A Little Ditty In Father Temperament

As Igs initially pointed out, 13-equal is cognitively comprehensible
in some sort of strange way that Rothenberg would have a field day
with. Here's a little iPhone ditty demonstrating the concept:

http://soundcloud.com/mikebattagliamusic/a-little-ditty-in-13-equal

For all the haters in the audience, I played this on my IPHONE, so
y'alls got to ease on up.

Here I'm using the 2 2 1 2 1 2 2 1 mode of Father[8]. The interesting
thing about this scale is that (assuming we're in the key of C) the
bottom 5 notes sound like C-D-E-F-G from the diatonic scale, and the
top 4 notes sound like G-A-B-C also from the diatonic scale. However,
the G from the top half is a sharp "father" G, and the G from the
bottom half is a flat "pelog" G. This scale contains both of them, and
they differ by 1\13, which is also the size of the small step in the
scale.

The end result of all of this is that it is extremely easy to "follow"
this scale mentally. This could be because it makes use of "diatonic
hearing," albeit in a way that expands on it xenharmonically. It might
also be that there's something special about half steps and whole
steps that makes their insertion into scales particularly magical, but
I don't know what exactly that might be.

What I found most interesting, however, is that this scale's departure
from JI doesn't seem to impact my ability to cognize it. This is just
met in my perception by mapping things such that there are just "two
fifths" - the "pelog" one and the "father" one. Now that I've mapped
it out like that, I have a brand new to to play with.

Thus there is something that determines the harmonic concordance of
the scales (HE), and something else that determines the end
comprehensibility of the map (????), and the Two are Not One. Father
has the second property, but not the first.

Thoughts?

-Mike

Another recording in 13-equal, this time a free improv around various "modes"

http://soundcloud.com/mikebattagliamusic/modal-improvisation-in-13

Quality is pretty crappy because this is coming from my iPhone speaker
into my macbook microphone.

-Mike

On Wed, Jun 1, 2011 at 2:11 AM, Mike Battaglia <battaglia01@...> wrote:
> As Igs initially pointed out, 13-equal is cognitively comprehensible
> in some sort of strange way that Rothenberg would have a field day
> with. Here's a little iPhone ditty demonstrating the concept:
>
> http://soundcloud.com/mikebattagliamusic/a-little-ditty-in-13-equal
>
> For all the haters in the audience, I played this on my IPHONE, so
> y'alls got to ease on up.
>
> Here I'm using the 2 2 1 2 1 2 2 1 mode of Father[8]. The interesting
> thing about this scale is that (assuming we're in the key of C) the
> bottom 5 notes sound like C-D-E-F-G from the diatonic scale, and the
> top 4 notes sound like G-A-B-C also from the diatonic scale. However,
> the G from the top half is a sharp "father" G, and the G from the
> bottom half is a flat "pelog" G. This scale contains both of them, and
> they differ by 1\13, which is also the size of the small step in the
> scale.
>
> The end result of all of this is that it is extremely easy to "follow"
> this scale mentally. This could be because it makes use of "diatonic
> hearing," albeit in a way that expands on it xenharmonically. It might
> also be that there's something special about half steps and whole
> steps that makes their insertion into scales particularly magical, but
> I don't know what exactly that might be.
>
> What I found most interesting, however, is that this scale's departure
> from JI doesn't seem to impact my ability to cognize it. This is just
> met in my perception by mapping things such that there are just "two
> fifths" - the "pelog" one and the "father" one. Now that I've mapped
> it out like that, I have a brand new to to play with.
>
> Thus there is something that determines the harmonic concordance of
> the scales (HE), and something else that determines the end
> comprehensibility of the map (????), and the Two are Not One. Father
> has the second property, but not the first.
>
> Thoughts?
>
> -Mike
>

Neat. It suggests many possibilities to me. I found it most effective
towards the end where you just simplified the texture to single melody plus
drone...I thought the harmonies a little thick and muddy although I was
listen over my little Android speaker. I wonder how human singing would
sound on the same passage?

13 evokes a kind of surreal dream space for me. I immediately thought how
weird and wonderful it would be to hear this on the Chicago EL or NYC
subway...it would make people think they were dreaming, esp. if there were
strange visual elements.

AKJ
On Jun 1, 2011 2:57 AM, "Mike Battaglia" <battaglia01@...> wrote:
> Another recording in 13-equal, this time a free improv around various
"modes"
>
> http://soundcloud.com/mikebattagliamusic/modal-improvisation-in-13
>
> Quality is pretty crappy because this is coming from my iPhone speaker
> into my macbook microphone.
>
> -Mike
>
>
>
> On Wed, Jun 1, 2011 at 2:11 AM, Mike Battaglia <battaglia01@...>
wrote:
>> As Igs initially pointed out, 13-equal is cognitively comprehensible
>> in some sort of strange way that Rothenberg would have a field day
>> with. Here's a little iPhone ditty demonstrating the concept:
>>
>> http://soundcloud.com/mikebattagliamusic/a-little-ditty-in-13-equal
>>
>> For all the haters in the audience, I played this on my IPHONE, so
>> y'alls got to ease on up.
>>
>> Here I'm using the 2 2 1 2 1 2 2 1 mode of Father[8]. The interesting
>> thing about this scale is that (assuming we're in the key of C) the
>> bottom 5 notes sound like C-D-E-F-G from the diatonic scale, and the
>> top 4 notes sound like G-A-B-C also from the diatonic scale. However,
>> the G from the top half is a sharp "father" G, and the G from the
>> bottom half is a flat "pelog" G. This scale contains both of them, and
>> they differ by 1\13, which is also the size of the small step in the
>> scale.
>>
>> The end result of all of this is that it is extremely easy to "follow"
>> this scale mentally. This could be because it makes use of "diatonic
>> hearing," albeit in a way that expands on it xenharmonically. It might
>> also be that there's something special about half steps and whole
>> steps that makes their insertion into scales particularly magical, but
>> I don't know what exactly that might be.
>>
>> What I found most interesting, however, is that this scale's departure
>> from JI doesn't seem to impact my ability to cognize it. This is just
>> met in my perception by mapping things such that there are just "two
>> fifths" - the "pelog" one and the "father" one. Now that I've mapped
>> it out like that, I have a brand new to to play with.
>>
>> Thus there is something that determines the harmonic concordance of
>> the scales (HE), and something else that determines the end
>> comprehensibility of the map (????), and the Two are Not One. Father
>> has the second property, but not the first.
>>
>> Thoughts?
>>
>> -Mike
>>
>
>
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--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Here I'm using the 2 2 1 2 1 2 2 1 mode of Father[8].

Weren't we calling that Uncle temperament, or Step-Father or something? 8-EDO is Father, and the 5-note MOS might be Father, but that 8-note MOS has a clearly better 5/4 than the Father mapping gives.

> However, the G from the top half is a sharp "father" G, and the G
> from the bottom half is a flat "pelog" G. This scale contains both > of them, and they differ by 1\13, which is also the size of the
> small step in the scale.

Yeah, I remember the 'Wad had an example showing us how we hear both of them as a "fifth".

> The end result of all of this is that it is extremely easy to
> "follow" this scale mentally. This could be because it makes use of > "diatonic hearing," albeit in a way that expands on it
> xenharmonically. It might also be that there's something special
> about half steps and whole steps that makes their insertion into
> scales particularly magical, but I don't know what exactly that
> might be.

Time was, I found this scale totally mind-blowing because of the "extra" half-step. Like playing up and down the scale, there would always come a point where something "weird" would happen and I would totally freak out. Maybe because I'd play 2 2 1 2 2 and find myself at a minor 6th instead of a major 6th, I dunno. But after playing with this scale for a few years now, that doesn't happen any more. It sounds totally normal to me. I have "gone native" with this scale.

> What I found most interesting, however, is that this scale's
> departure from JI doesn't seem to impact my ability to cognize it. > This is just met in my perception by mapping things such that there > are just "two fifths" - the "pelog" one and the "father" one.

The fact that this scale does this with fifths makes it a particularly good example, but there are other scales that f*** with our intervallic perception just as heavily. Blackwood[10] in 20-EDO, for instance, gives us two "minor 7ths"--one at 960 cents, one at 1020 cents. The first one is from a stack of fourths, the second one is a fifth above the minor 3rd. Actually, you can also have two fifths in 20-EDO Blackwood, too--the 660-cent "pelog" fifth and the 720-cent "Blackwood" fifth. Thus two fourths as well. And two whole-tones (inversions of minor 7ths). That does a real job on me, mentally.

-Igs

I don't know why people bother with all these nomenclatures like "Father" at
all--if it's 8edo, why not just say 8edo? Done.

AKJ

You want a toe? I can get you a toe. There are ways, dude..... Hell, I can
get you a toe by 3 o'clock, with nail polish.
On Jun 1, 2011 10:35 AM, "cityoftheasleep" <igliashon@...> wrote:
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
>> Here I'm using the 2 2 1 2 1 2 2 1 mode of Father[8].
>
> Weren't we calling that Uncle temperament, or Step-Father or something?
8-EDO is Father, and the 5-note MOS might be Father, but that 8-note MOS has
a clearly better 5/4 than the Father mapping gives.
>
>> However, the G from the top half is a sharp "father" G, and the G
>> from the bottom half is a flat "pelog" G. This scale contains both > of
them, and they differ by 1\13, which is also the size of the
>> small step in the scale.
>
> Yeah, I remember the 'Wad had an example showing us how we hear both of
them as a "fifth".
>
>> The end result of all of this is that it is extremely easy to
>> "follow" this scale mentally. This could be because it makes use of >
"diatonic hearing," albeit in a way that expands on it
>> xenharmonically. It might also be that there's something special
>> about half steps and whole steps that makes their insertion into
>> scales particularly magical, but I don't know what exactly that
>> might be.
>
> Time was, I found this scale totally mind-blowing because of the "extra"
half-step. Like playing up and down the scale, there would always come a
point where something "weird" would happen and I would totally freak out.
Maybe because I'd play 2 2 1 2 2 and find myself at a minor 6th instead of a
major 6th, I dunno. But after playing with this scale for a few years now,
that doesn't happen any more. It sounds totally normal to me. I have "gone
native" with this scale.
>
>> What I found most interesting, however, is that this scale's
>> departure from JI doesn't seem to impact my ability to cognize it. > This
is just met in my perception by mapping things such that there > are just
"two fifths" - the "pelog" one and the "father" one.
>
> The fact that this scale does this with fifths makes it a particularly
good example, but there are other scales that f*** with our intervallic
perception just as heavily. Blackwood[10] in 20-EDO, for instance, gives us
two "minor 7ths"--one at 960 cents, one at 1020 cents. The first one is from
a stack of fourths, the second one is a fifth above the minor 3rd. Actually,
you can also have two fifths in 20-EDO Blackwood, too--the 660-cent "pelog"
fifth and the 720-cent "Blackwood" fifth. Thus two fourths as well. And two
whole-tones (inversions of minor 7ths). That does a real job on me,
mentally.
>
> -Igs
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
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>

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@...> wrote:
>
> I don't know why people bother with all these nomenclatures like "Father" at
> all--if it's 8edo, why not just say 8edo? Done.
>
> AKJ

Because temperament and tuning don't equate- they're not the same thing. A primary conceptual accomplishment of this list is steadfastly distinguishing between the two.

On Wed, Jun 1, 2011 at 1:30 PM, lobawad <lobawad@...> wrote:

>
>
> --- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@...> wrote:
> >
> > I don't know why people bother with all these nomenclatures like "Father"
> at
> > all--if it's 8edo, why not just say 8edo? Done.
> >
> > AKJ
>
> Because temperament and tuning don't equate- they're not the same thing. A
> primary conceptual accomplishment of this list is steadfastly distinguishing
> between the two.
>
>
Right, but I thought 'tuning' as used on this list was reserved for JI...and
temperament was any 'tuning' that used impure intervals

My point being that it's not just about this list....you go out there in the
world and talk to other musicians, saying "Father" temperament would elicit
a blank stare or a laugh, whereas 8edo has a chance of being understood. And
if you are talking about a linear temperament instead of an edo, you can
still give the size of the 'fifth' in terms of rational divisions of the
octave (e.g. 1/4 comma meantone temperament is pretty well described by
18\31 of an octave as a generator)

AKJ

>
>
>
>
>
>
>
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--
Aaron Krister Johnson
http://www.akjmusic.com
http://www.untwelve.org

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@...> wrote:

> >
> >
> Right, but I thought 'tuning' as used on this list was reserved for >JI...and
> temperament was any 'tuning' that used impure intervals
>
> My point being that it's not just about this list....you go out there in the
> world and talk to other musicians, saying "Father" temperament would elicit
> a blank stare or a laugh, whereas 8edo has a chance of being understood. And
> if you are talking about a linear temperament instead of an edo, you can
> still give the size of the 'fifth' in terms of rational divisions of the
> octave (e.g. 1/4 comma meantone temperament is pretty well described by
> 18\31 of an octave as a generator)
>
> AKJ
>

I think funky names are unnecessary, but the temperament schemes I use can be descibed in straightforward ways. "1/8 Wuerschmidt's comma" is only a few brief words of explanation from completely mainstream lingo, so is "minor thirds tempered to temper out the lesser diesis" instead of "Hanson" (the basics of this stuff is in MGG for crying out loud).

