Concordant Major/Minor Triad Pairs and Essential Tempering

We all know that the basis of meantone tonality is the contrasting major and minor triads, representing 4:5:6 and 10:12:15. Those of us searching for something that works like meantone, but differently, occasionally consider a triadic basis other than these two triads, but usually we only consider alternatives to the major triad and let the minor "sort itself out" as being maybe the utonal counterpart of the major triad. One problem with this is that the utonal counterparts of most triads more complex than 4:5:6 are much more discordant, at least if we go by the size of the numbers used to represent the utonal chords as a sequence of overtones. For instance, the utonal counterpart to 5:6:7 is 30:35:42, which should be fairly discordant. In practice, these utonal chords *aren't* discordant, and I suspect this is because many of them are in the "field of attraction" of a simpler identity. If we can work out what simpler identities might be, we can treat these utonal chords as being "essentially tempered" to them, and by figuring out what commas are involved, we might find good temperaments supporting both concordant otonal chords and essentially-tempered utonal chords that might get a boost in concordance by being closer to a simpler identity.

So, I've made a short list of some possibilities, showing a basis set, the otonal and utonal triads derived from it (in close voicings spanning less than a 2/1), some possible essential temperings of the utonal chords, and the commas involved. Some look better than others.

-------------

2:3:5--4:5:6 v 10:12:15

Possible essential tempering of utonal chord: 6:7:9, suggesting 36/35

(Note: I've often suspected this is how I hear 12-TET, and why minor triads in 19-TET always sounded a little bit "wrong" to me)

3:5:9--5:6:9 v 10:15:18

P.E.T.: 5:8:9, suggesting 16/15 (not likely, though!!)

3:7:9--6:7:9 v 14:18:21

P.E.T.: 6:8:9, suggesting 28/27

2:3:7--4:6:7 v 12:14:21

P.E.T.: 8:9:14, again suggesting 28/27 (5-ED2, anyone?)

3:5:7--5:6:7 v 30:35:42

P.E.T.: 15:17:21, suggesting 35/34; 5:6:7, suggesting 36/35 (probably a bit more likely, lame)

5:7:9--5:7:9 v 35:45:63

P.E.T.: 10:13:18, suggesting 91/90 (Deutone! This is a good one)

3:9:11--6:9:11 v 45:66:99

P.E.T.: 12:15:22, suggesting 45/44

3:5:11--6:10:11 v 60:66:110

P.E.T.: 12:13:22, suggesting 66/65

7:9:11--7:9:11 v 63:77:99

P.E.T.: 14:17:22, suggesting 154/153 (unlikely); 9:11:14, suggesting 99/98 (very likely); 5:6:8, suggesting 56/55 and 28/27 (not very likely)

5:7:11--7:10:11 v 70:77:110

P.E.T.: 14:15:22, suggesting 77/75; 9:10:14, suggesting 100/99 and 99/98

2:3:11--8:11:12 v 88:96:132

P.E.T.: 8:9:12, suggesting 33/32; 16:17:24, suggesting 192/187 (neither are very good)

2:7:11--8:11:14 v 88:112:154

P.E.T.: 4:5:7, suggesting 56/55 (Triforce yay!); 7:9:12, suggesting 49/48 and 99/98

9:11:13--9:11:13 v 99:117:143

P.E.T.: 18:21:26, suggesting 78/77; 11:13:16, suggesting 144/143 (both of these are still pushing it as far as concordance goes)

-------------

Feel free to add!

-Igs

If I win the bid on this:

http://www.ebay.com/itm/Scientology-E-meter-Signed-L-Ron-Hubbard-emeter-/300511415305?pt=LH_DefaultDomain_0&hash=item45f7e04c09#ht_4456wt_909

I'll be able to scientifically test your claims!

