Yahoo Tuning Groups Ultimate Backup tuning JI scales with different limits for numerators and denominators

Turns out I have a scale in the Scala archive. It's one of the "ClownTone" just scales I came up with through brainstorming years ago. They were various mostly otonal scales plus the same transposed by a fourth or fifth, filling out a twelve-note chromatic scale. This one is made up of 18:19:20:21:22:24 tetrachords a fifth apart plus a 17 below the higher one.

! wier_cl.scl
!
Danny Wier, ClownTone (2003)
12
!
19/18
10/9
7/6
11/9
4/3
17/12
3/2
19/12
5/3
7/4
11/6
2/1

I haven't written anything using this scale except stuff I made up in my head and long-forgotten bass solos.

Which leads me to my question: what is it called when you make a JI scale using a different prime limit for the numerator than the limit for denominator. The scale above has a 19-limit otonally and 3-limit utonally. A rectangular scale would also qualify.

~D.

🔗Herman Miller <hmiller@IO.COM>

🔗Danny Wier <dawiertx@sbcglobal.net>

----- Original Message ----- From: "Herman Miller" <hmiller@IO.COM>
To: <tuning@yahoogroups.com>
Sent: Thursday, March 29, 2007 7:31 PM
Subject: Re: [tuning] JI scales with different limits for numerators and denominators

> Danny Wier wrote:
>
>> Which leads me to my question: what is it called when you make a JI scale
>> using a different prime limit for the numerator than the limit for
>> denominator. The scale above has a 19-limit otonally and 3-limit >> utonally. A
>> rectangular scale would also qualify.
>
> I don't know if there _is_ a name for that, but maybe you could call it
> 19/3-limit. An overtone series would be x/2-limit (where x is unlimited,
> but the denominator is always a power of 2). The idea only makes sense
> if your 1/1 reference pitch has a special role in the scale: assigning a
> different note to be the 1/1 could change the limit of the scale.

I didn't think of that problem, and I did have tonal music in mind.

I also thought of names like "asymmetrical JI scale", and in cases where the o-limit is much higher than the u-limit (as in that 19/3-limit scale), "compound otonal". Just possibilities.

I also have a ten-note 11/3-limit "country-blues" scale as an idea for a harmonica a while back. Two 8:9:10:11:12:14 chords a fourth apart, but I forgot how I had the (imaginary) reeds laid out.

~D.

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

hi danny
you have used degrees of 36-ADO with prime limit for the numerator :

1/1
37/36
19/18
13/12
10/9
41/36
7/6
43/36
11/9
5/4
23/18
47/36
4/3
49/36
25/18
17/12
13/9
53/36
3/2
55/36
14/9
19/12
29/18
59/36
5/3
61/36
31/18
7/4
16/9
65/36
11/6
67/36
17/9
23/12
35/18
71/36
2/1

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 Danny Wier
Sent: Friday, March 30, 2007 1:50 AM
To: tuning@yahoogroups.com
Subject: [tuning] JI scales with different limits for numerators and denominators

Turns out I have a scale in the Scala archive. It's one of the "ClownTone"
just scales I came up with through brainstorming years ago. They were
various mostly otonal scales plus the same transposed by a fourth or fifth,
filling out a twelve-note chromatic scale. This one is made up of
18:19:20:21:22:24 tetrachords a fifth apart plus a 17 below the higher one.

! wier_cl.scl
!
Danny Wier, ClownTone (2003)
12
!
19/18
10/9
7/6
11/9
4/3
17/12
3/2
19/12
5/3
7/4
11/6
2/1

I haven't written anything using this scale except stuff I made up in my
head and long-forgotten bass solos.

Which leads me to my question: what is it called when you make a JI scale
using a different prime limit for the numerator than the limit for
denominator. The scale above has a 19-limit otonally and 3-limit utonally. A
rectangular scale would also qualify.

~D.

🔗Cameron Bobro <misterbobro@yahoo.com>

The "tonal center", or "key key" :-) of what Shaahin calls 36-ADO is
on the 16/9.

Your tuning is mostly centered on the 4/3, with a secondary center
on 4/3 above that, so it's lopsided.

A number of well-temperaments, when examined this way, turn out to
be very logical. For example, I made some this way: three groups of
consecutive fifths, each group centered in this way, ie as
overtones, on the first tone of the group, and did "compare file" in
Scala. One of the tunings I did was identical, within some
ridiculously tiny margin, to one of Tom Dent's tuning, and different
versions turned up Mercadier, Niedhart... a number of historical
WTs. If you shove your different fifths hither and about, you lose
this particular cohesion.

