Yahoo Tuning Groups Ultimate Backup tuning-math Re:John Farey's 1806 middel-unit 3^37/25/2^54, rediscovered as "Monz

--- In tuning-math@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> pi for musical tunings, which predate John 'Longitude' Harrison
> ( 1760's) in your historical researches.

hi Charles,
irrational proportions appear to be introduced
into the history of musical tunings in ancient china:

http://www.jstor.org/view/00043648/sp050043/05x1014z/0
"Which other conceivable motive could the artisan have for neatly
deforming a well-turned circular disk, except the musical tuning of
the Pi?"
Especially referring to
http://en.wikipedia.org/wiki/Zhu_Zaiyu
especially
http://links.jstor.org/sici?sici=0004-3648(1953)16%3A1%2F2%3C25%3ATMSOAC%3E2.0.CO%3B2-Z
p.48
"This interpretation of the sgmented 'PI-disk'...
...but was not understand by Prince Chu Tsai Yu..."

His 2^(1/12)semitone was then overtaken by Simon Stevin:
http://www.xs4all.nl/~huygensf/doc/singe.html

http://en.wikipedia.org/wiki/Pi
approximates the ratio inbetween
the 7th and octaved 11th partials:
http://en.wikipedia.org/wiki/Proof_that_22/7_exceeds_%CF%80

Why do you prefer to approximate rationals by irrationals?
I peronally see no need for that.

Yours Sincerely
A.S.

🔗Graham Breed <gbreed@gmail.com>

Andreas Sparschuh wrote:

> irrational proportions appear to be introduced > into the history of musical tunings in ancient china:
> > http://www.jstor.org/view/00043648/sp050043/05x1014z/0
> "Which other conceivable motive could the artisan have for neatly
> deforming a well-turned circular disk, except the musical tuning of
> the Pi?"

That page only gets me to the JSTOR home page with login options that I don't think will help me.

> Especially referring to
> http://en.wikipedia.org/wiki/Zhu_Zaiyu
> especially
> http://links.jstor.org/sici?sici=0004-3648(1953)16%3A1%2F2%3C25%3ATMSOAC%3E2.0.CO%3B2-Z
> p.48
> "This interpretation of the sgmented 'PI-disk'...
> ...but was not understand by Prince Chu Tsai Yu..."

Right, so it's pi disk or 璧(bi). Nothing to do with the number pi. At least from the front page that they let me see. So is this anything to do with 3.141592... or are you talking pi hua?

Here's a pi disk:

http://baike.baidu.com/view/487681.htm

And there appears to be a Wikipedia page:

http://zh.wikipedia.org/wiki/%E7%92%A7

I don't know if it'll help you. I can't reach it. There are plenty of links in Google.

> His 2^(1/12)semitone was then overtaken by Simon Stevin:
> http://www.xs4all.nl/~huygensf/doc/singe.html

Oh, we know about the calculation of equal temperament. But it wasn't found useful in practice.

Graham

🔗Charles Lucy <lucy@harmonics.com>

Thank you for the references Andreas and Graham.

>Why do you prefer to approximate rationals by irrationals?
>I peronally see no need for that.

>Yours Sincerely
>A.S.

I suppose if one is considering tunings from a strictly J.I. point of
view, one might find my approach to the arithmetic of musical tuning
to be somewhat alien.

[Although using irrational numbers as a mathematical starting point
for tunings does have the distinct advantage of tending to avoid J.I.
reruns.]

(pi (π) and phi (1+(5)^(1/2)/2, and e seem to date to have been the
most fruitful irrationals for musical tuning.

see this page and others for more info:

http://en.wikipedia.org/wiki/Irrational_number

I am sad to read that A.S. does not appreciate why I reject the
musical intervals generated by integer frequency ratios as a basis for
musical tuning.

Anyone who has followed tuning research as over the past quarter of a
century, as I have, and who has subscribed to tuning lists since
shortly after their inception, will have noticed that the majority of
the discussions in the tuning community centre around integer
frequency ratios.

These "landmarks" (as I consider them) have been and continue to be
used by many contributors as "Tuning Gospel" for various purposes:

1) To explain beating between diverse frequencies, which, I believe,
almost everyone can hear, appreciate, generally agree upon.

As frequencies approach an integer frequency ratio, beat frequencies
slow, and when at exact ratios are observably zero.
This is audibly obvious when the ratios approach unison or octaves
i.e. 1:1, 2:1, 4:1, 8:1, etc.
The beating (or lack of it) becomes progressively less blatantly
apparent when the integers increase e.g. 3:2, 4:3, 5:2, 5:3,
5:4,....... etc.
Nevertheless integer ratios "are supposed to" exhibit zero beating.

[I always expect noise from the usual tunanik dissenters, although I
doubt that even my most severe critics will find this "purpose"
particularly controversial.]

2) To judge the validity of any tuning system. Integer frequency
ratios are the only basis from which musical intervals should be
selected and evaluated;

i.e. if an interval has zero beating it is a "perfect" interval.

This seems to be the perspective from which A.S. is asking his
question, and assumes that "Good" tunings should be "Just". There are
Gb's of text in the tuning archives "judging"/evaluating various
musical intervals and tunings by how closely they conform to JI
principles.

3) To devise musical intervals and tunings with the aim of minimising
beating.

I choose to use and advocate the use of pi, as I believe that beating
is inevitable and desirable in musical tuning, and it enables me to
use a system which conforms to the general rules of Western harmony,
can be considered as a "meantone-type", or an equal interval tuning
(88edo or 1420edo), dependent upon your point of view and level of
precision.

Anyone who has looked at the literature of tuning will be familiar
with the paradoxes found in the use of only
Just intervals as a basis of selecting interval and tunings.

They are well documented in many places: lemmas,

e.g. "Should four fourth plus one third equal an octave?" etc.

http://www.lucytune.com/tuning/just_intonation.html

As far as I am concerned, JI is an old horse that has been "beaten" to
death. Time to make music. (A requiem for JI?)

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

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🔗monz <joemonz@yahoo.com>

🔗Carl Lumma <carl@lumma.org>

🔗Graham Breed <gbreed@gmail.com>

monz wrote:

> JSTOR's generous license allows *any* visitor to an
> institution which has a JSTOR account (i.e., a library)
> to access the complete articles.

So how is that generous on the part of JSTOR? The institutions have to pay for that access. From what I know of academic pricing, they probably have to pay a great deal (for articles the authors paid to have published of course). That ensures that only rich institutions can afford it and the institute I live and work at isn't one of them. Sure, there may be a way, but it isn't simple enough when the chances are the article's completely irrelevant anyway. (Probably mentions a Chinese word transliterated as "pi" and not the Greek letter pi.)

I'm sure there are generous institutions that allow the public to share the JSTOR access they paid for. If there's one in your city have fun with it!

Graham

Re:John Farey's 1806 middel-unit 3^37/25/2^54, rediscovered as "Monz

🔗Charles Lucy <lucy@harmonics.com>

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

🔗Graham Breed <gbreed@gmail.com>

🔗Charles Lucy <lucy@harmonics.com>

🔗monz <joemonz@yahoo.com>

🔗Carl Lumma <carl@lumma.org>

🔗Graham Breed <gbreed@gmail.com>