I'd certainly never use a moniker like "father" temperament outside this list. But: I don't use "father temperament". I don't think it evens qualifies as "temperament" in any way that would fly outside these lists. However, I think people who cook up kooky stuff are perfectly entitled to give it kooky names, and if I were digging "father temperament" I might even use the moniker out of sheer uppitiness. It's a lot more vigorous, interesting and less bizarre than adding a second to a triad and calling it a "mu-chord" and having noone say get outta here you clown you, just because it's officially approved by being a Steely Dan chord, woooo-wooooo!

--- In tuning@yahoogroups.com, Aaron Krister Johnson <aaron@...>

> Right, but I thought 'tuning' as used on this list was reserved for > JI...andtemperament was any 'tuning' that used impure intervals
>

A tuning is a specific instance of any general tuning system. "Meantone" is a temperament but not a tuning; 1/3-comma meantone is a temperament and a tuning. 7-limit JI is not a tuning, but Centaur is a 7-limit JI tuning. Tuning is a set of concrete pitch relationships, expressible in cents values, temperament is a set of abstract (and somewhat flexible) pitch relationships, expressible in terms of a mapping (which defines a set of commas).

> My point being that it's not just about this list....you go out
> there in the world and talk to other musicians, saying "Father"
> temperament would elicit a blank stare or a laugh, whereas 8edo has > a chance of being understood.

But we're not "out in the world", we're on this list. We engage in academic discussions here, would you demand an academic physics journal to put everything in layman's terms? Here these terms have concrete and well-understood meanings and are useful in our discussions. Why would we abandon them? We don't talk to each other as if talking to musicians who know nothing of microtonality. I'd never use the terminology I use here on outsiders. So your "point" is totally invalid.

> And if you are talking about a linear temperament instead of an
> edo, you can still give the size of the 'fifth' in terms of
> rational divisions of the octave (e.g. 1/4 comma meantone
> temperament is pretty well described by
> 18\31 of an octave as a generator)

It's not simple when dealing with other temperaments. The regular mapping paradigm means that some tunings can be interpreted as multiple mappings, and the question of which temperament best describes a certain tuning is not always straightforward to answer. In the case of Father, you can define the "fifth" as being 5\8 of an octave, but when you look at something very near (but not exactly) that value like 17\27 or 13\21 it becomes questionable whether the Father mapping really applies, because in some cases you get a better 5/4 further along the generator chain than the one the Father mapping gives you.

If we're going to talk about linear temperaments, it's helpful to know if what we're talking about is musical reality or numerical fancy. So while 18\31 may be a good estimation of the Meantone generator, it's not clear that the Father generator can really be "estimated" at all, or if it *only* applies to 8-EDO. People have been in the habit of calling 13-EDO a Father temperament, when in reality other 5-limit mappings describe it much better, since the Father mapping says the ~461-cent interval is the 5/4, whereas there's a much better 5/4 at around ~369 cents.

Seriously, Aaron, I don't know why you poke your nose into the jargon-fest just to decry our use of jargon. The only way we could do away with the silly names is by specifying the mapping or the commas of every temperament we talk about. The names are there to save us the trouble of typing out a mapping every time we want to talk about various temperaments. I should think a discussion liberally punctuated by what basically look like matrices would be even more of a turn-off to musicians than a discussion peppered with obscure nomenclature. What looks nicer to you: the word "Father", or

[1 1 3]
[0 1 -1]

?

What would you even call that in speech?

Can you imagine what a discussion of planar temperaments would look like, or subgroups? Or if we were doing commas instead of mappings, is that really any better? I can't even remember the commas to most of the temperaments that get talked about here. Do you know the ratio to the schisma by heart? I don't. It would be a nightmare. The names exist for good reason, and the xenwiki is there for anyone who doesn't know what a given temperament name refers to. So quit yer belly-achin'.

-Igs

On Wed, Jun 1, 2011 at 10:01 AM, Aaron Krister Johnson
<aaron@...> wrote:
>
> Neat. It suggests many possibilities to me. I found it most effective towards the end where you just simplified the texture to single melody plus drone...I thought the harmonies a little thick and muddy although I was listen over my little Android speaker. I wonder how human singing would sound on the same passage?

Probably awesome. There are lots of ways to clean up what I did
though, it was a bit messy.

-Mike

On Wed, Jun 1, 2011 at 11:35 AM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Here I'm using the 2 2 1 2 1 2 2 1 mode of Father[8].
>
> Weren't we calling that Uncle temperament, or Step-Father or something? 8-EDO is Father, and the 5-note MOS might be Father, but that 8-note MOS has a clearly better 5/4 than the Father mapping gives.

It technically fits the Uncle mapping, but everyone just keeps calling
it Father[8], where "everyone" is "the average guy in the Xenharmonic
Alliance group chat." And for that matter, everyone seems to call the
3\11 generator MOS in 11-equal Hanson/Kleismic, even though it's
probably closer to this "Orgone" mapping we keep talking about.

This was why I recommended just picking the uber-temperament for an
MOS and giving that one the MOS name: because no matter how elegant of
a terminology system we come up with, if it's too confusing people
aren't going to give a damn about it and just use whatever they want.
In this case, they seem to have opted into calling any 4L3s MOS with a
minor third generator "hanson" (which is what I call it as well) and,
as we all know, sharp fifths comprise "father" temperament.

Lastly, I think this example shows that there isn't "a single" 5/4 in
this scale, nor is there a a single 3/2. And, as you are always so
adept at pointing out, we don't even know if this perception of "a
fifth" has anything to do with 3/2 to begin with. I guess that if you
want to assume so, we'd end up with some kind of 2.3.3b.5.5b rank-2
temperament that somehow includes both father and uncle.

> > However, the G from the top half is a sharp "father" G, and the G
> > from the bottom half is a flat "pelog" G. This scale contains both > of them, and they differ by 1\13, which is also the size of the
> > small step in the scale.
>
> Yeah, I remember the 'Wad had an example showing us how we hear both of them as a "fifth".

The Wad is as usual ahead of his time.

> > The end result of all of this is that it is extremely easy to
> > "follow" this scale mentally. This could be because it makes use of > "diatonic hearing," albeit in a way that expands on it
> > xenharmonically. It might also be that there's something special
> > about half steps and whole steps that makes their insertion into
> > scales particularly magical, but I don't know what exactly that
> > might be.
>
> Time was, I found this scale totally mind-blowing because of the "extra" half-step. Like playing up and down the scale, there would always come a point where something "weird" would happen and I would totally freak out. Maybe because I'd play 2 2 1 2 2 and find myself at a minor 6th instead of a major 6th, I dunno. But after playing with this scale for a few years now, that doesn't happen any more. It sounds totally normal to me. I have "gone native" with this scale.

It took me a couple days to go native with it. Try this one too

2 2 1 2 2 2 1 2

Or maybe the 22-equal version is better

3 3 1 3 3 3 1 3

This is hedgehog. Now, if you notice, the C-D-E-F-G has been smushed
in such a fashion that the C-D-E is ~10:11:12, the E-G is now 7/6, and
the C-G is 1/2 octave. You need to snap your perception into hearing
the 3 3 1 3 as a really, really flat C-D-E-F-G from the diatonic
scale.

The crazy thing now is that this ultra-flat "G" is in a sense the
"dominant" of the tonic, but then the dominant of the dominant is the
tonic again. Don't worry about ratios and just focus on perception. If
you are curious about ratios, the idea here is that 4:5:6 is replaced
by 5:6:7, and 8:9:10:12 is replaced by 10:11:12:14, and 4/3 is
replaced by 9/7.

Something about the 2 2 1 2 pattern is trippy, but I'm not sure what it is.

> The fact that this scale does this with fifths makes it a particularly good example, but there are other scales that f*** with our intervallic perception just as heavily. Blackwood[10] in 20-EDO, for instance, gives us two "minor 7ths"--one at 960 cents, one at 1020 cents.

Yes, but Blackwood tends to confuse the hell out of me, whereas this
scale doesn't. That's where I'm at with this now.

>The first one is from a stack of fourths, the second one is a fifth above the minor 3rd. Actually, you can also have two fifths in 20-EDO Blackwood, too--the 660-cent "pelog" fifth and the 720-cent "Blackwood" fifth. Thus two fourths as well. And two whole-tones (inversions of minor 7ths). That does a real job on me, mentally.

YMMV, but father[8] for some reason does NOT do a real job on me,
mentally. It's just that we don't get the benefit of having concordant
harmonies everywhere, which sucks. But there's something about this
scale that's especially coherent, which perhaps means coherent
"melodically."

-Mike

On Wed, Jun 1, 2011 at 4:07 PM, lobawad <lobawad@...> wrote:
>
>
> I'd certainly never use a moniker like "father" temperament outside this list. But: I don't use "father temperament". I don't think it evens qualifies as "temperament" in any way that would fly outside these lists. However, I think people who cook up kooky stuff are perfectly entitled to give it kooky names, and if I were digging "father temperament" I might even use the moniker out of sheer uppitiness.

It sucks as far as concordant harmonies are concerned, but there's
something about the scalar structure that makes it really
comprehensible for me. Seems quite a few people on the XA facebook
group think the same thing. If we could figure out what this
Mysterious Property is, then we could generate scales around it that
DO have concordant harmonies, because the converse of this is scales
with concordant harmonies that have a ridiculously unintelligible
scale structure, and nobody wants that.

-Mike

On Wed, Jun 1, 2011 at 12:05 PM, Aaron Krister Johnson
<aaron@...> wrote:
>
> I don't know why people bother with all these nomenclatures like "Father" at all--if it's 8edo, why not just say 8edo? Done.

This isn't 8EDO, this is the 5L3s scale from 13-equal, generator is a
sharp perfect fifth.

-Mike

> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > Here I'm using the 2 2 1 2 1 2 2 1 mode of Father[8].

When I see something like this, I think of whether it maps to my 31EDO guitar, and in this case, it does (5 5 2 5 2 5 5 2). So,
whatever Father[8] is, is it supported by 31?

> It took me a couple days to go native with it. Try this one too
>
> 2 2 1 2 2 2 1 2
>
> Or maybe the 22-equal version is better
>
> 3 3 1 3 3 3 1 3
>
> This is hedgehog.

And now we have a different structure in a different EDOs. A very different structure, these are symmetric around the 12et tritone. Other than '8 notes' what is the similarity?

On Thu, Jun 2, 2011 at 4:05 AM, bobvalentine1 <bob.valentine@...> wrote:
>
> > > > Here I'm using the 2 2 1 2 1 2 2 1 mode of Father[8].
>
> When I see something like this, I think of whether it maps to my 31EDO guitar, and in this case, it does (5 5 2 5 2 5 5 2). So,
> whatever Father[8] is, is it supported by 31?

Sure, if you use the sharp mapping for 3/2.

> > It took me a couple days to go native with it. Try this one too
> >
> > 2 2 1 2 2 2 1 2
> >
> > Or maybe the 22-equal version is better
> >
> > 3 3 1 3 3 3 1 3
> >
> > This is hedgehog.
>
> And now we have a different structure in a different EDOs. A very different structure, these are symmetric around the 12et tritone. Other than '8 notes' what is the similarity?

I screwed up the second one - I meant 3 3 2 3 3 3 2 3, which puts you
at 22-equal. All of these scales share the same superficial structure,
which is LLsLLLsL. For the 20-equal version, where L = 3s, the
harmonic structure is a bit different than the 22-equal, where L:s =
3:2 - but something about the melodic structure of the scale remains
the same nonetheless.

-Mike

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

> A tuning is a specific instance of any general tuning system.

That seems like a perfect definition to me.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Jun 1, 2011 at 4:07 PM, lobawad <lobawad@...> wrote:
> >
> >
> > I'd certainly never use a moniker like "father" temperament outside this list. But: I don't use "father temperament". I don't think it evens qualifies as "temperament" in any way that would fly outside these lists. However, I think people who cook up kooky stuff are perfectly entitled to give it kooky names, and if I were digging "father temperament" I might even use the moniker out of sheer uppitiness.
>
> It sucks as far as concordant harmonies are concerned, but there's
> something about the scalar structure that makes it really
> comprehensible for me. Seems quite a few people on the XA facebook
> group think the same thing. If we could figure out what this
> Mysterious Property is, then we could generate scales around it that
> DO have concordant harmonies, because the converse of this is scales
> with concordant harmonies that have a ridiculously unintelligible
> scale structure, and nobody wants that.
>
> -Mike
>

I think "concordant harmonies" is pretty much a golden hammer, as far as comprehensibility of pitch structures, psychoacoustic validity of tunings, etc. etc., goes.

Oh-
http://en.wikipedia.org/wiki/Law_of_the_instrument

I've noticed that those who point out that spectrum isn't the magic key to all musical structure and comprehension tend to make the much sillier error of claiming that spectrum has nothing at all to do with musical structure and comprehension.

