Twinkletits in 23-EDO

http://soundcloud.com/cityoftheasleep/twinkletits

Enjoy. My first little guitar improv in 23-EDO, featuring the Pelogic heptatonic. I like this better than the 16-EDO version, definitely. Those near-Just 5/3's are just so damn sweet, and for some reason I also find the 4ths and 5ths drastically less objectionable despite a mere 3-4 cents difference.

I am completely in love with 23-EDO. This is definitely my "desert island" tuning. I have a sinking feeling that I may come to neglect my other microtonal guitars in the future. It does pretty much everything I want, and I keep finding these neat little easter-eggs in it, for instance it's really cool that the neutral 2nd works as both a 12/11 and an 11/10, because I can play 5:6:11 triads and they sound really awesome. Also I think I can tune a 21/16 by ear now. It's a little dip in beating right before the 4/3 and at least on guitar it locks in pretty solidly for me. It's complex but regular in some way. And oh man the two major 3rds are playing mega tricks on my mind. The one around 365 cents definitely screams "5/4" to me, but when I play a Ripple-tempered version of the major scale the 417-cent major 3rd feels just as natural.

-Igs

On Fri, Jun 10, 2011 at 2:47 AM, cityoftheasleep
<igliashon@...> wrote:
>
> http://soundcloud.com/cityoftheasleep/twinkletits
>
> Enjoy. My first little guitar improv in 23-EDO, featuring the Pelogic heptatonic. I like this better than the 16-EDO version, definitely. Those near-Just 5/3's are just so damn sweet, and for some reason I also find the 4ths and 5ths drastically less objectionable despite a mere 3-4 cents difference.

I feel the same way sometimes about the fifths. I think it has to do
with the fact that because the 5/4's are also so flat, it warps your
brain into hearing the flat 3/2's as being "right" in a way that
16-EDO doesn't accomplish. I've noticed a similar effect under lots of
different circumstances, where sharper fifths demand sharper thirds
and etc. 23-equal is also a lot closer to the POTE-optimal tuning for
mavila; POTE likewise has it set up so that flatter 5/4's demand
flatter 3/2's and so on (one of the reasons why the father mapping for
13-EDO kept winning out over the uncle one as well; the algorithm
suggested a sharper 5/4 to go with the sharper 3/2). I think that
23-equal is the optimal patent val for mavila as well.

But as for 16-EDO - the schizophrenia of the way intervals are
mistuned is actually I think a huge asset to 16-EDO. The 3/2's are so
flat so as to be almost stifling, depressing perhaps, but the 5/4's
are much less so and the 7/4's are actually a bit sharp, and suddenly
these intervals lend the tuning some brightness and color (relatively
speaking). This contradiction seems to contribute much to the
"feeling" of 16-EDO, where it's somehow very confining, and yet
freeing in a way; it has almost a gothic sort of feel to it. It feels
like you're floating around in a fog, or maybe that you're a ghost or
something, but the 5/4's can penetrate through the fog. I find it to
have a more immediate meaning than most other EDOs, to be honest.

23-EDO on the other hand, by virtue of its uniformly flat major triad,
doesn't have the same kind of schizophrenic "bad fifth good third"
type thing going on, but rather the entire thing has a more cohesive
feel to it. It is more uniformly "mavila." The whole thing blends into
a new sound in which all intervals are uniformly flat. At least that's
my interpretation.

This also reinforces my understanding of mistuning as one of the
"primary foundations" of a single harmonic percept, with flatness and
sharpness representing the two different polarities that this can go.
It lastly also suggests to me that the absurd and oversimplified
paradigm whereby mistuning is "bad" and pure tuning is "good" is in
fact absurd and oversimplified after all.

> I am completely in love with 23-EDO. This is definitely my "desert island" tuning. I have a sinking feeling that I may come to neglect my other microtonal guitars in the future. It does pretty much everything I want, and I keep finding these neat little easter-eggs in it, for instance it's really cool that the neutral 2nd works as both a 12/11 and an 11/10, because I can play 5:6:11 triads and they sound really awesome. Also I think I can tune a 21/16 by ear now. It's a little dip in beating right before the 4/3 and at least on guitar it locks in pretty solidly for me. It's complex but regular in some way. And oh man the two major 3rds are playing mega tricks on my mind.

It doesn't have too bad of a 15/8 either, so maybe 16:21:30 will work
out for you.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> I am completely in love with 23-EDO. This is definitely my "desert island" tuning.

I'm still awaiting a reply on the question of where your past music has run off to, and whether and how I can fix the broken links on the Xenwiki. But now I have to ask if I can link to your new Soundcloud stuff as well.

On Fri, Jun 10, 2011 at 3:19 AM, Mike Battaglia <battaglia01@...> wrote:
>
> I feel the same way sometimes about the fifths. I think it has to do
> with the fact that because the 5/4's are also so flat, it warps your
> brain into hearing the flat 3/2's as being "right" in a way that

Also, I don't know how into punk you are, but I was throwing around
some mavila comma pumps with Ron Sword the other day, and there were
some pretty awesome ones

||: Cmaj -> Gmaj -> Bm -> Fmaj :|| (where B->F is actually 4/3, so the
progression is like 1/1 -> up 3/2 -> up 5/4 -> down 4/3 -> down 4/3).
This is kind of a mavila-evolved version of the more standard punk
Cmaj -> Gmaj -> Am -> Fmaj. It's from the sLssLss mode.

||: Cmaj -> Em -> Bmaj -> Fmaj :|| - B->F is down 4/3 again, same as
above, so it's 1/1 -> up 5/4 -> up 3/2 -> down 4/3 -> down 4/3. This
is from the ssLssLs mixolydian mode. The more evolved version of Cmaj
-> Em -> Am

||: Cmaj -> Gmaj -> Dmaj -> F(#)m :|| - the crazy thing is that the
F#-A from the Dmaj and the F-Ab from the Fm are actually the same
thing, so this is 1/1 -> up 3/2 -> down 4/3 -> up 5/4 -> down 4/3.

Enjoy.

-Mike

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> I'm still awaiting a reply on the question of where your past music has run off to, and whether and how I can fix the broken links on the Xenwiki. But now I have to ask if I can link to your new Soundcloud stuff as well.
>

By "past music", do you mean the stuff I posted to the files section here? I took those tracks down so as not to be a space hog. I can re-upload to my sound cloud account if there are any you particularly miss, and you can link from there. I'm using the soundcloud account primarily for non-album unpolished demo tracks.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> By "past music", do you mean the stuff I posted to the files section here? I took those tracks down so as not to be a space hog. I can re-upload to my sound cloud account if there are any you particularly miss, and you can link from there. I'm using the soundcloud account primarily for non-album unpolished demo tracks.

I emailed you about these:

A Calamitous Simultaneity
Ideas on the Waterfall of Expression
Dragged by a Storm Across the Desert Years
Numerology
Revenge of the inorganic compounds
A Walk Through the Valley of Ashes
Paint in the Water 29

But I guess you didn't get it. Rather than messing with Soundcloud, if you were to email me any mp3 files less than 25MB in size, or upload them to a temporary location with a file-sharing service, I would be happy to put them up on Chris's site.

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

> A Calamitous Simultaneity
> Ideas on the Waterfall of Expression
> Dragged by a Storm Across the Desert Years
> Numerology
> Revenge of the inorganic compounds
> A Walk Through the Valley of Ashes

These can all be found at my last.fm page, http://www.last.fm/music/City+Of+The+Asleep/+albums , and are either on "Early Microtonal Works" or "Map of an Internal Landscape". You can download them all free and put them up somewhere else if you don't want to muck about with last.fm for the links.

> Paint in the Water 29

This one I can e-mail you if you PM me your address, I'll be on the watch for it so it doesn't get lost amongst the spam.

> But I guess you didn't get it.

I did not. If it went to my yahoo address, that one is mostly a spam bucket these days and it's really easy for me to miss messages there unless I'm expecting one.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> I feel the same way sometimes about the fifths. I think it has to do
> with the fact that because the 5/4's are also so flat, it warps your
> brain into hearing the flat 3/2's as being "right" in a way that
> 16-EDO doesn't accomplish.

That makes a lot of sense. I've suspected that before...like maybe that's what I like about 20-EDO, or something, or why I like 5-limit triads in 19-EDO better than 22-EDO. Damned if I know how significant this may actually be.

> 23-equal is also a lot closer to the POTE-optimal tuning for
> mavila;

O RLY?

http://xenharmonic.wikispaces.com/Pelogic+family

It's near POTE-optimal for Pelogic, not Mavila. 25-EDO is more of an optimal Mavila. I know what I said about not enforcing consistent terminology, but when you're talking about specific temperaments and POTE generators, and when there is an authoritative source cataloging these, there can be no argument in favor of ignoring the proper terminology.

> But as for 16-EDO - the schizophrenia of the way intervals are
> mistuned is actually I think a huge asset to 16-EDO.

I agree, I think the difference between 23 and 16 for 2L5s is much like the difference between 19 and 12 for 5L2s. The weird haze of 16-EDO is really striking, and the fact that 5 and 7 are both very clearly represented while 3 is not makes it rather unique to work with. I actually prefer to conceive of 16 as 2.5.7.27, frankly, as that better describes what I use as consonances. I almost always avoid the fifth in 16, except as a root movement or a melodic movement.

> This also reinforces my understanding of mistuning as one of the
> "primary foundations" of a single harmonic percept, with flatness
> and sharpness representing the two different polarities that this
> can go.
> It lastly also suggests to me that the absurd and oversimplified
> paradigm whereby mistuning is "bad" and pure tuning is "good" is in
> fact absurd and oversimplified after all.

I have been suggesting this off and on for a while but Carl and Paul always tell me I need more rigorous evidence.

> It doesn't have too bad of a 15/8 either, so maybe 16:21:30 will
> work out for you.

Maybe, I'll see how that feels.

-Igs

On Fri, Jun 10, 2011 at 2:27 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I feel the same way sometimes about the fifths. I think it has to do
> > with the fact that because the 5/4's are also so flat, it warps your
> > brain into hearing the flat 3/2's as being "right" in a way that
> > 16-EDO doesn't accomplish.
>
> That makes a lot of sense. I've suspected that before...like maybe that's what I like about 20-EDO, or something, or why I like 5-limit triads in 19-EDO better than 22-EDO. Damned if I know how significant this may actually be.

That's also why I think I like 20-EDO, although 20-EDO overshoots its
mark a bit for this. But yeah, I've always liked the extreme sharp
thirds of 20-EDO, thinking that they go well with the sharp fifths.
22-EDO is also a bit schizophrenic in terms of its having a sharp 3/2
and a slightly flat but pretty much just 5/4, but it's the sharpness
of the 6/5 that gets to me more than anything. Maybe it just has to do
with minimizing dyadic error.

> > 23-equal is also a lot closer to the POTE-optimal tuning for
> > mavila;
>
> O RLY?
>
> http://xenharmonic.wikispaces.com/Pelogic+family
>
> It's near POTE-optimal for Pelogic, not Mavila. 25-EDO is more of an optimal Mavila. I know what I said about not enforcing consistent terminology, but when you're talking about specific temperaments and POTE generators, and when there is an authoritative source cataloging these, there can be no argument in favor of ignoring the proper terminology.

Those names are backwards from what I learned. Mavila is the 5-limit
temperament, and Pelogic is its 7-limit extension which suggests an
even flatter fifth. This usage is consistent with this here

/tuning/database?method=reportRows&tbl=10

also consistent with Graham's temperament finder

http://x31eq.com/cgi-bin/rt.cgi?ets=7_2p&limit=5
http://x31eq.com/cgi-bin/rt.cgi?ets=9_16&limit=7

I believe that's how it's called in "A Middle Path" as well. It also
doesn't look like the 5-limit version is called "Pelogic" even in the
xenharmonic wiki page, Gene says "The 5-limit temperament is (5-limit)
mavila, or pelogic, whose generator is a very flat fifth."

I think what happened was that the temperament was originally called
"Pelogic," and then it was discovered that Kraig Grady had discovered
the temperament earlier by going to the Chopi village of Mavila in
Africa and measured the tuning for the xylophones they were using, so
they called it "Mavila" as a nod to that. Something along those lines
anyway. Either way, the point is that actual "pelog" tunings are
flatter than "mavila" ones.

