Topic: JI scales with different limits for numerators and denominators
1 scales
| File | Description | Notes | Period (ยข) | Limit |
|---|---|---|---|---|
| wier_cl | Danny Wier, ClownTone (2003) | 12 | 1200.0 | 19 |
Thread (7 messages)
From: Danny Wier (2007-03-29) Subject: 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.
From: Herman Miller (2007-03-30) 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.
From: Danny Wier (2007-03-30) Subject: Re: [tuning] JI scales with different limits for numerators and denominators ----- Original Message ----- From: "Herman Miller" <[email protected]> To: <[email protected]> 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.
From: Mohajeri Shahin (2007-04-03) Subject: RE: [tuning] JI scales with different limits for numerators and denominators 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: [email protected] [mailto:[email protected]] On Behalf Of Danny Wier Sent: Friday, March 30, 2007 1:50 AM To: [email protected] 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.
From: Cameron Bobro (2007-04-03) Subject: 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. 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 [email protected], "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: [email protected] [mailto:[email protected]] On Behalf Of Danny Wier > Sent: Friday, March 30, 2007 1:50 AM > To: [email protected] > 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. >
From: Mohajeri Shahin (2007-04-03) Subject: RE: [tuning] Re: JI scales with different limits for numerators and denominators 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: [email protected] [mailto:[email protected]] On Behalf Of Cameron Bobro Sent: Tuesday, April 03, 2007 12:52 PM To: [email protected] 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. 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 [email protected] <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: [email protected] <mailto:tuning%40yahoogroups.com> [mailto:[email protected] <mailto:tuning%40yahoogroups.com> ] On Behalf Of Danny Wier > Sent: Friday, March 30, 2007 1:50 AM > To: [email protected] <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. >
From: Cameron Bobro (2007-04-03) Subject: Re: JI scales with different limits for numerators and denominators --- In [email protected], "Mohajeri Shahin" <shahinm@...> wrote: > > hi cameron > why 16/9? That's the transposition where tuning is all overtones of the 1/1. .