Yahoo Tuning Groups Ultimate Backup makemicromusic Organ Study #1 in 26 edo

Cool piece! I was surprised at how relatively normal this sounded to me,
considering that I haven't heard of 26EDO being used before. What
characteristics of it are appealing to you? A quick check shows it does a
good job in 7 and 11, and a recognizable job at 3, and a pretty crummy job
at 5. This, of course, is a very simplistic way of looking at an equal
temperament.

On 2/11/07, Daniel Thompson <microtonaldan@...> wrote:
>
> I recently uploaded a little study for pipe organ in 26 edo.
>
> <http://www.microtonalmusic.net/audio/26edoorganstudy1.mp3>
>
> I would be interested in hearing if anyone else has done much
> experimenting in this temperament. I kept this study fairly simple, but
> I hope to finish a second one that will explore some of this
> temperament's more exotic harmonic possibilities.
>
> Thank You,
> Daniel Thompson
> http://danielthompson.blogspot.com
>
>
>

[Non-text portions of this message have been removed]

🔗Cameron Bobro <misterbobro@...>

Hehe, I like the piece.

You could make some very nice tetrachords in 26. Haven't tried 26-
ED0 until this very moment, but many of the intervals are very
familiar- there's 10/9, 14/11, 27/23 right off the bat, within tiny
ranges, this would be a good tuning for an almost-equal rational
tuning! Lessee, or hear rather... I really like the dark fifth,
too.

And there's no wanna-be 5/4, what a relief! :-)

Good choice of tuning, I dig it, let us know when you do some
modulations!

-Cameron Bobro

--- In MakeMicroMusic@yahoogroups.com, "Daniel Thompson"
<microtonaldan@...> wrote:
>
> I recently uploaded a little study for pipe organ in 26 edo.
>
> <http://www.microtonalmusic.net/audio/26edoorganstudy1.mp3>
>
> I would be interested in hearing if anyone else has done much
> experimenting in this temperament. I kept this study fairly
simple, but
> I hope to finish a second one that will explore some of this
> temperament's more exotic harmonic possibilities.
>
> Thank You,
> Daniel Thompson
> http://danielthompson.blogspot.com
>

🔗Daniel Thompson <microtonaldan@...>

Thanks for the comments. There's a lot that I like about 26 edo. I
enjoy the triad 0, 277, 692 (in cents). It has an approximation of
7/6 that's about 10 cents sharp and an approximation of 3/2 that is
about 10 cents flat. The directions of the discrepancies, however,
seem to produce a triad that is a little more spatially balanced than
the corresponding justly tuned triad, while still having a nice
flavor of septimal harmony.

The distance from 277 to 692 is about 415 cents. You can modulate to
a mode that uses 415 cents as a sort of approximation of a major
third (perhaps a Pythagorean major third), but it is pretty sharp.
There seems to be a pretty strong urge to modulate back to the
septimal minor mode. When I compose in 12 edo I feel the opposite
urge to go from minor to major. You could also use a minor third of
323 and a major third of 369, but the minor is still closer than the
major. The minor modes sound strong and powerful to me. You can also
have some interesting modulations where you go from one type of minor
to the other or one type of major to the other.

26 edo has an equally tempered tritone. The tritone seems to me to
have a stronger function in 26 edo. I speculate that this may have
something to do with the fact that the fifth is pretty flat. A
perfectly tuned fifth divides the octave in a linear sense, while a
tempered tritone divides an octave in a logarithmic sense. Since the
fifth is flat, I wonder if the emphasis is shifted somewhat towards
the tritone as a sort of alternate point of symmetry. I also like the
way the tritone is asymmetrically divided into two different minor
like intervals (277 and 323 cents).

I don't know if any of this makes sense to any one but me. I'm still
trying to come to terms with this temperament. There is a lot of
speculation involved. I do know that I like the sound of it.