Anyway, finding what makes a scale work, against your expectations, seems like a great idea, it'll be interesting to see what you guys propose as the answers.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > On Wed, Jun 1, 2011 at 4:07 PM, lobawad <lobawad@> wrote:
> > >
> > >
> > > I'd certainly never use a moniker like "father" temperament outside this list. But: I don't use "father temperament". I don't think it evens qualifies as "temperament" in any way that would fly outside these lists. However, I think people who cook up kooky stuff are perfectly entitled to give it kooky names, and if I were digging "father temperament" I might even use the moniker out of sheer uppitiness.
> >
> > It sucks as far as concordant harmonies are concerned, but there's
> > something about the scalar structure that makes it really
> > comprehensible for me. Seems quite a few people on the XA facebook
> > group think the same thing. If we could figure out what this
> > Mysterious Property is, then we could generate scales around it that
> > DO have concordant harmonies, because the converse of this is scales
> > with concordant harmonies that have a ridiculously unintelligible
> > scale structure, and nobody wants that.
> >
> > -Mike
> >
>
> I think "concordant harmonies" is pretty much a golden hammer, as far as comprehensibility of pitch structures, psychoacoustic validity of tunings, etc. etc., goes.
>

--- In tuning@yahoogroups.com, "bobvalentine1" <bob.valentine@...> wrote:

> When I see something like this, I think of whether it maps to my 31EDO guitar, and in this case, it does (5 5 2 5 2 5 5 2). So,
> whatever Father[8] is, is it supported by 31?

Father is where you take a generator of about 456 cents, and pretend it is both a perfect fourth *and* a major third. To do it in 31edo, you'd use 12\31, which is 464.5 cents, making it even harder to hear anything like a third in it, but you can try, and the 5\13 generator is nearly that sharp. In meantone terms, this means you are using an augmented third, C-E#, as the father generator, and you get different values depending on your fifth--for instance, 462 cents in 1/4-comma meantone. In 50edo meantone, the augmented third is exactly 456 cents, and obviously you are in business.

Of course, in 31edo whatever you pick as a generator already has some named temperament attached to it, and none of them are father. The 12\31 generator you can also take to be a semisept generator. Instead of being less complex and accurate than what you'd normally associate to 31, it's more complex and accurate and also interesting as a way of
exploring higher-limit harmony, so the fact you can use the same generator for both is really irrelevant.

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

> It technically fits the Uncle mapping, but everyone just keeps
> calling it Father[8], where "everyone" is "the average guy in the
> Xenharmonic Alliance group chat." And for that matter, everyone
> seems to call the 3\11 generator MOS in 11-equal Hanson/Kleismic,
> even though it's probably closer to this "Orgone" mapping we keep
> talking about.

That sucks. That's a total misappropriation of the terminology. I don't think we should just lie back and accept this, I think you should be correcting people. The community is still small enough that we can stop the spread of inconsistent terminology before it gets much further. 13-EDO is not Father, 11-EDO is not Hanson, etc.

> This was why I recommended just picking the uber-temperament for an
> MOS and giving that one the MOS name: because no matter how elegant > of a terminology system we come up with, if it's too confusing
> people aren't going to give a damn about it and just use whatever
> they want. In this case, they seem to have opted into calling any
> 4L3s MOS with a minor third generator "hanson" (which is what I
> call it as well) and, as we all know, sharp fifths comprise
> "father" temperament.

Who are these people, and how many of them are there? There can't be THAT many people who know these temperament names but do not understand the temperaments well enough to know how they apply.

> Lastly, I think this example shows that there isn't "a single" 5/4 > in this scale, nor is there a a single 3/2.

Are you hearing the ~462-cent interval as a major 3rd at times? I guess I hear it that way if I play 738-554-462, or 738-646-462. Does the same thing happen when you play the scale in 23-EDO, where it's more like a ~470-cent interval? I'll have to check that out myself, because if I can hear ~470 cents as a major 3rd, that's a pretty incredible perceptual warping. That's almost a full semitone sharp of 5/4.

> And, as you are always so adept at pointing out, we don't even know > if this perception of "a fifth" has anything to do with 3/2 to
> begin with. I guess that if you want to assume so, we'd end up with > some kind of 2.3.3b.5.5b rank-2 temperament that somehow includes
> both father and uncle.

Ah, yes, I hadn't really thought much of that. I think you're right, actually--it's neither Father NOR Uncle, but it's also both, and something else (mapping 3 to the ~646-cent interval instead of the generator). Yeah, it's like four temperaments in one, based on how we're hearing it. THAT is far-out. This is why I love exotemperaments, because the high-entropy intervals can collapse in either direction and totally blow some minds.

> It took me a couple days to go native with it. Try this one too
>
> 2 2 1 2 2 2 1 2
>
> Or maybe the 22-equal version is better
>
> 3 3 1 3 3 3 1 3

I like the 14-EDO version. Haven't explored it much, I've only really explored Semaphore in 14, but this is pretty trippy.

> You need to snap your perception into hearing
> the 3 3 1 3 as a really, really flat C-D-E-F-G from the diatonic
> scale.

Reminds me of playing Mavila on my kalimba, and how sometimes it sounds like a whole-tone scale, sometimes it sounds like a major scale, and rarely does it actually sound like Mavila.

> The crazy thing now is that this ultra-flat "G" is in a sense the
> "dominant" of the tonic, but then the dominant of the dominant is
> the tonic again. Don't worry about ratios and just focus on
> perception.

Reminds me a little bit of chord progressions in Lemba. Two 4:5:7 triads a half-octave apart can sound like tonic and dominant to me sometimes.

> Something about the 2 2 1 2 pattern is trippy, but I'm not sure
> what it is.

The weird thing to me is that a 2 2 3 2 pattern (a la Mavila) works the same mojo for me. This could be insane, but I think I actually hear it as 2 2 1 2, or maybe 2 1 2 2. I mean seriously, WTF.

> Yes, but Blackwood tends to confuse the hell out of me, whereas this
> scale doesn't. That's where I'm at with this now.

It's less confusing in 15-EDO because the interval classes are further apart. I have a *hell* of a time soloing in 20-EDO Blackwood over chord progressions...although if you recall the last song on my album "Open Space", it's all 20-EDO Blackwood lead guitar over 17-EDO Superpyth rhythm guitar, and it sounded fine to me.

> It's just that we don't get the benefit of having
> concordant harmonies everywhere, which sucks. But there's something > about this scale that's especially coherent, which perhaps means
> coherent "melodically."

No concordant harmonies everywhere? Not a fan of 16:18:21 then, eh? Try the 18-EDO version, I think it sounds very concordant (although not super "restful" or "resolved"). As far as harmonies not based on 4:5:6 go, I quite enjoy the sound of these triads. Also there are two approximate 8:9:10 triads (which you can voice as 4:5:9 for added concordance), and also (in 13-EDO only) a couple "Orwell-esque" triads of 0-276-554 cents, where every dyad in the chord is an 11-limit consonance (these are both Paul's and Graham's words). There's also a couple of 8:11:13 triads to be had, too. Frankly I find this to be a very concordant scale as long as you're not trying to play the very out-of-tune "5-limit" Father triads of 0-462-738 cents, the Uncle triads of 0-369-738, or the unnamed triads of 0-369-646 cents.

I actually like the entire Father/Uncle pentatonic scale as a pentad, 0-185-462-646-923 cents, or even better in 23-EDO as 0-209-470-678-939 cents or 18-EDO as 0-200-466.67-666.67-933.33 cents. I think the smoothness of the dyads trumps the entropy of the pentad in this case, and although the result is not as smooth as 4:5:6:7:9 or something, I think it sounds pleasant and exotic nonetheless. YMMV.

-Igs

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
>
> > A tuning is a specific instance of any general tuning system.
>
> That seems like a perfect definition to me.
>

I think I would clean up the recursiveness of this definition and say that "a tuning is a specific instance of an abstractly-defined set of general pitch relationships". Hopefully the examples I gave clarified the sloppiness of the above definition.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > > A tuning is a specific instance of any general tuning system.
> >
> > That seems like a perfect definition to me.
> >
>
> I think I would clean up the recursiveness of this definition and say that "a tuning is a specific instance of an abstractly-defined set of general pitch relationships". Hopefully the examples I gave clarified the sloppiness of the above definition.
>
> -Igs
>

That's even better, but now that I think about it, maybe "realization" rather than "instance" would be better, what do you think?

The traditional Just augmented third is (5/4)*(25/24), 457 cents (rounded), so you can tune it in 31-edo right there as you describe. The 31-edo tuning of this is what I've been calling a "shadow interval" for several years here, the ideal tuning of this shadow "fird" or "thourth" being the region between 13/10 and 2phi(mod2), in my opinion. A truly fuzzy and ambiguous interval, great for thickening sonorities without either chugging beating (because it goes zhzhzhzhzhzh) or any definite implied direction of resolution.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In tuning@yahoogroups.com, "bobvalentine1" <bob.valentine@> wrote:
>
> > When I see something like this, I think of whether it maps to my 31EDO guitar, and in this case, it does (5 5 2 5 2 5 5 2). So,
> > whatever Father[8] is, is it supported by 31?
>
> Father is where you take a generator of about 456 cents, and pretend it is both a perfect fourth *and* a major third. To do it in 31edo, you'd use 12\31, which is 464.5 cents, making it even harder to hear anything like a third in it, but you can try, and the 5\13 generator is nearly that sharp. In meantone terms, this means you are using an augmented third, C-E#, as the father generator, and you get different values depending on your fifth--for instance, 462 cents in 1/4-comma meantone. In 50edo meantone, the augmented third is exactly 456 cents, and obviously you are in business.
>
> Of course, in 31edo whatever you pick as a generator already has some named temperament attached to it, and none of them are father. The 12\31 generator you can also take to be a semisept generator. Instead of being less complex and accurate than what you'd normally associate to 31, it's more complex and accurate and also interesting as a way of
> exploring higher-limit harmony, so the fact you can use the same generator for both is really irrelevant.
>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> That's even better, but now that I think about it, maybe "realization" rather than "instance" > would be better, what do you think?

Yes. That or "instantiation", which I think is what I was grasping for mentally when I came up with "instance".

I think of temperaments and/or JI as the Platonic forms of tunings. The regular mapping paradigm actually can express JI, the map of 7-limit JI would be:

[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]

So I tend to think of everything in terms of mapping. Mappings tell us how intervals are related mathematically, but not what scales or tunings to use. As long as a tuning satisfies the relationships defined by the mapping, the tuning is a specific realization of the abstract mapping.

-Igs

> That sucks. That's a total misappropriation of the terminology. I don't think we should just lie back and accept this, I think you should be correcting people. The community is still small enough that we can stop the spread of inconsistent terminology before it gets much further. 13-EDO is not Father, 11-EDO is not Hanson, etc.

May I volunteer to be the first one corrected? Why is 11-edo not Hanson? If I'm using the 327 cent generator as a 6/5 and six iterations as 3/1, how is it not Hanson? And if I'm using 13-edo the way Father prescribes why is it not Father?

Just because there is a better mapping (in your opinion) for the tuning doesn't mean any other is invalid. For instance, just because there is a better 5/4 in 53-tet doesn't mean that it can't be used for meantone to take advantage of the simpler (though less accurate) mapping.

> Are you hearing the ~462-cent interval as a major 3rd at times? I guess I hear it that way if I play 738-554-462, or 738-646-462. Does the same thing happen when you play the scale in 23-EDO, where it's more like a ~470-cent interval? I'll have to check that out myself, because if I can hear ~470 cents as a major 3rd, that's a pretty incredible perceptual warping. That's almost a full semitone sharp of 5/4.

I've definitely heard 480 cents of 5-edo as a 5/4, so it's not thaaat crazy.

John M

On Thu, Jun 2, 2011 at 1:47 PM, cityoftheasleep <igliashon@...> wrote:
>
> > It technically fits the Uncle mapping, but everyone just keeps
> > calling it Father[8], where "everyone" is "the average guy in the
> > Xenharmonic Alliance group chat." And for that matter, everyone
> > seems to call the 3\11 generator MOS in 11-equal Hanson/Kleismic,
> > even though it's probably closer to this "Orgone" mapping we keep
> > talking about.
>
> That sucks. That's a total misappropriation of the terminology. I don't think we should just lie back and accept this, I think you should be correcting people. The community is still small enough that we can stop the spread of inconsistent terminology before it gets much further. 13-EDO is not Father, 11-EDO is not Hanson, etc.

These are words that people are using to denote the MOS's in general.
If you want to be more specific you can always specify "Uncle" or
"Orgone" instead of "Hanson" and so on.

> Who are these people, and how many of them are there? There can't be THAT many people who know these temperament names but do not understand the temperaments well enough to know how they apply.

There was me, John M, Jacob Barton, Ron Sword, and I think Ryan Avella
all calling it "father." I didn't bother to correct anyone because the
concept of "hearing something as a 5/4" doesn't seem to have anything
to do with the nearest approximation to 5/4 in the EDO.

Furthermore, as per our recent conversation, we don't have any idea,
if when we hear something "as a major third," that that perception
even has anything to do with 5/4. I'd like to know that it does before
I go on and tell people they need to learn multiple names for the same
scale.