Wish me luck.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> We all know that the basis of meantone tonality is the contrasting major and minor triads, representing 4:5:6 and 10:12:15. Those of us searching for something that works like meantone, but differently, occasionally consider a triadic basis other than these two triads, but usually we only consider alternatives to the major triad and let the minor "sort itself out" as being maybe the utonal counterpart of the major triad. One problem with this is that the utonal counterparts of most triads more complex than 4:5:6 are much more discordant, at least if we go by the size of the numbers used to represent the utonal chords as a sequence of overtones. For instance, the utonal counterpart to 5:6:7 is 30:35:42, which should be fairly discordant. In practice, these utonal chords *aren't* discordant, and I suspect this is because many of them are in the "field of attraction" of a simpler identity. If we can work out what simpler identities might be, we can treat these utonal chords as being "essentially tempered" to them, and by figuring out what commas are involved, we might find good temperaments supporting both concordant otonal chords and essentially-tempered utonal chords that might get a boost in concordance by being closer to a simpler identity.
>
> So, I've made a short list of some possibilities, showing a basis set, the otonal and utonal triads derived from it (in close voicings spanning less than a 2/1), some possible essential temperings of the utonal chords, and the commas involved. Some look better than others.
>
> -------------
>
> 2:3:5--4:5:6 v 10:12:15
>
> Possible essential tempering of utonal chord: 6:7:9, suggesting 36/35
>
> (Note: I've often suspected this is how I hear 12-TET, and why minor triads in 19-TET always sounded a little bit "wrong" to me)
>
>
> 3:5:9--5:6:9 v 10:15:18
>
> P.E.T.: 5:8:9, suggesting 16/15 (not likely, though!!)
>
>
> 3:7:9--6:7:9 v 14:18:21
>
> P.E.T.: 6:8:9, suggesting 28/27
>
>
> 2:3:7--4:6:7 v 12:14:21
>
> P.E.T.: 8:9:14, again suggesting 28/27 (5-ED2, anyone?)
>
>
> 3:5:7--5:6:7 v 30:35:42
>
> P.E.T.: 15:17:21, suggesting 35/34; 5:6:7, suggesting 36/35 (probably a bit more likely, lame)
>
>
> 5:7:9--5:7:9 v 35:45:63
>
> P.E.T.: 10:13:18, suggesting 91/90 (Deutone! This is a good one)
>
>
> 3:9:11--6:9:11 v 45:66:99
>
> P.E.T.: 12:15:22, suggesting 45/44
>
>
> 3:5:11--6:10:11 v 60:66:110
>
> P.E.T.: 12:13:22, suggesting 66/65
>
>
> 7:9:11--7:9:11 v 63:77:99
>
> P.E.T.: 14:17:22, suggesting 154/153 (unlikely); 9:11:14, suggesting 99/98 (very likely); 5:6:8, suggesting 56/55 and 28/27 (not very likely)
>
>
> 5:7:11--7:10:11 v 70:77:110
>
> P.E.T.: 14:15:22, suggesting 77/75; 9:10:14, suggesting 100/99 and 99/98
>
>
> 2:3:11--8:11:12 v 88:96:132
>
> P.E.T.: 8:9:12, suggesting 33/32; 16:17:24, suggesting 192/187 (neither are very good)
>
>
> 2:7:11--8:11:14 v 88:112:154
>
> P.E.T.: 4:5:7, suggesting 56/55 (Triforce yay!); 7:9:12, suggesting 49/48 and 99/98
>
>
> 9:11:13--9:11:13 v 99:117:143
>
> P.E.T.: 18:21:26, suggesting 78/77; 11:13:16, suggesting 144/143 (both of these are still pushing it as far as concordance goes)
>
>
> -------------
>
> Feel free to add!
>
> -Igs
>

On Mon, Jan 23, 2012 at 2:08 PM, cityoftheasleep
<igliashon@...> wrote:
>
> We all know that the basis of meantone tonality is the contrasting major and minor triads, representing 4:5:6 and 10:12:15.

I only agree with this if you mean something very specific by "basis
of." What exactly do you mean?

> In practice, these utonal chords *aren't* discordant, and I suspect this is because many of them are in the "field of attraction" of a simpler identity.

Using your operational definition, isn't everything in the field of
attraction of a simpler identity?

> If we can work out what simpler identities might be, we can treat these utonal chords as being "essentially tempered" to them, and by figuring out what commas are involved, we might find good temperaments supporting both concordant otonal chords and essentially-tempered utonal chords that might get a boost in concordance by being closer to a simpler identity.

I think that you have a good list; one you might want to add is 91/90,
which turns 1/6:7:9 into 10:13:15. Of course, you may not like or care
about 10:13:15, but you can always fit it into something like
10:11:13:15 if you want.