--- In MakeMicroMusic@yahoogroups.com, "Cody Hallenbeck"
<codyhallenbeck@...> wrote:
>
> Cool piece! I was surprised at how relatively normal this sounded
to me,
> considering that I haven't heard of 26EDO being used before. What
> characteristics of it are appealing to you? A quick check shows it
does a
> good job in 7 and 11, and a recognizable job at 3, and a pretty
crummy job
> at 5. This, of course, is a very simplistic way of looking at an
equal
> temperament.
>
> On 2/11/07, Daniel Thompson <microtonaldan@...> wrote:
> >
> > I recently uploaded a little study for pipe organ in 26 edo.
> >
> > <http://www.microtonalmusic.net/audio/26edoorganstudy1.mp3>
> >
> > I would be interested in hearing if anyone else has done much
> > experimenting in this temperament. I kept this study fairly
simple, but
> > I hope to finish a second one that will explore some of this
> > temperament's more exotic harmonic possibilities.
> >
> > Thank You,
> > Daniel Thompson
> > http://danielthompson.blogspot.com
> >
> >
> >
>
>
> [Non-text portions of this message have been removed]
>

🔗Herman Miller <hmiller@...>

Daniel Thompson wrote:
> I recently uploaded a little study for pipe organ in 26 edo.
> > <http://www.microtonalmusic.net/audio/26edoorganstudy1.mp3>

Nice! This sort of dark "subminor" feel is one of the things that 26-ET is good at.

> I would be interested in hearing if anyone else has done much > experimenting in this temperament. I kept this study fairly simple, but > I hope to finish a second one that will explore some of this > temperament's more exotic harmonic possibilities.

I've only done one piece specifically in 26-ET.

http://www.io.com/~hmiller/midi/26tet.mid

It starts out sounding relatively traditional, but with some chromatic alterations from the usual diatonic scale. The chord progressions start going in some unusual directions, eventually introducing approximations of higher overtones in the harmonic series (11 and 13).

More recently I've been exploring a kind of temperament called "lemba" which has a characteristic 16-note scale. One of the tunings I use for this is very close to an octave-stretched 26-ET. These examples aren't actually tuned in 26-ET, but they could be adapted without much trouble.

http://www.io.com/~hmiller/music/ex/lemba.mid
http://www.io.com/~hmiller/midi/lemba2.mid
http://home.comcast.net/~teamouse/lemba-galatsia.mp3

The basic 10-note lemba scale in 26-ET has alternating steps of 2 and 3 degrees of 26-ET (3 2 3 2 3 3 2 3 2 3). You get the 16-note scale by splitting the 3-steps into smaller steps of 1 and 2 degrees of 26-ET (2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2). Instead of a chain of fifths, lemba has a chain of approximate 8/7 intervals (5 steps of 26-ET); a fifth is approximated by three of those intervals (15 steps of 26-ET).

Another temperament of interest is injera, which repeats at the half-octave (like lemba), but is based on a chain of fifths or fourths (like meantone). The generator of injera temperament is 2 steps of 26-ET. One nice thing about this temperament is that it has a 12-note scale which can easily be adapted to the traditional piano keyboard.

Also of theoretical possibility, there's cynder (aka mothra), which has a 5-step generator (like lemba), but repeats at the octave, and superkleismic, with a 7-step generator. I don't know whether these are useful in the context of 26-ET, but it might be worth a try.

🔗Aaron Krister Johnson <aaron@...>

🔗Cameron Bobro <misterbobro@...>

--- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
<aaron@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Cameron Bobro"
>
> > And there's no wanna-be 5/4, what a relief! :-)
>
> I'm curious from whence comes the fashionable hatred of this
interval?
>
> -A.

Hahaha! I am not aware of any fashion for hating 5/4, nor do I hate
this lovely interval. Your comment is a classic case of the "straw
man".

Jury-rigging a tuning for triadic harmony with an "approximation" of
5/4 is a fine recipe for a seasick sound.

🔗Cameron Bobro <misterbobro@...>

--- In MakeMicroMusic@yahoogroups.com, "Daniel Thompson"
<microtonaldan@...> wrote:
>
> Thanks for the comments. There's a lot that I like about 26 edo. I
> enjoy the triad 0, 277, 692 (in cents). It has an approximation of
> 7/6 that's about 10 cents sharp and an approximation of 3/2 that
>is
> about 10 cents flat.

