612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

Hi dear Cameron Bobro

I have uploaded an excel spreadsheet to approximate any EDO with any EDL system:
http://240edo.googlepages.com/EDOandEDL.xls

For any constant string length you can find also place of any fret of any EDO according to this simulation.
612-EDL approximate very good 53-EDO with errors between -2 and +2.5 cent.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Cameron Bobro
Sent: Wednesday, July 04, 2007 1:01 PM
To: tuning@yahoogroups.com
Subject: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

Servus Andreas,

Yes those sources state that the 612 refers to equal divisions of
the octave, but what about this "coincidence":

1/1---------------0.000
-----------------------------------
181.132 cents 181.132
612/551 181.775
=0.643 cents difference
-------------------------------------
203.774 cents 203.774
9/8 203.910
=0.136 cents difference
-------------------------------------
294.340 cents 294.340
51/43 295.393
=1.053 cents difference
--------------------------------------
306/245 384.900
384.906 cents 384.906
=.006 cents difference
--------------------------------------
4/3 498.045
498.113 cents 498.113
=.068 cents difference
--------------------------------------
153/109 587.044
588.679 cents 588.679
=1.635 cents difference
--------------------------------------
679.245 cents 679.245
612/413 680.868
=1.623 cents difference
---------------------------------------
701.887 cents 701.887
3/2 701.955
=.068 cents difference
--------------------------------------
792.453 cents 792.453
68/43 793.438
=0.985 cents difference
--------------------------------------
883.019 cents 883.019
612/367 885.302
(886.020 cents 886.020)
=2.283 cents difference (0.718 from 77/76 stepsize)
--------------------------------------
204/121 904.275
905.660 cents 905.660
=1.385 cents difference
-------------------------------------
996.226 cents 996.226
153/86 997.348
=1.122 cents difference
--------------------------------------
204/109 1085.089
1086.792 cents 1086.792
=1.703 cents difference
-------------------------------------
1177.358 cents 1177.358
306/155 1177.516
=0.158 cents difference
-------------------------------------

53-equal is represented in cents, and the ratios are all from 612
equal divisions of a string length.

I knew before calculating this that it would work out this way, that
612 equal divisions of length gives a simple, practical and very
accurate way to fret 53 "equal" (whether its truly equal, or
rationally concieved). How? Common sense (what's with the sudden
leap in size of the supposedly equal divisions?) and by immediately
noticing that the "612" is the "same" as the 196-EDL Werckmeister
used (as detailed by Tom Dent here); it is the "same" in a certain
very simple rules-of-thumb-for-craftsmen kind of way.

So I suspect that the 53 does refer to equal divisions, but the 612
refers to a practical way of marking a monochord in order to get
that tuning.

-Cameron Bobro

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> , "Andreas Sparschuh" <a_sparschuh@...>
wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> , "Cameron Bobro" <misterbobro@>
> asked:
> > tell me what you think the "612"
> > refers to.
> >
> Dear Cameron,
> here literature
> about N's 612 division:
> http://www.bach-cantatas.com/Topics/Genius.htm <http://www.bach-cantatas.com/Topics/Genius.htm>
>
> "Newton played pretty well the viola, and invented for instance in
> tuning theory the 612-division of the octave.
> Lit: new Grove 2nd Ed. Vol.17 p.815-4"
>
>
> Mark Lindley, in
> "Geschichte der Musik-Thorie" (History of music-theory)
> in his article
> "Stimmung und Temperatur" , Darmstadt 1987
> ISBN 3-534-01206-2 (Band/Vol. 6)
> "Hören, Messen und Rechnen in der frühen Neuzeit"
> refers in his review of N's paper short to 612 on p. 206:
> "Er (N.) beschäftigt sich dann mit der Teilung der Oktave in
> 20, 24, 25, 29, 36, 41, 53, 60, 100, 120 und 612 gleiche Teile,
> entscheidet sich für die 53tönige Teilung als die beste und gibt
das
> in Abb.30 wiedergebene Diagramm"
>
> 'He (N.) then considers divisions of the octave into .... and 612
> parts, opts for 53tone div. as the best and presents the
> Diagramm in Fig.30b.'
>
> Has anybody here in that group access to N's original paper?
>
> The next reference that i found on that
> in my tuning-libary in:
> http://diapason.xentonic.org/ttl/ttl04.html <http://diapason.xentonic.org/ttl/ttl04.html>
> p.68
> "....represent 1/51 of an E.T. semitone, the whole system
> constitute a div. of the octave into 612 equal intervals*...
>
> footnote:
> * The importance of this system was pointed out by Captain
J.Herschel,
> R.R.S.
>
> the astronomer:
> http://en.wikipedia.org/wiki/J._Herschel_ <http://en.wikipedia.org/wiki/J._Herschel_> (crater)
> http://www.answers.com/topic/j-herschel <http://www.answers.com/topic/j-herschel>
> http://www.solstation.com/stars/hj5173ab.htm <http://www.solstation.com/stars/hj5173ab.htm>
>
>
> A.S.
>

