A minimal 38-tone tuning for maqam music with strong septimal flavours

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Voila! Has anyone discovered this before?

Oz.

--- 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?

--- 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.

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

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 04 Kas�m 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.

--- 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