Yahoo Tuning Groups Ultimate Backup tuning interesting about 34-edo

Has anyone noticed that 1 step of 34-edo is very close to a 49:48 comma?

Interesting b/c 34 is a decent 5-limit system that, to my ear, is 'tinged' with 7-limit sound, without being a strong 7-limit system.

This is related to 1 step of 44-edo being close to 64:63, making 22-edo a similar 'tinged' system, b/c unlike others, I find the 7/4 interval here quite compromised, but notheless very cool sounding, and it retains it's distinct flavor.

I think there might be something to the idea of a 'tinged' system for musical purposes---a sense of new color coming from an ambigious new direction (from a 12-edo or 5-limit POV) without being explicit.

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Aaron K. Johnson <aaron@akjmusic.com>

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
> >> Has anyone noticed that 1 step of 34-edo is very close to a 49:48 >> > comma?
>
> Even closer to 50/49.
>
> >> I think there might be something to the idea of a 'tinged' system for >> musical purposes---a sense of new color coming from an ambigious new >> direction (from a 12-edo or 5-limit POV) without being explicit.
>> >
> How would it work? That is, by what mechanism to you propose we might > hear the tinging?

My first thought is that a n-limit temperament is tinged by a given p-limit interval when there is an interval in the temperament that is (close-to) halfway between the nearest approximation to that p-limit interval and the p-limit interval itself (e.g. the way 22-edo tempers out 64/63, i.e. 16/9 and 7/4 are the 'same').

That's of course, saying nothing abouta given temperament encompassing more than one 'tinge'.

I'm sure you can come up with something more rigorous--that's off the top of my head....

-A.

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>
> Has anyone noticed that 1 step of 34-edo is very close to a 49:48
comma?

I guess you don't read my posts very much, not that I blame you,
hehe. A little while ago I wrote that you can simply alternate
50/49 and 49/48 steps and make a 34 with a minutely stretched
octave. It's very good IMO and George Secor said he'd check it
out.

>
> Interesting b/c 34 is a decent 5-limit system that, to my ear, is
> 'tinged' with 7-limit sound, without being a strong 7-limit system.
>
> This is related to 1 step of 44-edo being close to 64:63, making
>22-edo
> a similar 'tinged' system, b/c unlike others, I find the 7/4
interval
> here quite compromised, but notheless very cool sounding, and it
retains
> it's distinct flavor.
>
> I think there might be something to the idea of a 'tinged' system
>for
> musical purposes---a sense of new color coming from an ambigious
new
> direction (from a 12-edo or 5-limit POV) without being explicit.

Yes this is exactly one of things I'm refering to when I've been go
on about "character families" and "things that make a tuning
cohesive", and something I believe is important to expanding
harmonic possibilities. As I've said before, 34 is amazingly
precise and complete in representing a "simple JI" interlaced
with more complex intervals which are the harmonic means of JI
intervals. Hearing it this way you have to completely dump
the literal 7/x and x/7 intervals, IMO- it's an aseptimal
framework, though exactly as you say it is somehow "tinged" with
"7" sound, perhaps because it is full of gentle relations to
the 7th and 14th partials without getting close enough to
them to create conflict? I don't know, but anyway- sounds good
to me.

-Cameron Bobro

🔗Aaron K. Johnson <aaron@akjmusic.com>

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>
> Cameron Bobro wrote:
> > --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@> wrote:
> >
> >> Has anyone noticed that 1 step of 34-edo is very close to a
49:48
> >>
> > comma?
> >
> > I guess you don't read my posts very much, not that I blame you,
> > hehe. A little while ago I wrote that you can simply alternate
> > 50/49 and 49/48 steps and make a 34 with a minutely stretched
> > octave. It's very good IMO and George Secor said he'd check it
> > out.
> >
> I have to admit, sometimes I skim posts....sounds cool to me!
>
> -A.

Maybe there's a "thing" about tunings that can be done this
way- I think 53 does this as well. Which is what you were
implying before, if I understood correctly. One, or two adjacent,
superparticular intervals stacked up to make an almost-pure octave.
I wonder what other tunings under about 50-60 tones or so do this?