What is the best EDL to approximate 159-EDO? Error for each pitch should be less than 0.5 cents.

Oz.
----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 04 Temmuz 2007 Çarşamba 15:00
Subject: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

Hi dear Cameron Bobro

I have uploaded an excel spreadsheet to approximate any EDO with any EDL system:
http://240edo.googlepages.com/EDOandEDL.xls

For any constant string length you can find also place of any fret of any EDO according to this simulation.
612-EDL approximate very good 53-EDO with errors between -2 and +2.5 cent.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ??????

My farsi page in Harmonytalk ???? ??????? ?? ??????? ???

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ????

Hi Shaahin, thanks! Nice!

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:
> 612-EDL approximate very good 53-EDO with errors between -2 and
>+2.5 cent.

The subset of 53-equal which is the steps in the Newton drawing are
approximated even better, with one +2.3 cent error and the rest
extremely close.

I was quite sure 612 would relate to 53 this way before reckoning
it, because of the handy "rule of thumb" that occurred to me doing
EDLs, which your spreadsheet as well seems to be confirming in the
first few EDO/EDL pairs I've tried.

Your pages are very interesting- because I'm trying to deeply relate
everything I do in tuning with the extended harmonic series, of
course I do these EDL/ADO etc. things continually.

-Cameron Bobro

Hi ozan
according to my EDO-EDL calculator , 3100-Edl is a good choic.3101-EDl cant satisfy you but 3102-EDL is better than 3100.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman
Sent: Wednesday, July 04, 2007 3:48 PM
To: tuning@yahoogroups.com
Subject: Re: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

What is the best EDL to approximate 159-EDO? Error for each pitch should be less than 0.5 cents.

Oz.

----- Original Message -----
From: Mohajeri Shahin <mailto:shahinm@kayson-ir.com>
To: tuning@yahoogroups.com <mailto:tuning@yahoogroups.com>
Sent: 04 Temmuz 2007 Çarşamba 15:00
Subject: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

Hi dear Cameron Bobro

I have uploaded an excel spreadsheet to approximate any EDO with any EDL system:
http://240edo.googlepages.com/EDOandEDL.xls <http://240edo.googlepages.com/EDOandEDL.xls>

For any constant string length you can find also place of any fret of any EDO according to this simulation.
612-EDL approximate very good 53-EDO with errors between -2 and +2.5 cent.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

Lessee, the rule-of-thumb, just takes a few seconds, gives me 1836,
with just a handful of errors over .5 cents, the worst of which
is .8 cents. That's the first octave- Shaahin's spreadsheet
calculates fretting errors, for more than one octave, so the errors
increase beyond the first octave of course.

Less than .5 cent error... what EDL would be better I don't know.

-Cameron Bobro

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> What is the best EDL to approximate 159-EDO? Error for each pitch
should be less than 0.5 cents.
>
> Oz.
> ----- Original Message -----
> From: Mohajeri Shahin
> To: tuning@yahoogroups.com
> Sent: 04 Temmuz 2007 Çarþamba 15:00
> Subject: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53
drawing, as an extension of Re: pseudo-Odo _dialogus_
>
>
> Hi dear Cameron Bobro
>
> I have uploaded an excel spreadsheet to approximate any EDO with
any EDL system:
> http://240edo.googlepages.com/EDOandEDL.xls
>
> For any constant string length you can find also place of any
fret of any EDO according to this simulation.
> 612-EDL approximate very good 53-EDO with errors between -2 and
+2.5 cent.
>
> Shaahin Mohajeri
>
> Tombak Player & Researcher , Microtonal Composer
>
> My web site?? ???? ????? ??????
>
> My farsi page in Harmonytalk ???? ??????? ?? ??????? ???
>
> Shaahin Mohajeri in
Wikipedia ????? ?????? ??????? ??????? ???? ????
>

In the real "play the instrument" world, the errors in the sound you will get are not as significant as how hard you press or bend the strings when you play.