> > This also reinforces my understanding of mistuning as one of the
> > "primary foundations" of a single harmonic percept, with flatness
> > and sharpness representing the two different polarities that this
> > can go.
> > It lastly also suggests to me that the absurd and oversimplified
> > paradigm whereby mistuning is "bad" and pure tuning is "good" is in
> > fact absurd and oversimplified after all.
>
> I have been suggesting this off and on for a while but Carl and Paul always tell me I need more rigorous evidence.

What part of this specifically needs more rigorous evidence?

-Mike

On Fri, Jun 10, 2011 at 2:53 PM, Mike Battaglia <battaglia01@...> wrote:
>
> Those names are backwards from what I learned. Mavila is the 5-limit
> temperament, and Pelogic is its 7-limit extension which suggests an
> even flatter fifth. This usage is consistent with this here

Just to clarify, the one I called "Mavila" is what the xenwiki had
listed as nothing, and the one I called "Pelogic" is the one that the
xenwiki had listed as "Hexadecimal." I've edited the page to be
consistent with the other terminology, which was also on the xenwiki
(check the discussion I'm having with Graham in the other thread for
more on that).

So what I meant was that 23-equal was close to the POTE optimal
generator for 5-limit mavila, but after checking it seems to be more
analogous to 19-equal; 19-equal has a fifth that's 1.5 cents flatter
than optimal for meantone, and 23-equal has a fifth that's 1.6 cents
flatter than optimal for mavila. So 23-equal is "better than 16-equal"
for mavila, just like 19-equal is "better than 12-equal" for meantone.

30-equal fulfills the counterpart to 31-equal; both cases are less
than a cent off from the POTE generators for mavila and meantone,
respectively.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> I think what happened was that the temperament was originally called
> "Pelogic," and then it was discovered that Kraig Grady had
> discovered the temperament earlier by going to the Chopi village of > Mavila in Africa and measured the tuning for the xylophones they
> were using, so they called it "Mavila" as a nod to that. Something > along those lines anyway. Either way, the point is that actual
> "pelog" tunings are flatter than "mavila" ones.

I'm deferring everything to the Xenwiki, so whatever it says there is fine with me. I like the name "Pelogic" because it implies similarity to Pelog, rather than equivalence, whereas the name "Mavila" implies equivalence, but I don't actually care all that much about it. All I can say is that in 23-EDO, I treat the ~678-cent interval as a consonance, and hence an approximate 3/2, but I don't in 16 and probably wouldn't in 25 either.

> What part of this specifically needs more rigorous evidence?

All of it. We need more test-cases and more confirmations of the pattern and perhaps a more explicit formulation of how much conflicting error signs within a chord will affect discordance. But as I'm not interested really in generalizing these things, you're on your own (though I'll be happy to weigh in as a subject in listening tests etc.)

-Igs

On Fri, Jun 10, 2011 at 5:54 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I think what happened was that the temperament was originally called
> > "Pelogic," and then it was discovered that Kraig Grady had
> > discovered the temperament earlier by going to the Chopi village of > Mavila in Africa and measured the tuning for the xylophones they
> > were using, so they called it "Mavila" as a nod to that. Something > along those lines anyway. Either way, the point is that actual
> > "pelog" tunings are flatter than "mavila" ones.
>
> I'm deferring everything to the Xenwiki, so whatever it says there is fine with me. I like the name "Pelogic" because it implies similarity to Pelog, rather than equivalence, whereas the name "Mavila" implies equivalence, but I don't actually care all that much about it. All I can say is that in 23-EDO, I treat the ~678-cent interval as a consonance, and hence an approximate 3/2, but I don't in 16 and probably wouldn't in 25 either.

What do you mean "equivalence?"

I was talking about the 5-limit 138/125 tuning, which is called
"Mavila." The 7-limit 138/125 and 64/63 tuning, which is kind of like
mavila crossbred with dominant, is "Pelogic." There is apparently a
7-limit version of mavila, lowest in badness, which tempers out 21/20,
such that 5/3 and 7/4 get tempered to be the same thing; not sure why
that one beat out 64/63. As for the name, this apparently was a
discussion that took place years ago before I joined so I have no
comment on it.

> > What part of this specifically needs more rigorous evidence?
>
> All of it. We need more test-cases and more confirmations of the pattern and perhaps a more explicit formulation of how much conflicting error signs within a chord will affect discordance. But as I'm not interested really in generalizing these things, you're on your own (though I'll be happy to weigh in as a subject in listening tests etc.)

All of what? That flat fifths suggest flat thirds? Both TOP and TE
error suggest that that's how it works, so if this facet of life
hasn't been proven to everyone's satisfaction then it's time to throw
those out the window.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> What do you mean "equivalence?"

Equivalence to the tunings used in Mavila. Kraig has insisted that (especially in the case of 16-EDO) this is not the case. They might be Mavila-esque, but should not be confused with actual tunings of the region.

> All of what? That flat fifths suggest flat thirds? Both TOP and TE
> error suggest that that's how it works, so if this facet of life
> hasn't been proven to everyone's satisfaction then it's time to throw
> those out the window.

How does TOP suggest this?

-Igs

On Fri, Jun 10, 2011 at 7:31 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > What do you mean "equivalence?"
>
> Equivalence to the tunings used in Mavila. Kraig has insisted that (especially in the case of 16-EDO) this is not the case. They might be Mavila-esque, but should not be confused with actual tunings of the region.

OK. Well, the name for the 5-limit 135/128 rank-2 temperament, as far
as I know, is "mavila." That's all I got.

> > All of what? That flat fifths suggest flat thirds? Both TOP and TE
> > error suggest that that's how it works, so if this facet of life
> > hasn't been proven to everyone's satisfaction then it's time to throw
> > those out the window.
>
> How does TOP suggest this?

I'll discuss TE instead, because I know more about it, data on it is
readily available and because people are using it over TOP nowadays
anyway. Take the case of Blackwood, where you can set the major third
to be whatever you want. The POTE generators for Blackwood are 240
cents and 80.406 cents, which if you works it out gives you a fourth
of 399.59 cents. Note that the algorithm selects a sharper third to go
with a sharper fifth. The idea is that we want to optimize the error
for "all" intervals, and when you try to minimize dyadic error over
all intervals this is a pretty common behavior that results.*

Look here at the choice of 7/4 that minimizing TE error picks for 23-equal -

http://x31eq.com/cgi-bin/rt.cgi?ets=23&limit=7

The 23d mapping is the optimal mapping here, with 23p coming in second
place. That means that 18\23 is winning out over 19\23, despite that
19\23 is the choice you get by rounding 7/4 to its nearest match in
23-equal (the patent val).

18\23 is 939 cents, so that means the POTE-optimal 4:5:6:7 tuning for
23-equal is 0-365-678-939. 939 cents! In comparison, the closest match
to 7/4 directly is 991 cents, and the patent val 4:5:6:7 tuning is
0-365-678-991. So the question is, which one to you sounds more like a
just 4:5:6:7? To me it's the first one.

(*This obviously isn't the case for something like porcupine, though,
where the only way to get it as close to 4:5:6 as possible is to go
with a slightly flat 5/4 and a slightly sharp 3/2.)

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> It's near POTE-optimal for Pelogic, not Mavila. 25-EDO is more of an optimal Mavila.

Speaking of which, has anyone tried composing in 25? Or 28? Or, aside from me, in 27? I'd be interested to hear examples.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...>
> Speaking of which, has anyone tried composing in 25? Or 28? Or, aside > from me, in 27? I'd be interested to hear examples.

27: http://www.last.fm/music/City+Of+The+Asleep/Map+of+an+Internal+Landscape/Midnight+in+the+Garden+of+Missed+Connections

28: http://www.last.fm/music/City+Of+The+Asleep/Map+of+an+Internal+Landscape/The+Bittersweet+Orange+Glow+of+Nostalgia

25: http://www.last.fm/music/City+Of+The+Asleep/Map+of+an+Internal+Landscape/Audiospark+Spring+Bubbles+Turquoise

Didn't know you'd used 27 before...what did you use it for? Isn't it a bit inaccurate for your tastes?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> Didn't know you'd used 27 before...what did you use it for? Isn't it a bit inaccurate for your tastes?

Yes, sadly, it is a bit inaccurate for me. When I first looked at the numbers for equal temperaments, my only actual micro experience was a bit of futzing around with 7-limit JI, which for me at the time wasn't that easy. When I looked at the numbers for 27, and even 15, I thought I might like them. I thought 27, which tempered out both 64/63 and 126/125, looked very promising (that's augene temperament, but I didn't know to think in those terms back then.) I wanted to like 15 and 27, which I had never heard had even been considered, but sadly, when I got the chance I found I didn't like 15 at all, and 27 was pretty marginal.

Another system which caught my eye was 46, and that did turn out be something I liked, which made me happy. One thing 46 does is that using the relationship between 126/125 and 64/63, you can mutate 46 into 27 if you work it right. This is how I ended up with 27--varied a 46 piece a bit, transformed it to a 27 piece, varied that some more, transformed it back to 46 and messed about for a conclusion. With the right timbres 27 isn't too bad, so it all worked out.

On Sat, Jun 11, 2011 at 3:31 AM, genewardsmith
<genewardsmith@...> wrote:
>
> Yes, sadly, it is a bit inaccurate for me. When I first looked at the numbers for equal temperaments, my only actual micro experience was a bit of futzing around with 7-limit JI, which for me at the time wasn't that easy. When I looked at the numbers for 27, and even 15, I thought I might like them. I thought 27, which tempered out both 64/63 and 126/125, looked very promising (that's augene temperament, but I didn't know to think in those terms back then.) I wanted to like 15 and 27, which I had never heard had even been considered, but sadly, when I got the chance I found I didn't like 15 at all, and 27 was pretty marginal.

You recently said that you like 14-equal now. I'm still waiting for
what exactly it is you've come to like about 14-equal. Here's to
hoping you can similarly come around for 15-equal as well. Maybe
16-equal too.

Serious question, what exactly is it that you hate about higher error
temperaments? The beating? If you play them with flute-like timbres,
or something like a Rhodes, is it all that bad? Or is it more that you
like hearing chords fuse into a single VF? Because the more I go on
the more I realize that 15 and 16 are two of my favorite tunings on
the earth, specifically because their higher error makes for some
novel puns and generally stimulating tonal structures.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I'll discuss TE instead, because I know more about it, data on it is
> readily available and because people are using it over TOP nowadays
> anyway.

Well, I'm not. Should I?

> The 23d mapping is the optimal mapping here, with 23p coming in second
> place. That means that 18\23 is winning out over 19\23, despite that
> 19\23 is the choice you get by rounding 7/4 to its nearest match in
> 23-equal (the patent val).
>
> 18\23 is 939 cents, so that means the POTE-optimal 4:5:6:7 tuning for
> 23-equal is 0-365-678-939. 939 cents!

FWIW, close to isoharmonic 21:26:31:36.

Kalle

On Sat, Jun 11, 2011 at 5:27 AM, Kalle Aho <kalleaho@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > I'll discuss TE instead, because I know more about it, data on it is
> > readily available and because people are using it over TOP nowadays
> > anyway.
>
> Well, I'm not. Should I?

You only live once, Kalle...

Why do you prefer TOP to TE optimal?

> > 18\23 is 939 cents, so that means the POTE-optimal 4:5:6:7 tuning for
> > 23-equal is 0-365-678-939. 939 cents!
>
> FWIW, close to isoharmonic 21:26:31:36.

Beautiful. I sometimes wish we had some formulas for cranking out
isoharmonic-based well temperaments of regular and equal temperaments,
although I don't know if strict isoharmonicity is really necessary.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Jun 11, 2011 at 5:27 AM, Kalle Aho <kalleaho@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > I'll discuss TE instead, because I know more about it, data on it is
> > > readily available and because people are using it over TOP nowadays
> > > anyway.
> >
> > Well, I'm not. Should I?
>
> You only live once, Kalle...
>
> Why do you prefer TOP to TE optimal?

The reasoning behind TOP is beautiful (in particular the endnote xxvi
in Middle Path). TE is supposed to be easier to calculate but that's
no reason for me to prefer it. I particularly don't like POTE because
if I temper I want to temper all intervals, the sound will be
livelier.

> > > 18\23 is 939 cents, so that means the POTE-optimal 4:5:6:7 tuning for
> > > 23-equal is 0-365-678-939. 939 cents!
> >
> > FWIW, close to isoharmonic 21:26:31:36.
>
> Beautiful. I sometimes wish we had some formulas for cranking out
> isoharmonic-based well temperaments of regular and equal temperaments,
> although I don't know if strict isoharmonicity is really necessary.

The fundamentals will have the spacing for periodicity buzz but
perhaps the harmonics will obscure this?

