The 80 revolution

When George Secor and Margo Schulter were talking about the "17
revolution", did they discuss a fifth a little nearer to true, namely
the 80-equal fifth of 705 cents, or perhaps just slightly flatter,
around 704.96 cents, from the point of view of no-fives harmony and
temperaments involving chains of fifths? This came up in connection
to a scale Ozan Yarman has been considering.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> When George Secor and Margo Schulter were talking about the "17
> revolution", did they discuss a fifth a little nearer to true,
namely
> the 80-equal fifth of 705 cents, or perhaps just slightly flatter,
> around 704.96 cents, from the point of view of no-fives harmony and
> temperaments involving chains of fifths? This came up in connection
> to a scale Ozan Yarman has been considering.

The Blackwood R for an equal temperament with val h is
h(9/8)/h(256/243). For 80, this is 14/5, or 2.8, for 63, it is 11/4,
or 2.75. These are therefore a little sharper than Margo's e-system
of 2.718281828..., and sharper, or on the very edge, of her "gentle"
region for neo-Gothic. It seems like a pretty good neo-Gothic region,
but it doesn't seem to have gotten much attention, if any. Ozan
Yarman's scale suggests some people might like it. Ozan's scale is,
basically, the 12 note MOS using the fifths of 80-equal; the 17-note
MOS is an attractive alternative.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> The Blackwood R for an equal temperament with val h is
> h(9/8)/h(256/243). For 80, this is 14/5, or 2.8, for 63, it is
11/4,
> or 2.75. These are therefore a little sharper than Margo's e-system
> of 2.718281828..., and sharper, or on the very edge, of
her "gentle"
> region for neo-Gothic. It seems like a pretty good neo-Gothic
region,
> but it doesn't seem to have gotten much attention, if any.

If I recall correctly, the 46&63 system came up in connection with
something Margo was considering. In 13-limit sans 5, the 46&63 and
63&80 systems are the same, and the rms fifth, with just the no-fives
consonances, is 704.946969 cents, which is a little sharper than what
Margo seems to prefer for "gentle" systems. Anyway, this Ozan system
I think, if I am remembering this right, did come up as a no-fives
system. The R value for the above fifth is 2.7887, and for Ozan's
fifth, which is exactly 4000/3993 sharper than a pure fifth, we have
704.987 cents, for an R of 2.7973. It's all a bit above e.

Does this mean that I have finally come up with something worthwhile?
----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: 13 Mart 2005 Pazar 5:44
Subject: [tuning] Re: The 80 revolution

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> When George Secor and Margo Schulter were talking about the "17
> revolution", did they discuss a fifth a little nearer to true,
namely
> the 80-equal fifth of 705 cents, or perhaps just slightly flatter,
> around 704.96 cents, from the point of view of no-fives harmony and
> temperaments involving chains of fifths? This came up in connection
> to a scale Ozan Yarman has been considering.

The Blackwood R for an equal temperament with val h is
h(9/8)/h(256/243). For 80, this is 14/5, or 2.8, for 63, it is 11/4,
or 2.75. These are therefore a little sharper than Margo's e-system
of 2.718281828..., and sharper, or on the very edge, of her "gentle"
region for neo-Gothic. It seems like a pretty good neo-Gothic region,
but it doesn't seem to have gotten much attention, if any. Ozan
Yarman's scale suggests some people might like it. Ozan's scale is,
basically, the 12 note MOS using the fifths of 80-equal; the 17-note
MOS is an attractive alternative.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> Does this mean that I have finally come up with something worthwhile?

It looks great for neo-Gothic music; I don't know enough to tell you
if it is a grand idea for Turkish music but I suppose it might be. I
think 17 notes of it instead of 12 would be nice.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> When George Secor and Margo Schulter were talking about the "17
> revolution", did they discuss a fifth a little nearer to true,
namely
> the 80-equal fifth of 705 cents, or perhaps just slightly flatter,
> around 704.96 cents, from the point of view of no-fives harmony and
> temperaments involving chains of fifths? This came up in connection
> to a scale Ozan Yarman has been considering.

Margo and I each devised 17-tone tunings that contain a chain of
fifths of ~704.3770c (giving an exact 11:14) in about half the fifths
in the circle. In her temperament these fifths were in the most
common keys, whereas in mine they were in the remote part of the
circle. My 17-tone tuning is as follows:

! secor_17wt.scl
!
George Secor's well temperament with 5 pure 11/7 and 3 near just
11/6
17
!
66.74120
144.85624
214.44090
278.33864
353.61023
428.88181
492.77955
562.36421
640.47925
707.22045
771.11819
849.23324
921.66136
985.55910
1057.98722
1136.10226
2/1

With C=1/1, the best approximations of the 6:7:9:11:13 pentad are
built on F, C, G, D, and A.

Sorry, I owe you (Gene) and Ozan (on notation) both replies, but I
have had very little spare time lately (along with some Internet
access problems) and can answer things that require only brief
replies now. Hopefully, before long.

Best,

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> Margo and I each devised 17-tone tunings that contain a chain of
> fifths of ~704.3770c (giving an exact 11:14) in about half the fifths
> in the circle. In her temperament these fifths were in the most
> common keys, whereas in mine they were in the remote part of the
> circle.

From that point of view, the 17-note chain-of-fifths MOS of 46-equal
might be of interest. The wolf fifth is 28 steps of 46, not 27, and if
you are brave enough to interpret it in the 21-odd-limit, could be
32/21, which is one of the intervals 46 uses it for.

The no-fives 13-limit temperament this corresponds to is exactly the
same as in the case of 80; only the 5 mapping differs, and we ignore
that. Does it need a name, I wonder? It is the temperament, regarded
as a 13-limit no-fives temperament, which tempers out 169/168,
352/351, and 364/363. It has an octave period and a fifth generator,
and is supported by 17, 29, 46, 63, 80, 92, 109, 126, 172 and 189. It
can be extended to a complete 13-limit temperament in various ways;
for instance by adding 91/90 to the mix.

The 80-et version of this MOS has a wolf of 720 cents, which is the
fifth of 5-equal. We pay for that with sharper thirds, less near to
14/11; the 80-et version of a 14/11 third is 420 cents, whereas the
46-et version is 417.3 cents, and a pure 14/11 is 417.4 cents. The
80-et version of 9/7, however, is almost pure, and is much better than
the 46-et version, and this is significant because they appear in the
remote keys instead of 14/11. Margo targeted this for a few of her
thirds in her well-temperament.