Yahoo Tuning Groups Ultimate Backup tuning numerary nexus : re [tuning] Re: Otonal / Utonal

In arithematical series with a constant denominatore ( otonal systems )
which I call them "" increasing/constant rational system "" , the
denominator is like the cardinality of EDO system , showing the number
of degrees in system( denominator+1). so the chords for example 4:5:6
are related to a i/c rational or otonal system of:

4/4 5/4 6/4 7/4 8/4 . if we accept octave equivalency , it will be
simplified as : 1/1 5/4 3/2 7/4 2/1 so the real numerary nexus ,
according to my view , is 4 .

In the utonal system , ''''constant/decreasing rational system "" , with
constant nominator = 8 we have so : 8/8 8/7 8/6 8/5 8/4 and after
o.e we have : 1/1 8/7 4/3 8/5 2/1 so the real n.n is 8 and 8=2*4

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of wallyesterpaulrus
Sent: Tuesday, October 18, 2005 12:29 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: Otonal / Utonal

I believe the numerary nexus is 1 for both systems if each is related
to a fixed 1/1 common to both, in some kind of Partchian diamondic
system (and if not, "numerary nexus" doesn't have much meaning here).
Why do you think otherwise?

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:
>
> EXCUSE ME ...... I MADE A MISTAKE ......IN THESE 2 SYSTEMS ,WHICH
THE
> FIRST IS OTONAL AND THE LAST UTONAL THE NUMBER OF DEGREES ARE THE
SAME
> (=8) BUT THE RELATION BETWEEN THEIR NUMERARY NEXUS(N.N) OF IS SO :
>
>
>
> N.N OF UTONAL = 2 * N.N OF OTONAL
>
>
>
>
>
> 0: 1/1 0.000 unison, perfect prime
>
> 1: 9/8 203.910 major whole tone
>
> 2: 5/4 386.314 major third
>
> 3: 11/8 551.318 undecimal semi-augmented
fourth
>
> 4: 3/2 701.955 perfect fifth
>
> 5: 13/8 840.528 tridecimal neutral sixth
>
> 6: 7/4 968.826 harmonic seventh
>
> 7: 15/8 1088.269 classic major seventh
>
> 8: 2/1 1200.000 octave
>
> |
>
> 0: 1/1 0.000 unison, perfect prime
>
> 1: 16/15 111.731 minor diatonic semitone
>
> 2: 8/7 231.174 septimal whole tone
>
> 3: 16/13 359.472 tridecimal neutral third
>
> 4: 4/3 498.045 perfect fourth
>
> 5: 16/11 648.682 undecimal semi-diminished
fifth
>
> 6: 8/5 813.686 minor sixth
>
> 7: 16/9 996.090 Pythagorean minor seventh
>
> 8: 2/1 1200.000 octave
>
>
>
> ________________________________
>
> From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On
Behalf
> Of wallyesterpaulrus
> Sent: Thursday, October 13, 2005 12:37 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: Otonal / Utonal
>
>
>
> --- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...>
wrote:
>
> > 4-in otonal and utonal systems with same number of degrees ,
> > udentity=2*odentity.
>
> How did you come to that conclusion?
>
>
>
>
>
> You can configure your subscription by sending an empty email to one
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🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

Wouldn't it be simpler to just write 4/8 4/7 4/6 4/5 4/4 instead
of 8/8 8/7 8/6 8/5 8/4, so you can keep the Mohajeri Shahin n.n
the same for both?

Anyway, if we accept octave equivalence, 1, 4, and 8 all mean the
same thing.