Kalle

On Sat, Jun 11, 2011 at 6:11 AM, Kalle Aho <kalleaho@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > You only live once, Kalle...
> >
> > Why do you prefer TOP to TE optimal?
>
> The reasoning behind TOP is beautiful (in particular the endnote xxvi
> in Middle Path). TE is supposed to be easier to calculate but that's
> no reason for me to prefer it. I particularly don't like POTE because
> if I temper I want to temper all intervals, the sound will be
> livelier.

I can't believe I'm still awake, but

1) TE doesn't have to mean POTE, TE can temper octaves as well.
2) TE isn't only easier to calculate, but uses the L2 norm, which
means that... it uses the L2 norm.

Either way, does TOP display the same behavior? What's the TOP tuning
for Blackwood? I'm not at my computer with Scala to check.

> > > > 18\23 is 939 cents, so that means the POTE-optimal 4:5:6:7 tuning for
> > > > 23-equal is 0-365-678-939. 939 cents!
> > >
> > > FWIW, close to isoharmonic 21:26:31:36.
> >
> > Beautiful. I sometimes wish we had some formulas for cranking out
> > isoharmonic-based well temperaments of regular and equal temperaments,
> > although I don't know if strict isoharmonicity is really necessary.
>
> The fundamentals will have the spacing for periodicity buzz but
> perhaps the harmonics will obscure this?
>
> Kalle

For 21:26:31:36 they'll actually buzz even more, because the harmonics
will also beat in sync with everything else.* Try it, you'll see. RI
delivers buzz like no other. If you, for the sake of argument, assume
that the periodicity buzz = synchronized roughness paradigm, you'll
see why it all makes sense, and more importantly, that it makes the
correct predictions.

This has also been dealt with before under all of Jacques' work with
"equal beating" chords and the like; Gene also worked much of it out
and the term "omni-sync beating" was used at some points.

*Unless you're using inharmonic timbres. If the timbres are inharmonic
but still linear, say phi-based timbres that work off of the series
1:1+phi:1+2phi:1+3phi:etc, the phi-based ones will display the
strongest beating. If the timbres aren't linear, then the buzz will be
uneven and occur as an irrational polyrhythm.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Jun 11, 2011 at 6:11 AM, Kalle Aho <kalleaho@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > You only live once, Kalle...
> > >
> > > Why do you prefer TOP to TE optimal?
> >
> > The reasoning behind TOP is beautiful (in particular the endnote xxvi
> > in Middle Path). TE is supposed to be easier to calculate but that's
> > no reason for me to prefer it. I particularly don't like POTE because
> > if I temper I want to temper all intervals, the sound will be
> > livelier.
>
> I can't believe I'm still awake, but
>
> 1) TE doesn't have to mean POTE, TE can temper octaves as well.

I know, that's why I said "particularly".

> 2) TE isn't only easier to calculate, but uses the L2 norm, which
> means that... it uses the L2 norm.

So what?

> Either way, does TOP display the same behavior?

What behavior do you mean?

> What's the TOP tuning for Blackwood? I'm not at my computer with
> Scala to check.

5-limit: generator 80.088638, period 238.866863. Fifth is 716.601
cents and octave 1194.334 cents.

> > > > > 18\23 is 939 cents, so that means the POTE-optimal 4:5:6:7 tuning for
> > > > > 23-equal is 0-365-678-939. 939 cents!
> > > >
> > > > FWIW, close to isoharmonic 21:26:31:36.
> > >
> > > Beautiful. I sometimes wish we had some formulas for cranking out
> > > isoharmonic-based well temperaments of regular and equal temperaments,
> > > although I don't know if strict isoharmonicity is really necessary.
> >
> > The fundamentals will have the spacing for periodicity buzz but
> > perhaps the harmonics will obscure this?
> >
> > Kalle
>
> For 21:26:31:36 they'll actually buzz even more, because the harmonics
> will also beat in sync with everything else.* Try it, you'll see. RI
> delivers buzz like no other. If you, for the sake of argument, assume
> that the periodicity buzz = synchronized roughness paradigm, you'll
> see why it all makes sense, and more importantly, that it makes the
> correct predictions.
>
> This has also been dealt with before under all of Jacques' work with
> "equal beating" chords and the like; Gene also worked much of it out
> and the term "omni-sync beating" was used at some points.
>
> *Unless you're using inharmonic timbres. If the timbres are inharmonic
> but still linear, say phi-based timbres that work off of the series
> 1:1+phi:1+2phi:1+3phi:etc, the phi-based ones will display the
> strongest beating. If the timbres aren't linear, then the buzz will be
> uneven and occur as an irrational polyrhythm.

So chords don't really have to be isoharmonic to buzz. George Secor
claims that isoharmonic chords are somehow special but I don't know
why.

Kalle

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Serious question, what exactly is it that you hate about higher error
> temperaments? The beating? If you play them with flute-like timbres,
> or something like a Rhodes, is it all that bad? Or is it more that you
> like hearing chords fuse into a single VF?

I really don't know, but timbre does make a difference. Bell-like or flute-like timbres work better. What I don't like is the part where I'm listening and it's sort of making sense, and then I wince in pain. But I don't always wince in pain, and what factors make me do so I'm not clear on. Even when I don't, I usually get a serious "meh" feeling about it all.

> Because the more I go on
> the more I realize that 15 and 16 are two of my favorite tunings on
> the earth, specifically because their higher error makes for some
> novel puns and generally stimulating tonal structures.

I think the trouble with them is that they are close enough to JI to hear things as approximations, but not close enough for the approximations to sound any good. Near-just is like biting into a sweet, perfect peach. 12et is where the peach isn't quite ripe. What I don't like is when you bite into your music, and it tastes a little rotten, so you want to spit it out.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Serious question, what exactly is it that you hate about higher error
> temperaments?

Here's a question: check out the music on this page

http://xenharmonic.wikispaces.com/Quarter-comma+meantone

and tell me what is it you hate about low error temperaments.

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

> Here's a question: check out the music on this page
>
> http://xenharmonic.wikispaces.com/Quarter-comma+meantone
>
> and tell me what is it you hate about low error temperaments.
>

You mean "low-limit, low-error" temperaments.

And to that I say 5 centuries of exploration in this direction is enough.

I'm working on a paper right now (sort of a "book 2" of the Field Guide, which is almost done) that analyzes each EDO in terms of harmonics 32-64 and "bans" any approximations worse than 8 cents off. It's a different approach than the one used around here for the most part, not better or worse but it will probably reveal those lurking isoharmonic chords that treating everything in terms of "error from prime harmonics 2-13" obscures. In my approach, there are no high-error temperaments. Just high-harmonic ones.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> I'm working on a paper right now (sort of a "book 2" of the Field Guide, which is almost done) that analyzes each EDO in terms of harmonics 32-64 and "bans" any approximations worse than 8 cents off. It's a different approach than the one used around here for the most part, not better or worse but it will probably reveal those lurking isoharmonic chords that treating everything in terms of "error from prime harmonics 2-13" obscures. In my approach, there are no high-error temperaments. Just high-harmonic ones.

You and Johnny Reinhard. The trouble with it all is, do your ears know about these higher harmonics? When you confine yourself to 2-13, you're dealing with the real world. I like that.

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:

> I particularly don't like POTE because
> if I temper I want to temper all intervals, the sound will be
> livelier.

The reason I like pure-octaves tunings when discussing temperaments, especially in the rank one and two cases, is that it makes life a lot easier. For rank one, it surely helps the discussion along if I can say the error of 7/4 is so many cents, and from that everyone knows the error for 7/2 and 7 will be just the same. In the rank two case, if I give the number of periods in an octave and a tuning for the generator, I've specified the tuning. Moreover, pure octaves are generally acceptable. You may not prefer them, but I presume you don't hate them, whereas some people either don't like tempered octaves or just don't want to have to deal with them.

Of course, I am guilty of being an early proponent of octave tempering because of zeta tunings. Oh well.

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

> You and Johnny Reinhard. The trouble with it all is, do your ears know about these higher harmonics? When you confine yourself to 2-13, you're dealing with the real world. I like that.
>

Calling 480 cents a 4/3 leads to calling 960 cents a 16/9. Yet treating 960 cents as a 7/4 leads to calling 480 cents a 323/256. Doing both leads to saying 16/9 and 7/4 are the same thing, as are 4/3 and 323/256. How is that "the real world"?

In any case, some people (Mike and Kalle) are saying isoharmonic chords are psychoacoustically important and sound better than arbitrarily-tuned chords. So in answer to your question, it seems that *yes*, your ears do know about these higher harmonics, at least in some contexts.

-Igs

--- In tuning@yahoogroups.com, "genewardsmith" wrote

> Speaking of which, has anyone tried composing in 25? Or 28? Or, aside
> from me, in 27? I'd be interested to hear examples.

I don't think 25 is so unpopular, though aside from a thing or two from
Igs the only piece that comes to mind is my favorite "study" by Paul
Rappoport, which appeared on a Perspectives of new music CD from
the '90s.... not available online that I know of....

-Carl

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> > Here's a question: check out the music on this page
> >
> > http://xenharmonic.wikispaces.com/Quarter-comma+meantone
> >
> > and tell me what is it you hate about low error temperaments.
> >
>
> You mean "low-limit, low-error" temperaments.

Yep, that's a page on quarter-comma meantone. But elsewhere he
said up to 13 was reality, and I'm wondering what you don't like
about that (George Secor's music for instance, among numerous
other examples).

Even in the 5-limit, Petr showed there are new and interesting
waters to explore.

> I'm working on a paper right now (sort of a "book 2" of the Field Guide, which
> is almost done) that analyzes each EDO in terms of harmonics 32-64 and
> "bans" any approximations worse than 8 cents off. It's a different approach
> than the one used around here for the most part, not better or worse

Well it should be worse, since a lot of stuff up there simply isn't
audible outside of very specific listening conditions.

> but it will probably reveal those lurking isoharmonic chords

What are isoharmonic chords again?

-Carl

On Sat, Jun 11, 2011 at 8:23 AM, Kalle Aho <kalleaho@...> wrote:
>
> > What's the TOP tuning for Blackwood? I'm not at my computer with
> > Scala to check.
>
> 5-limit: generator 80.088638, period 238.866863. Fifth is 716.601
> cents and octave 1194.334 cents.

OK, so there you go. That maps the major third to 397.646 cents.
Despite that Blackwood tempers out a no-5's comma, the size of the 5/4
changes anyway. That was the point that I was making when I said that
existing optimization methods will already pick sharper thirds to go
with sharper fifths. I guess the exception would be something like
porcupine, where the temperament is such that the 3/2 and the 5/4 are
dragged in opposite directions.

> > *Unless you're using inharmonic timbres. If the timbres are inharmonic
> > but still linear, say phi-based timbres that work off of the series
> > 1:1+phi:1+2phi:1+3phi:etc, the phi-based ones will display the
> > strongest beating. If the timbres aren't linear, then the buzz will be
> > uneven and occur as an irrational polyrhythm.
>
> So chords don't really have to be isoharmonic to buzz. George Secor
> claims that isoharmonic chords are somehow special but I don't know
> why.

You and I already had this discussion! :)

/tuning/topicId_95699.html#95714

Look at the examples I gave (looks like the links have been changed)

http://www.mikebattagliamusic.com/music/161719buzz.wav
http://www.mikebattagliamusic.com/music/161719buzz.png

and

http://www.mikebattagliamusic.com/323437buzz.wav
http://www.mikebattagliamusic.com/323437buzz.png

The first one isn't isoharmonic, because the 19/17 will beat twice as
fast as the 17/16. The 37/34 will buzz 3:2 times as fast as the 34/32.
Isoharmonicity is great because it means that all of the dyads will
buzz in a 1:1 ratio to one another.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> Yep, that's a page on quarter-comma meantone. But elsewhere he
> said up to 13 was reality, and I'm wondering what you don't like
> about that (George Secor's music for instance, among numerous
> other examples).

Haven't heard much of George's music, but I tend to hate anything with full 13-limit otonalities (let alone utonalities...yuck), and it's my understanding of your perspective that you don't believe that 13-limit intervals in smaller and less-distinctly otonal contexts are "reality". A while back you were pretty adamant that a naked 11/9 or 11/8 isn't actually recognizable in reality as such.

> Even in the 5-limit, Petr showed there are new and interesting
> waters to explore.

You mean even in the *accurate* 5-limit. And sure, there are always interesting new waters to explore, nothing is ever completely *dead*. There's plenty of life left in 12-TET for that matter. What's your point? That I should continue milking the same tired old cow just because its udders aren't totally dry?

