72 ET

Dear All,
I'm thinking about putting together a webpage devoted to 72 ET unless
one already exists. The most important link I'm missing is Ezra Sims 72
ET notation website address. Thanks.
Rick

Rick Tagawa wrote,

>I'm thinking about putting together a webpage devoted to 72 ET unless
>one already exists. The most important link I'm missing is Ezra Sims 72
>ET notation website address. Thanks.

This site has Sims' notation but warning! it contains misinformation about
72-tET:
https://www.mindeartheart.org/micro.html

I'd love to contribute to your website an explanation and listing of the
uniquely articulated 11-limit and consistent 17-limit approximations in
72-tET.

Dear Paul,
Thanks for your interest. As a believer in carpe diem I'm responding with a
request for said articles even though I've just started assembling the page. I'd
love to see them. I'm new to the internet & website design so any input would be
appreciated. Right now the site is at
http://sites.netscape.net/ricktagawa/homepage At some point I'll change the
format & address.
RT

"Paul H. Erlich" wrote:

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> Rick Tagawa wrote,
>
> >I'm thinking about putting together a webpage devoted to 72 ET unless
> >one already exists. The most important link I'm missing is Ezra Sims 72
> >ET notation website address. Thanks.
>
> This site has Sims' notation but warning! it contains misinformation about
> 72-tET:
> https://www.mindeartheart.org/micro.html
>
> I'd love to contribute to your website an explanation and listing of the
> uniquely articulated 11-limit and consistent 17-limit approximations in
> 72-tET.
>
> --------------------------- ONElist Sponsor ----------------------------
>
> Live La Vida Loca at Amazon.com! Come browse Earth's Biggest Selection
> of Ricky Martin CDs, videos, and books! Save up to 30%.
> Check it out: <a href=" http://clickme.onelist.com/ad/amazon4 ">Click Here</a>
>
> ------------------------------------------------------------------------
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@onelist.com - subscribe to the tuning list.
> tuning-unsubscribe@onelist.com - unsubscribe from the tuning list.
> tuning-digest@onelist.com - switch your subscription to digest mode.
> tuning-normal@onelist.com - switch your subscription to normal mode.

Hi Rick,

You wrote:
>Message: 6
> Date: Sun, 27 Jun 1999 10:25:49 -0700
> From: Rick Tagawa <ricktagawa@earthlink.net>
>Subject: Re: 72 ET
>
>... I'm new to the internet & website design so any input would be
>appreciated. Right now the site is at
>http://sites.netscape.net/ricktagawa/homepage At some point I'll change the
>format & address.

As you're probably aware, your homepage messes with the alignment of
everything. If you were using straight HTML, you could fix it by
surrounding the text with "<pre>" and "</pre>" (which begins and ends
"preformatted" text).

But you're using some sort of web page "authoring tool" - whatever it is
that Netscape Site Central uses. I'll let you know if I figure out how to
fix it with Site Central.

By the way, I've been looking for a good place (i.e., free but not crappy)
to relocate my web pages. It looks like Site Central might be it. I'm
glad I tried out your site, which made me aware of Netscape's web hosting
service.

Thanks,

--Mark Nowitzky (nowitzky@alum.mit.edu, AKA tuning-owner@onelist.com)

+------------------------------------------------------+
| Mark Nowitzky |
| email: nowitzky@alum.mit.edu AIM: Nowitzky |
| www: http://www.pacificnet.net/~nowitzky |
| "If you haven't visited Mark Nowitzky's home |
| page recently, you haven't missed much..." |
+------------------------------------------------------+
________________________________________________________
NetZero - We believe in a FREE Internet. Shouldn't you?
Get your FREE Internet Access and Email at
http://www.netzero.net/download/index.html

Rick -- let me know if this is to your liking. Depending on the level of
difficulty and amount of detail of your webpage, this can be adjusted
accordingly:

This table shows which 72-tET intervals best approximate the just ratios of
the 17-limit within half an octave. "17-limit" here means the largest odd
factor of either of the numbers forming the ratio does not exceed 17, as in
Harry Partch's Tonality Diamonds. Intervals larger than half an octave are
easily calculated: for example, 7:4 is an octave minus 8:7, so it's 72 - 14
= 58 steps.

The table shows that all 11-limit ratios are represented uniquely; that is,
no 72-tET interval has to represent more than one of them. What the table
does not show is that the maximum error of the 72-tET approximations of the
11-limit ratios is 4 cents. The lowest ET that improves on that is 118-tET
where the largest error is 3 cents.

72-tET is consistent through the 17-limit. To explain what this means, let
me show why 72-tET is not consistent in the 19-limit. In 72-tET, the best
approximation of 13:8 is 50 steps, the best approximation of 19:8 is 90
steps, and the best approximation of 19:13 is 39 steps. That means that if
you try to play the chord 8:13:19 in 72-tET, you cannot use the best
approximation of all the intervals involved. That difficulty will never
arise in a chord all of whose intervals are within the 17-limit, thus the
term "consistency". 58-tET is also consistent through the 17-limit, but with
worse approximations; the lowest ET that is consistent through the 19-limit
is 80-tET, and the smallest that improves on 72-tET's 17-limit
approximations is 94-tET, which is also consistent through the 23-limit.