How you play will influence the pitch more than a millimetre or so error in the fret marking, cutting and placement.

Guitar players do all sorts of fancy movements as they play "hammer-ons", "hammer-offs", slides, bends etc. with their fretting hand,

plus various fancy techniques which can effect pitch with their
"plucking" hand.

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 4 Jul 2007, at 14:11, Cameron Bobro wrote:

> Lessee, the rule-of-thumb, just takes a few seconds, gives me 1836,
> with just a handful of errors over .5 cents, the worst of which
> is .8 cents. That's the first octave- Shaahin's spreadsheet
> calculates fretting errors, for more than one octave, so the errors
> increase beyond the first octave of course.
>
> Less than .5 cent error... what EDL would be better I don't know.
>
> -Cameron Bobro
>
>
> .
>
>

3100-EDL is a fine choice. But how do we include the error caused by the inclination of the string when fingers touch the frets?

Oz.
----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 04 Temmuz 2007 Çarşamba 15:43
Subject: RE: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

Hi ozan
according to my EDO-EDL calculator , 3100-Edl is a good choic.3101-EDl cant satisfy you but 3102-EDL is better than 3100.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ??????

My farsi page in Harmonytalk ???? ??????? ?? ??????? ???

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ????

------------------------------------------------------------------------------
From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman
Sent: Wednesday, July 04, 2007 3:48 PM
To: tuning@yahoogroups.com
Subject: Re: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

What is the best EDL to approximate 159-EDO? Error for each pitch should be less than 0.5 cents.

Oz.

Cameron,

Equal Divisions of the Octave (EDO's) have been around
a long time. Please define EDL's and ADO's.

Mark

--- Cameron Bobro <misterbobro@yahoo.com> wrote:

> Hi Shaahin, thanks! Nice!
>
> --- In tuning@yahoogroups.com, "Mohajeri Shahin"
> <shahinm@...> wrote:
> > 612-EDL approximate very good 53-EDO with errors
> between -2 and
> >+2.5 cent.
>
> The subset of 53-equal which is the steps in the
> Newton drawing are
> approximated even better, with one +2.3 cent error
> and the rest
> extremely close.
>
> I was quite sure 612 would relate to 53 this way
> before reckoning
> it, because of the handy "rule of thumb" that
> occurred to me doing
> EDLs, which your spreadsheet as well seems to be
> confirming in the
> first few EDO/EDL pairs I've tried.
>
> Your pages are very interesting- because I'm trying
> to deeply relate
> everything I do in tuning with the extended harmonic
> series, of
> course I do these EDL/ADO etc. things continually.
>
> -Cameron Bobro
>
>
>
>

____________________________________________________________________________________Ready for the edge of your seat?
Check out tonight's top picks on Yahoo! TV.
http://tv.yahoo.com/

Hi brother

I believe that in acoustic music , pitch error is an inavoidable thing because your control on instrument will change everything.
But ,an important thing to mention , as you know , is that it is mostly related to compensation as is discussed in http://www.mandolincafe.com/glossary/glossary_60.shtml and other related links.
EDL and many other measurements are for a physical ideal string but many other things have effect on these ratios: http://www.classicalandflamencoguitars.com/Compensation4.htm
My experience for fretting setar is that at first i must have compensated octave fret in its best condition due to my ear error and sound analyzer's result and then use EDL to fret other frets as compared with octave fret ( as mentioned in my EDO-EDL sheet).
So if anyone wants to fret instrument , firstly must compensate frets to delete errors as is done for guitars.
also uncertainty principle of frequency analysis http://www-gewi.uni-graz.at/staff/parncutt/PSYCHOACOUSTICS.pdf <javascript:document.form1[1].value="NO";document.form1.submit();> have somethings to say.
and this may be is useful for you :http://www.wellesley.edu/Physics/brown/pubs/vibPerF100P1728-P1735.pdf <javascript:document.form1[1].value="NO";document.form1.submit();>

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman
Sent: Wednesday, July 04, 2007 4:42 PM
To: tuning@yahoogroups.com
Subject: Re: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

3100-EDL is a fine choice. But how do we include the error caused by the inclination of the string when fingers touch the frets?

