Harrison Temperament (Jorgensen Book)

I've been going through "Tuning the Historical Temperaments By Ear"
(Jorgensen 1977), trying out tunings on my Zuckerman Virginal.

There are two tunings which mention "Harrison":

"Tuning the Theoretically Correct Harrison 3/10 Syntonic Comma
Meantone Temperament in the Acoustic Tonality of C Major and A Minor"
(pg. 149)

and:

"Tuning the Theoretically Correct Well Tempered Version of the
Harrison Temperament in the Acoustic Tonality of C Major" (pg. 291)

Does anyone have any references explaining who this
particular "Harrison" is? There's no cross reference I can find in
the book.

I've been slugging through the archives at:
/tuning/ but it's slow going.

Thanks.

toyoji@mills.edu

Hello!

>I've been going through "Tuning the Historical Temperaments By Ear"
>(Jorgensen 1977), trying out tunings on my Zuckerman Virginal.
>
>There are two tunings which mention "Harrison":
>
>"Tuning the Theoretically Correct Harrison 3/10 Syntonic Comma
>Meantone Temperament in the Acoustic Tonality of C Major and A Minor"
>(pg. 149)
>
>and:
>
>"Tuning the Theoretically Correct Well Tempered Version of the
>Harrison Temperament in the Acoustic Tonality of C Major" (pg. 291)
>
>Does anyone have any references explaining who this
>particular "Harrison" is? There's no cross reference I can find in
>the book.

I wonder if this is John "Longitude" Harrison? 3/10 is fairly
close to pi, and 3/10th syntonic comma is about right for LucyTuning.

>I've been slugging through the archives at:
>/tuning/ but it's slow going.

Be sure to ask whatever questions you have!

-Carl

hi toyoji and Carl,

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> > [toyoji:]
> >
> > I've been going through "Tuning the Historical
> > Temperaments By Ear" (Jorgensen 1977), trying out
> > tunings on my Zuckerman Virginal.
> >
> > There are two tunings which mention "Harrison":
> >
> > "Tuning the Theoretically Correct Harrison 3/10
> > Syntonic Comma Meantone Temperament in the Acoustic
> > Tonality of C Major and A Minor" (pg. 149)
> >
> > and:
> >
> > "Tuning the Theoretically Correct Well Tempered Version
> > of the Harrison Temperament in the Acoustic Tonality of
> > C Major" (pg. 291)
> >
> > Does anyone have any references explaining who this
> > particular "Harrison" is? There's no cross reference
> > I can find in the book.
>
> I wonder if this is John "Longitude" Harrison? 3/10 is
> fairly close to pi, and 3/10th syntonic comma is about
> right for LucyTuning.

yes, it is John "Longitude" Harrison. 3/10-comma meantone
is audibly indistinguishable from the pi-based tuning now
known as LucyTuning. see:

http://tonalsoft.com/enc/lucy.htm

(i've been having trouble accessing my own webpages today
... hopefully it's just a short-term server problem.)

-monz

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> I wonder if this is John "Longitude" Harrison?

Yes, it is.

> 3/10 is fairly
> close to pi,

It isn't, and though 3/10 fairly close to 1/pi,
LucyTuning/HarrisonTuning is not defined as (nor is it equal to) 1/pi-
comma meantone (which has fifths of 695.11 cents), if that's what you
had in mind.

> and 3/10th syntonic comma is about right for LucyTuning.

Yes, LucyTuning/HarrisonTuning is defined such that the major third
is 1/pi octave (logarithmically, of course). It has fifths of 695.49
cents.

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

> Yes, LucyTuning/HarrisonTuning is defined such that the major third
> is 1/pi octave (logarithmically, of course). It has fifths of
695.49
> cents.

Or 600 + 300/pi cents, to you pi fans. Why this exact value? This is
a "why a duck?" question, to which the standard answer, first given
by Groucho Marx, is "why not a duck?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
>
> > Yes, LucyTuning/HarrisonTuning is defined such that the major third
> > is 1/pi octave (logarithmically, of course). It has fifths of
> 695.49
> > cents.
>
> Or 600 + 300/pi cents, to you pi fans. Why this exact value? This is
> a "why a duck?" question, to which the standard answer, first given
> by Groucho Marx, is "why not a duck?

Of course, you might find something similar which seems better
motivated. In the neighborhood of the Lucy fifth, we find the
following meantone fifths:

69-et 695.652
Wilson 695.630
Pure 9/7's (224/9)^(1/8) 695.614
Lucy 600+300/pi 695.493
88-et 695.455

A little sharper are

Golden meantone 696.215
Woolhouse 696.165

A little flatter is

Pure 17/11 wolves (1408/17)^(1/11) 695.124