-Cameron Bobro

🔗Kalle Aho <kalleaho@mappi.helsinki.fi>

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@> wrote:
> >
> > Cameron Bobro wrote:
> > > --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@> wrote:
> > >
> > >> Has anyone noticed that 1 step of 34-edo is very close to a
> 49:48
> > >>
> > > comma?
> > >
> > > I guess you don't read my posts very much, not that I blame you,
> > > hehe. A little while ago I wrote that you can simply alternate
> > > 50/49 and 49/48 steps and make a 34 with a minutely stretched
> > > octave. It's very good IMO and George Secor said he'd check it
> > > out.
> > >
> > I have to admit, sometimes I skim posts....sounds cool to me!
> >
> > -A.
>
> Maybe there's a "thing" about tunings that can be done this
> way- I think 53 does this as well. Which is what you were
> implying before, if I understood correctly. One, or two adjacent,
> superparticular intervals stacked up to make an almost-pure octave.
> I wonder what other tunings under about 50-60 tones or so do this?

Hello Cameron,

these are octaves within 3 cents of pure made with single stacked
superparticular:

(25/24)^17
(38/37)^26
(48/47)^33
(51/50)^35
(54/53)^37
(61/60)^42
(64/63)^44
(67/66)^46
(74/73)^51
(77/76)^53
(80/79)^55
(84/83)^58
(87/86)^60

Kalle Aho

🔗Kraig Grady <kraiggrady@anaphoria.com>

I would be more interested in Alternating the 2 in some MOS pattern. This way each transposition would give you a slight yet unique variation.

Posted by: "Cameron Bobro" I guess you don't read my posts very much, not that I blame you,
hehe. A little while ago I wrote that you can simply alternate
50/49 and 49/48 steps and make a 34 with a minutely stretched
octave. It's very good IMO and George Secor said he'd check it
out.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Kraig Grady <kraiggrady@anaphoria.com>

One can take any segment of the harmonic or subharmonic series that spans an Octave and Shuffle them. or if that is too even one can subdivide any of these epimores these into 2,3 or more epimores.

Posted by: "Kalle Aho"

these are octaves within 3 cents of pure made with single stacked
superparticular:

(25/24)^17
(38/37)^26
(48/47)^33
(51/50)^35
(54/53)^37
(61/60)^42
(64/63)^44
(67/66)^46
(74/73)^51
(77/76)^53
(80/79)^55
(84/83)^58
(87/86)^60

Kalle Aho
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> One can take any segment of the harmonic or subharmonic series
>that
> spans an Octave and Shuffle them. or if that is too even one can
> subdivide any of these epimores these into 2,3 or more epimores.

So there are eight divisions of the octave that fit the bill
(superparticular or two consecutive superparticular intervals
stacking to a near perfect octave, with a limit on the sheer
number of intervals about 60-70).

I agree that arranging the intervals into some kind of MOS is
groovier. You would still get the modulation possibilities of an
equal division, at least AFAIC, but more pizzaz.

The pieces I've done using segments of the harmonic series (like
26 tones of x/26 for example) are
eerily consonant in overall feeling, to my ears, regardless of how
dissonant the music is "on paper". My wife finds the sound too
peaceful, "church-like" in her words, and at this point it
seems to me that such a tuning is more appropriate to wilder
timbres.

(thanks for the list by the way, Kalle!)

-Cameron Bobro
>
>
>
> Posted by: "Kalle Aho"
>
>
> these are octaves within 3 cents of pure made with single stacked
> superparticular:
>
> (25/24)^17
> (38/37)^26
> (48/47)^33
> (51/50)^35
> (54/53)^37
> (61/60)^42
> (64/63)^44
> (67/66)^46
> (74/73)^51
> (77/76)^53
> (80/79)^55
> (84/83)^58
> (87/86)^60
>
> Kalle Aho
> --
> Kraig Grady
> North American Embassy of Anaphoria Island
<http://anaphoria.com/index.html>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los
Angeles
>

🔗Cameron Bobro <misterbobro@yahoo.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

well all JI can do this. one merely modulates from one point to another. The more commas the more range of expression one has. In fact i want tunings with as many comma distinctions as possible!