The character of the dark third is distinctly different from 7/6.
More like the 27/23 dark third which is less than .7 cents away, I'd
say.

>The directions of the discrepancies, however,
> seem to produce a triad that is a little more spatially balanced >
>than
> the corresponding justly tuned triad, while still having a nice
> flavor of septimal harmony.

I agree that it's very nicely balanced.

> The distance from 277 to 692 is about 415 cents. You can modulate
>to
> a mode that uses 415 cents as a sort of approximation of a major
> third (perhaps a Pythagorean major third), but it is pretty sharp.

The Pythagorean third in this tuning is the 369 cent third (the
fourth fifth). The high third in 26 is 2 cents from 14/11, which is
a great third- the high third of 26 isn't an approximation of 5/4 or
81/64 at all.

Functionally, the 26 high third belongs in the region staked out
from about 14/11 to 9/7. With these high thirds, you might also want
to try using a scale with an augmented fourth, a kind of super-duper
Lydian. :-)

> There seems to be a pretty strong urge to modulate back to the
> septimal minor mode.

If you use a very broad second, minor or major, it will soften this.
Then soften the upper the upper tetrachord with a low seventh, not a
leading tone. It's a sweet and peaceful sound.

-Cameron Bobro

🔗aum <aum@...>

🔗Carl Lumma <ekin@...>

>I recently uploaded a little study for pipe organ in 26 edo.
>
><http://www.microtonalmusic.net/audio/26edoorganstudy1.mp3>
>
>I would be interested in hearing if anyone else has done much
>experimenting in this temperament. I kept this study fairly simple, but
>I hope to finish a second one that will explore some of this
>temperament's more exotic harmonic possibilities.
>
>Thank You,
>Daniel Thompson
>http://danielthompson.blogspot.com

Fantastic sound! Good use of 26. Boring composition. But
as a study, it succeeds splendidly.

-Carl

🔗Gene Ward Smith <genewardsmith@...>

--- In MakeMicroMusic@yahoogroups.com, Herman Miller <hmiller@...>
wrote:
> Daniel Thompson wrote:

> > I would be interested in hearing if anyone else has done much
> > experimenting in this temperament.

> I've only done one piece specifically in 26-ET.

> http://www.io.com/~hmiller/midi/26tet.mid

I think other people have given it a try. A very different
temperament with sharp rather than flat thirds is 27, and for some
reason that isn't tried as much. In fact, so far as I know I'm the
only one who has tried it. It's quite musically feasible, however.
26+27=53, showing the errors of the two cancelling out. However, 27
has better fifths (though of course very different ones) and much
better major and minor thirds. 26 has a much better 7/4, but taken as
a whole 27 does much better with septimal intervals also. Why it gets
ignored in favor of 26 all the time I don't know. Of course, George
Secor thinks it's a garbage tuning, but I suppose he'd say the same
about 26.

Just as Herman explained for 26, it's got some interesting
temperament possibilities. 27 is excellent for augene, good for
superpyth or beatles, and can be used for myna or sensi.