I don't understand this at all:

> 2:3:5--4:5:6 v 10:12:15
> Possible essential tempering of utonal chord: 6:7:9, suggesting 36/35
> (Note: I've often suspected this is how I hear 12-TET, and why minor triads in 19-TET always sounded a little bit "wrong" to me)

It's not at all clear what you mean by "how I hear 12-TET." Do you
mean that using your operational definition, if you were handed a
12-TET minor chord, you'd retune it to 6:7:9 if you tried to maximize
the """""""concordance,""""""" placed within seven scare quotes, and
that this would also apply to a minor chord in 19-TET as well?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > We all know that the basis of meantone tonality is the contrasting major and minor
> > triads, representing 4:5:6 and 10:12:15.
>
> I only agree with this if you mean something very specific by "basis
> of." What exactly do you mean?

What meaning would you agree with? It's probably that one.

> Using your operational definition, isn't everything in the field of
> attraction of a simpler identity?

Um...yes and no, I guess. What happens to HE when you really crank up s? Whether something is or isn't in something else's field of attraction depends largely on what we assume for s.

> I think that you have a good list; one you might want to add is 91/90,
> which turns 1/6:7:9 into 10:13:15. Of course, you may not like or care
> about 10:13:15, but you can always fit it into something like
> 10:11:13:15 if you want.

I included 91/90 as turning 1/(5:7:9) into 10:13:18, but I can see it would also be useful in the case you stated.

> It's not at all clear what you mean by "how I hear 12-TET." Do you
> mean that using your operational definition, if you were handed a
> 12-TET minor chord, you'd retune it to 6:7:9 if you tried to maximize
> the """""""concordance,""""""" placed within seven scare quotes, and
> that this would also apply to a minor chord in 19-TET as well?

Yeah. The 19-TET minor triad always sounded "wrong" to me, much more complex than the major triad; yet at the same time, the subminor triad as an approximation to 6:7:9 didn't sound like the proper foil to the major triad, since I can hear the dyads inside it are different and it's not the "inverse" of the major. But for instance in 21-ED2, the major and minor triads sound more evenly matched. In 12-TET if I wanted to adaptively tune 0-300-700, I'd tune it to a 6:7:9 rather than a 10:12:15.

-Igs

On Tue, Jan 24, 2012 at 3:58 AM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > > We all know that the basis of meantone tonality is the contrasting major and minor
> > > triads, representing 4:5:6 and 10:12:15.
> >
> > I only agree with this if you mean something very specific by "basis
> > of." What exactly do you mean?
>
> What meaning would you agree with? It's probably that one.

The only way I'd agree with it is if you're claiming that meantone
tunes major chords to 4:5:6 and minor chords to 10:12:15, which is a
trivial statement. It doesn't sound like that's what you were saying.
I'm not sure how to evaluate the statement "major and minor triads
represent 4:5:6 and 10:12:15."

> > Using your operational definition, isn't everything in the field of
> > attraction of a simpler identity?
>
> Um...yes and no, I guess. What happens to HE when you really crank up s? Whether something is or isn't in something else's field of attraction depends largely on what we assume for s.

OK, but you said that you suspect various utonal chords don't sound
discordant if they're in the field of attraction of something simpler.
But isn't everything is in the field of attraction of something
simpler, except things which are already simple?

> > It's not at all clear what you mean by "how I hear 12-TET." Do you
> > mean that using your operational definition, if you were handed a
> > 12-TET minor chord, you'd retune it to 6:7:9 if you tried to maximize
> > the """""""concordance,""""""" placed within seven scare quotes, and
> > that this would also apply to a minor chord in 19-TET as well?
>
> Yeah. The 19-TET minor triad always sounded "wrong" to me, much more complex than the major triad; yet at the same time, the subminor triad as an approximation to 6:7:9 didn't sound like the proper foil to the major triad, since I can hear the dyads inside it are different and it's not the "inverse" of the major. But for instance in 21-ED2, the major and minor triads sound more evenly matched. In 12-TET if I wanted to adaptively tune 0-300-700, I'd tune it to a 6:7:9 rather than a 10:12:15.

I see. I'm not entirely sure if the word "minor" is entirely
applicable to every inverse of an otonal chord, but I think the
concept of shooting for intonational purity for a chord and its
inverse is a neat idea. I still haven't found a better one of these
than the 91/90-tempered 6:7:9 -> 10:13:15 one though.

