick <rick_ballan@...>

🔗cameron <misterbobro@...>

🔗rick <rick_ballan@...>

🔗rick <rick_ballan@...>