TUNING IN errors

Errors in Scott Wilkinson: "Tuning In".

page 17:
"The nearest whole number ratio for this interval (12th root of 2) is
89/84."
"The nearest whole number ratio (for 1 cent) is 1731/1730."

Nearest whole number ratios to irrational numbers do not exist.
And 1732/1731 is closer to 1 cent.

page 20:
"Great Diesis"

The name Great Diesis for the interval 125:128 can be confusing
since there is a major diesis of 648/625 that is larger. It is
generally called "minor diesis" or only "diesis".

page 40, 120:
"Art Schnitger"

Arp Schnitger

page 43:
"Christiaan Huygens, a Dutch astronomer and philosopher of the 18th
century."

He was just as much a physicist and mathematian but not really a
philosopher. He lived from 14 April 1629 to 8 July 1695, so that's in
the 17th century.

page 65:
Four values in the Pythagorean scale are wrong.

page 67:
"... the primary fifths C-G-D-A-E are tuned flat by one quarter of the
Pythagorean comma."

This must be syntonic comma. The values in the scale are calculated with
the Pythagorean comma and then still four values wrong.

page 68:
The Werckmeister scale has five incorrect values.
The Vallotti scale has six incorrect values.

page 69:
"Raising the F# by 1/6 comma (3.91 cents) ..."

That's 3.58 comma. Six false notes here too.

page 74:
17th Century here too.

page 112:
"Denielou"

Danie'lou

page 113:
"Xenharmonicon ..."

Xenharmonikon. The editor is John Chalmers again now.

page 115:
The address of Grey Matter Response is out of date.

Manuel Op de Coul coul@ezh.nl

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-------------------- Begin Original Message --------------------

Message text written by INTERNET:tuning@ella.mills.edu

">I probably ought to let Neil speak for himself, but I suspect that he
meant
>less specifically than the harmonic series itself, but JI in general.

I see no difference here. I could say, "19 consistenly represents 9-limit
JI
and 34 consistenly represents 5-limit JI," but I didn't want to start the
odd vs. prime debate on the definition of "limit" again.
"


-------------------- End Original Message --------------------

I'm not sure about 19 or 34 right off the top of my head, but there is a
difference:

Approximating the harmonic series itself forces them to be represented
relative to the fundamental of that series. Two harmonic approximations in
some equal-temperament could, for example, be way flat of the harmonics
they are closest to, but if they are nearly equally flat, then that tuning
will have a pretty good approximation to that frequency ratio, but not of
either of those harmonics.

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From: PAULE

Gary wrote,

>>>I probably ought to let Neil speak for himself, but I suspect that he
meant
>>>less specifically than the harmonic series itself, but JI in general.

I wrote,

>>I see no difference here. I could say, "19 consistenly represents 9-limit
JI
>>and 34 consistenly represents 5-limit JI," but I didn't want to start the
>>odd vs. prime debate on the definition of "limit" again.

Gary wrote,

>I'm not sure about 19 or 34 right off the top of my head, but there is a
>difference:

>Approximating the harmonic series itself forces them to be represented
>relative to the fundamental of that series. Two harmonic approximations in
>some equal-temperament could, for example, be way flat of the harmonics
>they are closest to, but if they are nearly equally flat, then that tuning
>will have a pretty good approximation to that frequency ratio, but not of

>either of those harmonics.

Gary,
Yes, you are correct. There is a difference. My comments are meaningless
with respect to a "relations between the fundamental and other members of
the harmonic series" viewpoint, but they do apply to a "small-integer-ratio"
viewpoint. So why your comment above (first quote above)?

By the way, the difference between the two viewpoints leads to two different
JI lattice constructions. The RBFAOMOHS view leads to rectangular lattices,
while the SIR viewpoint leads to triangular lattices. Exploring the
relationship between these views in 5-dimensional lattices led me to some
interesting discoveries about the tiling of 5-dimensional space with regular
hyperpolyhedra (which happen to be various Wilson CPSs from [1,3,5,7,11]).

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