> > Lastly, I think this example shows that there isn't "a single" 5/4 > in this scale, nor is there a a single 3/2.
>
> Are you hearing the ~462-cent interval as a major 3rd at times? I guess I hear it that way if I play 738-554-462, or 738-646-462. Does the same thing happen when you play the scale in 23-EDO, where it's more like a ~470-cent interval? I'll have to check that out myself, because if I can hear ~470 cents as a major 3rd, that's a pretty incredible perceptual warping. That's almost a full semitone sharp of 5/4.

Yes, I hear 462 as a major third sometimes. I haven't tried it with
23-equal. To hear 462 as a major third in 13-equal, just start with
the octave and work your way down the "major scale," aka 2 steps for L
and 1 step for s, until you get to the 462 cent major third. Then go
one more step down and now the 369 cent major third will sound like a
minor third. That is, unless you conceptually believe that the 369
cent major third is supposed to be a major third because it's "5/4,"
at which point you'll force yourself to remap things mentally because
of this preconception, and then you have an artificially
self-fulfilling theory.

> > And, as you are always so adept at pointing out, we don't even know > if this perception of "a fifth" has anything to do with 3/2 to
> > begin with. I guess that if you want to assume so, we'd end up with > some kind of 2.3.3b.5.5b rank-2 temperament that somehow includes
> > both father and uncle.
>
> Ah, yes, I hadn't really thought much of that. I think you're right, actually--it's neither Father NOR Uncle, but it's also both, and something else (mapping 3 to the ~646-cent interval instead of the generator). Yeah, it's like four temperaments in one, based on how we're hearing it. THAT is far-out. This is why I love exotemperaments, because the high-entropy intervals can collapse in either direction and totally blow some minds.

So now you know why people have just decided to just call the whole
thing Father.

> > It took me a couple days to go native with it. Try this one too
> >
> > 2 2 1 2 2 2 1 2
> >
> > Or maybe the 22-equal version is better
> >
> > 3 3 1 3 3 3 1 3
>
> I like the 14-EDO version. Haven't explored it much, I've only really explored Semaphore in 14, but this is pretty trippy.

This isn't Semaphore, this is hedgehog.

> > You need to snap your perception into hearing
> > the 3 3 1 3 as a really, really flat C-D-E-F-G from the diatonic
> > scale.
>
> Reminds me of playing Mavila on my kalimba, and how sometimes it sounds like a whole-tone scale, sometimes it sounds like a major scale, and rarely does it actually sound like Mavila.

The flat fifth sounds like mavila, right? Except in this case it's a
half octave.

I will now refer to this pattern as the LLsL pentachord. The LLsL
pentachord seems to have some kind of special mojo no matter what the
outer dyad is (to a point), probably because we're used to LLsL
patterns from the major scale.

> > Something about the 2 2 1 2 pattern is trippy, but I'm not sure
> > what it is.
>
> The weird thing to me is that a 2 2 3 2 pattern (a la Mavila) works the same mojo for me. This could be insane, but I think I actually hear it as 2 2 1 2, or maybe 2 1 2 2. I mean seriously, WTF.

So does 1 1 1 1 a la 7-equal. I screwed up bigtime at one point and
did the experiment in 8-equal by mistake - I was reveling in how easy
I was able to follow the LLsL pentachord and then I realized it was
just 8-equal. And now we're back to hearing inflections of "major" and
"minor" in 7-EDO again, except now it's 8-edo. I'm confused, really.

> > Yes, but Blackwood tends to confuse the hell out of me, whereas this
> > scale doesn't. That's where I'm at with this now.
>
> It's less confusing in 15-EDO because the interval classes are further apart. I have a *hell* of a time soloing in 20-EDO Blackwood over chord progressions...although if you recall the last song on my album "Open Space", it's all 20-EDO Blackwood lead guitar over 17-EDO Superpyth rhythm guitar, and it sounded fine to me.

I have to listen to it again. I do remember it sounded fine, but not
as comprehensible as Father, which is LLsL s LLs. I can get Blackwood
to sound kind of comprehensible if I try to hear it as a really flat
diminished[8] or something like that.

> > It's just that we don't get the benefit of having
> > concordant harmonies everywhere, which sucks. But there's something > about this scale that's especially coherent, which perhaps means
> > coherent "melodically."
>
> No concordant harmonies everywhere? Not a fan of 16:18:21 then, eh? Try the 18-EDO version, I think it sounds very concordant (although not super "restful" or "resolved").

I'm a fan of it, and if you check out the "modal" improv I use it a
lot. But it's just one type of sound, and 12-equal lets you fit this
sound into a huge and expansive tonal structure that I haven't found a
counterpart to in 13-equal. Fifths are not concordant, and that makes
for interesting harmonies. It sounds like there's a "hole" in the
chord if you play 6:7:9. Which is great, it's just not what the word
"concordant" signifies.

> There's also a couple of 8:11:13 triads to be had, too.

The modal improv I just did in 13-equal starts with 8:11:13 in the
form of 0-6-9, and then resolves it to 0-4-8, and then turns it into a
vaguely middle eastern thing that spoofs 12-equal's mixob6 mode. Feel
free to confirm that the first chord readily resolves to the second
chord, even though the first chord is the magically concordant
8:11:13, and the second is basically an augmented chord.

There is something magical about half steps.

> I actually like the entire Father/Uncle pentatonic scale as a pentad, 0-185-462-646-923 cents, or even better in 23-EDO as 0-209-470-678-939 cents or 18-EDO as 0-200-466.67-666.67-933.33 cents. I think the smoothness of the dyads trumps the entropy of the pentad in this case, and although the result is not as smooth as 4:5:6:7:9 or something, I think it sounds pleasant and exotic nonetheless. YMMV.

Father[5] is amazing.

-Mike

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
> May I volunteer to be the first one corrected? Why is 11-edo not Hanson? If I'm using the
> 327 cent generator as a 6/5 and six iterations as 3/1, how is it not Hanson?

Because calling anything in 11-EDO a 3/1 is psychoacoustically nonsense. Especially an interval of 763.64 cents. Moreover, if you take something written in 19-EDO Hanson temperament and try to play it in 11-EDO, it is going to sound like a completely different piece of music.

> And if I'm using 13-edo the way Father prescribes why is it not Father?

Because physics, psychoacoustics, and perception in general dictate whether we can hear tempered intervals "as" approximating Just intervals. We cannot just arbitrarily call any interval an approximation of any ratio, or else we are allowing all kinds of useless absurdities into what should be a sensible and useful paradigm. To blatantly ignore that there is an interval in 13-EDO that sounds much more like a 5/4 than does the interval prescribed by the Father mapping is, well, stupid.

> Just because there is a better mapping (in your opinion) for the tuning doesn't mean any > other is invalid. For instance, just because there is a better 5/4 in 53-tet doesn't mean
> that it can't be used for meantone to take advantage of the simpler (though less
> accurate) mapping.

It is not a matter of opinion, it is a matter of the limits of perception. There are limits to how badly we can temper something before it no longer becomes a sensible approximation. Some tunings support multiple mappings--23-EDO, for instance, supports two mappings of 3, and two mappings of 5, among other things. These mappings work because both approximations are equally sensible (or insensible, depending on your personal tolerance for mistuning). Even in 22-EDO, it makes some sense to apply a meantone mapping to the superpyth major scale, because in that 7-note scale, the closest thing to a 5/4 is a 9/7, so if we wanted to be obstinate we could reasonably call it a 5/4. This stops being true when we get to the 12-note MOS of superpyth, and at that point we'd be foolish to insist on calling the 9/7 a 5/4, since there is a near-Just 5/4 staring us in the face at another place in the scale.

In 13-EDO, in the 5L+3s scale, there are two instances of an interval that are much closer to a 5/4 than the Father generator, and it's stupid to ignore that. You have on one hand an interval that's about 17 cents flat, and on the other an interval that's about 74 cents sharp. Are you telling me that you can think of a reason to ignore the better approximation and insist that the 74-cent sharp interval is the 5/4 in the scale?? That is just **STUPID**. ON THE OTHER HAND, In the 3L+2s pentatonic scale, the Father generator *is* the closest thing to a 5/4 that appears, so we may call that pentatonic scale a "Father" pentatonic.

We have to exercise good sense when talking about mappings and scales. This is the same reason that calling the 5L+2s scale in 29-EDO "Schismatic/Helmholtz" is stupid, because the mapping for Helmholtz takes 8 generators to produce the approximation to 5/4, thus the Schismatic 5/4 doesn't appear in the 7-note MOS. Strictly-speaking, Schismatic doesn't exist as a temperament below a certain size of MOS, unless you're using a MODMOS or something where the Schismatic 5/4 is actually present in the scale.

> I've definitely heard 480 cents of 5-edo as a 5/4, so it's not thaaat crazy.

In 5-EDO, 480 cents is the closest thing to a 5/4 you've got, so it's not unreasonable to map 5/4 to 480 cents (if you are insisting on mapping it to anything, which is a questionable thing to insist on in 5-EDO). But the real important thing is, given a set of intervals in a particularly-tuned tempered scale, the sensible mapping is the one that maps the JI intervals to their nearest tempered approximants *available in the scale*. To fail to do this is to contradict your own ears in the mapping--why would anyone *want* to do that? What is to be gained from ignoring the presence of audibly better approximations and insisting on a perceptually-invalid mapping?

-Igs

Igs:
>> The community is still small enough that we can stop the spread of inconsistent
>> terminology before it gets much further. 13-EDO is not Father, 11-EDO is not Hanson,
>> etc.

John:
> Why is 11-edo not Hanson?

Respectfully: because Hanson is an abstract temperament, and 11-EDO is
a specific, concrete scale that instantiates it.

> If I'm using the 327 cent generator as a 6/5 and six iterations as 3/1, how is it not
> Hanson? And if I'm using 13-edo the way Father prescribes why is it not Father?

In those cases, you *are* playing in Hanson and Father, respectively.
And if you play traditional music in 12 EDO, you are playing in
meantone.

However, 12 EDO is not the *same thing* as meantone, because you can
also play in meantone in 19 EDO or 31 EDO. Moreover, you don't have to
play "in meantone" just because you're in 12-EDO. You could play, say,
serial music instead.

Similarly, 11 EDO is not Hanson, because you can play in Hanson in
other ways, and because you can play 11 EDO without playing Hanson.
And 13 EDO is not Father, for analogous reasons.

So you're actually doing to Igs what you think he's doing to you:
> Just because there is a better mapping (in your opinion) for the tuning doesn't mean any
> other is invalid.

The fact that you like to play Father in 13 doesn't mean "that's
Father". The fact that you like to use the 327-cent generator for
Hanson doesn't mean "that's Hanson". And there's certainly no "better"
or "worse" at issue. There's just abstract and concrete. Hanson,
Father, and Meantone are all abstract, while 11, 13, 12, and 19 EDO
are all concrete.

I agree with Igs that this is important to keep straight. As casual
shorthand I can see calling 13 EDO "Father", but we should know why
it's *not* Father even as we say it.

Regards,
Jake

On 6/2/11, jlmoriart <JlMoriart@...> wrote:
>> That sucks. That's a total misappropriation of the terminology. I don't
>> think we should just lie back and accept this, I think you should be
>> correcting people. The community is still small enough that we can stop
>> the spread of inconsistent terminology before it gets much further.
>> 13-EDO is not Father, 11-EDO is not Hanson, etc.
>
> May I volunteer to be the first one corrected? Why is 11-edo not Hanson? If
> I'm using the 327 cent generator as a 6/5 and six iterations as 3/1, how is
> it not Hanson? And if I'm using 13-edo the way Father prescribes why is it
> not Father?
>
> Just because there is a better mapping (in your opinion) for the tuning
> doesn't mean any other is invalid. For instance, just because there is a
> better 5/4 in 53-tet doesn't mean that it can't be used for meantone to take
> advantage of the simpler (though less accurate) mapping.
>
>> Are you hearing the ~462-cent interval as a major 3rd at times? I guess I
>> hear it that way if I play 738-554-462, or 738-646-462. Does the same
>> thing happen when you play the scale in 23-EDO, where it's more like a
>> ~470-cent interval? I'll have to check that out myself, because if I can
>> hear ~470 cents as a major 3rd, that's a pretty incredible perceptual
>> warping. That's almost a full semitone sharp of 5/4.
>
> I've definitely heard 480 cents of 5-edo as a 5/4, so it's not thaaat crazy.
>
> John M
>
>
>
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On Fri, Jun 3, 2011 at 12:13 AM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
> > May I volunteer to be the first one corrected? Why is 11-edo not Hanson? If I'm using the
> > 327 cent generator as a 6/5 and six iterations as 3/1, how is it not Hanson?
>
> Because calling anything in 11-EDO a 3/1 is psychoacoustically nonsense. Especially an interval of 763.64 cents. Moreover, if you take something written in 19-EDO Hanson temperament and try to play it in 11-EDO, it is going to sound like a completely different piece of music.