Oz.

----- Original Message -----
From: Mohajeri Shahin <mailto:shahinm@kayson-ir.com>
To: tuning@yahoogroups.com <mailto:tuning@yahoogroups.com>
Sent: 04 Temmuz 2007 Çarşamba 15:43
Subject: RE: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

Hi ozan
according to my EDO-EDL calculator , 3100-Edl is a good choic.3101-EDl cant satisfy you but 3102-EDL is better than 3100.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman
Sent: Wednesday, July 04, 2007 3:48 PM
To: tuning@yahoogroups.com
Subject: Re: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

What is the best EDL to approximate 159-EDO? Error for each pitch should be less than 0.5 cents.

Oz.

Ozan, try 3538, which I got from going to your original "79" paper and
checking out what it really is all about- 79/159 is just a very
accurate approximation of offset 4:3/33s, and not the original tuning,
isn't it? I think a tuning from 3538-EDL might even more accurate for
you 79 tones, but all these monster EDLs are pretty useless- it's the
<650 or so ones that can be happily applied with millimeters or 1/32"
to a real monochord, for example, while still having a chance to
reduce down to something that could reasonably be viewed as rational
intonation rather than splitting angel's hairs.

The very low EDLs are pretty fun- you can get things like an very good
1/8 Pyth. meantone fifth with nothing but a decent ruler and 148-EDL,
etc.

-Cameron Bobro

Where on earth did you get 3538 from?

There are at least four ways to achieve Ozmosis, all of which are detailed
in my yet incomplete thesis.

No need to equally divide a string if 1006-ADO yields accurate results.

Oz.

----- Original Message -----
From: "Cameron Bobro" <misterbobro@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 05 Temmuz 2007 Per�embe 15:36
Subject: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as
an extension of Re: pseudo-Odo _dialogus_

> Ozan, try 3538, which I got from going to your original "79" paper and
> checking out what it really is all about- 79/159 is just a very
> accurate approximation of offset 4:3/33s, and not the original tuning,
> isn't it? I think a tuning from 3538-EDL might even more accurate for
> you 79 tones, but all these monster EDLs are pretty useless- it's the
> <650 or so ones that can be happily applied with millimeters or 1/32"
> to a real monochord, for example, while still having a chance to
> reduce down to something that could reasonably be viewed as rational
> intonation rather than splitting angel's hairs.
>
> The very low EDLs are pretty fun- you can get things like an very good
> 1/8 Pyth. meantone fifth with nothing but a decent ruler and 148-EDL,
> etc.
>
>
> -Cameron Bobro
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Where on earth did you get 3538 from?

Same way I knew at a glance that 612-EDL would yield a good 53-EDO.
3538: is it or is it not a very accurate EDL for your tuning?
>
> There are at least four ways to achieve Ozmosis, all of which are
>detailed
> in my yet incomplete thesis.

Is Ozmosis your tuning? I'm really looking forward to your thesis.
I haven't noticed anything mentioned about a certain delightful
property of your tuning, let's see if it's in your thesis.
>
> No need to equally divide a string if 1006-ADO yields accurate
>results.

I certainly agree.
>
> Oz.
>
> ----- Original Message -----
> From: "Cameron Bobro" <misterbobro@...>
> To: <tuning@yahoogroups.com>
> Sent: 05 Temmuz 2007 Perþembe 15:36
> Subject: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53
drawing, as
> an extension of Re: pseudo-Odo _dialogus_
>
>
> > Ozan, try 3538, which I got from going to your original "79"
paper and
> > checking out what it really is all about- 79/159 is just a very
> > accurate approximation of offset 4:3/33s, and not the original
tuning,
> > isn't it? I think a tuning from 3538-EDL might even more
accurate for
> > you 79 tones, but all these monster EDLs are pretty useless-
it's the
> > <650 or so ones that can be happily applied with millimeters or
1/32"
> > to a real monochord, for example, while still having a chance to
> > reduce down to something that could reasonably be viewed as
rational
> > intonation rather than splitting angel's hairs.
> >
> > The very low EDLs are pretty fun- you can get things like an
very good
> > 1/8 Pyth. meantone fifth with nothing but a decent ruler and 148-
EDL,
> > etc.
> >
> >
> > -Cameron Bobro
> >
>