> Well it should be worse, since a lot of stuff up there simply isn't
> audible outside of very specific listening conditions.

Worse in what way? You're assuming a uniform set of goals according to which the efficacy of a conceptual approach to organizing pitches can be judged. All intervals have a sound. 43/32 sounds, well, like the 7-EDO fourth, in a way that 4/3 doesn't. Rather than assuming the ear can only identify a handful of ratios, I'm giving people the benefit of the doubt that they can usefully use higher ratios as qualitative musical landmarks, from which they might be able to construct some useful musical systems--particularly systems whose existence would not be apparent within the usual approach. If no one's interested in setting hard-and-fast rules about when various temperament mappings can be validly applied to various tunings, why should anyone care about setting hard-and-fast rules about which harmonics describe musically-relevant identities?

> What are isoharmonic chords again?

http://tinyurl.com/5so2sng

-Igs

On Sat, Jun 11, 2011 at 11:24 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Serious question, what exactly is it that you hate about higher error
> > temperaments?
>
> Here's a question: check out the music on this page
>
> http://xenharmonic.wikispaces.com/Quarter-comma+meantone
>
> and tell me what is it you hate about low error temperaments.

I don't hate them. But it took some time getting used to something
like porcupine when you've spent your whole life listening to
meantone. It even took some time getting used to something like JI: I
at first heard the 7/4 in 4:5:6:7 as being woefully flat, and I noted
that a lot of other kids in my school did as well. Non-musicians
seemed to be quicker to adjust.

Either way, I didn't notice much of a difference in whether I was
trying to adjust to mavila or porcupine; both required adjustments of
categorical perception more than anything. Now that I have a fairly
decent handle on mavila, I don't notice or care about the higher
entropy of the fifths - I just snap them into 3/2 mode and that's it.
I don't even care about beating anymore - I've learned to separate the
figure from the ground, so to speak. The only thing stopping me from
adapting in this way before was that I was convinced that my existing
set of 12-equal/meantone adaptations were actually maladaptations, and
that I needed to "unadapt" and understand that low HE was the way for
easy musical cognition because it means your brain is less confused. I
was way off.

Maybe it has more to do with "Uncanny Valley" than anything.

-Mike

On Sat, Jun 11, 2011 at 11:50 AM, cityoftheasleep
<igliashon@...> wrote:
>
> I'm working on a paper right now (sort of a "book 2" of the Field Guide, which is almost done) that analyzes each EDO in terms of harmonics 32-64 and "bans" any approximations worse than 8 cents off. It's a different approach than the one used around here for the most part, not better or worse but it will probably reveal those lurking isoharmonic chords that treating everything in terms of "error from prime harmonics 2-13" obscures. In my approach, there are no high-error temperaments. Just high-harmonic ones.

Is the goal to optimize for periodicity buzz or something? Because
when you say you hate 11-limit harmony, but you're also trying to
analyze things in terms of harmonics 32-64, that confuses the heck out
of me.

Assuming you really are getting at periodicity buzz, then it might be
worthwhile to note that 19-equal is full of hidden chords like that
that sound discordant, but buzz really nicely. I had a list of them
somewhere, but I can't find it now. All I'll say is that 19 might be a
goldmine for that approach.

-Mike

"cityoftheasleep" <igliashon@...> wrote:

> Haven't heard much of George's music, but I tend to hate
> anything with full 13-limit otonalities

Ok, well, Gene asked you why. He compare high-error music
to eating rotten fruit so feel free to be descriptive.

> and it's my understanding of your perspective that you don't
> believe that 13-limit intervals in smaller and less-
> distinctly otonal contexts are "reality". A while back you
> were pretty adamant that a naked 11/9 or 11/8 isn't actually
> recognizable in reality as such.

A truly naked 11/9, yes. 11/4 has something going on.
But most music isn't composed of bare dyads separated
by long rests.

> > Even in the 5-limit, Petr showed there are new and interesting
> > waters to explore.
>
> You mean even in the *accurate* 5-limit. And sure, there are
> always interesting new waters to explore, nothing is ever
> completely *dead*.

Yes.

> There's plenty of life left in 12-TET for that matter. What's
> your point?

Petr's progressions are truly new and have not be touched
in the three centuries of common-practice music you complained
about.

> > Well it should be worse, since a lot of stuff up there
> > simply isn't audible outside of very specific listening
> > conditions.
>
> Worse in what way?

Abstract models (such as analyzing an equal temperament
in terms of a harmonic series) should aid us in reaching
consistent conclusions about reality. Using harmonics
32-64 with a brick wall 8-cent error cutoff won't do that.

> > What are isoharmonic chords again?
>
> http://tinyurl.com/5so2sng

WTF is an "equal-hertz" chord and why is this bullshit
in the wiki?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> > Haven't heard much of George's music, but I tend to hate
> > anything with full 13-limit otonalities
>
> Ok, well, Gene asked you why. He compare high-error music
> to eating rotten fruit so feel free to be descriptive.

Large otonalities in the 13-limit feel like sticking my finger in a light socket. I find the sound jarring, clangorous, emotionally ambiguous and somewhat distressing. On the other hand I find harmonies that beat moderately, such as those in 14, 20, and 23-EDO to be soothing, watery, exotic, and sweet.

> A truly naked 11/9, yes. 11/4 has something going on.
> But most music isn't composed of bare dyads separated
> by long rests.

Right, well, whatever. What does it take for an 11/9 to enter "reality"?

> Petr's progressions are truly new and have not be touched
> in the three centuries of common-practice music you complained
> about.

I'm not complaining. I've got nothing against common-practice music or those who choose to continue working in the (accurate) 5-limit. Whatever floats your boat. Me, I'm interested in other things. I find that the "texture" of accurate 5-limit music is pretty much the same, whether it's rendered in Porcupine or Meantone or Diaschismic or Negri...though I think calling Porcupine 5-limit is silly since there are serious 11-limit implications everywhere in it.

> Abstract models (such as analyzing an equal temperament
> in terms of a harmonic series) should aid us in reaching
> consistent conclusions about reality. Using harmonics
> 32-64 with a brick wall 8-cent error cutoff won't do that.

I disagree. The "reality" is that harmonics 32-64 each have a sound (or at least a texture) that people can and have learned to recognize. How easily they can be recognized is of no more concern than how much mistuning a 7/4 can tolerate before it stops sounding like a 7/4--these are issues that depend on listener and listening environment. Admittedly the 8-cent error cutoff is mutable, but it's arrived at from a reasonably sensitive proposition. If you combine two tempered intervals with an error of 8 cents (of the same sign), you get a new interval whose error is 16 cents, which is about as much as the worst 12-TET deviation from a 5-limit consonance. Insisting on no more than 8 cents of error ensures that any given temperament will be at least as accurate as 12-TET. But in any case there are always many ways to interpret a tuning, and I'm offering my approach as a supplement to, rather than a replacement for, the approach used and pioneered here.

In any case, I don't subscribe to the view that as musicians, we must shackle ourselves to hard psychoacoustic truths about "reality" and ignore an approach just because it is not substantiated under the current state of psychoacoustic knowledge. Tuning systems are validated by music made with them, and the only reason to subscribe to any paradigm of alternative tunings is as a guide for making music. You may say people are fooling themselves into thinking higher harmonics are identifiable, but thinking in terms of higher harmonics allows people to organize pitches in different ways than restricting to the lower ones. If those methods lead to good music (as they seem to do, in the case of Kraig Grady and Johnny Reinhard and Dante Rosati, among others), then the real fool is the person who insists against the use of such approaches.

> WTF is an "equal-hertz" chord and why is this bullshit
> in the wiki?

Presumably it is a chord in which the first-order difference tones all share the same frequency. Seems like you're the only one calling bullshit on it.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Is the goal to optimize for periodicity buzz or something? Because
> when you say you hate 11-limit harmony, but you're also trying to
> analyze things in terms of harmonics 32-64, that confuses the heck out
> of me.

The goal is more related to conceptual organization rather than any particular perceptual gestalt. I also have no intention of leaving out something just because *I* don't like the sound of it. Other people appear to like such chords just fine. In any case, it's not high-limit harmony I hate, just particularly the 11- or 13-limit otonality. I like plenty of smaller 11- and 13-limit chords. And 15- and 17- etc.

> Assuming you really are getting at periodicity buzz, then it might be
> worthwhile to note that 19-equal is full of hidden chords like that
> that sound discordant, but buzz really nicely. I had a list of them
> somewhere, but I can't find it now. All I'll say is that 19 might be a
> goldmine for that approach.

Maybe. I think 23 is as well.

-Igs

Igs:
> Carl:
> WTF is an "equal-hertz" chord and why is this bullshit
> in the wiki?
"Presumably it is a chord in which the first-order difference tones all
share the same frequency. Seems like you're the only one calling bullshit on
it."

If going by count, I'll mention that the name is pretty confusing.

On 6/10/2011 2:53 PM, Mike Battaglia wrote:

> Those names are backwards from what I learned. Mavila is the 5-limit
> temperament, and Pelogic is its 7-limit extension which suggests an
> even flatter fifth. This usage is consistent with this here
>
> /tuning/database?method=reportRows&tbl=10
>
> also consistent with Graham's temperament finder
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=7_2p&limit=5
> http://x31eq.com/cgi-bin/rt.cgi?ets=9_16&limit=7
>
> I believe that's how it's called in "A Middle Path" as well. It also
> doesn't look like the 5-limit version is called "Pelogic" even in the
> xenharmonic wiki page, Gene says "The 5-limit temperament is (5-limit)
> mavila, or pelogic, whose generator is a very flat fifth."
>
> I think what happened was that the temperament was originally called
> "Pelogic," and then it was discovered that Kraig Grady had discovered
> the temperament earlier by going to the Chopi village of Mavila in
> Africa and measured the tuning for the xylophones they were using, so
> they called it "Mavila" as a nod to that. Something along those lines
> anyway. Either way, the point is that actual "pelog" tunings are
> flatter than "mavila" ones.

Yes, pelogic was just the older name that was replaced by mavila. There were different 7-limit extensions of pelogic, and there may have been conflicting opinions over which one should get the "pelogic" name. At any rate, one of them had the alternative name "hexadecimal", so that one caught on, and the other one was left with "pelogic" (later replaced by "mavila"). Any distinction between 7-limit "mavila" and "pelogic" is probably just a result of combining names from different lists.

Igs actually suggested that the one we're calling Hexadecimal/Pelogic
should actually be called Armodue, for obvious reasons. I would
definitely support this. He also suggested calling Mavila Hornbostel,
but I think that the folks in the Mavila village were probably using
that tuning before Hornbostel figured it out, so I say keep it Mavila.

-Mike

On Sat, Jun 11, 2011 at 10:56 PM, Herman Miller <hmiller@...> wrote:
>
> On 6/10/2011 2:53 PM, Mike Battaglia wrote:
>
> > Those names are backwards from what I learned. Mavila is the 5-limit
> > temperament, and Pelogic is its 7-limit extension which suggests an
> > even flatter fifth. This usage is consistent with this here
> >
> > /tuning/database?method=reportRows&tbl=10
> >
> > also consistent with Graham's temperament finder
> >
> > http://x31eq.com/cgi-bin/rt.cgi?ets=7_2p&limit=5
> > http://x31eq.com/cgi-bin/rt.cgi?ets=9_16&limit=7
> >
> > I believe that's how it's called in "A Middle Path" as well. It also
> > doesn't look like the 5-limit version is called "Pelogic" even in the
> > xenharmonic wiki page, Gene says "The 5-limit temperament is (5-limit)
> > mavila, or pelogic, whose generator is a very flat fifth."
> >
> > I think what happened was that the temperament was originally called
> > "Pelogic," and then it was discovered that Kraig Grady had discovered
> > the temperament earlier by going to the Chopi village of Mavila in
> > Africa and measured the tuning for the xylophones they were using, so
> > they called it "Mavila" as a nod to that. Something along those lines
> > anyway. Either way, the point is that actual "pelog" tunings are
> > flatter than "mavila" ones.
>
> Yes, pelogic was just the older name that was replaced by mavila. There
> were different 7-limit extensions of pelogic, and there may have been
> conflicting opinions over which one should get the "pelogic" name. At
> any rate, one of them had the alternative name "hexadecimal", so that
> one caught on, and the other one was left with "pelogic" (later replaced
> by "mavila"). Any distinction between 7-limit "mavila" and "pelogic" is
> probably just a result of combining names from different lists.
>
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> He also suggested calling Mavila Hornbostel,
> but I think that the folks in the Mavila village were probably using
> that tuning before Hornbostel figured it out, so I say keep it
> Mavila.
>
> -Mike

I would love to have a peek at the data from the Mavila village to know what their actual tuning is. That would settle it for me. Kraig has said it's not very much like 16-EDO, but I haven't heard him weigh in on 23-EDO. The name "Hornbostel" has the advantage of being known outside of our little circle, although he was certainly not well respected as an ethnomusicologist. But I am impartial.