That 16/11 sometimes sounds like a fifth to me. And you said you heard
the 13-equal version as sounding like a pelog fifth.

> > And if I'm using 13-edo the way Father prescribes why is it not Father?
>
> Because physics, psychoacoustics, and perception in general dictate whether we can hear tempered intervals "as" approximating Just intervals. We cannot just arbitrarily call any interval an approximation of any ratio, or else we are allowing all kinds of useless absurdities into what should be a sensible and useful paradigm. To blatantly ignore that there is an interval in 13-EDO that sounds much more like a 5/4 than does the interval prescribed by the Father mapping is, well, stupid.

Firstly, who says that we have to pick one and only one approximation
to 5/4 in a scale, and why should the brain hear things that way?

Secondly, we don't know wtf "hearing tempered intervals as
approximating just intervals" means. At least I don't, and you didn't
seem to last week either.

> Even in 22-EDO, it makes some sense to apply a meantone mapping to the superpyth major scale, because in that 7-note scale, the closest thing to a 5/4 is a 9/7, so if we wanted to be obstinate we could reasonably call it a 5/4. This stops being true when we get to the 12-note MOS of superpyth, and at that point we'd be foolish to insist on calling the 9/7 a 5/4, since there is a near-Just 5/4 staring us in the face at another place in the scale.

What if you still hear the 9/7 as 5/4? Why can't the 9/7 just be a
sharp 5/4, and the more just 5/4 be a more just 5/4? Who says the
brain only assigns 5/4 to one dyad in a scale?

> In 13-EDO, in the 5L+3s scale, there are two instances of an interval that are much closer to a 5/4 than the Father generator, and it's stupid to ignore that.

What tuning for father ends up with the generator being a closer
approximation to 5/4 than -6 generators?

> You have on one hand an interval that's about 17 cents flat, and on the other an interval that's about 74 cents sharp. Are you telling me that you can think of a reason to ignore the better approximation and insist that the 74-cent sharp interval is the 5/4 in the scale?? That is just **STUPID**.

What do you mean "the" 5/4 in the scale?

-Mike

Hi Igs,

> Because calling anything in 11-EDO a 3/1 is psychoacoustically nonsense. Especially an interval of 763.64 cents. Moreover, if you take something written in 19-EDO Hanson temperament and try to play it in 11-EDO, it is going to sound like a completely different piece of music.

I disagree:
/tuning/files/JohnMoriarty/SoundTheSame.mp3

> Because physics, psychoacoustics, and perception in general dictate whether we can hear tempered intervals "as" approximating Just intervals. We cannot just arbitrarily call any interval an approximation of any ratio, or else we are allowing all kinds of useless absurdities into what should be a sensible and useful paradigm. To blatantly ignore that there is an interval in 13-EDO that sounds much more like a 5/4 than does the interval prescribed by the Father mapping is, well, stupid.

But is it not all a spectrum or preference? You go on to say that some tunings support multiple mappings, and I assume for you they are both close enough or similar enough to consider both, but in this situation you call one the right choice and the other stupid. Maybe my limits are just different than yours, and we'd have to get even more extreme before I wouldn't bother considering two different mappings.

> It is not a matter of opinion, it is a matter of the limits of perception. There are limits to how badly we can temper something before it no longer becomes a sensible approximation.

Yes but, again, this is a different spectrum for each person with no lines pre-drawn.

>Some tunings support multiple mappings--23-EDO, for instance, supports two mappings of 3, and two mappings of 5, among other things. These mappings work because both approximations are equally sensible (or insensible, depending on your personal tolerance for mistuning). Even in 22-EDO, it makes some sense to apply a meantone mapping to the superpyth major scale, because in that 7-note scale, the closest thing to a 5/4 is a 9/7, so if we wanted to be obstinate we could reasonably call it a 5/4. This stops being true when we get to the 12-note MOS of superpyth, and at that point we'd be foolish to insist on calling the 9/7 a 5/4, since there is a near-Just 5/4 staring us in the face at another place in the scale.

Again, this is part of that same spectrum of tolerance. If 23-edo has two "sensible" mappings, then this example of 22-edo is just your deciding where to draw a line for what is "sensible" enough to consider two optional mappings, and what is foolish.

> In 13-EDO, in the 5L+3s scale, there are two instances of an interval that are much closer to a 5/4 than the Father generator, and it's stupid to ignore that. You have on one hand an interval that's about 17 cents flat, and on the other an interval that's about 74 cents sharp. Are you telling me that you can think of a reason to ignore the better approximation and insist that the 74-cent sharp interval is the 5/4 in the scale?? That is just **STUPID**. ON THE OTHER HAND, In the 3L+2s pentatonic scale, the Father generator *is* the closest thing to a 5/4 that appears, so we may call that pentatonic scale a "Father" pentatonic.

Yes, I'm telling you that I can think of a reason to ignore the better approximation and to insist on using the 74-cent sharp 5/4 as such, even when extending the MOS I'm using beyond the 3L2S scale, and I don't think it's *that* dumb :P

In my experience, I've found that I can come to associate a scale and a mapping very closely. For example, in meantone I'm used to hearing two major seconds add up to a 5/4, and then a major and minor second on top of that being a 3/2. Combining the root and these two gives me the 4/5/6 triad sound, even when in 22-edo. I'm not "forcing" myself to tolerate a worse 5/4 in 22-edo at all, I'm taking advantage of the 5/4 (which I still hear as so from the melodic context) being so expressively wide, if anything.

In fact, when playing in 22-edo meantone for long enough, the "sharp" 5/4 actually sounds MORE like 5/4 than the "purer" one. No Joke! The other, "better" 5/4 sounds SOUR when played after using the other one, probably because I've 1. simply gotten used to it and 2. come to connect the scalar structures with a meantone mapping. Melodically replacing the major third with the purer interval sounds off as well, probably because it's introducing another step size. Interestingly, it doesn't sound quite as bad (melodically) if I replace the major seventh of a major scale in addition to the major third, but it still sounds a little "off".

So if I want my meantone mapping in 22-edo specifically because it lines up with the mapping and melodic expectations I've built up from other tunings of the same scale structure, I see nothing foolish, stupid, or wrong with that.

Following that, if I want my Father mapping specifically because it lines up with the mapping and melodic expectation I've built up from other tunings of the same scale structure, I see nothing wrong with that.

John M

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

> I disagree:
> /tuning/files/JohnMoriarty/SoundTheSame.mp3

Not sold. Not even a little bit. For starters, the timbre makes it hard for me to even discern the chords being played, for two I hear very clear differences between the different progressions. I take it you were using TransFormSynth and sliding along the "Hanson" continuum?

> But is it not all a spectrum or preference? You go on to say that some tunings support
> multiple mappings, and I assume for you they are both close enough or similar enough > to consider both, but in this situation you call one the right choice and the other stupid. > Maybe my limits are just different than yours, and we'd have to get even more extreme
> before I wouldn't bother considering two different mappings.

Are you honestly telling me that if you heard a 462-cent interval and a a 369-cent interval, you would consider the first one a 5/4 and not the second one?

> Yes but, again, this is a different spectrum for each person with no lines pre-drawn.

That is patently false. Yes, there are variations from person to person, and if you use artificial/obscured timbres that blur harmonic identities, then things go up in the air. But there are definite limits, especially when directly comparing two intervals. Can 600 cents sound like a 3/2? Maybe under some extreme circumstances, but put it next to 700 cents, and it's obvious that 600 cents is NOT a 3/2. And anyway the regular mapping paradigm is not meant to vary from person to person, or to account for "extreme" listening environments generated by artificial scale-mapped timbres. It is meant to fit the most commonly agreed-upon consensus of reasonable "average" listeners listening to "normal" harmonic timbres. That's the only way to consistently define the paradigm, and if you're not interested in the consensus view of it, I'd suggest that there's no point in using it, because you're obviously taking it into territory it is not suited for.

> Again, this is part of that same spectrum of tolerance. If 23-edo has two "sensible"
> mappings, then this example of 22-edo is just your deciding where to draw a line for
> what is "sensible" enough to consider two optional mappings, and what is foolish.

Well of course decisions have to be made. The question is are they sensible, and that is a question determined by consensus. So far you haven't given any reason as to why these "lines" are not sensible.

> Yes, I'm telling you that I can think of a reason to ignore the better approximation and to > insist on using the 74-cent sharp 5/4 as such, even when extending the MOS I'm using > beyond the 3L2S scale, and I don't think it's *that* dumb :P

Well, let's hear the reason, then.

> In my experience, I've found that I can come to associate a scale and a mapping very
> closely. For example, in meantone I'm used to hearing two major seconds add up to a
> 5/4, and then a major and minor second on top of that being a 3/2. Combining the root > and these two gives me the 4/5/6 triad sound, even when in 22-edo. I'm not "forcing"
> myself to tolerate a worse 5/4 in 22-edo at all, I'm taking advantage of the 5/4 (which I > still hear as so from the melodic context) being so expressively wide, if anything.

What evidence is there that you're hearing it as a 5/4? Don't make the mistake of thinking that just because you hear "major triad" that that means you're hearing "4:5:6".

> In fact, when playing in 22-edo meantone for long enough, the "sharp" 5/4 actually
> sounds MORE like 5/4 than the "purer" one. No Joke! The other, "better" 5/4 sounds
> SOUR when played after using the other one, probably because I've 1. simply gotten
> used to it and 2. come to connect the scalar structures with a meantone mapping.
> Melodically replacing the major third with the purer interval sounds off as well, probably > because it's introducing another step size. Interestingly, it doesn't sound quite as bad
> (melodically) if I replace the major seventh of a major scale in addition to the major
> third, but it still sounds a little "off".

You're making the mistake of conflating melodic hearing (which the regular temperament paradigm and/or H.E. does not model or concern itself with at all) with harmonic hearing. Try playing in 22-EDO diaschismic a bit instead and see if you still hear the "sharp" 9/7 as a 5/4 in comparison to the true 5/4. In any case this still has nothing to do with Father.

> So if I want my meantone mapping in 22-edo specifically because it lines up with the
> mapping and melodic expectations I've built up from other tunings of the same scale
> structure, I see nothing foolish, stupid, or wrong with that.

Like I said, if you're using the 7-note MOS, that Superpyth 9/7 is the closest thing to a 5/4 in the scale, so if you had to describe the scale in the 5-limit, it would fit the meantone mapping. OTOH, it's also arguable that you're NOT hearing a 5/4, because that interval *is* a 9/7, and those triads *are* 14:18:21. You *are* hearing major triads and something about the diatonic structure actually biases your perception such that when presented with a 5/4, it sounds too "low" to be a major 3rd. But this is as much evidence for the conclusion that "major 3rd-ness" has nothing to do with 5/4 as it is evidence for the conclusion that a 9/7 can sound like a 5/4. Personally, I think if we want to accept the latter, we have to throw out JI as a load of hogwash, because if we can conflate ratios that easily, the ratios themselves are actually psychoacoustically meaningless. And if that's the case, we have to toss the regular temperament paradigm too, because if the ratios are mutable then tempered versions of them are doubly so.

> Following that, if I want my Father mapping specifically because it lines up with the
> mapping and melodic expectation I've built up from other tunings of the same scale
> structure, I see nothing wrong with that.

You have to ask yourself what you're really mapping and what the significance of mapping actually is, then. If you are hearing 462 cents as "more" of a 5/4 than 369 cents, what that means right there, plain as day, is that error is meaningless and temperament and mapping are a farce. It's as insane as looking at a black square on the left and a white square on the right, and saying "as I see it, the square on the left is white, and the square on the right is black." It basically means our perception of intervals has *nothing* to do with how they are tuned and everything to do with some other factor--melodic cues, preattentive bias, etc.--and if that's the case, there's no point in even TALKING about JI anymore. The ratio 5/4 is psychoacoustically meaningless if something 74 cents from a 5/4 sounds somehow "more like" a 5/4 than something 17 cents away from a 5/4. If that is in fact the case, then what you are hearing has nothing to do with frequency ratios at all, so "temperament" as we understand it is irrelevant as a descriptor for what is happening in that scale.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> That 16/11 sometimes sounds like a fifth to me. And you said you heard
> the 13-equal version as sounding like a pelog fifth.

Sounding "like a fifth" and sounding "like a 3/2" have not been conclusively proven to be the same. The tritone sounds like a fifth--a *diminished* fifth. The pelog fifth is a pelog fifth, and it does not sound like a 3/2. You can map a 3/2 to it in absence of something better, but it's stretching the validity of the mapping, I'd say.

> Firstly, who says that we have to pick one and only one approximation
> to 5/4 in a scale, and why should the brain hear things that way?

Well, last time I checked, Father temperament only supplies us with one 5/4 and one 3/2. If we're hearing two types of 5/4 and two types of 3/2, then we're still definitely not in Father temperament.

> Secondly, we don't know wtf "hearing tempered intervals as
> approximating just intervals" means. At least I don't, and you didn't
> seem to last week either.