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...> wrote:
>
> In arithematical series with a constant denominatore ( otonal
systems )
> which I call them "" increasing/constant rational system "" , the
> denominator is like the cardinality of EDO system , showing the
number
> of degrees in system( denominator+1). so the chords for example
4:5:6
> are related to a i/c rational or otonal system of:
>
> 4/4 5/4 6/4 7/4 8/4 . if we accept octave equivalency , it
will be
> simplified as : 1/1 5/4 3/2 7/4 2/1 so the real numerary nexus ,
> according to my view , is 4 .
>
> In the utonal system , ''''constant/decreasing rational system "" ,
with
> constant nominator = 8 we have so : 8/8 8/7 8/6 8/5 8/4 and
after
> o.e we have : 1/1 8/7 4/3 8/5 2/1 so the real n.n is 8 and 8=2*4
>
>
>
> ________________________________
>
> From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On
Behalf
> Of wallyesterpaulrus
> Sent: Tuesday, October 18, 2005 12:29 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: Otonal / Utonal
>
>
>
> I believe the numerary nexus is 1 for both systems if each is
related
> to a fixed 1/1 common to both, in some kind of Partchian diamondic
> system (and if not, "numerary nexus" doesn't have much meaning
here).
> Why do you think otherwise?
>
>
> --- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...>
wrote:
> >
> > EXCUSE ME ...... I MADE A MISTAKE ......IN THESE 2 SYSTEMS ,WHICH
> THE
> > FIRST IS OTONAL AND THE LAST UTONAL THE NUMBER OF DEGREES ARE THE
> SAME
> > (=8) BUT THE RELATION BETWEEN THEIR NUMERARY NEXUS(N.N) OF IS
SO :
> >
> >
> >
> > N.N OF UTONAL = 2 * N.N OF OTONAL
> >
> >
> >
> >
> >
> > 0: 1/1 0.000 unison, perfect prime
> >
> > 1: 9/8 203.910 major whole tone
> >
> > 2: 5/4 386.314 major third
> >
> > 3: 11/8 551.318 undecimal semi-augmented
> fourth
> >
> > 4: 3/2 701.955 perfect fifth
> >
> > 5: 13/8 840.528 tridecimal neutral sixth
> >
> > 6: 7/4 968.826 harmonic seventh
> >
> > 7: 15/8 1088.269 classic major seventh
> >
> > 8: 2/1 1200.000 octave
> >
> > |
> >
> > 0: 1/1 0.000 unison, perfect prime
> >
> > 1: 16/15 111.731 minor diatonic semitone
> >
> > 2: 8/7 231.174 septimal whole tone
> >
> > 3: 16/13 359.472 tridecimal neutral third
> >
> > 4: 4/3 498.045 perfect fourth
> >
> > 5: 16/11 648.682 undecimal semi-diminished
> fifth
> >
> > 6: 8/5 813.686 minor sixth
> >
> > 7: 16/9 996.090 Pythagorean minor seventh
> >
> > 8: 2/1 1200.000 octave
> >
> >
> >
> > ________________________________
> >
> > From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On
> Behalf
> > Of wallyesterpaulrus
> > Sent: Thursday, October 13, 2005 12:37 AM
> > To: tuning@yahoogroups.com
> > Subject: [tuning] Re: Otonal / Utonal
> >
> >
> >
> > --- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@k...>
> wrote:
> >
> > > 4-in otonal and utonal systems with same number of degrees ,
> > > udentity=2*odentity.
> >
> > How did you come to that conclusion?
> >
> >
> >
> >
> >
> > You can configure your subscription by sending an empty email to
one
> > of these addresses (from the address at which you receive the
list):
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - leave the group.
> > tuning-nomail@yahoogroups.com - turn off mail from the group.
> > tuning-digest@yahoogroups.com - set group to send daily digests.
> > tuning-normal@yahoogroups.com - set group to send individual
> emails.
> > tuning-help@yahoogroups.com - receive general help information.
> >
> >
> >
> >
> >
> > SPONSORED LINKS
> >
> > Music education
> > <http://groups.yahoo.com/gads?
> t=ms&k=Music+education&w1=Music+education&
> >
>
w2=Music+production+education&w3=Music+education+degree&w4=Degree+educ
> at
> >
>
ion+music+online&w5=Music+business+education&w6=Music+education+online
> &c
> > =6&s=174&.sig=zMNRfOOOdo7nVqxhYS_0Yg>
> >
> > Music production education
> > <http://groups.yahoo.com/gads?
> t=ms&k=Music+production+education&w1=Music
> >
>
+education&w2=Music+production+education&w3=Music+education+degree&w4=
> De
> >
>
gree+education+music+online&w5=Music+business+education&w6=Music+educa
> ti
> > on+online&c=6&s=174&.sig=xvNPUlceIGAdVcjAsHH8JA>
> >
> > Music education degree
> > <http://groups.yahoo.com/gads?
> t=ms&k=Music+education+degree&w1=Music+edu
> >
>
cation&w2=Music+production+education&w3=Music+education+degree&w4=Degr
> ee
> >
>
+education+music+online&w5=Music+business+education&w6=Music+education
> +o
> > nline&c=6&s=174&.sig=lrDYh_-yrdu524mpql-csg>
> >
> > Degree education music online
> > <http://groups.yahoo.com/gads?
> t=ms&k=Degree+education+music+online&w1=Mu
> >
>
sic+education&w2=Music+production+education&w3=Music+education+degree&
> w4
> >
>
=Degree+education+music+online&w5=Music+business+education&w6=Music+ed
> uc
> > ation+online&c=6&s=174&.sig=SVm8lC0-Q2tryy6Hv14ihQ>
> >
> > Music business education
> > <http://groups.yahoo.com/gads?
> t=ms&k=Music+business+education&w1=Music+e
> >
>
ducation&w2=Music+production+education&w3=Music+education+degree&w4=De
> gr
> >
>
ee+education+music+online&w5=Music+business+education&w6=Music+educati
> on
> > +online&c=6&s=174&.sig=pCxzd_uR0dRaYO3MB1Fpvw>
> >
> > Music education online
> > <http://groups.yahoo.com/gads?
> t=ms&k=Music+education+online&w1=Music+edu
> >
>
cation&w2=Music+production+education&w3=Music+education+degree&w4=Degr
> ee
> >
>
+education+music+online&w5=Music+business+education&w6=Music+education
> +o
> > nline&c=6&s=174&.sig=DaqBb8P8ErSmB8MxxA-ePw>
> >
> >
> >
> > ________________________________
> >
> > YAHOO! GROUPS LINKS
> >
> >
> >
> > * Visit your group "tuning
> </tuning>
> > " on the web.
> >
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> > Service <http://docs.yahoo.com/info/terms/> .
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> > ________________________________
> >
>
>
>
>
>
>
> You can configure your subscription by sending an empty email to one
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>
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> YAHOO! GROUPS LINKS
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>
>
> * Visit your group "tuning
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> " on the web.
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> ________________________________
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🔗Mohajeri Shahin <shahinm@kayson-ir.com>

