Yahoo Tuning Groups Ultimate Backup tuning the 'official' Harmonic Entropy webpage

> [Paul Erlich, TD 297.1]
>
> Glen wrote,
>
>> I am slowly making my way through "on Harmonic Entropy by
>> Paul Erlich"
>>
>> http://www.uq.net.au/~zzdkeena/Erlich/index.htm
>>
>> [...]
>
>> Here are some quotes from the site with my comments:
>>
>>> "Recent speculation among tuning theorists has raised the
>>> idea that consonance and dissonance may actually be two
>>> separate and not mutually-exclusive dimensions of sonance.
>>> I have extrapolated this to the idea that each prime may in
>>> fact be responsible for a separate dimension of sonance that
>>> does not necessarily exclude any of the others."
>>
>> What about saying each odd factor instead of each prime?
>> I have found in my experiments that n/3 will be consonant with
>> n/6 and n/9, but n/6 and n/9 are not so consonant with each
>> other. All are related by a factor 3, but the relationship
>> doesn't carry over between 2*3 and 3*3.
>
>
> I totally agree and would say "odd" where Joe Monzo said
> "prime". Unfortunately it is not so clear on the site which is
> my original text and which is Joe's commentary. Joe, perhaps it
> would be helpful to put the initials of the author in front of
> each paragraph?

I would continue to say 'prime', and add that 'odd' may also
be admissible as yet another 'separate dimension of sonance that
does not necessarily exclude any of the others'.

While Paul Erlich maintains that odd-limits are a more important
consideration in tuning than prime-limits, he himself has
admitted that primes do form a separate 'dimension' in tuning,
in that each one has a unique sound that is required for
tuning even when one is concerned mainly with thinking in
terms of odd-limits, that is, including composites (i.e.,
non-prime odds) as delimiters.

The fact that this is true is why I speak of primes as possibly
constituting the separate dimensions of sonance. Intervals
that are measured as composite odd ratios are ultimately
reducible aurally to their constituent primes.

(This is not to argue the merits of thinking in terms of
odd-limits when composing, performing, or listening.)

As far as making clear on the webpage what is original with
Paul Erlich and what is added commentary by me, Paul's original
postings are indented and appear in Times New Roman font,
where my commentary starts at the margin and appears in
the more modern-looking Arial font. I try to make this a
standard procedure when quoting someone else's material.

The URL being tossed around for the Harmonic Entropy webpage
is an old and outdated one. The 'official' address for the
Harmonic Entropy page is:

http://www.ixpres.com/interval/td/erlich/entropy.htm

I have added the information about the fonts at the beginning,
and have finally included the graphs that were on Dave Keenan's
page but were missing from mine.

There is also a link to the unedited original text of the
postings by Paul Erlich.

Many thanks to Dave for graciously hosting this page when I
had FTP problems in the the spring, and even more for his
patience with me while I took so long to update my site.
Dave, you can now delete those files. Anyone who had the
Dave Keenan address bookmarked for Harmonic Entropy should
replace it with the one given above. Any future updates will
be done at that URL.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

___________________________________________________________________
Get the Internet just the way you want it.
Free software, free e-mail, and free Internet access for a month!
Try Juno Web: http://dl.www.juno.com/dynoget/tagj.

> [Paul Erlich, TD 301.2]
>
> Joe Monzo wrote,
>
>> The URL being tossed around for the Harmonic Entropy webpage
>> is an old and outdated one. The 'official' address for the
>> Harmonic Entropy page is:
>>
>> http://www.ixpres.com/interval/td/erlich/entropy.htm
>>
>> I have added the information about the fonts at the beginning,
>> and have finally included the graphs that were on Dave Keenan's
>> page but were missing from mine.
>
> Thanks, Joe. Maybe the best way to clarify would be to change
> the "by Paul Erlich" on the second line to "by Joe Monzo and
> Paul Erlich"?

Well... OK, if that's how *you* really want it. :)

Since my commentary is based on what you told me face-to-face,
I really felt that your name should be the one getting the credit.
But the whole Harmonic Entropy idea is your baby; whatever you
prefer is OK with me.

-monz

the 'official' Harmonic Entropy webpage

🔗Joe Monzo <monz@xxxx.xxxx>

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

🔗Joe Monzo <monz@xxxx.xxxx>

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

🔗Joe Monzo <monz@xxxx.xxxx>