-Igs

On Sat, Jun 11, 2011 at 11:25 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > He also suggested calling Mavila Hornbostel,
> > but I think that the folks in the Mavila village were probably using
> > that tuning before Hornbostel figured it out, so I say keep it
> > Mavila.
> >
> > -Mike
>
> I would love to have a peek at the data from the Mavila village to know what their actual tuning is. That would settle it for me. Kraig has said it's not very much like 16-EDO, but I haven't heard him weigh in on 23-EDO. The name "Hornbostel" has the advantage of being known outside of our little circle, although he was certainly not well respected as an ethnomusicologist. But I am impartial.

See here:

http://www.anaphoria.com/meantone-mavila.PDF

Note that for (meta-)meantone, +4 (generators) = "5" (prime) and then
for (meta-)mavila, -3 (generators) = "5" (prime). So in Erv Wilson's
view, regardless of intonation, the fundamental characteristic of
mavila is that three tempered 4/3's get you to "5," just as the
fundamental characteristic of meantone is that four tempered 3/2's get
you to "5." So if you have a problem with the 135/128 linear
temperament being called "mavila," then you should take it up with
him.

I would be curious to find out how the folks in the Mavila village
actually did tune their xylophones, to see whether or not they got
closer to the POTE tuning by spreading the error out (closer to 23),
or if they instead wanted greater difference between the major and
minor thirds (closer to 16 or 25-equal).

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> See here:
>
> http://www.anaphoria.com/meantone-mavila.PDF

There's no data here, and in any case this is meta-mavila, not mavila. You bracket the meta- as if it's unimportant, but how do we know? Has Erv himself ever weighed in on the 135/128 temperament? Why didn't we call it meta-mavila temperament?

> I would be curious to find out how the folks in the Mavila village
> actually did tune their xylophones, to see whether or not they got
> closer to the POTE tuning by spreading the error out (closer to 23),
> or if they instead wanted greater difference between the major and
> minor thirds (closer to 16 or 25-equal).

Like I said. Data would be nice.

-Igs

--- "cityoftheasleep" <igliashon@...> wrote:

> Large otonalities in the 13-limit feel like sticking my
> finger in a light socket. I find the sound jarring,
> clangorous, emotionally ambiguous and somewhat distressing.
> On the other hand I find harmonies that beat moderately,
> such as those in 14, 20, and 23-EDO to be soothing, watery,
> exotic, and sweet.

OK thanks. Though I wouldn't say intervals in those EDOs
beat moderately... I think of moderate beating as being in
the 2-8 Hz range roughly.

> > Abstract models (such as analyzing an equal temperament
> > in terms of a harmonic series) should aid us in reaching
> > consistent conclusions about reality. Using harmonics
> > 32-64 with a brick wall 8-cent error cutoff won't do that.
>
> I disagree. The "reality" is that harmonics 32-64 each have
> a sound (or at least a texture) that people can and have
> learned to recognize.

Who? Is there any reason to believe such a statement?
I don't think so...

> In any case, I don't subscribe to the view that as musicians,

Writing about ratios and cents isn't musicianship, it's
quantitative music theory. Like any quantitative endeavor,
it must produce consistent conclusions about reality or it's
useless-- or worse, misleading. Hate to "shackle" you but
nothing can free us from this basic fact.

> If those methods lead to good music (as they seem to do,
> in the case of Kraig Grady and Johnny Reinhard and
> Dante Rosati, among others), then the real fool is the
> person who insists against the use of such approaches.

I haven't heard any of them claim to be able to recognize
every harmonic up to 64 or that such a skill has been
useful in music-making. Other outlandish claims have been
made though (such as the ability to distinguish and perform
at will on a variety of instruments any interval with
1-cent accuracy).

> > WTF is an "equal-hertz" chord and why is this bullshit
> > in the wiki?
>
> Presumably it is a chord in which the first-order difference
> tones all share the same frequency.
> Seems like you're the only one calling bullshit on it.

I know, it's terrible.

-Carl

Herman Miller <hmiller@...> wrote:

> Yes, pelogic was just the older name that was replaced by mavila.

That's what I thought, until I popped over to facebook just
now and saw Paul Erlich going apeshit about how only 5-limit
pelogic is mavila and nothing else should be called mavila.

As if music from mavila had anything to do with the 5-limit!

-Carl

Mike Battaglia <battaglia01@...> wrote:

> Igs actually suggested that the one we're calling
> Hexadecimal/Pelogic should actually be called Armodue,
> for obvious reasons.

Are you joking? If not, what are the reasons? I'm ignorant.

-Carl

On Sun, Jun 12, 2011 at 12:42 AM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > See here:
> >
> > http://www.anaphoria.com/meantone-mavila.PDF
>
> There's no data here, and in any case this is meta-mavila, not mavila. You bracket the meta- as if it's unimportant, but how do we know? Has Erv himself ever weighed in on the 135/128 temperament? Why didn't we call it meta-mavila temperament?

The "meta" prefix has to do with recurrent sequences and proportional
beating, which is kind of like a devolved form of periodicity buzz
(unless you're playing with sine waves, at which point it is
periodicity buzz).

So here we have a diagram showing 7-tet, which tempers out 25/24, and
then showing the choice of the two fifth-based systems that exist in
7-tet - mavila and meantone. One of them requires 4 generators to get
to E/Eb, which he called "5" in what is basically an intuitive use of
dicot temperament, and the other requires -3 generators to get to the
E/Eb "5" point. He then treats the two as separate tonal systems,
which in modern parlance means he's now detempering the 25/24, and
works out the "meta" generator for each of them, labeling the results
"meta-mavila" and "meta-meantone" in the same way we might talk about
"TOP mavila" or "TOP meantone." There are other fifth-based systems in
7-tet (what about the one where four fifths gets you to 125/96) but
these are the main points.

One interesting thing you can do with the meta-tunings is to start by
figuring out the meta-generator for a linear temperament, and then do
some secret voodoo math, and somehow you then end up with the
recurrent sequence of harmonics that approaches that generator. For
example, 2000:2992:4464:6672:9984 is a meta-meantone chain of fifths
derived in this way. This means that the major chord is
2000:2496:2992, which is actually 125:156:187, which an "isoharmonic"
chord with a constant difference of 31. You can work out some
interesting unequal temperaments this way, although it might just be
the case that 125:156:187 is too complex for the buzz to be audible (I
don't have scala set up atm to test) and that it might be handled
differently.

But that's what Erv Wilson was getting at. For the record I believe he
was actually shooting for optimizing around converging "combination
tones" rather than periodicity buzz (and I think that the latter fits
more into modern psychoacoustics anyway, where inner-ear combination
tones aren't talked about all the time anymore).

> > I would be curious to find out how the folks in the Mavila village
> > actually did tune their xylophones, to see whether or not they got
> > closer to the POTE tuning by spreading the error out (closer to 23),
> > or if they instead wanted greater difference between the major and
> > minor thirds (closer to 16 or 25-equal).
>
> Like I said. Data would be nice.

The point is that Erv Wilson called the 138/125 linear temperament
"mavila." Then he called the recurrent sequence proportional beating
version based on it "Meta-mavila." I would also love to know what size
of generator this culture used, or whether they tended towards
well-temperaments or whatever it is, but if you're claiming that
people have bastardized Kraig's work by fitting it into the 138/125
linear temperament, then you should take it up with Erv Wilson,
because that's the guy who did it first.

-Mike

On Sun, Jun 12, 2011 at 1:48 AM, Carl Lumma <carl@...> wrote:
>
> > I disagree. The "reality" is that harmonics 32-64 each have
> > a sound (or at least a texture) that people can and have
> > learned to recognize.
>
> Who? Is there any reason to believe such a statement?
> I don't think so...

You want to make the argument that you can dismiss, a priori, the
statement that anyone on planet Earth can set up a map for harmonics
32-64? Even despite that 64/63 is 27 cents, and that there are ear
training classes in 72-TET?

How? Why?

> > > WTF is an "equal-hertz" chord and why is this bullshit
> > > in the wiki?
> >
> > Presumably it is a chord in which the first-order difference
> > tones all share the same frequency.
> > Seems like you're the only one calling bullshit on it.
>
> I know, it's terrible.

Chords like that are going to be maximally "spiky," in your parlance,
so you're now calling bullshit on yourself. :)

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> How? Why?

Extraordinary claims require extraordinary evidence.
But in all my years of questioning this particular claim,
no evidence of any kind has ever been presented.

-Carl

Ah, I see

http://xenharmonic.wikispaces.com/Armodue+theory

It's very similar to what my recent suggestion would
produce for a 9-of-16 scale like that. -Carl

I wrote:

> Mike Battaglia <battaglia01@> wrote:
>
> > Igs actually suggested that the one we're calling
> > Hexadecimal/Pelogic should actually be called Armodue,
> > for obvious reasons.
>
> Are you joking? If not, what are the reasons? I'm ignorant.

On Sun, Jun 12, 2011 at 1:52 AM, Carl Lumma <carl@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > Igs actually suggested that the one we're calling
> > Hexadecimal/Pelogic should actually be called Armodue,
> > for obvious reasons.
>
> Are you joking? If not, what are the reasons? I'm ignorant.

Because much of the Armodue paper was about the 7-limit implications
of 16-equal, and the main diatonic scale in the system is mavila[9].
Therefore

- Because the Armodue way of thinking seems to be very influential,
and people like it and often cite it, especially on the XA Facebook
group
- And the name "Pelogic" is even more overloaded than "diatonic," in
that now we have a Mavila/Pelogic, and then a 7-limit "Mavila," and
also a "Hexadecimal/Pelogic," etc
- And because the name "Hexadecimal" already suggests that we're aware
that this is basically the only 7-limit mavila extension that makes
sense in 16-equal
- And also because Paul Erlich was going apeshit about calling
Hexadecimal "Pelogic"

I say might as well call this specific 7-limit mapping Armodue. But
there's going to be a riot if you want people to start calling Mavila
"Hornbostel," I'll tell you that right now.

-Mike

On Sun, Jun 12, 2011 at 2:07 AM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > How? Why?
>
> Extraordinary claims require extraordinary evidence.
> But in all my years of questioning this particular claim,
> no evidence of any kind has ever been presented.

What's extraordinary about it? If Igs had said that people were
perceiving 64/63 as resolving correctly to the correct VF, I could see
why you'd be skeptical. But he said that it's a useful structure for
people to think in and conceptually organize music, and you're saying
that that's impossible. That's the extraordinary claim. But since
we're all pressed for time these days, it'd be okay if you could give
some normal, non-extraordinary evidence for it.

-Mike

Mike Battaglia <battaglia01@...> wrote:

> > Extraordinary claims require extraordinary evidence.
> > But in all my years of questioning this particular claim,
> > no evidence of any kind has ever been presented.
>
> What's extraordinary about it? If Igs had said that people
> were perceiving 64/63

Unless I misunderstood, he said that all dyads between
harmonics up to 64 produce a unique "texture" that can
be recognized.

-Carl

On Sun, Jun 12, 2011 at 2:47 AM, Carl Lumma <carl@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > > Extraordinary claims require extraordinary evidence.
> > > But in all my years of questioning this particular claim,
> > > no evidence of any kind has ever been presented.
> >
> > What's extraordinary about it? If Igs had said that people
> > were perceiving 64/63
>
> Unless I misunderstood, he said that all dyads between
> harmonics up to 64 produce a unique "texture" that can
> be recognized.

Given the original conversation between him and Johnny R on Facebook,
I thought he meant effectively all "rooted" harmonics up to 64. As in,
all dyads between 32 and 64 with 32 as the denominator, not all
permutations of total dyads between 32 and 64. I'll leave it up to him
to clarify.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> > > Here's a question: check out the music on this page
> > >
> > > http://xenharmonic.wikispaces.com/Quarter-comma+meantone
> > >
> > > and tell me what is it you hate about low error temperaments.
> > >
> >
> > You mean "low-limit, low-error" temperaments.
>
> Yep, that's a page on quarter-comma meantone.

