41-EDO

It just occurred to me that 41-EDO is one of the best EDOs (it's the
first one that represents all the ratios of the 9-limit differently
and consistently) but I've never heard anything written in it. Anyone
have any listening suggestions?

Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> It just occurred to me that 41-EDO is one of the best EDOs (it's the
> first one that represents all the ratios of the 9-limit differently
> and consistently) but I've never heard anything written in it. Anyone
> have any listening suggestions?

I wrote a piece in it, Magic Rondo, but I don't think it is one of my
better ones. Maybe I should try again.

As the name suggests, one of the nifty featues of 41 is that it is a
good tuning for magic temperament. Another, as you note, is that it
gives us the 9-limit diamond, and is an excellent 9-limit system overall.

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> It just occurred to me that 41-EDO is one of the best EDOs (it's the
> first one that represents all the ratios of the 9-limit differently
> and consistently) but I've never heard anything written in it. Anyone
> have any listening suggestions?
>
> Keenan

If you want see and hear a very short (7-measure) example piece (13-
limit) that will allow you to compare it to some other tunings, go to:
http://dkeenan.com/sagittal/exmp/index.htm

Another interesting thing about 41-ET is that it's a subset of 2460-ET
(27-limit consistent, and also a multiple of 12). 2460 is the division
in which we're able to map most of the smallest intervals that can be
notated in the Sagittal notation. For example, we can distinguish
between 26:27 (difference between a Pythagorean A and 13/8 of C),
8192:8505 (difference between the apotome and the sum of 80:81 and
63:64), and 51200:531441 (three 80:81 commas) -- steps of < 1/2 cent.
If you were to build flexible-pitch acoustic instruments in 41-ET, you
could approximate any of the 27-limit consonances to better than 1/6
cent (and most of them considerably better than that) by pitch-bending
in increments of 1/60 degree (you might call them "minutes", but we
already call them "minas", which is short for "schisminas"). I think
it's an excellent reference framework for defining pitches for
electronic music.

--George

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

> I think
> it's an excellent reference framework for defining pitches for
> electronic music.

It could also, of course, be used notationally in ways other than
Sagittal. There's no compelling reason why Reinhard notation needs to
be referred to 1200edo; and both 612 (dividing the semitone into 51
parts) and 2460 (dividing it into 205 parts) are self-recommending
alternatives. Put them together and you get atomic temperament,
incidentally.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@> wrote:
>
> > I think
> > it's an excellent reference framework for defining pitches for
> > electronic music.
>
> It could also, of course, be used notationally in ways other than
> Sagittal. There's no compelling reason why Reinhard notation needs
to
> be referred to 1200edo; and both 612 (dividing the semitone into 51
> parts) and 2460 (dividing it into 205 parts) are self-recommending
> alternatives. Put them together and you get atomic temperament,
> incidentally.

The only problem is that it's not as easy to think of something
divided into 51 or 205 parts as it is into 50 or 200 parts. The nice
thing about 41 into 2460 is that 60 parts is reasonably easy, so the
combination of 41-ET instruments and a Reinhard-style notation (in
2460th-octave increments) would be a good match.

--George