-Mike

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

> > What meaning would you agree with? It's probably that one.
>
> The only way I'd agree with it is if you're claiming that meantone
> tunes major chords to 4:5:6 and minor chords to 10:12:15, which is a
> trivial statement. It doesn't sound like that's what you were saying.

It is, though. In meantone, a major triad is the same thing as a representation of 4:5:6 in the temperament; a minor triad is the same thing as a representation of 10:12:15 in the temperament.

> OK, but you said that you suspect various utonal chords don't sound
> discordant if they're in the field of attraction of something simpler.
> But isn't everything is in the field of attraction of something
> simpler, except things which are already simple?

Well, what things are "already simple"?

> I see. I'm not entirely sure if the word "minor" is entirely
> applicable to every inverse of an otonal chord, but I think the
> concept of shooting for intonational purity for a chord and its
> inverse is a neat idea. I still haven't found a better one of these
> than the 91/90-tempered 6:7:9 -> 10:13:15 one though.

I wouldn't say the word "major" is entirely applicable to every otonal chord, either. But if we buy that meantone tonality functions by contrasting otonal triads with their utonal counterparts to create tension and resolve, we can generalize that concept for application to other temperaments and other basis chords and see what happens. Maybe it's a red herring, this otonal/utonal pairing thing? Who knows?

-Igs

On Tue, Jan 24, 2012 at 4:40 AM, cityoftheasleep
<igliashon@...> wrote:
>
> > OK, but you said that you suspect various utonal chords don't sound
> > discordant if they're in the field of attraction of something simpler.
> > But isn't everything is in the field of attraction of something
> > simpler, except things which are already simple?
>
> Well, what things are "already simple"?

Using your operational definition, things which aren't "heard as"
something else are already simple. It seems like you were saying that
things are more concordant than their tuning would suggest because
you're "hearing them as" something simpler, but by your definition
everything is heard as something simpler except things which are
already concordant.

> > I see. I'm not entirely sure if the word "minor" is entirely
> > applicable to every inverse of an otonal chord, but I think the
> > concept of shooting for intonational purity for a chord and its
> > inverse is a neat idea. I still haven't found a better one of these
> > than the 91/90-tempered 6:7:9 -> 10:13:15 one though.
>
> I wouldn't say the word "major" is entirely applicable to every otonal chord, either. But if we buy that meantone tonality functions by contrasting otonal triads with their utonal counterparts to create tension and resolve, we can generalize that concept for application to other temperaments and other basis chords and see what happens. Maybe it's a red herring, this otonal/utonal pairing thing? Who knows?

Which of these do you think is more consonant?

http://soundcloud.com/mikebattagliamusic/consonance-example-4

http://soundcloud.com/mikebattagliamusic/consonance-example-7

-Mike

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

> Using your operational definition, things which aren't "heard as"
> something else are already simple. It seems like you were saying that
> things are more concordant than their tuning would suggest because
> you're "hearing them as" something simpler, but by your definition
> everything is heard as something simpler except things which are
> already concordant.

Right. It's based on the same principle as 301/299 sounding concordant because we hear it as a 3/2.

> Which of these do you think is more consonant?
>
> http://soundcloud.com/mikebattagliamusic/consonance-example-4
>
> http://soundcloud.com/mikebattagliamusic/consonance-example-7

Too close to call.

-Igs

On Tue, Jan 24, 2012 at 4:50 AM, cityoftheasleep
<igliashon@...> wrote:
>
> > Which of these do you think is more consonant?
> >
> > http://soundcloud.com/mikebattagliamusic/consonance-example-4
> >
> > http://soundcloud.com/mikebattagliamusic/consonance-example-7
>
> Too close to call.

XA was split on it: exactly half the folks polled said 4, and half the
folks polled said 7. The first is a 4-EDO diminished chord, voiced in
open sixths, and the second is two of those placed directly inside of
one another, so it's a stack of 7 450 cent intervals. However, to my
ears, the latter sounds less dissonant than the first, and apparently
half the folks polled agree. What didn't happen is that there was a
clear response that the latter was more dissonant, despite it having
even more harmonic data placed in a way that makes even less sense.
From my own, personal perspective, the evil diminishedness of the
first one vanishes for the second example, making it sound more spacey
and BPlike or what have you.

This sort of thing makes me wary to assign a psychoacoustic
explanation for something like minorness.