I apologize to anyone who thought the musical examples were not xen enough for a Xenharmonic Wiki. I've added five xenharmonic canons and a piece by Vicentino to the mix.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> Haven't heard much of George's music, but I tend to hate anything with full 13-limit otonalities (let alone utonalities...yuck)

Who is it who composes in those? Whereas lots of people are flocking to the banner of high-error temperaments.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Herman Miller <hmiller@> wrote:
>
> > Yes, pelogic was just the older name that was replaced by mavila.
>
> That's what I thought, until I popped over to facebook just
> now and saw Paul Erlich going apeshit about how only 5-limit
> pelogic is mavila and nothing else should be called mavila.

Brings a smile to my face--he's still the same Paul. I'm hoping to get some new music out of his basement, especially if it isn't in mavila. Or pelogic, or armodue, or whatever.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > Unless I misunderstood, he said that all dyads between
> > harmonics up to 64 produce a unique "texture" that can
> > be recognized.
>
> Given the original conversation between him and Johnny R on
> Facebook, I thought he meant effectively all "rooted"
> harmonics up to 64. As in, all dyads between 32 and 64
> with 32 as the denominator, not all permutations of total
> dyads between 32 and 64. I'll leave it up to him
> to clarify.

My criticism would stand either way but it should be
noted that this is not Facebook. Continuing discussions
from there over here is likely to confuse.

-Carl

On Sun, Jun 12, 2011 at 3:15 AM, Carl Lumma <carl@...> wrote:
>
> My criticism would stand either way

Why?

> but it should be
> noted that this is not Facebook. Continuing discussions
> from there over here is likely to confuse.

Igs said this:
> I disagree. The "reality" is that harmonics 32-64 each have a sound (or at least a texture) that people can and have learned to recognize.

Not 61-limit harmony, but harmonics 32-64, with "each one" having its
own sound, meaning not random dyads between them. That's pretty clear
to me even without Facebook, but maybe not to you. But since you seem
to claim that even this is psychoacoustically impossible, go on, let's hear
it.

-Mike

Mike Battaglia <battaglia01@...> wrote:

> > My criticism would stand either way
>
> Why?

For reasons already stated. -Carl

On Sun, Jun 12, 2011 at 3:28 AM, Carl Lumma <carl@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > > My criticism would stand either way
> >
> > Why?
>
> For reasons already stated. -Carl

Can you state them publicly? -Mike

On Sun, Jun 12, 2011 at 3:31 AM, Mike Battaglia <battaglia01@...> wrote:
> On Sun, Jun 12, 2011 at 3:28 AM, Carl Lumma <carl@...> wrote:
>>
>> Mike Battaglia <battaglia01@...> wrote:
>>
>> > > My criticism would stand either way
>> >
>> > Why?
>>
>> For reasons already stated. -Carl
>
> Can you state them publicly? -Mike

Hey also, when you do, can you make sure to take into consideration
the things I've already said about the a priori dismissal of ideas and
"extraordinary claims," so that we don't waste time by going in
circles? Thanks, Mike

Mike Battaglia <battaglia01@...> wrote:

> Hey also, when you do, can you make sure to take into
> consideration the things I've already said about the a priori
> dismissal of ideas and "extraordinary claims," so that
> we don't waste time by going in circles? Thanks, Mike

You should have taken into account the comments you were
replying to when you made those nonsense remarks in the
first place, and you should have taken them into account
again before you made the above blabber. Please stop before
you hurt yourself.

-Carl

On Sun, Jun 12, 2011 at 3:43 AM, Carl Lumma <carl@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > Hey also, when you do, can you make sure to take into
> > consideration the things I've already said about the a priori
> > dismissal of ideas and "extraordinary claims," so that
> > we don't waste time by going in circles? Thanks, Mike
>
> You should have taken into account the comments you were
> replying to when you made those nonsense remarks in the
> first place, and you should have taken them into account
> again before you made the above blabber. Please stop before
> you hurt yourself.

I took them into account when I replied to them, by definition.

But I didn't get a response from you on those replies; not after the
rootedness miscommunication was cleared up. So far I've there's only
been remarks from you stating you'd already explained your reasoning,
and now a further response saying my questioning of that incomplete
reasoning is nonsensical blabber.

Still waiting for a straightforward exposition of your logic,
Mike

Mike Battaglia <battaglia01@...> wrote:

> > > > My criticism would stand either way
> > >
> > > Why?
> >
> > For reasons already stated. -Carl
>
> Can you state them publicly? -Mike

Just did, open your eyes. -Carl

On Sun, Jun 12, 2011 at 3:36 AM, Carl Lumma <carl@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > > > > My criticism would stand either way
> > > >
> > > > Why?
> > >
> > > For reasons already stated. -Carl
> >
> > Can you state them publicly? -Mike
>
> Just did, open your eyes. -Carl

You got this message late, this was supposed to be a few messages ago.
I haven't seen an explanation of why you think it's impossible for
someone to work out a categorical, Rothenberg-style perception based
around harmonics 32-64. If you've posted one, then mea culpa, but I
don't see it, so a link would be helpful.

-Mike

"cityoftheasleep" <igliashon@...> wrote:

> Large otonalities in the 13-limit feel like sticking my
> finger in a light socket. I find the sound jarring,
> clangorous, emotionally ambiguous and somewhat
> distressing. On the other hand I find harmonies that
> beat moderately, such as those in 14, 20, and 23-EDO to
> be soothing, watery, exotic, and sweet.

What a vivid picture you paint! With rhetoric like that,
you might spark a 13-limit explosion. What composer
wouldn't want to harness the raw, primal energy of those
large otonalities? If only there were music to back it up.
And how witheringly you dismiss those washed out EDOs.

Graham

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> OK thanks. Though I wouldn't say intervals in those EDOs
> beat moderately... I think of moderate beating as being in
> the 2-8 Hz range roughly.

I consider the fifths of 5- and 7-EDO to beat "moderately", while the fifth of 16-EDO beats "hectically", and the fifths of 26-EDO and 27-EDO beat "mildly" and the fifths of 19 or 22-EDO beat "barely".

> Who? Is there any reason to believe such a statement?
> I don't think so...

What are you actually trying to accomplish with this attitude, Carl? Do you want to put Johnny Reinhard in a lab, run some tests on him, prove to him that no he can't tell the 171st harmonic from the 85th and then force him to admit that his entire approach to making music is a fiction, so that he abandons it and hops on the regular temperament band-wagon with everyone else? Do you want to force Dante Rosati to admit that the intervals on his prime harmonics 17-199 guitar are not any different than randomly-tuned intervals, so that he scrapes the frets off it and replaces them with Blackjack? Are you going to start charging into discussions of 5-limit JI and decrying the existence of the 40/27 wolf-fifth..."sorry guys, 40/27 is no different in sound than any other randomly-tuned dissonance, so you guys have to stop using that ratio in your discussions because it's psychoacoustically meaningless."

> Writing about ratios and cents isn't musicianship, it's
> quantitative music theory. Like any quantitative endeavor,
> it must produce consistent conclusions about reality or it's
> useless-- or worse, misleading. Hate to "shackle" you but
> nothing can free us from this basic fact.

Bullshit. This is music, not science. The constraint placed upon music theory has nothing to do with "reality" and everything to do with "aesthetics". We're not making "conclusions", we're making ART.

But in any case, just because it might be difficult to recognize a bare dyadic high-harmonic ratio in isolation, that does not mean music made with said harmonics will be difficult to recognize. I can tell the difference between 14-EDO and 12-EDO and 17-EDO and 19-EDO, and I suspect you can too. And hey, guess how we do that? By recognize the characteristic sounds of the tunings of the intervals in each tuning. I can tell the sound of 14-EDO because it's got 4ths and 5ths that beat moderately, a piquant supermajor 3rd that doesn't quite buzz, a slightly awkward submajor 2nd, a flat subminor 3rd that's a bit rough, etc. If I can recognize those intervals as being characteristic of 14-EDO, why should it be any harder for me to recognize music made with, say, harmonics 25, 37, 39, 41, and 43? As it turns out, those harmonics all sound almost exactly like intervals from 14-EDO. Wow, I guess this means if I can recognize those intervals as being from 14-EDO, I should just as easily be able to recognize them as being those harmonics, as long as I do a little bit of mental training so that I think "41st harmonic" instead of "14-EDO supermajor 3rd" when I hear that interval.

Seems like in your view, I shouldn't be able to hear that interval as anything but a 9/7...or maybe even a 5/4. But it's obviously not a Just version of either of those, it's mistuned in a particular and audible way. Saying I can't recognize the 41st harmonic is basically saying I can't tell the difference between a 9/7 that's tuned 8 cents flat and one that's tuned 16 cents flat.

> I haven't heard any of them claim to be able to recognize
> every harmonic up to 64 or that such a skill has been
> useful in music-making. Other outlandish claims have been
> made though (such as the ability to distinguish and perform
> at will on a variety of instruments any interval with
> 1-cent accuracy).

And yet, there they go, making music with those higher harmonics. They clearly find something useful about thinking in terms of them, and even if it's true that no one can recognize them, that doesn't actually matter, because (as I keep saying), the important thing is how the theory leads to music. We're not trying to build a fucking space elevator or cure brain cancer here. Music does not deal in reality, music deals in fantasy. Music theory guides people in making music, which is to say it guides people in constructing fantasies. FANTASY, Carl.

And hey, you know what else is a fantasy? That 11-EDO is a Hanson temperament. Or that Father temperament exists. Or that 12-EDO is a 7-limit temperament.

-Igs

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> Who is it who composes in those? Whereas lots of people are flocking > to the banner of high-error temperaments.

If by "lots" you mean me, Mike, and maybe Herman.

I don't know anyone using full 13-limit otonalities in their music, but I gather that as far as Carl is concerned, unless they are doing so, their music is not truly 13-limit, because 13-limit intervals are not recognizable on their own.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > Who is it who composes in those? Whereas lots of people are flocking > to the banner of high-error temperaments.
>
> If by "lots" you mean me, Mike, and maybe Herman.

Chris counts as lots all by himself.

On Sun, Jun 12, 2011 at 12:08 PM, cityoftheasleep
<igliashon@...> wrote:
>
> But in any case, just because it might be difficult to recognize a bare dyadic high-harmonic ratio in isolation, that does not mean music made with said harmonics will be difficult to recognize. I can tell the difference between 14-EDO and 12-EDO and 17-EDO and 19-EDO, and I suspect you can too. And hey, guess how we do that? By recognize the characteristic sounds of the tunings of the intervals in each tuning.

1) The average person can't identify every interval in 12-EDO from one
another. That's why people need to take ear training classes to learn
to identify intervals. I believe I've read that either the major sixth
or the minor 7th is the hardest to identify, usually. So by this
reasoning, 12-EDO is a scam, and the average person can't identify
12-EDO music.

2) The above is absurd, obviously, because music does not consist of
bare dyads separated by long spaces of silence, as a wise man once put
it. But when you play a major third, and then you go up a half step to
a fourth, the average person will be able to figure out where you've
moved to in the scale - as evidenced by the fact that people can carry
simple melodies.

Whether or not someone can identify a bare dyad offhand from the
harmonic series means nothing. The ability to find your way in a
musical setting means everything. There's more going on than just
harmonic entropy in musical cognition.

If you play an octave, and then you move down 17 cents, a listener
with enough training will probably be able to figure out that this
melodic motion has put you at the 63rd harmonic. And if they all start
to blend together somewhere in the middle, then that would just become
part of the music - you'd know not to just start off playing random
harmonics in the middle because you'd lose your place and not be able
to follow. You know, just like people have learned to not play random
ass notes in 12-equal because then they can't figure out what's going
on.

But you could, even so, start off in the middle, so long as you have a
way to find your way around. Luckily, since 64 is a power of 2, there
are low-entropy "guide tones" all over the place, with higher-entropy
or ambiguous ones interspersed logarithmically in between them. If you
lose your way, mentally, you can always get back on track as soon as
someone hits a simpler interval that you recognize, like 7/4. Then you
have a good strategy for finding your way. If you used a strong enough
timbre, the periodicity buzz alone would be a hell of a clue you for
when you've hit a simpler harmonic. Who knows what kinds of (possibly
redundant) coding strategies someone would come up with to map this
space out if this is what they wanted to do?