----- Original Message -----
From: "Cameron Bobro" <misterbobro@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 06 Temmuz 2007 Cuma 16:00
Subject: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as
an extension of Re: pseudo-Odo _dialogus_

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Where on earth did you get 3538 from?

Same way I knew at a glance that 612-EDL would yield a good 53-EDO.
3538: is it or is it not a very accurate EDL for your tuning?

Anything that voluminous would be accurate, no?

>
> There are at least four ways to achieve Ozmosis, all of which are
>detailed
> in my yet incomplete thesis.

Is Ozmosis your tuning? I'm really looking forward to your thesis.
I haven't noticed anything mentioned about a certain delightful
property of your tuning, let's see if it's in your thesis.
>

Well, it has Oz in it, so it must have something to do with me. That
property you are talking about... could it be Myhill's?

> No need to equally divide a string if 1006-ADO yields accurate
>results.

I certainly agree.
>
> Oz.
>

> > Where on earth did you get 3538 from?
>
> Same way I knew at a glance that 612-EDL would yield a good 53-EDO.

Which way is that?

-Carl

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:

> Is Ozmosis your tuning?

It's a linear temperament. 79 notes of it give the scale of the The
Great and Powerful Oz.

Yours truly.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 06 Temmuz 2007 Cuma 22:04
Subject: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as
an extension of Re: pseudo-Odo _dialogus_

> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> > Is Ozmosis your tuning?
>
> It's a linear temperament. 79 notes of it give the scale of the The
> Great and Powerful Oz.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> Anything that voluminous would be accurate, no?

Yes and no, what about your <.5 cents demand?

918-EDL, for example, gives you less than 2 cents maximum errors for
159-EDO, with almost all intervals just dandy, and it "breaks down"
rationally, ie you can see at a glance that there are a huge number
of classic intervals in your tuning, which seems to be exceptionally
strong in the 11-family for example.

The use of EDLs in my opinion is physical on one hand- fretting- and
as a tool in doing rational intonation. Lower numbers which break
down nicely rationally, numbers that relate elegantly to
appropriate ADOs for interlacing so to speak, are what interest me.

> Well, it has Oz in it, so it must have something to do with me.
>That
> property you are talking about... could it be Myhill's?

Yes and no, but you guessed what I was refering to- one delightful
aspect, among many, is that it has "Myhill's property" on one level,
and yet does not at a deeper level, because it can viewed, almost
perfectly, as the product of a single low (all things considered)
superparticular interval.

Carl asked "what way", and I mean something so bonehead simple it
seems silly, but seems to work quite well: if you take a "key"
superparticuar ratio, either the ratio equivalent of the EDO
step size, the smallest important interval, or other step with je
nais se quois vis a vis the tuning, add the terms and use that as
your "unit", multiply by four for example, you can get a good EDL.
So when I saw 612, I thought, oh, 612/4 is 77+76. 196 is (25+24)4.
I knew 148-EDL would do something old-fashioned and groovy before
trying it, being an EDL appropriate, by this rule of thumb, for
19/18, and sure enough it gives an excellent -1/8 Pyth. fifth.
Sometimes the superparticular rational equivalent is too far from
the EDO step size, for example doing this for 82-EDO gives you a
good EDL for 41-EDO, etc. Now Carl and Gene can scoff away, hahaha!

Anyway, "ozmosis" is a great tuning (it's not a scale).

-Cameron Bobro

----- Original Message -----
From: "Cameron Bobro" <misterbobro@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 08 Temmuz 2007 Pazar 14:49
Subject: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as
an extension of Re: pseudo-Odo _dialogus_

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> > Anything that voluminous would be accurate, no?
>
> Yes and no, what about your <.5 cents demand?
>

It stands.

