a reference pitch (was: A common notation for JI and ETs)

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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>

--- 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