In fact, it might even be that the harmonics with root 64 would
function best as "chromatic" notes, whereas the ones that reduce to
denominator 32 or even 16 work as the main ones. Then you'd learn not
to hang around on the /64 harmonics for too long, because they sound
ambiguous and you lose your cognitive foothold on what's going on, so
they might work best as passing tones between the more important and
simpler harmonics. I don't know exactly how people would learn to get
around, but I do know that any psychoacoustic limitations would become
part of the model; people would become aware of them, and they'd just
be met with people learning to cognize things in other ways. If one
coding strategy fails, that doesn't mean another can't take its place.

-Mike

On 6/11/2011 11:01 PM, Mike Battaglia wrote:
> Igs actually suggested that the one we're calling Hexadecimal/Pelogic
> should actually be called Armodue, for obvious reasons. I would
> definitely support this. He also suggested calling Mavila Hornbostel,
> but I think that the folks in the Mavila village were probably using
> that tuning before Hornbostel figured it out, so I say keep it Mavila.

Also, I ran across a different Hornbostel tuning with a 261 cent generator (pelog_pb.scl in the Scala archive) back when I was investigating a 14-note MOS scale I called "superpelog". That one gives me the impression of being a better approximation to a pelog tuning than the mavila one (to the extent that any regular temperament can approximate the various pelog tunings). So if we want to use the name "hornbostel" for any RT, I'd suggest one with a generator around 261 cents (e.g., 5-limit bug, 7-limit beep or superpelog).

On 6/12/2011 3:12 AM, genewardsmith wrote:
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep"<igliashon@...>
> wrote:
>
>> Haven't heard much of George's music, but I tend to hate anything
>> with full 13-limit otonalities (let alone utonalities...yuck)
>
> Who is it who composes in those? Whereas lots of people are flocking
> to the banner of high-error temperaments.

Prent Rodgers has used the 15-limit tonality diamond.

http://prodgers13.home.comcast.net/~prodgers13/liner/DryHoleCanyon.htm

On Sun, Jun 12, 2011 at 12:56 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > > Who is it who composes in those? Whereas lots of people are flocking > to the banner of high-error temperaments.
> >
> > If by "lots" you mean me, Mike, and maybe Herman.
>
> Chris counts as lots all by himself.

FWIW, before you joined the list, Carl sent me a huge zip file of your
MIDIs, and I spent lots of time obsessively listening to them over and
over again to get the sound in my head, especially Chromosounds. I
think that you could be the equivalent of Stravinsky for the 21st
century, except that we don't have a real orchestra to play your stuff
yet, and I've had discussions with a lot of people about this fact.
Someday, when I have an infinite amount of time, I'll arrange
Chromosounds out for orchestra, because I've had the vision in my head
for how to do that since like 2008 or so. In fact, I think it quite
likely that you'll be very well-known for your pioneering role in all
of this, both theoretically and compositionally, but let's hope that
both of those happen before the year 2300. So if I haven't brownnosed
enough let that set the record straight.

Our present discussion is coming as part of a general low-accuracy
revolution in the community overall, which is being spearheaded by
folks like Igs with his use of exotemperaments, Ron Sword with his
16-equal stuff, etc. People have figured out that low error doesn't
immediately correspond to high intelligibility, and high error doesn't
immediately correspond to low intelligibility. If you've spent time
working out a cognitive map for low-error JI type tunings, then that
might be the case, but you had to build that map at one point, so you
might as well work it out for some crazy exotemperaments as well. The
rottenness of the fruit, when processed properly, becomes a part of
the music, as has processed rotten fruit become a part of dinner. In
fact, the Catholic Church says that processed rotten fruit is actually
a necessary part of bringing you in communion with God! You can't come
to appreciate rotten fruit more than that.

And now I'm going to stop, because I'm again not here, which is why
I'm still behind on the stuff about cubic lattices. But the next thing
I do will likely be a 19-limit sort of thing built around 19-equal
negri, and then I'll move onto something really high accuracy
afterward.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Jun 12, 2011 at 12:08 PM, cityoftheasleep
> <igliashon@...> wrote:
> >
> > But in any case, just because it might be difficult to recognize a bare dyadic high-harmonic ratio in isolation, that does not mean music made with said harmonics will be difficult to recognize. I can tell the difference between 14-EDO and 12-EDO and 17-EDO and 19-EDO, and I suspect you can too. And hey, guess how we do that? By recognize the characteristic sounds of the tunings of the intervals in each tuning.
>
> 1) The average person can't identify every interval in 12-EDO from >one
> another.

The average person can't carry a tune in a bucket, or notice "wrong notes" or when something's "off key"? That's simply not true. What you mean is, the average person can't give every 12-tET interval presented out of context it's "proper name".

>That's why people need to take ear training classes to learn
> to identify intervals. I believe I've read that either the major >sixth
> or the minor 7th is the hardest to identify, usually.

My experience has been that mistakes, overwhelmingly, are made by incorrectly guessing which interval of a particular "character class " is presented- confusing octave and fifth, or major third and sixth.

>So by this
> reasoning, 12-EDO is a scam, and the average person can't identify
> 12-EDO music.

Well said. Aside from being deeply unmusical, the judgement of tuning and intervallic "validity" by isolated dyad is pseudo-scientific.
>
> 2) The above is absurd, obviously, because music does not consist of
> bare dyads separated by long spaces of silence, as a wise man once put
> it. But when you play a major third, and then you go up a half step to
> a fourth, the average person will be able to figure out where you've
> moved to in the scale - as evidenced by the fact that people can >carry
> simple melodies.

Not just simple melodies. By nature, humans have excellent pitch and melody abilities. Twice in my life I've been privileged to overhear, by accident, two different allegedly "tone deaf" teenagers (continually mocked and told to shut up by their families) singing when they weren't aware anyone was hearing: singing with enviable strength and precision, "my jaw dropped" as they say. My little son is the solist in his choir, but let me tell you, one third of the kids have effortlessly excellent ears, and another third I'm dead certain would have great ears with time and some work at scraping off inherited social burdens, timidity, etc.

>
> Whether or not someone can identify a bare dyad offhand from the
> harmonic series means nothing. The ability to find your way in a
> musical setting means everything. There's more going on than just
> harmonic entropy in musical cognition.

Once again well said. And, right off the bat the grid of reference presented by the harmonic series, regardless of the weight of its relevance to musical cognition, is more fine-grained than the rigged ethnocentric tripe of "harmonic entropy" would have it. In these internet groups, and in these internet groups ONLY, have I not found "no duh" consensus that moderately high harmonic ratios such as 11/9 and 13/8 are "of a kind" with lower ratios, that is, clearly "Just", and that the 12-tET M3 very obviously is completely different in character from 5/4. Actually I think that "civilian" sensitivity to "Justness" tends to be greater than mine.

On Mon, Jun 13, 2011 at 5:07 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > 1) The average person can't identify every interval in 12-EDO from >one
> > another.
>
> The average person can't carry a tune in a bucket, or notice "wrong notes" or when something's "off key"? That's simply not true. What you mean is, the average person can't give every 12-tET interval presented out of context it's "proper name".

I'm not saying that. I'm saying that the usual logic I hear against
someone learning to make sense of something like harmonics 32-64 is
that they wouldn't be able to identify which is which in a blind
listening test. Which is like, OK, I'm not sure Johnny Reinhardt can
do that, and I've also seen plenty of people screw up and say that a
fifth is an octave. Big deal. Melody and context is everything.

> >That's why people need to take ear training classes to learn
> > to identify intervals. I believe I've read that either the major >sixth
> > or the minor 7th is the hardest to identify, usually.
>
> My experience has been that mistakes, overwhelmingly, are made by incorrectly guessing which interval of a particular "character class " is presented- confusing octave and fifth, or major third and sixth.

Yeah, the octave and fifth confusion is pretty common.

> >So by this
> > reasoning, 12-EDO is a scam, and the average person can't identify
> > 12-EDO music.
>
> Well said. Aside from being deeply unmusical, the judgement of tuning and intervallic "validity" by isolated dyad is pseudo-scientific.

It's doubly unscientific because it's not that hard to find your way
around harmonics 16-32, for example, and then 32-64 are just in
between those. And when it really does get ambiguous - say you're apt
to confuse 61/64 and 62/64 or something, because they're so close
together - then that will work its way into the way that people
cognize the music, because people will know not to just start randomly
playing harmonics near the top, just like they know that playing
random notes in 12-tet sounds confusing and terrible. You'd have to
start with some kind of identifiable signpost to help someone mentally
find their way throughout the scale, like a just 7/4 or something, and
then move around from there.

It would be pretty confusing if I played a melody consisting of random
notes on a 12-tet piano. If, on the other hand, I had a melody that
was mostly diatonic, but interspersed chromatic notes between the
diatonic ones, it'll be much less confusing. Maybe it'd naturally work
out that people would think of harmonics 8-16 would be the "diatonic"
ones, there to help you "find your way" so to speak, that the
remainders from 16-32 would be more like the "chromatic" ones that
pass between 8-16, and then that the ones left over 32-64 would be the
equivalent of quartertones or something like that. And although
something like 41/32 would probably sound exactly like 4/3, there's
nothing stopping you from also being aware of how it fits to nearby
intervals like 21/16 and 11/8 in the harmonic series - just like
you're aware of how things in meantone can function more than one way
because of the 81/80 pun. I would expect so.

> Not just simple melodies. By nature, humans have excellent pitch and melody abilities. Twice in my life I've been privileged to overhear, by accident, two different allegedly "tone deaf" teenagers (continually mocked and told to shut up by their families) singing when they weren't aware anyone was hearing: singing with enviable strength and precision, "my jaw dropped" as they say. My little son is the solist in his choir, but let me tell you, one third of the kids have effortlessly excellent ears, and another third I'm dead certain would have great ears with time and some work at scraping off inherited social burdens, timidity, etc.

I do know, unfortunately, a lot of people who couldn't carry a melody
to save their lives. They get "up" vs "down" and step vs leap, and
other than that it's ready fire aim for them. Somehow, though, my
friend Sean has learned to sing in 13-tet - he liked Sevish's tune
"Sean's Bits" and sings the melody from it - something like Ab Bb Ab,
E F# E, except the Ab-E is a father-tempered fifth. He nails the leap
as being right between 3/2 and 8/5 every single time. It's crazy.

> > Whether or not someone can identify a bare dyad offhand from the
> > harmonic series means nothing. The ability to find your way in a
> > musical setting means everything. There's more going on than just
> > harmonic entropy in musical cognition.
>
> Once again well said. And, right off the bat the grid of reference presented by the harmonic series, regardless of the weight of its relevance to musical cognition, is more fine-grained than the rigged ethnocentric tripe of "harmonic entropy" would have it. In these internet groups, and in these internet groups ONLY, have I not found "no duh" consensus that moderately high harmonic ratios such as 11/9 and 13/8 are "of a kind" with lower ratios, that is, clearly "Just", and that the 12-tET M3 very obviously is completely different in character from 5/4. Actually I think that "civilian" sensitivity to "Justness" tends to be greater than mine.

What do you mean by 11/9 being "of a kind" with lower ratios?

As for 400 cents and 386 cents being completely different in character
- I notice that if I'm playing in 12-equal, the 400 cent major third
sounds "right," and then a sudden shift to the 386 cent major third
will sound "wrong." Then, if I shift to 31-equal, and play around the
circle of fifths for a bit, suddenly the 386 cent one will sound
right, and the 193 cent whole step will sound right too. Then, if I
shift back to 12-equal, suddenly the 400 cent major third will sound
wrong, and the 200 cent whole step as well. After a few seconds I
adjust again. This seems to apply even if we're dealing with diatonic
scales as diverse as 17-equal and 26-equal. Although you seem to have
spent much of your time learning to distinguish between different
intervals - my recent explorations into exotemperaments have led me to
try and identify their similarities. So I might say that things sound
similar in more ways than you might.

Lastly, I should say that I'm not sure how useful the grid of
reference provided by the harmonic series up around the highest part
of the chunk we're looking at, like 54-64 say, will be - I think I'd
find it very confusing if you hit random harmonics and asked me to
guess which is which. But I think that where it gets ambiguous, I'd
just develop another coding strategy to find my way mentally around
the scale; I'd find some kind of undeniably familiar intervals (like
56/24, which would be 7/4) and then I'd get a handle on what's going
on that way. You don't need to know every single note in 31-tet to be
able to find your way around it, and I don't think you'd need to learn
all of the harmonics from 32-64 to get the gist of how to move around
the 32-note scale either.