Posted by: "Cameron Bobro
I agree that arranging the intervals into some kind of MOS is
groovier. You would still get the modulation possibilities of an
equal division, at least AFAIC, but more pizzaz.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
wrote:
> >
> > --- In tuning@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@>
> > wrote:
> >
> > > How would it work? That is, by what mechanism to you propose
we
> > >might
> > > hear the tinging?
>
> > By what fantasy mechanism would we NOT hear timbre?
>
> This isn't an answer to the question.

No- nor is it what I wrote. What I wrote was:

"By what fantasy mechanism would we NOT hear timbre? Every harmony
or even entire piece of music can be considered and analized as a
complex spectrum for the simple reason that that is one of things
that it "is". The human ear is extremely finely tuned to timbre."

Which answers your question- by what mechanism would we hear
sound colors? By hearing sound color, timbre, the same as
always. If you meant, how would we go about testing and
cataloguing the "tinging", the answer is even simpler:
"just listen".

>Go read the question, try to
> understand what I said,
>and if you want to respond construcitively then
> do.

The very idea of you speaking to me in that way is pretty
damn funny.

-Cameron Bobro

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Cameron Bobro <misterbobro@yahoo.com>

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

> I think you may be coming down with Dunning-Kruger syndrome. An
> emergency proceedure to unswell your head may be in order.
>

Whatever the size of my head, the hat that fits it must be doffed
to you, oh master of internet sophistry. Your ability
to change the subject, completely avoid any unpleasant questions,
failure to acknowledge even the possible validity of any
viewpoints that don't agree with yours, and generally sidetrack
any discussion that doesn't fit into your interpretation
of temperament is simply dazzling.

Anyway, for those living higher than the geneosphere, ie, have
unravelled such Gordian knots as "3:1 is not the same as 3:2", Aaron
was saying, in reference to curious things about 34 equal divisions
of an octave

"My first thought is that a n-limit temperament is tinged by a given
p-limit interval when there is an interval in the temperament that is
(close-to) halfway between the nearest approximation to that p-limit
interval and the p-limit interval itself (e.g. the way 22-edo tempers
out 64/63, i.e. 16/9 and 7/4 are the 'same')."

which is something I tried to discuss here some time ago, with
Gene no less, or should I say, no more. And I think there's
something to what Aaron says, which I can express in this crude but
perhaps musical (therefore probably of little interest here) way:
rather than ignoring or poorly approximating intervals
related to a particular partial, it is a good idea to deal
with them by substituting them, so to speak, with intervals
that have a rhyme and reason of their own, in relation to
strong interval families in the tuning.

For example, the fact that the seventh partial is so poorly
incorporated, in a literal fashion, into 34 equal may actually
be an advantage, superior to sloppy representations of intervals
incorporating the seventh partial, as long as the intervals
which are near where the x/7s and 7/xs "might have been" are
well and consistently related to the tuning as a whole and good in
and of themselves.

In 34, 9/7 and 7/4 can be taken this way ("substituted" respectively
by the mediants of 14/11 and 9/7, and of 7/4 and 16/9). Where 7/6
"might have been" we find the mediant of 7/6 and 13/11, and so
on. The spanner in the works might be 11/7, which is closely
enough represented in 34 that it can be used pure in a 34 well- or
ill-temperament. But maybe it's a "key" rather than a clunker, for
the hypothetically "7s-tempered-toward-11s" intervals certainly
sound lovely with it.

This brings in the idea of tempering-away-by-tempering-towards.
For example, take the intervals you wish to temper, temporarily
overly another offset scale and temper to, say, the harmonic
means of the first and second set of intervals, moving in the
directions you desire. The overlayed scale would be designed to
hammer the original towards an ideal, whatever that might be.

-Cameron Bobro