> 918-EDL, for example, gives you less than 2 cents maximum errors for
> 159-EDO, with almost all intervals just dandy, and it "breaks down"
> rationally, ie you can see at a glance that there are a huge number
> of classic intervals in your tuning, which seems to be exceptionally
> strong in the 11-family for example.
>
> The use of EDLs in my opinion is physical on one hand- fretting- and
> as a tool in doing rational intonation. Lower numbers which break
> down nicely rationally, numbers that relate elegantly to
> appropriate ADOs for interlacing so to speak, are what interest me.
>

I am very pleased that 1006-ADO approximates Ozmosis splendidly.

> > Well, it has Oz in it, so it must have something to do with me.
> >That
> > property you are talking about... could it be Myhill's?
>
> Yes and no, but you guessed what I was refering to- one delightful
> aspect, among many, is that it has "Myhill's property" on one level,
> and yet does not at a deeper level, because it can viewed, almost
> perfectly, as the product of a single low (all things considered)
> superparticular interval.
>
> Carl asked "what way", and I mean something so bonehead simple it
> seems silly, but seems to work quite well: if you take a "key"
> superparticuar ratio, either the ratio equivalent of the EDO
> step size, the smallest important interval, or other step with je
> nais se quois vis a vis the tuning, add the terms and use that as
> your "unit", multiply by four for example, you can get a good EDL.
> So when I saw 612, I thought, oh, 612/4 is 77+76. 196 is (25+24)4.
> I knew 148-EDL would do something old-fashioned and groovy before
> trying it, being an EDL appropriate, by this rule of thumb, for
> 19/18, and sure enough it gives an excellent -1/8 Pyth. fifth.
> Sometimes the superparticular rational equivalent is too far from
> the EDO step size, for example doing this for 82-EDO gives you a
> good EDL for 41-EDO, etc. Now Carl and Gene can scoff away, hahaha!
>

79+80*4=636

> Anyway, "ozmosis" is a great tuning (it's not a scale).
>

Yep.

> -Cameron Bobro
>

Oz.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
>
> ----- Original Message -----
> From: "Cameron Bobro" <misterbobro@...>
> To: <tuning@yahoogroups.com>
> Sent: 08 Temmuz 2007 Pazar 14:49
> Subject: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53
drawing, as
> an extension of Re: pseudo-Odo _dialogus_
>
>
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > > Anything that voluminous would be accurate, no?
> >
> > Yes and no, what about your <.5 cents demand?

> It stands.

Good- but do you mean .5 deviation from your actual tuning or its
subset of 159 approximation?

> I am very pleased that 1006-ADO approximates Ozmosis splendidly.

That's the lowest ADO you've found? By lowest I also mean the most
divisible.

> 79+80*4=636

You lost me here, 636-EDL doesn't meet your demand at all, and 80/79
is not an embracing superparticular interval for your tuning,
whereas...other intervals are.

-Cameron Bobro

----- Original Message -----
From: "Cameron Bobro" <misterbobro@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 08 Temmuz 2007 Pazar 15:13
Subject: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as
an extension of Re: pseudo-Odo _dialogus_

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> >
> > ----- Original Message -----
> > From: "Cameron Bobro" <misterbobro@...>
> > To: <tuning@yahoogroups.com>
> > Sent: 08 Temmuz 2007 Pazar 14:49
> > Subject: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53
> drawing, as
> > an extension of Re: pseudo-Odo _dialogus_
> >
> >
> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > > > Anything that voluminous would be accurate, no?
> > >
> > > Yes and no, what about your <.5 cents demand?
>
> > It stands.
>
> Good- but do you mean .5 deviation from your actual tuning or its
> subset of 159 approximation?
>

159-EDO approximation.

> > I am very pleased that 1006-ADO approximates Ozmosis splendidly.
>
> That's the lowest ADO you've found? By lowest I also mean the most
> divisible.
>
>

I found it by Farey minimax interval difference approximation of 79/80 MOS
159-tET in Scala. The simple frequencies version can be approximated by
decently 943-ADO.

> > 79+80*4=636
>
> You lost me here, 636-EDL doesn't meet your demand at all, and 80/79
> is not an embracing superparticular interval for your tuning,
> whereas...other intervals are.
>

Forget it then.

> -Cameron Bobro
>
>

Oz.