I will say that my belief in HE as a strict law of the universe has
waned a bit since I got my AXiS and set up my iPhone synth and started
playing more music. It's pretty simple - in 17-equal, when I was
trying to get a grip on what was going on, I first figured out that
7\17 was obviously the 4/3 (or the "fourth"), and that 9\17 was the
tritone, and then 8\17 was the ambiguous interval between them,
sometimes sounding kind of like a tritone. So now that I know all of
this theory, I'm aware that this ambiguous interval can actually
function as a really awesome, rooted, "otonal"-sounding interval in
chords, because it's also 11/8. After playing with such chords in
17-equal for a while, and while writing the etude, I started
experimenting with the bare dyad outside of the chord. I wasn't all
that surprised to find that the otonal sound of 11/8, the one I was
exploring in chords, started then to then carry over to the dyad; it
started sounding less ambiguous, which says something about how
learning affects psychoacoustics. It's kind of like how when you sing
C-E, it still sounds like a major third, even though you never
actually play notes in the dyad at the same time. "Root-finding" is
what we're after here, and it's very influenced by learning. Have I
sent you the "Frere Jacques" study yet, btw? You'd probably appreciate
it.

I should point out that I'm not really sure that you hate the HE model
as much as you think that you do - you mainly seem to disagree with
certain aspects of specifically Carl's interpretation of the HE curve.
You should try asking Paul about it directly and see if you find his
interpretation more appealing. In some ways he has a very different
take on it, and being as he's the one who invented it it's worth
hearing what he has to say. For instance, he's always encouraging me
to get into Javanese singing and other "high-entropy" forms of music,
because he thinks it just requires a little bit of adaptation to get
used to, and he didn't intend for the model to have anything to do
with learning - it's an intentionally basic model that doesn't take
learning into account at all.

As for Carl's interpretation, I think if pressed you guys would find
that you agree more than you think you do. After all, it's a fairly
odd experience for me, as an outsider, to watch Carl talk about
rank-order matrices and tell me how everything's not about HE, and
then for you to also tell me on the same thing, but then for you guys
to to somehow disagree when you talk directly to one another. I don't
get it.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Jun 13, 2011 at 5:07 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > 1) The average person can't identify every interval in 12-EDO from >one
> > > another.
> >
> > The average person can't carry a tune in a bucket, or notice "wrong notes" or when something's "off key"? That's simply not true. What you mean is, the average person can't give every 12-tET interval presented out of context it's "proper name".
>
> I'm not saying that. I'm saying that the usual logic I hear against
> someone learning to make sense of something like harmonics 32-64 is
> that they wouldn't be able to identify which is which in a blind
> listening test. Which is like, OK, I'm not sure Johnny Reinhardt can
> do that, and I've also seen plenty of people screw up and say that a
> fifth is an octave. Big deal. Melody and context is everything.

We're in agreement, I was just rewording your argument to show illustrate the fallacy you point out in a slightly different way. I remember kids from school who found the simplest of ear-training tests a struggle but could sing and perform just fine, even very well.

>
> > >That's why people need to take ear training classes to learn
> > > to identify intervals. I believe I've read that either the major >sixth
> > > or the minor 7th is the hardest to identify, usually.
> >
> > My experience has been that mistakes, overwhelmingly, are made by incorrectly guessing which interval of a particular "character class " is presented- confusing octave and fifth, or major third and sixth.
>
> Yeah, the octave and fifth confusion is pretty common.

Seconds and sevenths, too. I must say, and I teacher of mine pointed this out to me long ago, there's a difference between students who get things wrong in a consistent way and those whose errors are pretty much random. There's wrong-but-musical and just wrong. Plain old wrong is pretty rare, according to this (quite successful) teacher, and a real "tin ear" is very rare.

>
> I do know, unfortunately, a lot of people who couldn't carry a >melody
> to save their lives.

A friend of mine startled me one time: I'd always thought he couldn't carry a tune at all. Not oddly, he's an excellent professional sound engineer, and his spectral hearing (oh, that's such and such an amp, equing, etc.) is great. We were listening to a recording of a choir singing Justly and bam, for the first time I heard him sing along dead on. Scared the heck out of me, LOL. I speculate that he's just totally tuned into some kind of spectral way of listening.

>They get "up" vs "down" and step vs leap, and
> other than that it's ready fire aim for them. Somehow, though, my
> friend Sean has learned to sing in 13-tet - he liked Sevish's tune
> "Sean's Bits" and sings the melody from it - something like Ab Bb Ab,
> E F# E, except the Ab-E is a father-tempered fifth. He nails the leap
> as being right between 3/2 and 8/5 every single time. It's crazy.

A well-constructed melody is singable in all kinds of tunings, I've found.

.
>
> What do you mean by 11/9 being "of a kind" with lower ratios?

Soft, church/choir-like, calming, sleepy... I've heard all kinds of related descriptions when presenting "just intonation" to civilians, and find that these general character descriptions, recognizing simple ratios as "of a kind" go quite high- 13/8, all the 11/n ratios.
Mixing irrationals into the lisenting experience, they make the distinction, via character (that's like a choir, that's not... this region is exceptionally big on acappella vocal groups it's true).

>
> As for 400 cents and 386 cents being completely different in character
> - I notice that if I'm playing in 12-equal, the 400 cent major third
> sounds "right," and then a sudden shift to the 386 cent major third
> will sound "wrong." Then, if I shift to 31-equal, and play around the
> circle of fifths for a bit, suddenly the 386 cent one will sound
> right, and the 193 cent whole step will sound right too. Then, if I
> shift back to 12-equal, suddenly the 400 cent major third will sound
> wrong, and the 200 cent whole step as well. After a few seconds I
> adjust again. This seems to apply even if we're dealing with diatonic
> scales as diverse as 17-equal and 26-equal. Although you seem to have
> spent much of your time learning to distinguish between different
> intervals - my recent explorations into exotemperaments have led me to
> try and identify their similarities. So I might say that things sound
> similar in more ways than you might.

Oh I think peception can flip around in all kinds of ways, that's part of the fun.

Eh, gotta go.

>
> Lastly, I should say that I'm not sure how useful the grid of
> reference provided by the harmonic series up around the highest part
> of the chunk we're looking at, like 54-64 say, will be - I think I'd
> find it very confusing if you hit random harmonics and asked me to
> guess which is which. But I think that where it gets ambiguous, I'd
> just develop another coding strategy to find my way mentally around
> the scale; I'd find some kind of undeniably familiar intervals (like
> 56/24, which would be 7/4) and then I'd get a handle on what's going
> on that way. You don't need to know every single note in 31-tet to be
> able to find your way around it, and I don't think you'd need to learn
> all of the harmonics from 32-64 to get the gist of how to move around
> the 32-note scale either.

Mike B:
"As for 400 cents and 386 cents being completely different in character
- I notice that if I'm playing in 12-equal, the 400 cent major third
sounds "right," and then a sudden shift to the 386 cent major third
will sound "wrong." Then, if I shift to 31-equal, and play around the
circle of fifths for a bit, suddenly the 386 cent one will sound
right, and the 193 cent whole step will sound right too. Then, if I
shift back to 12-equal, suddenly the 400 cent major third will sound
wrong, and the 200 cent whole step as well. After a few seconds I
adjust again. This seems to apply even if we're dealing with diatonic
scales as diverse as 17-equal and 26-equal. Although you seem to have
spent much of your time learning to distinguish between different
intervals - my recent explorations into exotemperaments have led me to
try and identify their similarities. So I might say that things sound
similar in more ways than you might."

To me the equal/Pythagorean third sounds slightly sugary. I wonder how many
music students begin their ear training without even understanding the
harmonic sequence. In high school, our teacher would play the approximations
on a piano and say, "These are the notes that play when the bottom note is
played". Not knowing much about wave analysis, I didn't know if he was
talking about sympathetic vibration of the strings or not, nor about how the
timbre was composed of its own spectrum so the statement wasn't actually
true, nor that those fundamentals were actually only approximations, etc,
but it seemed to make sense to everyone else. So harmony winds up mastering
the player instead of being the tools of the player. Even worse, it leads an
interested student right past a treasure trove of theory. End complaining.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> It's doubly unscientific because it's not that hard to find your way
> around harmonics 16-32, for example, and then 32-64 are just in
> between those.

Remember that I'm not proposing using the entire gamut of harmonics 32-64 itself, I'm talking about using that gamut as a basis for describing intervals in EDOs. The most harmonics approximated by any EDO from 41 down is 19, in 41 itself (no surprise). If you can tell the difference between steps of 41, you can tell the difference between the 61st and the 63rd harmonic.

And in any case, the point of the exercise is more to find ways of treating EDOs like JI, i.e. to use pitch organization techniques the JI folks use (tonality diamonds, CPS's, etc.) in the context of an EDO. I got the idea from someone on the xenharmonic NING, I think it was Mark L. Vines but I'm not sure anymore because it's been awhile. I think he was using a lower error threshold than I am, though, because by his metric he was looking for at least 5 harmonics and 22-EDO didn't make his list, but by my count 22-EDO has about 9 harmonics within bounds. Maybe I should be a little more strict.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> I think that you could be the equivalent of Stravinsky for the 21st
> century, except that we don't have a real orchestra to play your stuff
> yet, and I've had discussions with a lot of people about this fact.

Wow, Mike, what can I say?

> In fact, I think it quite
> likely that you'll be very well-known for your pioneering role in all
> of this, both theoretically and compositionally, but let's hope that
> both of those happen before the year 2300.

I don't know. In 2300, computers will be writing the music and it will be in 12et because they can't actually hear like humans and the human simulations they use, which were based on 12 in the first place though they don't know that, say 12 is perfect. Performers mostly prefer 2, 3, or 4 equal because it's easier as you don't need to worry about chords and stuff, and of course no funny-looking keyboards.

People have figured out that low error doesn't
> immediately correspond to high intelligibility, and high error doesn't
> immediately correspond to low intelligibility.

Depends on how low the error goes, for me. I don't know that I hear this stuff the way you do.

> And now I'm going to stop, because I'm again not here, which is why
> I'm still behind on the stuff about cubic lattices.

What stuff about cubic latticies??

But the next thing
> I do will likely be a 19-limit sort of thing built around 19-equal
> negri, and then I'll move onto something really high accuracy
> afterward.

Good!

Herman Miller <hmiller@...> wrote:

> Prent Rodgers has used the 15-limit tonality diamond.
>
> http://prodgers13.home.comcast.net/~prodgers13/liner/DryHoleCanyon.htm

And George Secor, Jules Siegel, Hans Andre-Stamm, and
Arnold Dreyblatt, three of which I'd already named in
this thread. -Carl

Mike Battaglia <battaglia01@...> wrote:

> > > > > > My criticism would stand either way

> You got this message late, this was supposed to be a few
> messages ago. I haven't seen an explanation of why you
> think it's impossible for someone to work out a categorical,
> Rothenberg-style perception based around harmonics 32-64.
> If you've posted one, then mea culpa, but I don't see it,
> so a link would be helpful.

I have no idea what you mean by "Rothenberg-style" here but
it's pretty much been the entire history of this list, a
starting point, to discard rational intonation numerology.

-Carl

On Thu, Jun 16, 2011 at 3:26 AM, Carl Lumma <carl@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> I have no idea what you mean by "Rothenberg-style" here but
> it's pretty much been the entire history of this list, a
> starting point, to discard rational intonation numerology.

Please ditch the romanticization of tuning list history and science
and give me a straightforward explanation of why someone can't learn
to navigate around harmonics 32-64, which is a scale that contains 32
notes.

-Mike

Mike Battaglia <battaglia01@...> wrote:

> > I have no idea what you mean by "Rothenberg-style" here but
> > it's pretty much been the entire history of this list, a
> > starting point, to discard rational intonation numerology.
>
> Please ditch the romanticization of tuning list history and science
> and give me a straightforward explanation of why someone can't learn
> to navigate around harmonics 32-64, which is a scale that contains 32
> notes.

No need to fix what ain't broke. You can read the archives
like anyone else. -Carl

I wrote:

> > Speaking of which, has anyone tried composing in 25? Or 28?
> > Or, aside from me, in 27? I'd be interested to hear examples.
>
> I don't think 25 is so unpopular, though aside from a thing or
> two from Igs the only piece that comes to mind is my favorite
> "study" by Paul Rappoport, which appeared on a Perspectives of
> new music CD from the '90s.... not available online that
> I know of....

Now that I'm back from my little field trip, I've taken the
liberty of temporarily posting this piece here

http://lumma.org/temp/StudyInFives.mp3

It's the best piece I can think of in 25. -Carl