The only way I know how to make that make sense to me is by saying that a tempered interval is heard "as" approximating a given Just interval iff given the ability to retune the tempered interval to a Just interval, you'd tune it to the interval in question. So for instance if you take an interval of 462 cents and hold it, and then try to tweak the tuning to make the beating stop, if you tune it down to a 5/4 and think "there, that's what it's supposed to sound like", then you're hearing it as a 5/4. If you'd tune it up to a 4/3, then that's what you're hearing it as. I think of it like the brain noticing that the interval is "off", and calculating what it "would be" if it *wasn't* off. Like looking at a crookedly-hung picture and thinking "the left side needs to come up a bit to make it straight".

> What if you still hear the 9/7 as 5/4? Why can't the 9/7 just be a
> sharp 5/4, and the more just 5/4 be a more just 5/4? Who says the
> brain only assigns 5/4 to one dyad in a scale?

If you're hearing both 9/7 and 5/4 as a 5/4, even when they're right next to each other, that to me says something very bad about the meaning of ratios. It means that the identity of a ratio has nothing to do with its tuning, and therefore, nothing to do with the actual quantitative relationship between the frequencies impinging on the ear. It means ratios are themselves a fiction and we should just discard them wholesale, because we no longer even know what it means to hear a "5/4". If 9/7 sounds like a 5/4, and maybe (let's say) 11/9 sounds like 5/4, to me that means that there is no "sound" of a 5/4, and that frequency relationships tell us nothing about intervallic perceptual identity.

> What tuning for father ends up with the generator being a closer
> approximation to 5/4 than -6 generators?

8-EDO. -6g in 8-EDO = 300 cents, 86 cents flat of 5/4. 450 cents is only 64 cents sharp by comparison.

> What do you mean "the" 5/4 in the scale?

If we're dealing with multiple mappings of 5/4, we're not dealing with Father temperament.

-Igs

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

> If we're dealing with multiple mappings of 5/4, we're not dealing with Father temperament.

By definition. But I also think there's a distinction to be made between something like Father and Hanson. Hanson isn't really something which can be heard as what it is if you subject it to a lot of tuning abuse. The POTE/minimax generator of 317 cents is not as flexible as the Father generator, because it's a part of the nature of Hanson that it gives accurate 5-limit triads--that's the sort of temperament it is. So, 53edo pretty well nails it and 34edo is fine, but 19edo is already stretching the point--stretching it more than using 19 for Meantone is stretching it, as Hanson is more accurate. 15edo really won't do, and 11edo is orbiting another star entirely. 11edo does not have pure, sweet 5-limit triads. The val <11 18 26| belongs to Hanson algebraically, but as I've remarked before the val <36 65 116| belongs to Meantone algebraically. So I would regard Catakleismic as a natural extension of Hanson, but Keemun as something a bit different.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
>
> > If we're dealing with multiple mappings of 5/4, we're not dealing with Father temperament.
>
> By definition. But I also think there's a distinction to be made between something like Father and Hanson. Hanson isn't really something which can be heard as what it is if you subject it to a lot of tuning abuse. The POTE/minimax generator of 317 cents is not as flexible as the Father generator, because it's a part of the nature of Hanson that it gives accurate 5-limit triads--that's the sort of temperament it is. So, 53edo pretty well nails it and 34edo is fine, but 19edo is already stretching the point--stretching it more than using 19 for Meantone is stretching it, as Hanson is more accurate. 15edo really won't do, and 11edo is orbiting another star entirely. 11edo does not have pure, sweet 5-limit triads. The val <11 18 26| belongs to Hanson algebraically, but as I've remarked before the val <36 65 116| belongs to Meantone algebraically. So I would regard Catakleismic as a natural extension of Hanson, but Keemun as something a bit different.
>

I agree. This reasoning will stand outside internet speculation.

There are practical differences between innovation and unhitching your caboose from the train of history and letting it slow to a stop near Bedlam or Babel. In the case of "hanson", we're taking our tools to a well-documented facet of temperament history: "hanson" is presented, in negative form, in the MGG article, which is mainstream "required basic knowledge" stuff, on Stimmung und Temperatur.

It is an understandable mistake to conflate 5/4, the ditone, and "major third", as they are tempered to unity in 1/4 comma meantone, one of the several centers of western music, its notation, and its conception.

It is still a mistake, though. There's nothing heaven-born about this unity, whatever Hindemith or whoever may have implied.

I think it is easy to clear things up by making the distinction between point of identity and point of reference. Without specific timbral monkeyshines, there's no getting away from the fact that intervals within a goodly region of tuning will beat primarily around the 5th and 4th partials, right where 5/4 fuses. So "5/4" is pretty inescapable as a point of spectral reference for intervals within this region, but this does not mean it's a point of identity (rather the opposite I should think), unless the interval in question is close enough to have the slow beating of "almost fusing", in which case it seems completely reasonable to think of the thing as a kind of 5/4.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > That 16/11 sometimes sounds like a fifth to me. And you said you heard
> > the 13-equal version as sounding like a pelog fifth.
>
> Sounding "like a fifth" and sounding "like a 3/2" have not been conclusively proven to be the same. The tritone sounds like a fifth--a *diminished* fifth. The pelog fifth is a pelog fifth, and it does not sound like a 3/2. You can map a 3/2 to it in absence of something better, but it's stretching the validity of the mapping, I'd say.
>
> > Firstly, who says that we have to pick one and only one approximation
> > to 5/4 in a scale, and why should the brain hear things that way?
>
> Well, last time I checked, Father temperament only supplies us with one 5/4 and one 3/2. If we're hearing two types of 5/4 and two types of 3/2, then we're still definitely not in Father temperament.
>
> > Secondly, we don't know wtf "hearing tempered intervals as
> > approximating just intervals" means. At least I don't, and you didn't
> > seem to last week either.
>
> The only way I know how to make that make sense to me is by saying that a tempered interval is heard "as" approximating a given Just interval iff given the ability to retune the tempered interval to a Just interval, you'd tune it to the interval in question. So for instance if you take an interval of 462 cents and hold it, and then try to tweak the tuning to make the beating stop, if you tune it down to a 5/4 and think "there, that's what it's supposed to sound like", then you're hearing it as a 5/4. If you'd tune it up to a 4/3, then that's what you're hearing it as. I think of it like the brain noticing that the interval is "off", and calculating what it "would be" if it *wasn't* off. Like looking at a crookedly-hung picture and thinking "the left side needs to come up a bit to make it straight".
>
> > What if you still hear the 9/7 as 5/4? Why can't the 9/7 just be a
> > sharp 5/4, and the more just 5/4 be a more just 5/4? Who says the
> > brain only assigns 5/4 to one dyad in a scale?
>
> If you're hearing both 9/7 and 5/4 as a 5/4, even when they're right next to each other, that to me says something very bad about the meaning of ratios. It means that the identity of a ratio has nothing to do with its tuning, and therefore, nothing to do with the actual quantitative relationship between the frequencies impinging on the ear. It means ratios are themselves a fiction and we should just discard them wholesale, because we no longer even know what it means to hear a "5/4". If 9/7 sounds like a 5/4, and maybe (let's say) 11/9 sounds like 5/4, to me that means that there is no "sound" of a 5/4, and that frequency relationships tell us nothing about intervallic perceptual identity.
>
> > What tuning for father ends up with the generator being a closer
> > approximation to 5/4 than -6 generators?
>
> 8-EDO. -6g in 8-EDO = 300 cents, 86 cents flat of 5/4. 450 cents is only 64 cents sharp by comparison.
>
> > What do you mean "the" 5/4 in the scale?
>
> If we're dealing with multiple mappings of 5/4, we're not dealing with Father temperament.
>
> -Igs
>

Oh, Igliashon actually already said what I just said, I'm just restating in a summary and blunt way.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> It is an understandable mistake to conflate 5/4, the ditone, and "major third", as they are tempered to unity in 1/4 comma meantone, one of the several centers of western music, its notation, and its conception.
>
> It is still a mistake, though. There's nothing heaven-born about this unity, whatever Hindemith or whoever may have implied.
>
> I think it is easy to clear things up by making the distinction between point of identity and point of reference. Without specific timbral monkeyshines, there's no getting away from the fact that intervals within a goodly region of tuning will beat primarily around the 5th and 4th partials, right where 5/4 fuses. So "5/4" is pretty inescapable as a point of spectral reference for intervals within this region, but this does not mean it's a point of identity (rather the opposite I should think), unless the interval in question is close enough to have the slow beating of "almost fusing", in which case it seems completely reasonable to think of the thing as a kind of 5/4.
>
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > > That 16/11 sometimes sounds like a fifth to me. And you said you heard
> > > the 13-equal version as sounding like a pelog fifth.
> >
> > Sounding "like a fifth" and sounding "like a 3/2" have not been conclusively proven to be the same. The tritone sounds like a fifth--a *diminished* fifth. The pelog fifth is a pelog fifth, and it does not sound like a 3/2. You can map a 3/2 to it in absence of something better, but it's stretching the validity of the mapping, I'd say.
> >
> > > Firstly, who says that we have to pick one and only one approximation
> > > to 5/4 in a scale, and why should the brain hear things that way?
> >
> > Well, last time I checked, Father temperament only supplies us with one 5/4 and one 3/2. If we're hearing two types of 5/4 and two types of 3/2, then we're still definitely not in Father temperament.
> >
> > > Secondly, we don't know wtf "hearing tempered intervals as
> > > approximating just intervals" means. At least I don't, and you didn't
> > > seem to last week either.
> >
> > The only way I know how to make that make sense to me is by saying that a tempered interval is heard "as" approximating a given Just interval iff given the ability to retune the tempered interval to a Just interval, you'd tune it to the interval in question. So for instance if you take an interval of 462 cents and hold it, and then try to tweak the tuning to make the beating stop, if you tune it down to a 5/4 and think "there, that's what it's supposed to sound like", then you're hearing it as a 5/4. If you'd tune it up to a 4/3, then that's what you're hearing it as. I think of it like the brain noticing that the interval is "off", and calculating what it "would be" if it *wasn't* off. Like looking at a crookedly-hung picture and thinking "the left side needs to come up a bit to make it straight".
> >
> > > What if you still hear the 9/7 as 5/4? Why can't the 9/7 just be a
> > > sharp 5/4, and the more just 5/4 be a more just 5/4? Who says the
> > > brain only assigns 5/4 to one dyad in a scale?
> >
> > If you're hearing both 9/7 and 5/4 as a 5/4, even when they're right next to each other, that to me says something very bad about the meaning of ratios. It means that the identity of a ratio has nothing to do with its tuning, and therefore, nothing to do with the actual quantitative relationship between the frequencies impinging on the ear. It means ratios are themselves a fiction and we should just discard them wholesale, because we no longer even know what it means to hear a "5/4". If 9/7 sounds like a 5/4, and maybe (let's say) 11/9 sounds like 5/4, to me that means that there is no "sound" of a 5/4, and that frequency relationships tell us nothing about intervallic perceptual identity.
> >
> > > What tuning for father ends up with the generator being a closer
> > > approximation to 5/4 than -6 generators?
> >
> > 8-EDO. -6g in 8-EDO = 300 cents, 86 cents flat of 5/4. 450 cents is only 64 cents sharp by comparison.
> >
> > > What do you mean "the" 5/4 in the scale?
> >
> > If we're dealing with multiple mappings of 5/4, we're not dealing with Father temperament.
> >
> > -Igs
> >
>

So it seems that LLsLLsLs is 'father' and (heres where I think there is
an argument going on) the LLs should either be unambiguously hearable as the 'best 5/4' OR the usage model should be such that LLs takes the appearance of the 'best 5/4'.

So if I do a quick excel and say 'either the LLs is the best 5/4 OR the LL is sufficiently below 5/4 (<360 cents) that LL might appear 'minor' relative to the LLs 'major', then I get the following EDOs

8 21 29 34 37 45 47 50 53 55

If I made the fudge factor 370, 13 would appear. In fact the rule
with 360 is that s < L < 1.8 * s.

Back to 31, 55255252 has a SO MUCH BETTER 5/4 at 10\31 that it would
be hard to think that a piece of music could make the 12\31 work as a '5/4'.

BUT... that doesn't mean that a piece of music that did whatever a 'father' piece of music did wouldn't still do something 'fatherly' mapped to a not so father-like tuning in the same way that 'Happy Birthday' is recognizable when sung minor (and it is ALWAYS sung as a dirge anyhow),

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

> If you're hearing both 9/7 and 5/4 as a 5/4, even when
> they're right next to each other, that to me says
> something very bad about the meaning of ratios. It means
> that the identity of a ratio has nothing to do with its
> tuning, and therefore, nothing to do with the actual
> quantitative relationship between the frequencies
> impinging on the ear. It means ratios are themselves a
> fiction and we should just discard them wholesale,
> because we no longer even know what it means to hear a
> "5/4". If 9/7 sounds like a 5/4, and maybe (let's say)
> 11/9 sounds like 5/4, to me that means that there is no
> "sound" of a 5/4, and that frequency relationships tell
> us nothing about intervallic perceptual identity.

Oh, please, spare us the slippery slopes. It's quite
plausible for 5/4 to be heard as a consonance but not 9/7.
Partly it depends on the timbre. 9:7 clearly has higher
complexity. Even if you can find a contradiction (and
surely there must be one: human perception's a complicated
business) it wouldn't mean that no ratio has any meaning
ever.