🔗Gene Ward Smith <genewardsmith@...>

🔗Daniel Thompson <microtonaldan@...>

--- In MakeMicroMusic@yahoogroups.com, Herman Miller <hmiller@...>
wrote:
>
> Daniel Thompson wrote:
> > I recently uploaded a little study for pipe organ in 26 edo.
> >
> > <http://www.microtonalmusic.net/audio/26edoorganstudy1.mp3>
>
> Nice! This sort of dark "subminor" feel is one of the things that
26-ET
> is good at.
>
> > I would be interested in hearing if anyone else has done much
> > experimenting in this temperament. I kept this study fairly
simple, but
> > I hope to finish a second one that will explore some of this
> > temperament's more exotic harmonic possibilities.
>
> I've only done one piece specifically in 26-ET.
>
> http://www.io.com/~hmiller/midi/26tet.mid
>
> It starts out sounding relatively traditional, but with some
chromatic
> alterations from the usual diatonic scale. The chord progressions
start
> going in some unusual directions, eventually introducing
approximations
> of higher overtones in the harmonic series (11 and 13).
>
> More recently I've been exploring a kind of temperament
called "lemba"
> which has a characteristic 16-note scale. One of the tunings I use
for
> this is very close to an octave-stretched 26-ET. These examples
aren't
> actually tuned in 26-ET, but they could be adapted without much
trouble.
>
> http://www.io.com/~hmiller/music/ex/lemba.mid
> http://www.io.com/~hmiller/midi/lemba2.mid
> http://home.comcast.net/~teamouse/lemba-galatsia.mp3
>
> The basic 10-note lemba scale in 26-ET has alternating steps of 2
and 3
> degrees of 26-ET (3 2 3 2 3 3 2 3 2 3). You get the 16-note scale
by
> splitting the 3-steps into smaller steps of 1 and 2 degrees of 26-
ET (2
> 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2). Instead of a chain of fifths, lemba
has
> a chain of approximate 8/7 intervals (5 steps of 26-ET); a fifth is
> approximated by three of those intervals (15 steps of 26-ET).
>
> Another temperament of interest is injera, which repeats at the
> half-octave (like lemba), but is based on a chain of fifths or
fourths
> (like meantone). The generator of injera temperament is 2 steps of
> 26-ET. One nice thing about this temperament is that it has a 12-
note
> scale which can easily be adapted to the traditional piano keyboard.
>
> Also of theoretical possibility, there's cynder (aka mothra), which
has
> a 5-step generator (like lemba), but repeats at the octave, and
> superkleismic, with a 7-step generator. I don't know whether these
are
> useful in the context of 26-ET, but it might be worth a try.
>

Thanks for the information and music examples. I especially liked the
first one in 26 edo. It has a kind of sound that I've never achieved
in this temperament. It's nice to get a better idea of what some of
the possibilities are.

Thanks,
Daniel Thompson

🔗Herman Miller <hmiller@...>

Gene Ward Smith wrote:

> I think other people have given it a try. A very different > temperament with sharp rather than flat thirds is 27, and for some > reason that isn't tried as much. In fact, so far as I know I'm the > only one who has tried it. It's quite musically feasible, however. > 26+27=53, showing the errors of the two cancelling out. However, 27 > has better fifths (though of course very different ones) and much > better major and minor thirds. 26 has a much better 7/4, but taken as > a whole 27 does much better with septimal intervals also. Why it gets > ignored in favor of 26 all the time I don't know. Of course, George > Secor thinks it's a garbage tuning, but I suppose he'd say the same > about 26.

I did a 27-ET version of Galticeran which is a nice change from the 21-ET version. It has a nice shimmering quality, not as gloomy as the one in 21-ET.

http://www.io.com/~hmiller/midi/Galticeran27.mid

http://www.io.com/~hmiller/midi/Galticeran21.mid

In the end I preferred the 21-ET version since it was a better match for the particular mood I was trying to achieve, but there's a lot of good qualities in the 27-ET version (and both of these turned out better than the previous retunings I tried).

Organ Study #1 in 26 edo

🔗Daniel Thompson <microtonaldan@...>

🔗Cody Hallenbeck <codyhallenbeck@...>

🔗Cameron Bobro <misterbobro@...>

🔗Daniel Thompson <microtonaldan@...>

🔗Herman Miller <hmiller@...>

🔗Aaron Krister Johnson <aaron@...>

🔗Cameron Bobro <misterbobro@...>

🔗Cameron Bobro <misterbobro@...>

🔗aum <aum@...>

🔗Carl Lumma <ekin@...>

🔗Gene Ward Smith <genewardsmith@...>

🔗Gene Ward Smith <genewardsmith@...>

🔗Daniel Thompson <microtonaldan@...>

🔗Herman Miller <hmiller@...>