Re: [tuning] Digest Number 3455 - Reply to Monz - re: granularity of 88edo - combing your hares

Quote from Monz.
<start>
so, with that out of the way ... now i must address
the fact that your calculations of the "granularity"
of 88-edo misrepresent how closely it approximates
LucyTuning.

the *maximum* amount of error of "any 88 edo interval
is + or - 6.818182 cents from any chosen interval" --
but it's totally incorrect to state that "any 88edo
interval *is* + or - 6.818182 cents from any chosen
interval".

in fact, even a 101-tone LucyTuning chain of 5ths will
*still* present less than 2 cents error from 88edo.
i'm not trying to make any enemies here, Charles, but
i've said it before, and apparently you find it hard
to believe, so here's the (long) proof:

generator . LucyTuning ... 88-edo ......... error

.. 50 .. 1174.648293 .. 1172.727273 ... - 1.92102003
<end>

Yes I agree with your calculations, yet not with your "totally incorrect", and philosophical perspective.

Lucy says:
<the *maximum* amount of error of "any 88 edo interval
is + or - 6.818182 cents from any chosen interval" -->
Monz says:
<but it's totally incorrect to state that "any 88edo
interval *is* + or - 6.818182 cents from any chosen
interval".>

My point here was to criticise the inherent granularity of 88edo.

My use of "any chosen interval" said nothing about the "chosen interval" being from any specific tuning system.
I was emphasising the limitation of having a set number of intervals per octave.
Maybe I should have used the word "random" or "chance".
What I stated was/is entirely correct.

"The greater the distance between the teeth of your comb (rake?); the fewer the hairs (hares?) you are likely to catch."

--- In tuning@yahoogroups.com, Charles Lucy <lucy@h...> wrote:
> "The greater the distance between the teeth of your comb (rake?); the
> fewer the hairs (hares?) you are likely to catch."

Then again, you could place the teeth so close together that you risk
yanking out big swatches of hair. At this point in my life, I don't
need that kind of worry. Which is one of the philosophical reasons I
just laugh at all these many-hundreds-of-steps tunings!

Cheers,
Jon

hi Charles,

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

> My point here was to criticise the inherent granularity
> of 88edo.
>
> My use of "any chosen interval" said nothing about the
> "chosen interval" being from any specific tuning system.
> I was emphasising the limitation of having a set number
> of intervals per octave.
> Maybe I should have used the word "random" or "chance".
> What I stated was/is entirely correct.
>
> "The greater the distance between the teeth of your comb
> (rake?); the fewer the hairs (hares?) you are likely to catch."

i understand what you're saying about the granularity of
88-edo, and also about the philosophical difference between
Harrison's conception (and presumably yours) of LucyTuning.

but i fail to see the point of your "criticism", because
in most cases a musician is not going to use more than
say a 19 or 31 note subset of either 88-edo or LucyTuning,
and if that's the case, there won't be any real audible
difference between the two.

as i point out on my webpage, a 31-tone chain of 88-edo
exhibits only a little more than a 1/2-cent error from
the same chain in LucyTuning. for a 19-tone chain, the
error is little more than 1/3-cent.

philosopical difference, yes.
mathematical difference, yes.
audible difference, no.

and thanks for the link to Harrison's description of
the tuning. that's exactly what i wanted from you.

-monz

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

very strange ... Yahoo posted two copies of my post.
i deleted the second one.

-monz

I already gave examples of maqams that require 41 or 53 tones including modulations. I would never object to instances of higher granularity.

----- Original Message -----
From: Kraig Grady
To: tuning@yahoogroups.com
Sent: 24 Mart 2005 Perşembe 20:19
Subject: [tuning] Re: Digest Number 3455 - Reply to Monz - re: granularity of 88edo - combing your hares

I fine such arguments dangerous and resembles the one that put mircotonality back maybe 50 years. being the one that 1.5 cents no one is going to note the difference of which gave us 768. the worst , most unusable piece of ________ one can have. throws all types of beats that override the very tuning one wishes to hear. just throw it in the trash folks, there is no way you can use it and have any idea what it is you are tuning.
It is also dangerous that no one will use more than 31 or 19 tones. Someone like Dan Sterns might use that many at once