Graham

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

> > Secondly, we don't know wtf "hearing tempered intervals
> > as approximating just intervals" means. At least I
> > don't, and you didn't seem to last week either.
>
> The only way I know how to make that make sense to me is
> by saying that a tempered interval is heard "as"
> approximating a given Just interval iff given the ability
> to retune the tempered interval to a Just interval, you'd
> tune it to the interval in question. So for instance if
> you take an interval of 462 cents and hold it, and then
> try to tweak the tuning to make the beating stop, if you
> tune it down to a 5/4 and think "there, that's what it's
> supposed to sound like", then you're hearing it as a
> 5/4. If you'd tune it up to a 4/3, then that's what
> you're hearing it as. I think of it like the brain
> noticing that the interval is "off", and calculating what
> it "would be" if it *wasn't* off. Like looking at a
> crookedly-hung picture and thinking "the left side needs
> to come up a bit to make it straight".

Note that it's impossible, by this rule, for the same
pitch to be heard as both 4/3 and 5/4. But that doesn't
mean father temperament is logically impossible: you might
have both 5/4 and 3/2 in the scale.

Given your psychoacoustic rule, then, it looks like 503.4
cents must be within the field of attraction of a 5:4.
That's how suspended fourth resolutions work, after all.
Two voices end up a perfect fourth apart -- which is a
dissonance according to Renaissance musical grammar. The
upper voice corrects the mistake by moving down. With just
intonation, the target is a 5:4. When the pattern was
adapted to keyboard instruments tuned to quarter comma
meantone, the target was also an exact 5:4.

There is a precedent in psychoacoustics for intervals
having a wide field of attraction. At least one
psycoacoustician explains a minor triad as being a mistuned
4:5:6:

http://www.mmk.ei.tum.de/persons/ter/top/basse.html

"This implies that the root of musical chords is not merely
a theoretical . . . concept, but that it is an attribute of
auditory sensation, i.e., virtual pitch."

"In summary, there can be hardly any doubt
that Rameau's basse fondamentale, i.e., the root of chords,
has got its psychophysical explanation in the above
findings."

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> Note that it's impossible, by this rule, for the same
> pitch to be heard as both 4/3 and 5/4.

Not so; context can determine whether that interval gets heard as 5/4 or 4/3. It's not always heard as the same interval.

> Given your psychoacoustic rule, then, it looks like 503.4
> cents must be within the field of attraction of a 5:4.

Also not so. I'm not talking about tuning an interval to "resolve it", I'm talking about tuning it to make the beating stop. As if your mind is a virtual choir director telling one of the singers "you're a bit flat". A suspended 4th chord in JI is 6:8:9, which is plenty beatless.

> There is a precedent in psychoacoustics for intervals
> having a wide field of attraction. At least one
> psycoacoustician explains a minor triad as being a mistuned
> 4:5:6:
>
> http://www.mmk.ei.tum.de/persons/ter/top/basse.html
>
> "This implies that the root of musical chords is not merely
> a theoretical . . . concept, but that it is an attribute of
> auditory sensation, i.e., virtual pitch."
>
> "In summary, there can be hardly any doubt
> that Rameau's basse fondamentale, i.e., the root of chords,
> has got its psychophysical explanation in the above
> findings."

Ah, perhaps here we have found the identity of the mysterious "Dr. Gilbert Sullivan", then?

-Igs

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> Oh, please, spare us the slippery slopes. It's quite
> plausible for 5/4 to be heard as a consonance but not 9/7.
> Partly it depends on the timbre. 9:7 clearly has higher
> complexity. Even if you can find a contradiction (and
> surely there must be one: human perception's a complicated
> business) it wouldn't mean that no ratio has any meaning
> ever.

Perhaps not, but it would mean that the whole business of "error" is not actually as telling as we've been treating it. If John is right about his own hearing (which I actually doubt, but nevertheless), in that in 22-EDO he frequently hears the interval of 436.36 cents as sounding "more like" 5/4 than the interval of 381.82 cents, well, that's pretty huge if you ask me. Because 5/4 is an interval of 386.31 cents, and if an interval which approximates it with an error of almost 50 cents sounds *more* like it than an interval that approximates it with an error of less than 5 cents, that has a tremendous significance for the regular temperament paradigm.

However, that is a VERY big "if", and I don't actually believe that this is how John (or anyone) is hearing things. I think people have made the mistake of conflating "major 3rd" and "5/4"; the former identity is more contingent on scalar and/or progressional cues than on any harmonic properties, whereas the latter identity is contingent exclusively on harmonic properties. I say this because I *know* that if John simply heard the two chords (the ~14:18:21 and the ~4:5:6) in isolation, he would undoubtedly identify the ~4:5:6 as being the better approximation of 4:5:6--barring any wacky timbral/spectral tricks, of course.

-Igs

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>"hanson" is presented, in negative form, in the MGG article

MGG = ?

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

>
By definition. But I also think there's a distinction to be made
between something like Father and Hanson. Hanson isn't really something which can be heard as what it is if you subject it to a lot of tuning abuse. The POTE/minimax generator of 317 cents is not as flexible as the Father generator, because it's a part of the nature of Hanson that it gives accurate 5-limit triads--that's the sort of temperament it is. So, 53edo pretty well nails it and 34edo is fine, but 19edo is already stretching the point--stretching it more than using 19 for Meantone is stretching it, as Hanson is more accurate. 15edo really won't do, and 11edo is orbiting another star entirely. 11edo does not have pure, sweet 5-limit triads. The val <11 18 26| belongs to Hanson algebraically, but as I've remarked before the val <36 65 116| belongs to Meantone algebraically. So I would regard Catakleismic as a natural extension of Hanson, but Keemun as something a bit different.
>

I agree, and I'm glad you're backing me up on this. However, I don't agree that the Hanson generator is less flexible than the Father generator, I think perhaps even the opposite is the case. I don't actually even think the POTE generator for Father is consistent with Father temperament, because you get a better 5 than the mapping gets you very quickly in the generator chain--at +7 generators, and in fact as soon as you get flat of a 750-cent generator, +7 is going to be a better 5 than -1 generator. In fact between 741-742 cents you get a Just 5/4 at +7, and then slowly -6 starts to look better, until -7g=+6g (at 13-EDO, in fact), and after that -6 becomes the better 5, being near-Just between 736 and 735 cents. Getting sharp of a 750-cent generator, OTOH, moves you quickly into Sensi territory. So I'd say that if octaves are kept pure, the only consistent generator for Father temperament is an exact 450 cents, unless we are confining ourselves to the 3L+2s pentatonic scale, in which case we never get to the better approximations of 5 within the scale and the Father mapping remains consistent.

-Igs

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >"hanson" is presented, in negative form, in the MGG article
>
> MGG = ?
>

http://en.wikipedia.org/wiki/Musik_in_Geschichte_und_Gegenwart

It looks like you can find it in English, too. Better than Grove's at least for "hands on" musicians, in my opinion.

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

> Ah, perhaps here we have found the identity of the mysterious
> "Dr. Gilbert Sullivan", then?

? Are you suggesting it's Terhardt?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
>
> > Ah, perhaps here we have found the identity of the mysterious
> > "Dr. Gilbert Sullivan", then?
>
> ? Are you suggesting it's Terhardt?

Ha ha ha, no, not really. But didn't that guy say something equally absurd, like minor chords just being maj7 chords with the root omitted or something?

-Igs

> > I disagree:
> > /tuning/files/JohnMoriarty/SoundTheSame.mp3
>
> Not sold. Not even a little bit. For starters, the timbre makes it hard for me to even discern the chords being played, for two I hear very clear differences between the different progressions. I take it you were using TransFormSynth and sliding along the "Hanson" continuum?

At first I had trouble discerning the actual pitches of warped timbres too, but that's something I've come to recognize more and more easily the more I use them. I probably should have made a second version with harmonic timbres taking that into account, but the point I was trying to make was that the chord progression was comparable in each example, and I thought the timbres highlighted that the most. I guess the amount the timbres helped me hear it hurt your chances. It was made in 2032.

> Are you honestly telling me that if you heard a 462-cent interval and a a 369-cent interval, you would consider the first one a 5/4 and not the second one?

Not without context. And I haven't become very familiar with the MOS scales we're referring to when it comes to father, so I haven't had time to associate the scale structure with a specific mapping, so chances are I would have trouble hearing the first one as more of a 5/4 than the second. But given my experiences with meantone, I imagine I could.

> > Yes but, again, this is a different spectrum for each person with no lines pre-drawn.
>
> That is patently false. Yes, there are variations from person to person, and if you use artificial/obscured timbres that blur harmonic identities, then things go up in the air. But there are definite limits, especially when directly comparing two intervals. Can 600 cents sound like a 3/2? Maybe under some extreme circumstances, but put it next to 700 cents, and it's obvious that 600 cents is NOT a 3/2.

What if you were to get that 700 cents to sound like say... a 25/16? or an 8/5 even? Then the 600 cent interval might sound way more like a 3/2.

> And anyway the regular mapping paradigm is not meant to vary from person to person, or to account for "extreme" listening environments generated by artificial scale-mapped timbres.

I'm not saying the paradigm needs to vary. I'm saying the paradigm itself has definitions with no limits, and to what extremes you stretch the paradigm is a judgment call: Harmonic or modified timbres, no previous exposure to a mapping or long term exposure, what have you.

> > Again, this is part of that same spectrum of tolerance. If 23-edo has two "sensible"
> > mappings, then this example of 22-edo is just your deciding where to draw a line for
> > what is "sensible" enough to consider two optional mappings, and what is foolish.
>
> Well of course decisions have to be made. The question is are they sensible, and that is a question determined by consensus.

I think that's just false. No decisions HAVE to be made, or at least not on the subject of drawing these lines. All you need is a consensus on the existence of a spectrum of limits, limits that vary person to person due to individual factors. Then sure, we could look into what those individual factors are, and that could lead to interesting insight.

If we really went by consensus, would this list even exist?

> So far you haven't given any reason as to why these "lines" are not sensible.

So far, all I have is what I hear, which does say (to me) that the lines are not sensible.

Problem is, YOU'RE the one proposing the limits, and I think that's the position that needs defending. Why are these lines YOU'VE drawn defensible? What evidence have you that says there is a specific line to draw and that you have drawn it correctly somewhere between you and me, or that there is even need for this line at all and not just the recognition of a spectrum?

> What evidence is there that you're hearing it as a 5/4? Don't make the mistake of thinking that just because you hear "major triad" that that means you're hearing "4:5:6".

> OTOH, it's also arguable that you're NOT hearing a 5/4, because that interval *is* a 9/7, and those triads *are* 14:18:21. You *are* hearing major triads and something about the diatonic structure actually biases your perception such that when presented with a 5/4, it sounds too "low" to be a major 3rd. But this is as much evidence for the conclusion that "major 3rd-ness" has nothing to do with 5/4 as it is evidence for the conclusion that a 9/7 can sound like a 5/4.

Of course my (and our) understanding of what hearing something "as a 3/2" actually means is not very solid. But there is a reason I'm confident I'm hearing this major triad in 22-edo as 4:5:6.
When I play other temperaments besides meantone like magic, anti-diatonic, and even bug, I hear a sort of harmonic identity in each's 4:5:6 that I link to both their respective scale structures AND to each other. That is, I hear the "same thing" when I play the 4:5:6 of multiple temperaments (all of which have the 5/4 and 3/2 line up with a different melodic combinations of L and S), and I manage to hear them all as this same thing even when I mess around with the tuning of each temperament's.

I feel like they are all inherently similar, and that makes me think that I'm not just hearing some "other" just triad like 14:18:21 when I mess with the tuning in meantone. It still "sounds like" it did in other meantone tunings (which COULD be melodic training), but it also sounds like it does in completely different temperaments and their different tunings (which coud NOT be melodic training.)

> Personally, I think if we want to accept the latter, we have to throw out JI as a load of hogwash, because if we can conflate ratios that easily, the ratios themselves are actually psychoacoustically meaningless.

Why? Again, I'm only saying that they are MORE conflatable than you are saying. What about the person who says that if YOU call 700 cents a 3/2 then we might as well throw out JI as a load of hogwash because if we can conflate ratios that easily, the ratios are psychoacoustically meaningless? Would you say that he is drawing the line to close to the actual just ratios?

John

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

> At first I had trouble discerning the actual pitches of warped
> timbres too, but that's something I've come to recognize more and
> more easily the more I use them. I probably should have made a
> second version with harmonic timbres taking that into account, but > the point I was trying to make was that the chord progression was
> comparable in each example, and I thought the timbres highlighted
> that the most. I guess the amount the timbres helped me hear it
> hurt your chances. It was made in 2032.

I suppose this goes to show that with repeated exposure, anything can come to sound "normal".

> > Are you honestly telling me that if you heard a 462-cent interval > > and a a 369-cent interval, you would consider the first one a 5/4 > > and not the second one?

> Not without context.