72-tET steps Tones 11-limit ratio Remaining 17-limit ratios
0 0 1:1
6 1/2 18:17, 17:16
7 7/12 16:15, 15:14
8 2/3 14:13, 13:12
9 3/4 12:11
10 5/6 11:10
11 11/12 10:9
12 1 9:8
13 1 1/12 17:15
14 1 1/6 8:7
15 1 1/4 15:13
16 1 1/3 7:6
17 1 5/12 13:11, 20:17
19 1 7/12 6:5
20 1 2/3 17:14
21 1 3/4 11:9
22 1 5/6 16:13
23 1 11/12 5:4
25 2 1/12 14:11
26 2 1/6 9:7
27 2 1/4 13:10, 22:17
28 2 1/3 17:13
30 2 1/2 4:3
32 2 2/3 15:11
33 2 3/4 11:8
34 2 5/6 18:13
35 2 11/12 7:5
36 3 17:12, 24:17

Hi Everyone,
I finally got Dreamweaver and found some space to resurrect 72 tone equal temperament. The new address is: 72note.com

What an ordeal.

Yours,
Rick

>> >>
> >

--- In tuning@y..., Rick Tagawa <ricktagawa@e...> wrote:

> Hi Everyone,
> I finally got Dreamweaver and found some space to resurrect 72 tone
> equal temperament. The new address is: 72note.com
>
> What an ordeal.

Thanks for undergoing it. You might want to know that the "Information about other microtonal groups" link is broken; perhaps Manuel could help. Also, the link to Ted Mook's font page works fine, but the link to fonts on it is broken.

Here's a question--does Blackjack automatically count as 72-et related? You might want to link to the Blackjack page on mp3.com.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:

> Thanks for undergoing it. You might want to know that the "Information about other microtonal groups" link is broken; perhaps Manuel could help. Also, the link to Ted Mook's font page works fine, but the link to fonts on it is broken.

Some of the links under "Subsets of 72-et" are broken also.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
>
> > Thanks for undergoing it. You might want to know that
the "Information about other microtonal groups" link is broken;
perhaps Manuel could help. Also, the link to Ted Mook's font page
works fine, but the link to fonts on it is broken.
>
> Some of the links under "Subsets of 72-et" are broken also.

ok, guys, here are some comments:

rick -- congrats on 72note.com. this is great!!

gene -- where are you seeing "Subsets of 72-et"? i can't find this
anywhere on 72note.com . . .

. . . however, i *do* see them on rick's old page,

http://sonic-arts.org/tagawa/72edo.htm -- which has other material i
don't see on the new page, but where these links:

12 Tone Equal Temperament
24 Tone Equal Temperament
36 Tone Equal Temperament

are broken . . . as, of course, are the links to monz's pages, which
have moved from ixpres to sonic-arts.org . . .

on the new page, i notice that the link to

Graham Breed's Decimal Notation

is the same as the link to

Dave Keenan's "mystery circle" of Graham Breed's Decimal Notation

("mystery circle"??? don't know what that is, but maybe you meant to
point to
http://www.uq.net.au/~zzdkeena/Music/Miracle/MiraclePitchChart.gif . .
. )

the songs in 72-equal don't seem to have the pitch bends implemented
correctly -- in any case, there's so much vibrato on the patch
selected that one probably couldn't hear the difference anyway . . .

p.s. rick -- here are some graphics i made that you're welcome and
encouraged to reproduce on your webpage:

/tuning/files/perlich/secor.gif
/tuning/files/perlich/secor2.gif
/tuning/files/perlich/72.gif

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:

> gene -- where are you seeing "Subsets of 72-et"? i can't find this
> anywhere on 72note.com . . .

I found it there, but can't seem to find it again.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:

/tuning/topicId_3754.html#40985

> --- In tuning@y..., Rick Tagawa <ricktagawa@e...> wrote:
>
> > Hi Everyone,
> > I finally got Dreamweaver and found some space to resurrect 72
tone
> > equal temperament. The new address is: 72note.com
> >
> > What an ordeal.
>
> Thanks for undergoing it. You might want to know that
the "Information about other microtonal groups" link is broken;
perhaps Manuel could help. Also, the link to Ted Mook's font page
works fine, but the link to fonts on it is broken.
>
> Here's a question--does Blackjack automatically count as 72-et
related? You might want to link to the Blackjack page on mp3.com.

***Well, actually this problem is on *Mook's* page, and I don't
believe Rick has any control over it. I've noticed this for some
time. At first I couldn't access the font, and sometimes the Mook
site asks me for a *password* when I believe he has it set up as a
*public* domain. Fortunately, I already have a copy of the font, and
have stored it other places for safekeeping.

