hi George,

good to be back in contact with you.

i proposed my "C" standards in the interests

of mathematical simplicity, and still stand by

them because of that reason. it doesn't get

much simpler than C n^0 = 1 Hz.

-monz

"all roads lead to n^0"

----- Original Message -----

From: "gdsecor" <gdsecor@yahoo.com>

To: <tuning-math@yahoogroups.com>

Sent: Friday, September 20, 2002 8:10 AM

Subject: [tuning-math] Re: A common notation for JI and ETs

> --- In tuning-math@y..., "monz" <monz@a...> wrote:

> > hi Gene,

> >

> > > From: "Gene Ward Smith" <genewardsmith@j...>

> > > To: <tuning-math@y...>

> > > Sent: Thursday, September 19, 2002 9:28 PM

> > > Subject: [tuning-math] Re: A common notation for JI and ETs

> > >

> > > --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote:

> > > > --- In tuning-math@y..., David C Keenan <d.keenan@u...> wrote

> > >

> > > > An irrational-number frequency as a tuning standard?

> > > > I thought that we could do better than that.

> > >

> > > If simplicity is what you want, I suggest the Verdi

> > > middle C of 256 Hz, beloved of physics teachers.

> > > Why do you need a tuning standard, BTW?

> >

> > i'm interested in this "Verdi middle C" of which you speak.

> > can you please give more details? (who's Verdi?)

> >

> > i too proposed a middle-C of 256 Hz = n^0 (= 1/1) as one of

> > two alternates for a reference frequency, in the original

> > paper i wrote about my notational system:

> >

> > http://www.ixpres.com/interval/monzo/article/article.htm#reference

> >

> > the other alternative was C n^0 = 1 Hz, which still gives

> > a middle-C of 256 Hz, but in this case middle-C = n^8. this

> > reference has been adopted by a few other microtonalists

> > (a couple of whom wrote to me to say so).

> >

> > i can't really give an answer as to why a reference is needed ...

> > just seemed the right thing to do to me.

>

> You guys didn't get my statement in its complete context. The

> problem that we discussed involves notating some ETs as subsets of

> others, in which case their native fifths might not be notated as

> such. It would therefore be necessary to specify which natural note

> would be kept, since all of the other tones related to it by native

> fifths would be modified by symbols from the superset ET. Hence the

> notation for the subset ET would probably not contain any natural

> note other than the one chosen.

>

> Dave proposed that "D" be the standard natural note for any and all

> of these. I then observed that most pitch standards are geared

> to "A" or "C" and that there might be some difficulty arriving at an

> appropriate pitch standard for D.

>

> So your comments, while well-intentioned, do not address the problem.

>

> In response to your comments, C=256 would be fine if we were still in

> a previous century when the prevailing musical pitch was close to

> that, but the forces of evil have driven it progressively higher.

>

> In the 1970s there was an unofficial consensus of C=264 among most of

> the microtonalists that I was in contact with. This is a 3:5

> relationship with A=440, and all of the frequencies of a "just" C

> major scale starting on 264 are integers, which would make it easy to

> present in a music theory class.

>

> --George

>

>

>

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>

>

>

> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

>

>

--- In tuning-math@y..., "monz" <monz@a...> wrote:

> hi George,

>

>

> good to be back in contact with you.

Likewise.

> i proposed my "C" standards in the interests

> of mathematical simplicity, and still stand by

> them because of that reason. it doesn't get

> much simpler than C n^0 = 1 Hz.

And how does that translate into a pitch standard for ETs (including

12-ET)?

--George

hi George,

> From: "gdsecor" <gdsecor@yahoo.com>

> To: <tuning-math@yahoogroups.com>

> Sent: Monday, September 23, 2002 11:32 AM

> Subject: [tuning-math] Re: a reference pitch

> (was: A common notation for JI and ETs)

>

>

> --- In tuning-math@y..., "monz" <monz@a...> wrote:

> > hi George,

> >

> >

> > good to be back in contact with you.

>

> Likewise.

>

> > i proposed my "C" standards in the interests

> > of mathematical simplicity, and still stand by

> > them because of that reason. it doesn't get

> > much simpler than C n^0 = 1 Hz.

>

> And how does that translate into a pitch standard for ETs

> (including 12-ET)?

>

> --George

umm ... well ... it only means that "middle-C" is 256 Hz.

this would make the 12edo "A" = ~430.5 Hz.

it was just my thinking that since this is not too far

off from most of the pitch-standards already in use today,

it makes more sense as a basis from a logical point of view.

we commonly use "C" as the reference anyway instead of "A",

so why not simply equate it with 1 Hz?

-monz

"all roads lead to n^0"

--- In tuning-math@y..., "monz" <monz@a...> wrote:

> > From: "gdsecor" <gdsecor@y...>

> > --- In tuning-math@y..., "monz" <monz@a...> wrote:

> > > i proposed my "C" standards in the interests

> > > of mathematical simplicity, and still stand by

> > > them because of that reason. it doesn't get

> > > much simpler than C n^0 = 1 Hz.

> >

> > And how does that translate into a pitch standard for ETs

> > (including 12-ET)?

> >

> > --George

>

> umm ... well ... it only means that "middle-C" is 256 Hz.

> this would make the 12edo "A" = ~430.5 Hz.

>

> it was just my thinking that since this is not too far

> off from most of the pitch-standards already in use today,

> it makes more sense as a basis from a logical point of view.

> we commonly use "C" as the reference anyway instead of "A",

> so why not simply equate it with 1 Hz?

>

> -monz

> "all roads lead to n^0"

The two main obstacles are 1) getting wind instruments to play in

tune and 2) getting others to accept this. I have a feeling that the

second one is the more formidable obstacle.

--George