-Mike

I do not think we mean the same thing by "minor". To me, major and minor are qualities defined in opposition to each other, but unfortunately I don't know what "in opposition" means. I do think any chord can be "major" or "minor", it's only made one or the other by
means of contrast with something else.

Consider the case of Lemba[6] in 16-ED2, where if you take the 1-3-6 pattern and move it up and down the scale, you get "minor" triads representing 4:5:7 and "major" triads representing 1/1-13/10-11/6 (or are they representing 6:8:11? 7:9:13? 13:17:24? I haven't a clue). These two triad types contrast as effectively as anything, I think...but they are only related in this scale, there's not otonal/utonal juju going on. Rare are the scales where the same pattern of steps produces both an otonal chord and its utonal counterpart (essentially=tempered or not) in various positions...but does this even matter? I just don't know.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Jan 24, 2012 at 4:50 AM, cityoftheasleep
> <igliashon@...> wrote:
> >
> > > Which of these do you think is more consonant?
> > >
> > > http://soundcloud.com/mikebattagliamusic/consonance-example-4
> > >
> > > http://soundcloud.com/mikebattagliamusic/consonance-example-7
> >
> > Too close to call.
>
> XA was split on it: exactly half the folks polled said 4, and half the
> folks polled said 7. The first is a 4-EDO diminished chord, voiced in
> open sixths, and the second is two of those placed directly inside of
> one another, so it's a stack of 7 450 cent intervals. However, to my
> ears, the latter sounds less dissonant than the first, and apparently
> half the folks polled agree. What didn't happen is that there was a
> clear response that the latter was more dissonant, despite it having
> even more harmonic data placed in a way that makes even less sense.
> From my own, personal perspective, the evil diminishedness of the
> first one vanishes for the second example, making it sound more spacey
> and BPlike or what have you.
>
> This sort of thing makes me wary to assign a psychoacoustic
> explanation for something like minorness.
>
> -Mike
>

On Tue, Jan 24, 2012 at 5:20 AM, cityoftheasleep
<igliashon@...> wrote:
>
> I do not think we mean the same thing by "minor". To me, major and minor are qualities defined in opposition to each other, but unfortunately I don't know what "in opposition" means. I do think any chord can be "major" or "minor", it's only made one or the other by
> means of contrast with something else.
>
> Consider the case of Lemba[6] in 16-ED2, where if you take the 1-3-6 pattern and move it up and down the scale, you get "minor" triads representing 4:5:7 and "major" triads representing 1/1-13/10-11/6 (or are they representing 6:8:11? 7:9:13? 13:17:24? I haven't a clue). These two triad types contrast as effectively as anything, I think...but they are only related in this scale, there's not otonal/utonal juju going on. Rare are the scales where the same pattern of steps produces both an otonal chord and its utonal counterpart (essentially=tempered or not) in various positions...but does this even matter? I just don't know.

Oh, so you're talking about the same sort of thing that Carl is. Yes,
I agree with this and I like it a lot. Once you pick two sounds out of
the sea of chaos that perception normally is, and you crystallize them
in something concrete like a scale, it's rather easy for one to be
defined in a certain way in opposition to the other.

I still feel like the holy grail of this approach is to get 4:6:7 and
6:9:11 working together in a decently-sized scale. Maqamic/beatles was
cool, but not the best possible I think.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> We all know that the basis of meantone tonality is the contrasting major and minor triads, representing 4:5:6 and 10:12:15.

I don't know that. That's a simplified version of how it's been used, is all.

> Those of us searching for something that works like meantone, but differently, occasionally consider a triadic basis other than these two triads, but usually we only consider alternatives to the major triad and let the minor "sort itself out" as being maybe the utonal counterpart of the major triad. One problem with this is that the utonal counterparts of most triads more complex than 4:5:6 are much more discordant, at least if we go by the size of the numbers used to represent the utonal chords as a sequence of overtones. For instance, the utonal counterpart to 5:6:7 is 30:35:42, which should be fairly discordant.

"Should be" only if you assume this overtone-based measure of consonance is a good one.

> In practice, these utonal chords *aren't* discordant, and I suspect this is because many of them are in the "field of attraction" of a simpler identity.

I suspect the totally obvious--it's because the dyads are all the same, and ignoring that is a flawed model of chord consonance.