Yes , good idea for homogenizing, but this system is a way of for
example equally-dividing string and nominator is the number of
divisions. in this 8-rdo(c/d) or utonal system you divide string into 8
equal segments and 8/7 means that 7 segments of string is vibrating.

We can costruct these two systems also with superparticular ratio:

1- y/b ------ a/x (y/b < a/x , y=2x) , now costruct system from 1/1 with
numerary nexus = y , you will have utonal system

2- a/x ------ y/b (y/b < a/x , y=2x) , now costruct system from 1/1 with
numerary nexus = x , you will have otonal system

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of wallyesterpaulrus
Sent: Tuesday, October 18, 2005 11:53 PM
To: tuning@yahoogroups.com
Subject: numerary nexus : re [tuning] Re: Otonal / Utonal

Wouldn't it be simpler to just write 4/8 4/7 4/6 4/5 4/4 instead
of 8/8 8/7 8/6 8/5 8/4, so you can keep the Mohajeri Shahin n.n
the same for both?

Anyway, if we accept octave equivalence, 1, 4, and 8 all mean the
same thing.

________________________________

YAHOO! GROUPS LINKS

* Visit your group "tuning </tuning>
" on the web.

* To unsubscribe from this group, send an email to:
tuning-unsubscribe@yahoogroups.com
<mailto:tuning-unsubscribe@yahoogroups.com?subject=Unsubscribe>

* Your use of Yahoo! Groups is subject to the Yahoo! Terms of
Service <http://docs.yahoo.com/info/terms/> .

________________________________