That's the rub, here: context. The regular mapping paradigm has no way to handle "context" and the attendant varieties of preattentive perceptual biases; it is all about straight-up error. The relevance of error to perception of course varies depending on all sorts of wacky circumstances that we are just now becoming aware of, and the result is that there are places where the paradigm gets a bit messy. It is precisely at these boundary-condition places that it becomes questionable whether or not we should even continue to use the paradigm, because if it's messy and inconsistent and contradicts our listening experience, what good is it doing us?

> What if you were to get that 700 cents to sound like say... a
> 25/16? or an 8/5 even? Then the 600 cent interval might sound way
> more like a 3/2.

That would be impossible, unless you use some kind of warped timbre. But if you're using warped timbres, ratios are pretty much meaningless anyway.

> I'm not saying the paradigm needs to vary. I'm saying the paradigm > itself has definitions with no limits, and to what extremes you
> stretch the paradigm is a judgment call: Harmonic or modified
> timbres, no previous exposure to a mapping or long term exposure,
> what have you.

Just because the paradigm does not deal in explicitly-defined limits, that does not mean there are no limits. There's some wiggle-room, yes, and the world's not going to end if you go waaaay out into interstellar space, but the real question is, what is to be gained by stretching the limits like that? *Why* would you want to insist that 11-EDO as a super-high-error Hanson temperament? That's as sensible as saying 16-EDO is a Meantone.

> I think that's just false. No decisions HAVE to be made, or at
> least not on the subject of drawing these lines.

If no decisions are made, then you could call any tuning any temperament you like, which wouldn't actually do you any good. What makes the regular temperament paradigm useful is that it shows us ways to approximate JI with tunings that are simpler than JI and within reasonable limits of accuracy. This is based on the idea that people cannot functionally distinguish tempered intervals from JI within a certain threshold of mistuning, and that even beyond that threshold, the "identity" or "character" of the JI interval is still retained within a wider threshold of mistuning. This assumes that JI intervals do actually possess distinct psychoacoustic identities related to their actual tuning, which we now know to be somewhat false--intervallic identity recognition depends on more than pure frequency relationship, many many MANY factors can bias perception and/or create auditory illusions. But we have to assume that JI intervals *do* have distinct identities related to their actual tuning, or else we're up shit creek without a paddle in terms of trying to figure out how to approximate them. And in any case, there are definite limits even to the illusions that can be created with warped timbres.

> All you need is a consensus on the existence of a spectrum of
> limits, limits that vary person to person due to individual
> factors. Then sure, we could look into what those individual
> factors are, and that could lead to interesting insight.

More important is the existence of a limit to the "spectrum of limits". Surely no one will mistake 200 cents or 1000 cents for a 3/2, so if we can put those "off limits", why can't we draw the limits a bit closer? Surely you can't believe that there are really NO absolutes?

> If we really went by consensus, would this list even exist?

There is plenty of consensus as regards the regular temperament paradigm. Not 100%, but no one doubts that 53-EDO is a Hanson temperament. No one doubts that 22-EDO is a Magic temperament. No one doubts that 72-EDO is a Miracle temperament. Until recently, no one has also doubted that a lower-error approximation sounds more like the approximated interval than a high-error approximation. Where there are discrepancies (some say 13-EDO is an Orwell temperament, some say it's not; some say 23-EDO is a Myna temperament, some say it's not; etc.), the sensible thing to do is to acknowledge that boundaries are being stretched and the application of a particular mapping to a particular tuning is questionable.

> So far, all I have is what I hear, which does say (to me) that the > lines are not sensible.

From what you've said, it sounds like what you hear is:
1) 436.36 cents sounds more like 5/4 than 381.82 cents.
2) ~461 cents sounds more like 5/4 than ~370 cents.
3) 763.64 cents sounds like an acceptable approximation of 3/2. Presumably that means it also does not sound to you like a 14/9, 11/7, or 8/5, either. Since 763.64 cents pretty much IS a 14/9, then that would also be saying 14/9 doesn't actually exist as an identity in its own right, it's just a point on the continuum of "detuned 3/2". Also that it's not subsumed into the nearer simpler identities of 11/7 or 8/5.

If this is how you hear things, I do not understand why you are interested in the regular mapping paradigm, because approximation of intervals seems to have absolutely nothing to do with, well, proximity for you. Or maybe has something to do with proximity some percentage of the time, but not often enough for proximity to be a reliable indicator of approximation strength.

> Problem is, YOU'RE the one proposing the limits, and I think that's > the position that needs defending. Why are these lines YOU'VE drawn > defensible? What evidence have you that says there is a specific
> line to draw and that you have drawn it correctly somewhere between > you and me, or that there is even need for this line at all and not > just the recognition of a spectrum?

Because the differentiation of temperaments (or temperament families, if you prefer the term) requires that there be limits. There has to be a point where Meantone ends and Pelogic begins. There has to be a point where Hanson ends and Amity begins, and where Amity ends and Dicot begins, etc.

The sensible place for boundaries to be drawn is where one mapping becomes lower-error than another one. If you look at the error of 16-EDO in terms of a Meantone mapping, its error is much higher than if you look at it in terms of a Pelogic mapping. Ergo, 16-EDO should be called a Pelogic temperament rather than a Meantone. In the case of 11-EDO, there are plenty of other (mostly subgroup) temperaments that describe it with a lower error than if you look at it as a Hanson temperament. In 13-EDO, the Uncle mapping describes it with a lower error than the Father mapping. There's nothing arbitrary about this at all, it's pure math, totally objective. And if you want to continue arguing that we should hold fast to categorizing tunings according higher-error mappings, I'm going to ask you again what is to be gained by that.

And for the record, I will say that at least one person (Mike B.) has been confused--by a very strong perceptually-biasing cue--into thinking Mavila/Pelogic was a really out-of-tune Meantone, such that he was hearing minor triads as badly out-of-tune major triads. Does that mean we ought to be open to considering the possibility that the tuning range for Meantone actually extends into Pelogic territory? No, it does not. It just means that, like the eyes, the ears too can be fooled by illusions.

> When I play other temperaments besides meantone like magic,
> anti-diatonic, and even bug, I hear a sort of harmonic identity in > each's 4:5:6 that I link to both their respective scale structures > AND to each other. That is, I hear the "same thing" when I play the > 4:5:6 of multiple temperaments (all of which have the 5/4 and 3/2
> line up with a different melodic combinations of L and S), and I
> manage to hear them all as this same thing even when I mess around > with the tuning of each temperament's.

And yet, the only way you hear the ~14:18:21 in 22-EDO as a 4:5:6 is when it's in the context of the diatonic scale. If I played you, out of context, the 22-EDO 4:5:6 and the 22-EDO 14:18:21, are you really going to claim that the latter would sound more like a 4:5:6 than the former? Absent any scalar or melodic cues, in a total sonic vacuum? Unless the answer is "yes", my point stands that it is the scalar cues biasing your perception. If the answer *is* yes, then you are effectively telling me that 14:18:21 sounds more like 4:5:6 than 4:5:6 itself does. That is absurd, and my reductio ad absurdum is complete.

> Why? Again, I'm only saying that they are MORE conflatable than you > are saying.

Just ratios, barring perceptually-biasing extrinsic factors, are not conflatable. Absent any extrinsic factors (melodic cues, progressional cues, etc.), 6/5 and 5/4 are not going to be mistaken for the same interval, nor will 5/4 and 9/7, 9/7 and 4/3, 3/2 and 14/9, etc. Extrinsic factors are capable of playing all manner of tricks on our perception, of course, but the point is they are *tricks*. Illusions. The possibility of these illusions of course does have ramifications for the validity of the regular temperament paradigm in general, but the paradigm has no way of addressing these tricks. In order to use the paradigm *consistently*, one has to ignore the tricks that music can play. Using remapped timbres basically invalidates the whole paradigm anyway, because ratios lose their psychoacoustic significance almost entirely.

> What about the person who says that if YOU call 700 cents a 3/2
> then we might as well throw out JI as a load of hogwash?

There is no Just ratio at 700 cents that could be conflated with 3/2. I'm fairly certain everyone on this list concurs that 700 cents is a very obvious (and very accurate) approximation of 3/2. Anyone who doesn't buy that doesn't buy the idea of approximation in general, and won't have any use for the regular temperament paradigm in general.

-Igs

I know I'm not quite keeping up with the pace of the conversation, but there are a few points I'd still like to make.

> The sensible place for boundaries to be drawn is where one mapping becomes lower-error than another one.

I don't like this because, in the 22-edo example, the diatonic MOS is Meantone whereas the chromatic MOS isn't because it contains the better 5/4 elsewhere. But even if you are playing "chromatic music", it usually involves a diatonic scale nested into the chromatic framework. Even when exposed to the D# in a C major piece, it'd only ever be used in harmonic context where it is a 5/4 above B (as part of a 4:5:6, as a secondary dominant of Em), and we'd probably never get the chance to even hear the D# as a 5/4 above C because we wouldn't run into them melodically together.

So even when exposed to scale structures large enough to contain much better approximations of a just interval, I still see the original mapping as viable, and definitely not contradictory.

> There has to be a point where Hanson ends and Amity begins, and where Amity ends and Dicot begins, etc.

If you remember from a while back, I have a theory that as long as the harmonic series derived from a tuning and a mapping has static or decreasing interval sizes consecutively from partial to partial, we should far more *easily* hear the tuning as has having the Just characteristics the mapping describes. Basically, make it so that 2/1 > 3/2 > 4/3 > 5/4 > 6/5 > 7/6 > 8/7 etc.

With this definition, every tempered comma has a definite range not having to do with how big an MOS you take into account.
Some 5-limit commas:
Syntonic=81/80=7-edo to 5-edo
Pelogic=135/128 = 2-edo to 7-edo
Porcupine=250/243= 8-edo to 7-edo
Magic=3125/3072= 10-edo to 3-edo
Hanson=15625/15552= 4-edo to 11-edo
etc.
Each boundary is going to be an edo because 5/4=6/5 or 4/3=5/4, reducing the dimensionality. Each boundary also lines up with a boundary of an MOS.

At 11-edo with a Hanson mapping, 5/4=4/3. Above 11-edo, 5/4>4/3 so I wouldn't expect someone to easily hear Hanson above 11-edo, but I can imagine 11-edo working as Hanson, and I hear it too.

> Surely you can't believe that there are really NO absolutes?

Not with some of the weird stuff I've heard stretching generators AND periods. All I ever expect to see is a rough correlation between:
1. The likelihood of being able to hear something as you describe it
And
2. The lack of error in what you are describing.

-John M

Hey John,
I've given up on telling people what to call things. Everyone is on their own trip with this stuff and no amount of arguing from me is going to change that, so I've resolved to get back to being on my own trip with it. Whatever floats your boat, mate.

-Igs

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
>
> I know I'm not quite keeping up with the pace of the conversation, but there are a few points I'd still like to make.
>
> > The sensible place for boundaries to be drawn is where one mapping becomes lower-error than another one.
>
> I don't like this because, in the 22-edo example, the diatonic MOS is Meantone whereas the chromatic MOS isn't because it contains the better 5/4 elsewhere. But even if you are playing "chromatic music", it usually involves a diatonic scale nested into the chromatic framework. Even when exposed to the D# in a C major piece, it'd only ever be used in harmonic context where it is a 5/4 above B (as part of a 4:5:6, as a secondary dominant of Em), and we'd probably never get the chance to even hear the D# as a 5/4 above C because we wouldn't run into them melodically together.
>
> So even when exposed to scale structures large enough to contain much better approximations of a just interval, I still see the original mapping as viable, and definitely not contradictory.
>
> > There has to be a point where Hanson ends and Amity begins, and where Amity ends and Dicot begins, etc.
>
> If you remember from a while back, I have a theory that as long as the harmonic series derived from a tuning and a mapping has static or decreasing interval sizes consecutively from partial to partial, we should far more *easily* hear the tuning as has having the Just characteristics the mapping describes. Basically, make it so that 2/1 > 3/2 > 4/3 > 5/4 > 6/5 > 7/6 > 8/7 etc.
>
> With this definition, every tempered comma has a definite range not having to do with how big an MOS you take into account.
> Some 5-limit commas:
> Syntonic=81/80=7-edo to 5-edo
> Pelogic=135/128 = 2-edo to 7-edo
> Porcupine=250/243= 8-edo to 7-edo
> Magic=3125/3072= 10-edo to 3-edo
> Hanson=15625/15552= 4-edo to 11-edo
> etc.
> Each boundary is going to be an edo because 5/4=6/5 or 4/3=5/4, reducing the dimensionality. Each boundary also lines up with a boundary of an MOS.
>
> At 11-edo with a Hanson mapping, 5/4=4/3. Above 11-edo, 5/4>4/3 so I wouldn't expect someone to easily hear Hanson above 11-edo, but I can imagine 11-edo working as Hanson, and I hear it too.
>
> > Surely you can't believe that there are really NO absolutes?
>
> Not with some of the weird stuff I've heard stretching generators AND periods. All I ever expect to see is a rough correlation between:
> 1. The likelihood of being able to hear something as you describe it
> And
> 2. The lack of error in what you are describing.
>
> -John M
>