Topic: A minimal 38-tone tuning for maqam music with strong septimal flavours
1 scales
| File | Description | Notes | Period (ยข) |
|---|---|---|---|
| undeviginti57 | Undeviginti[57] (152&171) in 171-et tuning | 57 | 1200.0 |
Thread (6 messages)
From: Ozan Yarman (2007-11-03) Subject: A minimal 38-tone tuning for maqam music with strong septimal flavours In SCALA, type: Equal 19 Copy 0 1 Move 14.24 Normalize Merge 1 Voila! Has anyone discovered this before? Oz.
From: Gene Ward Smith (2007-11-04) Subject: Re: A minimal 38-tone tuning for maqam music with strong septimal flavours --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > Voila! Has anyone discovered this before? Could you first explain more precisely what you mean--for instance, two chains of 19-et 14.24 centr apart?
From: Gene Ward Smith (2007-11-04) Subject: Re: A minimal 38-tone tuning for maqam music with strong septimal flavours --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > Voila! Has anyone discovered this before? > > Could you first explain more precisely what you mean--for instance, two > chains of 19-et 14.24 centr apart? > If so, it looks suspiciously like part of the 76&95 temperament. This may as well be tuned to 171-et, where Oz's scale would be two rows of 19-equal (9 steps of 171-et) separated by two steps of 171-et. The kernel is generated by 2401/2400 and the 19-comma. The wedgie is <<76 76 57 -56 -123 -81|| and if Oz is willing to go to a 76-note scale, there will be a ton more septimal harmony. Along the same lines is the 152&171 temperament, which has come up before. It tempers out the 19-comma and 4375/4374, and separates the chains of 19-et by one step of 171-et rather than two. The wedgie for that is <<19 19 57 -14 37 79|| and it is considerably more efficient, with a ton of septimal harmony already with the 57 note scale, which is three chains of 19.
From: Herman Miller (2007-11-05) Subject: Re: [tuning] Re: A minimal 38-tone tuning for maqam music with strong septimal flavours Gene Ward Smith wrote: > --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> > wrote: >> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: >> >>> Voila! Has anyone discovered this before? >> Could you first explain more precisely what you mean--for instance, > two >> chains of 19-et 14.24 centr apart? >> > > If so, it looks suspiciously like part of the 76&95 temperament. This > may as well be tuned to 171-et, where Oz's scale would be two rows of > 19-equal (9 steps of 171-et) separated by two steps of 171-et. The > kernel is generated by 2401/2400 and the 19-comma. The wedgie is > > <<76 76 57 -56 -123 -81|| > > and if Oz is willing to go to a 76-note scale, there will be a ton > more septimal harmony. The generator mapping of this is [<19, 31, 45, 54|, <0, -4, -4, -3|]; you'd need 5 chains of 19-et just to get 5-limit harmony. With only two chains of 19-ET, there's a 19&57 temperament that might work, and the generators are about the right size. <<0, 0, 19, 0, 30, 44|| [<19, 30, 44, 53|, <0, 0, 0, 1|] TOP-Max P = 63.277969, G = 15.093567 TOP-RMS P = 63.293581, G = 14.266095 > Along the same lines is the 152&171 temperament, which has come up > before. It tempers out the 19-comma and 4375/4374, and separates the > chains of 19-et by one step of 171-et rather than two. The wedgie for > that is > > <<19 19 57 -14 37 79|| > > and it is considerably more efficient, with a ton of septimal harmony > already with the 57 note scale, which is three chains of 19. That one looks a bit more manageable than the 76&95, and it has a generator size about half the size (around 7.14 - 7.15 cents). There's also a 19&95 which is more accurate than the 19&57, but not as complex as the 151&171. Its generator isn't the right size, but it could be useful for comparison. <<19, 19, 38, -14, 7, 35|| [<19, 30, 44, 53|, <0, 1, 1, 2|] TOP-Max P = 63.099661, G = 10.718850 TOP-RMS P = 63.139998, G = 9.426707
From: Ozan Yarman (2007-11-05) Subject: Re: [tuning] Re: A minimal 38-tone tuning for maqam music with strong septimal flavours ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@sbcglobal.net> To: <tuning@yahoogroups.com> Sent: 04 Kas\ufffdm 2007 Pazar 22:09 Subject: [tuning] Re: A minimal 38-tone tuning for maqam music with strong septimal flavours > --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> > wrote: > > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > > > Voila! Has anyone discovered this before? > > > > Could you first explain more precisely what you mean--for instance, > two > > chains of 19-et 14.24 centr apart? > > > > If so, it looks suspiciously like part of the 76&95 temperament. This > may as well be tuned to 171-et, where Oz's scale would be two rows of > 19-equal (9 steps of 171-et) separated by two steps of 171-et. What you say seems true enough. The > kernel is generated by 2401/2400 and the 19-comma. The wedgie is > > <<76 76 57 -56 -123 -81|| > > and if Oz is willing to go to a 76-note scale, there will be a ton > more septimal harmony. > I am trying to minimize the number of tones involved. > Along the same lines is the 152&171 temperament, which has come up > before. It tempers out the 19-comma and 4375/4374, and separates the > chains of 19-et by one step of 171-et rather than two. The wedgie for > that is > > <<19 19 57 -14 37 79|| > > and it is considerably more efficient, with a ton of septimal harmony > already with the 57 note scale, which is three chains of 19. > > > Can you give this new 57 note scale as a mode of 171-et in SCALA? Oz.
From: Gene Ward Smith (2007-11-06) Subject: Re: A minimal 38-tone tuning for maqam music with strong septimal flavours --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > Can you give this new 57 note scale as a mode of 171-et in SCALA? Lots of near-just major, minor, supermajor and subminor triads if that makes any difference. ! undeviginti57.scl Undeviginti[57] (152&171) in 171-et tuning 57 ! 7.017544 14.035088 63.157895 70.175439 77.192982 126.315790 133.333333 140.350877 189.473684 196.491228 203.508772 252.631579 259.649123 266.666667 315.789474 322.807018 329.824561 378.947368 385.964912 392.982456 442.105263 449.122807 456.140351 505.263158 512.280702 519.298246 568.421053 575.438596 582.456140 631.578947 638.596491 645.614035 694.736842 701.754386 708.771930 757.894737 764.912281 771.929825 821.052632 828.070175 835.087719 884.210526 891.228070 898.245614 947.368421 954.385965 961.403509 1010.526316 1017.543860 1024.561404 1073.684211 1080.701754 1087.719298 1136.842105 1143.859649 1150.877193 1200.000000