FW: [tuning] Re: JI scales with different limits for numerators and denominators

hi cameron

a problem: i can choose 12-note subsets of this 36-ado and make modes with different tonal centers of gravity.so what about this one? can you explain more?
scale of danny is based on tetrachord of (19/18*20/19*21/20*22/21*24/22) and pentachord of 17/16*18/17*(19/18*20/19*21/20*22/21*24/22).
tetrachord is based on 18-ADO and pentachord starts from sixth degree of 12-ADO and all these two are subsets of 36-ADO.
and note that begining part of graph for 18-ADO (C-F) and this part of 12-ado (G-C)have the same trend.
we can also have repeating blocks of notes in ADo,EDL and ....
for example consider 55-ADO.we have these cents:
0.
31.7667
64.1271
97.104
130.7212
165.0042
199.9798
with this superparticular block:
55/54
54/53
53/52
52/51
51/50
50/49
now after 6 repeating of this superparticular block we have octave of 1199.87906 cent:
0
34.976
31.7667
64.1271
97.104
130.7212
165.0042
199.9798
231.7465
264.107
297.0838
330.7011
364.9841
399.9597
431.7263
464.0868
497.0637
530.6809
564.9639
599.9395
631.7062
664.0666
697.0435
730.6608
764.9438
799.9194
831.686
864.0465
897.0234
930.6406
964.9236
999.8992
1031.6659
1064.0263
1097.0032
1130.6205
1164.9034
1199.8791
here you have quasi-equal intervals.so you see that you can do many thing with this new system.

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: Tuesday, April 03, 2007 4:14 PM
To: tuning@yahoogroups.com
Subject: [tuning] Re: JI scales with different limits for numerators and denominators

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> , "Mohajeri Shahin" <shahinm@...> wrote:
>
> hi cameron
> why 16/9?

That's the transposition where tuning is all overtones of the 1/1. .

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:
>
>
> hi cameron
>
> a problem: i can choose 12-note subsets of this 36-ado and make
modes with different tonal centers of gravity.so what about this
one? can you explain more?

Hi to you Shaahin, I'm talking about the center that "subsumes" this
entire tuning within one overtone series. Within the tuning you
could make different modes with musically different centers.

> scale of danny is based on tetrachord of
>(19/18*20/19*21/20*22/21*24/22) and pentachord of
>17/16*18/17*(19/18*20/19*21/20*22/21*24/22).
> tetrachord is based on 18-ADO and pentachord starts from sixth
>degree of 12-ADO and all these two are subsets of 36-ADO.

They're subsets of 36-ADO but the tone which would subsume them into
it is missing from the tuning, so they're disjointed (but joined by
a phantom center).

> we can also have repeating blocks of notes in ADo,EDL and ....
> for example consider 55-ADO.we have these cents:
> 0.
> 31.7667
> 64.1271
> 97.104
> 130.7212
> 165.0042
> 199.9798
> with this superparticular block:
> 55/54
> 54/53
> 53/52
> 52/51
> 51/50
> 50/49
> now after 6 repeating of this superparticular block we have octave
of 1199.87906 cent:
> 0
> 34.976
> 31.7667
> 64.1271
> 97.104
> 130.7212
> 165.0042
> 199.9798
> 231.7465
> 264.107
> 297.0838
> 330.7011
> 364.9841
> 399.9597
> 431.7263
> 464.0868
> 497.0637
> 530.6809
> 564.9639
> 599.9395
> 631.7062
> 664.0666
> 697.0435
> 730.6608
> 764.9438
> 799.9194
> 831.686
> 864.0465
> 897.0234
> 930.6406
> 964.9236
> 999.8992
> 1031.6659
> 1064.0263
> 1097.0032
> 1130.6205
> 1164.9034
> 1199.8791
> here you have quasi-equal intervals.so you see that you can do
many thing with this new system.

It's interesting that you post this because I was debating a few
days ago whether I should post the exact same thing, in response to
Joe Monzo's post on the 55 tuning of Mozart (the page he has up on
this is really good). It is my personal opinion that the "55-EDO" of
Mozart's time was precisely what you have just posted.

-Cameron Bobro

>
>
> 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: Tuesday, April 03, 2007 4:14 PM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: JI scales with different limits for
numerators and denominators
>
>
>
> --- In tuning@yahoogroups.com <mailto:tuning%
40yahoogroups.com> , "Mohajeri Shahin" <shahinm@> wrote:
> >
> > hi cameron
> > why 16/9?
>
> That's the transposition where tuning is all overtones of the
1/1. .
>