I guess people should e-mail Ted Mook *directly* if they want the
font, and probably he could send it as an attachment. He should
probably know, though, that people can't access it. I've already
mentioned it to him myself.

Personally I would vote that Blackjack, as a subset of 72, should be
considered "related..." However, I wouldn't link everything related
to 12-tET to the site, even though that also is a subset... :)

J. Pehrson

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_3754.html#40987

the difference anyway . . .
>
> p.s. rick -- here are some graphics i made that you're welcome and
> encouraged to reproduce on your webpage:
>
> /tuning/files/perlich/secor.gif
> /tuning/files/perlich/secor2.gif
> /tuning/files/perlich/72.gif

***I really hope that these beautiful graphics can be linked to the
page. Quite frankly, I've always enjoyed music theory to a degree,
but some of the theories associated with microtonality and Harmonic
Entropy, particularly, as developed by Paul Erlich, have been the
*most* interesting ideas of *any* kind of music theory I have yet
encountered. (What I can *understand* of it, of course... :)

J. Pehrson

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
>
> /tuning/topicId_3754.html#40987
>
> the difference anyway . . .
> >
> > p.s. rick -- here are some graphics i made that you're welcome
and
> > encouraged to reproduce on your webpage:
> >
> > /tuning/files/perlich/secor.gif
> > /tuning/files/perlich/secor2.gif
> > /tuning/files/perlich/72.gif
>
> ***I really hope that these beautiful graphics can be linked to the
> page. Quite frankly, I've always enjoyed music theory to a degree,
> but some of the theories associated with microtonality and Harmonic
> Entropy, particularly, as developed by Paul Erlich, have been the
> *most* interesting ideas of *any* kind of music theory I have yet
> encountered. (What I can *understand* of it, of course... :)
>
> J. Pehrson

thanks joseph! fans of harmonic entropy, i have great news: possibly
because of my urging, Matlab now allows one to directly access the
voronoi cell associated with any given point in a voronoi diagram.
this means i'll soon be able to observe the pattern (or lack thereof)
for triads that is analogous to my finding of

width ~ 1/sqrt(p*q)

for dyads . . . meaning that a calculation of harmonic entropy for
triads is finally within sight.

i.e., a yummier pizza!

stay tuned on the harmonic entropy list.

Many thanks for the graphics. I'll put them up today. I took off all of the midi files and substituted mp3 files. Of course at the cost of download time & file size. Still not completely happy with the sounds. Canright seems to think he can tinker with the midi files to make them more stable pitchwise. Anybody have any suggestions for a neutral stable sound for demonstrating pitch on the internet?

I'm using Finale's ability to link an "expression" with a pitch wheel value. It also seems to remember the metronome marking if I use the "set-up Wizard."

But like I said, I'm losing the midi files because of the "cheese" aspect.

--Rick

wallyesterpaulrus wrote:

><snip>
>
>the songs in 72-equal don't seem to have the pitch bends implemented >correctly -- in any case, there's so much vibrato on the patch >selected that one probably couldn't hear the difference anyway . . .
>
>p.s. rick -- here are some graphics i made that you're welcome and >encouraged to reproduce on your webpage:
>
>/tuning/files/perlich/secor.gif
>/tuning/files/perlich/secor2.gif
>/tuning/files/perlich/72.gif
>
>
>
> >

How do I credit these? and what should I title these? Maybe you could add a few lines of explanation?

Thanks!

rick

>
>wallyesterpaulrus wrote:
>
> >
>><snip>
>>
>>the songs in 72-equal don't seem to have the pitch bends implemented >>correctly -- in any case, there's so much vibrato on the patch >>selected that one probably couldn't hear the difference anyway . . .
>>
>>p.s. rick -- here are some graphics i made that you're welcome and >>encouraged to reproduce on your webpage:
>>
>>/tuning/files/perlich/secor.gif
>>/tuning/files/perlich/secor2.gif
>>/tuning/files/perlich/72.gif
>>
>>
>>
>> >>
>> >>
>
>
>
>You do not need web access to participate. You may subscribe through
>email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery on hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily digest mode.
> tuning-normal@yahoogroups.com - change your subscription to individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> >
>Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/ >
>
>
> >

--- In tuning@y..., Rick Tagawa <ricktagawa@e...> wrote:
>
> How do I credit these? and what should I title these? Maybe you
could
> add a few lines of explanation?
>
> Thanks!
>
> rick

hi rick,

these are by me (paul erlich), and two of them already have titles
("intervallic continuum" and "blackjack interval matrix"), and are (i
hope) self-explanatory. the "bingo card" is just like james
mccartney's, except that by using hexagons, i can indicate 5:3 and
6:5 as adjacencies, just like the other 5-limit consonances.