Re: [tuning] Digest Number 3453 - Sources of Harrison tuning system - something wrong here?

On 21 Mar 2005, at 14:56, tuning@yahoogroups.com wrote:
>
>
> 1. LucyTuning and 88-edo (was: History of 50 equal)
> From: "monz" <monz@tonalsoft.com>
>
> Message: 1
> Date: Sun, 20 Mar 2005 15:39:16 -0000
> From: "monz" <monz@tonalsoft.com>
> Subject: LucyTuning and 88-edo (was: History of 50 equal)
>
>
> hi Gene,
>
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
>> Another tidbit from Jorgensen is that he deciphers
>> Harrison in the same way as Lucy does, with a fifth of
>> 600+300/pi cents; his cited source being the same,
>> Smith's _Harmonics_.

Something's wrong here Monz,
Smith and Harrison were "enemies"; judging by what Harrison wrote about the clergy and academics.

Smith wrote "Harmonics", which as far as I remember was in the British Library.

My source of Harrison info. was his book "Concerning Such Mechanism........", which I found in the ClockMakers Library under the Guildhall in the City of London.
Transcript is here:
http://www.lucytune.com/academic/csm_transcription.html

New Scientist published my letter about the "found missing" final manuscript.

http://www.newscientist.com/article.ns?id=mg18524911.100

and I have rec'd a few responses, one very interesting from the bell tuner at Eayre and Smith Ltd

http://www.eayreandsmith.co.uk/

>
>
> i mention on my webpage that LucyTuning resembles
> 88-edo and 3/10-comma meantone:

Approximately correct, but to my mind misses the point.

1. 88 edo is circular
2. The maths of 3/10 comma is derived from integer frequency ratios logic.

Neither of which accurately describes what Harrison derived from pi.

>
> http://tonalsoft.com/enc/lucy.htm
>
>
>
> -monz
>
>
Charles Lucy - lucy@harmonics.com
------------ Promoting global harmony through LucyTuning -------
for information on LucyTuning go to: http://www.lucytune.com
for LucyTuned Lullabies go to http://www.lullabies.co.uk
Buy/download/CD from: http://www.cdbaby.com/cd/lucytuned2

hi Charles (and Gene),

--- In tuning@yahoogroups.com, Charles Lucy <lucy@h...> wrote:

> > Message: 1
> > Date: Sun, 20 Mar 2005 15:39:16 -0000
> > From: "monz" <monz@t...>
> > Subject: LucyTuning and 88-edo (was: History of 50 equal)
> >
> >
> > hi Gene,
> >
> >
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> >
> >> Another tidbit from Jorgensen is that he deciphers
> >> Harrison in the same way as Lucy does, with a fifth of
> >> 600+300/pi cents; his cited source being the same,
> >> Smith's _Harmonics_.
>
> Something's wrong here Monz, Smith and Harrison were
> "enemies"; judging by what Harrison wrote about
> the clergy and academics.

you quoted my post, but that bit is me quoting Gene ...

> > i mention on my webpage that LucyTuning resembles
> > 88-edo and 3/10-comma meantone:
>
> Approximately correct, but to my mind misses the point.
>
> 1. 88 edo is circular
> 2. The maths of 3/10 comma is derived from integer
> frequency ratios logic.
>
> Neither of which accurately describes what Harrison
> derived from pi.

yes, you're right ... in the new version of "LucyTuning"
which will appear when i'm finished converting the
Tonalsoft Encyclopedia, i'll add a statement to that
effect.

however, would you be so kind as to post here exactly
*why* my equivocations of Harrison/LucyTuning to 88-edo
and 3/10-comma meantone do not "accurately describe
what Harrison derived from pi"? i'd like to add *that*
to the updated Encyclopedia entry, but i'm simply too busy
now to dig deeply into Harrison's writings. thanks.

-monz

--- In tuning@yahoogroups.com, Charles Lucy <lucy@h...> wrote:

> My source of Harrison info. was his book "Concerning Such
> Mechanism........", which I found in the ClockMakers Library under the
> Guildhall in the City of London.
> Transcript is here:
> http://www.lucytune.com/academic/csm_transcription.html

Ah; I thought you'd found in Harmonics, which is what Jorgensen cites.
Jorgensen writes "Robert Smith's own temperament of 1749 was more
practicable to tune than was Harrison's, and it was an almost exact
compromise between the Harrison and Aaron [1/4-comma meantone]
meantone temperaments: \sqrt(1.49441151 x 1.49534872) = 1.49488072."
The value he gives for Harrison's fifth is the Lucy-tuned fifth, and
he cites Harmonics, where Smith does mention Harrison, as his source.

Incidentally, another Smith idea is using a fifth of 643/430 in the
place of 1/4-comma and counting beats; in general if this was a
consideration you can replace an irrational fifth with a nearby
rational one. How well this would actually work in practice I have no
idea.

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> however, would you be so kind as to post here exactly
> *why* my equivocations of Harrison/LucyTuning to 88-edo
> and 3/10-comma meantone do not "accurately describe
> what Harrison derived from pi"?

They don't exactly describe Harrison's tuning, because the fifth is
very slightly different. Harrison's fifth is, precisely, 600+300/pi
cents. A fifth 3/10 comma flat is 0.0104813... cents sharper than
this, and an 88-et meantone fifth (as opposed to the one it shares
with 22) is 0.0384204... cents flatter. Hence both are accurate, but
not exact. If you want to go totally overboard, 2^(823/1420) is
8.108658 x 10^(-4) cents flatter.