about table 31 of cris work

Dear cris

I cant find Table 31
of _Musical Mathematics: A Practice in the
Mathematics of Tuning Instruments and Analyzing
Scales_

Shaahin Mohaajeri

Tombak Player & Researcher , Microtonal Composer

My web site , click picture : <http://240edo.tripod.com/index.html>

My tombak musics in Rhythmweb: <http://www.rhythmweb.com/gdg>
www.rhythmweb.com/gdg

My articles in Harmonytalk:

- <http://www.harmonytalk.com/archives/000296.html>
www.harmonytalk.com/archives/000296.html

- <http://www.harmonytalk.com/archives/000288.html>
www.harmonytalk.com/archives/000288.html

My article in DrumDojo:

<http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>
www.drumdojo.com/world/persia/tonbak_acoustics.htm

My musics in Wikipedia, the free encyclopedia :

- A composition based on a
<http://www.xenharmony.org/mp3/shaahin/shur.mp3> folk melody of Shiraz
region, in shur-dastgah by Mohajeri Shahin

- An experiment in <http://www.xenharmony.org/mp3/shaahin/homayun.mp3>
Iranian homayun and chahargah modes by Mohajeri Shahin

_____

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of Cris Forster
Sent: Sunday, June 18, 2006 5:41 PM
To: tuning@yahoogroups.com
Subject: [tuning] Re: about a work of cris forster about zarlino and
ibnsina

>1- farabi , Ibn-sina and then zarlino were affected
>by equal divisions of length system(EDL) which
>firstly was used by ptolemy .

This observation, which took years to unearth and
systematize, I demonstrate in full detail (in Table 31
of _Musical Mathematics: A Practice in the
Mathematics of Tuning Instruments and Analyzing
Scales_) with interval ratios and frequency ratios as
found in the works of Ptolemy, Al-Farabi, and Ibn
Sina.

Cris Forster, Music Director
www.chrysalis-foundation.org

--- In tuning@yahoogroups. <mailto:tuning%40yahoogroups.com> com,
"Mohajeri Shahin" <shahinm@...> wrote:
>
> After reading :
>
> http://www.chrysali
<http://www.chrysalis-foundation.org/Ibn-Sina_Stifel_&_Zarlino.htm>
s-foundation.org/Ibn-Sina_Stifel_&_Zarlino.htm
>
> I noticed that :
>
>
>
> 1- farabi , Ibn-sina and then zarlino were affected by equal
divisions
> of length system(EDL) which firstly was used by ptolemy .
>
> He used a string length of 120 units (90 for the 4/3, 80/ for the
3/2)
> to define both individual tetrachords and full octave scales (
thanks to
> john chalmers for giving me valuable information about this
system. They
> will be uploaded in my site ).
>
>
>
> 2- using 4:3:2 means 4-EDL , dividing string length of L to 4 equal
> parts to have 1/1(4/4) , 4/3 ,2/1(4/2) and to have superparticular
> ratios as
>
> 4/3 and 3/2. in 6:4:3 we have 1/1(6/6) , 3/2(6/4) ,2/1(6/3) and
> superparticulars as 3/2 and 4/3.
>
>
>
> 3- arithmetic divisions of octave , there , means , arithmetic
mean of
> harmonics In harmonic acoustical series. in 2:3:4 we have 3 as
(2+4)/2
> : third harmonic lies between second and fourth. And in 4:3:2 then
> (4+2)/2 . in the first the superpartcular trend is descending and
in the
> next , ascending. In the first we move in direction of harmonic
> acoustical series and in the next in reverse direction.
>
> Considering divisions , Arithmetic divisions of octave or my term
as ADO
> , is an arithmetic progression with frequency ratios as terms.(
EDO has
> equal frequency ratios as equal divisions) so 3:4:5:6 is 3-ADO
besed on
> third degree of harmonic acoustical series.
>
> So in arithmetic and harmonic mean we use degrees of harmonic
acoustical
> series and not divisions but define divisions og octave or length.
>
>
>
> 4- so what about geometric mean in 4:?:2
>
> We have (4*2)^(1/2) = 2.8284271247461900976033774484194
>
> So we can have 40:28:20 or 400:282:200 or 4000:2828:2000 with t
> divisions of 617.488 cent , 582.512cent or 605.166cent and
> 594.834cent or 600.261cent and 599.834 cent.
>
> We see that we are going to Have EDO.
>
> Shaahin Mohaajeri
>
> Tombak Player & Researcher , Microtonal Composer
>
> My web site , click picture :
<http://240edo. <http://240edo.tripod.com/index.html>
tripod.com/index.html>
>
> My tombak musics in Rhythmweb: www.rhythmweb.com/gdg
> <http://www.rhythmwe <http://www.rhythmweb.com/gdg> b.com/gdg>
>
> My articles in Harmonytalk:
>
> - www.harmonytalk.com/archives/000296.html
> <http://www.harmonyt <http://www.harmonytalk.com/archives/000296.html>
alk.com/archives/000296.html>
>
> - www.harmonytalk.com/archives/000288.html
> <http://www.harmonyt <http://www.harmonytalk.com/archives/000288.html>
alk.com/archives/000288.html>
>
> My article in DrumDojo:
>
> www.drumdojo.com/world/persia/tonbak_acoustics.htm
> <http://www.drumdojo
<http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>
.com/world/persia/tonbak_acoustics.htm>
>
> My musics in Wikipedia, the free encyclopedia :
>
> - A composition based on a folk melody of Shiraz region, in shur-
dastgah
> by Mohajeri Shahin
<http://www.xenharmo <http://www.xenharmony.org/mp3/shaahin/shur.mp3>
ny.org/mp3/shaahin/shur.mp3>
>
> - An experiment in Iranian homayun and chahargah modes by Mohajeri
> Shahin <http://www.xenharmo
<http://www.xenharmony.org/mp3/shaahin/homayun.mp3>
ny.org/mp3/shaahin/homayun.mp3>
>