-Cameron Bobro

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:
>
> hi danny
> you have used degrees of 36-ADO with prime limit for the
numerator :
>
> 1/1
> 37/36
> 19/18
> 13/12
> 10/9
> 41/36
> 7/6
> 43/36
> 11/9
> 5/4
> 23/18
> 47/36
> 4/3
> 49/36
> 25/18
> 17/12
> 13/9
> 53/36
> 3/2
> 55/36
> 14/9
> 19/12
> 29/18
> 59/36
> 5/3
> 61/36
> 31/18
> 7/4
> 16/9
> 65/36
> 11/6
> 67/36
> 17/9
> 23/12
> 35/18
> 71/36
> 2/1
>
>
> 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 Danny Wier
> Sent: Friday, March 30, 2007 1:50 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] JI scales with different limits for numerators
and denominators
>
>
>
> Turns out I have a scale in the Scala archive. It's one of
the "ClownTone"
> just scales I came up with through brainstorming years ago. They
were
> various mostly otonal scales plus the same transposed by a fourth
or fifth,
> filling out a twelve-note chromatic scale. This one is made up of
> 18:19:20:21:22:24 tetrachords a fifth apart plus a 17 below the
higher one.
>
> ! wier_cl.scl
> !
> Danny Wier, ClownTone (2003)
> 12
> !
> 19/18
> 10/9
> 7/6
> 11/9
> 4/3
> 17/12
> 3/2
> 19/12
> 5/3
> 7/4
> 11/6
> 2/1
>
> I haven't written anything using this scale except stuff I made up
in my
> head and long-forgotten bass solos.
>
> Which leads me to my question: what is it called when you make a
JI scale
> using a different prime limit for the numerator than the limit for
> denominator. The scale above has a 19-limit otonally and 3-limit
utonally. A
> rectangular scale would also qualify.
>
> ~D.
>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

hi cameron
why 16/9?

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 12:52 PM
To: tuning@yahoogroups.com
Subject: [tuning] Re: JI scales with different limits for numerators and denominators

The "tonal center", or "key key" :-) of what Shaahin calls 36-ADO is
on the 16/9.

Your tuning is mostly centered on the 4/3, with a secondary center
on 4/3 above that, so it's lopsided.

-Cameron Bobro

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> , "Mohajeri Shahin" <shahinm@...> wrote:
>
> hi danny
> you have used degrees of 36-ADO with prime limit for the
numerator :
>
> 1/1
> 37/36
> 19/18
> 13/12
> 10/9
> 41/36
> 7/6
> 43/36
> 11/9
> 5/4
> 23/18
> 47/36
> 4/3
> 49/36
> 25/18
> 17/12
> 13/9
> 53/36
> 3/2
> 55/36
> 14/9
> 19/12
> 29/18
> 59/36
> 5/3
> 61/36
> 31/18
> 7/4
> 16/9
> 65/36
> 11/6
> 67/36
> 17/9
> 23/12
> 35/18
> 71/36
> 2/1
>
>
> Shaahin Mohajeri
>
> Tombak Player & Researcher , Microtonal Composer
>
> My web site?? ???? ????? ?????? <http://240edo.googlepages.com/ <http://240edo.googlepages.com/> >
>
> My farsi page in Harmonytalk ???? ??????? ?? ??????? ???
<http://www.harmonytalk.com/mohajeri <http://www.harmonytalk.com/mohajeri> >
>
> Shaahin Mohajeri in
Wikipedia ????? ?????? ??????? ??????? ???? ????
<http://en.wikipedia.org/wiki/Shaahin_mohajeri <http://en.wikipedia.org/wiki/Shaahin_mohajeri> >
>
>
>
> ________________________________
>
> From: tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> [mailto:tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> ] On
Behalf Of Danny Wier
> Sent: Friday, March 30, 2007 1:50 AM
> To: tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>
> Subject: [tuning] JI scales with different limits for numerators
and denominators
>
>
>
> Turns out I have a scale in the Scala archive. It's one of
the "ClownTone"
> just scales I came up with through brainstorming years ago. They
were
> various mostly otonal scales plus the same transposed by a fourth
or fifth,
> filling out a twelve-note chromatic scale. This one is made up of
> 18:19:20:21:22:24 tetrachords a fifth apart plus a 17 below the
higher one.
>
> ! wier_cl.scl
> !
> Danny Wier, ClownTone (2003)
> 12
> !
> 19/18
> 10/9
> 7/6
> 11/9
> 4/3
> 17/12
> 3/2
> 19/12
> 5/3
> 7/4
> 11/6
> 2/1
>
> I haven't written anything using this scale except stuff I made up
in my
> head and long-forgotten bass solos.
>
> Which leads me to my question: what is it called when you make a
JI scale
> using a different prime limit for the numerator than the limit for
> denominator. The scale above has a 19-limit otonally and 3-limit
utonally. A
> rectangular scale would also qualify.
>
> ~D.
>