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

> XA was split on it: exactly half the folks polled said 4, and half the
> folks polled said 7. The first is a 4-EDO diminished chord, voiced in
> open sixths, and the second is two of those placed directly inside of
> one another, so it's a stack of 7 450 cent intervals. However, to my
> ears, the latter sounds less dissonant than the first, and apparently
> half the folks polled agree.

It's certainly less annoying than the first.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> > We all know that the basis of meantone tonality is the contrasting major and minor
> > triads, representing 4:5:6 and 10:12:15.
>
> I don't know that. That's a simplified version of how it's been used, is all.

What if I had said it like this: "the most basic component of meantone tonality is contrasting major and minor triads, representing 4:5:6 and 10:12:15"?

> > Those of us searching for something that works like meantone, but differently, occasionally consider a triadic basis other than these two triads, but usually we only consider alternatives to the major triad and let the minor "sort itself out" as being maybe the utonal counterpart of the major triad. One problem with this is that the utonal counterparts of most triads more complex than 4:5:6 are much more discordant, at least if we go by the size of the numbers used to represent the utonal chords as a sequence of overtones. For instance, the utonal counterpart to 5:6:7 is 30:35:42, which should be fairly discordant.
>
> "Should be" only if you assume this overtone-based measure of consonance is a good
> one.

Correct.

> I suspect the totally obvious--it's because the dyads are all the same, and ignoring that > is a flawed model of chord consonance.

Compare the 11-limit otonality to (some voicing of) its utonal inverse. Same dyads, same concordance? I believe the observation that utonal chords are in some way less concordant than otonal chords is one of the things that led to the formulation of harmonic entropy.

In any case, I'm probably mistaken in my hypothesis anyway. Most of the temperings I suggested involve rather large commas, and thus don't end up improving the concordance. If moving a complex utonal chord closer to some nearby simpler otonal chord does not increase the consonance, then something's wrong with either the model or my understanding of it, indicating an area deserving further work.

-Igs

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

> Oh, so you're talking about the same sort of thing that Carl is. Yes,
> I agree with this and I like it a lot. Once you pick two sounds out of
> the sea of chaos that perception normally is, and you crystallize them
> in something concrete like a scale, it's rather easy for one to be
> defined in a certain way in opposition to the other.

Yeah, the trick is finding the right two sounds. You are dead-on that we focus too much on otonal/utonal and not nearly enough on chords that share a step-pattern in the scale but contrast effectively with each other. In my Lemba[6] example, the otonal 4:5:7 chord is the "minor" one, and the ambiguous one is "major".

> I still feel like the holy grail of this approach is to get 4:6:7 and
> 6:9:11 working together in a decently-sized scale. Maqamic/beatles was
> cool, but not the best possible I think.

Betcha can't find a better one! You need to find a scale where 7/4 and 11/6 share an interval class, and with copious near-pure 3/2s. Generators that produce a good amount of near-pure 3/2s are 3/2, (3/2)^(1/2), (4/3)^(1/2), (4/3)^(1/3), (3/2)^(1/3), (4/3)^(1/4), and (3/2)^(1/4). Your holy grail is hidden among them somewhere, if it exists. Or am I leaving something out?

-Igs

On Tue, Jan 24, 2012 at 7:32 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > XA was split on it: exactly half the folks polled said 4, and half the
> > folks polled said 7. The first is a 4-EDO diminished chord, voiced in
> > open sixths, and the second is two of those placed directly inside of
> > one another, so it's a stack of 7 450 cent intervals. However, to my
> > ears, the latter sounds less dissonant than the first, and apparently
> > half the folks polled agree.
>
> It's certainly less annoying than the first.

Alright, but do you see what I'm saying? The first is made up of three
900 cent dyads, and the second is made up of seven 450 cent dyads. The
second, in other words, is made up of two copies of the first, placed
450 cents apart. And that makes the "annoyingness", at least for you,
go down.

-Mike

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

> Alright, but do you see what I'm saying? The first is made up of three
> 900 cent dyads, and the second is made up of seven 450 cent dyads. The
> second, in other words, is made up of two copies of the first, placed
> 450 cents apart. And that makes the "annoyingness", at least for you,
> go down.
>
> -Mike
>

It's been mentioned a number of times on this list that increasing noise and ambiguity does not always equal increasing dissonance, but can actually create an alternative "consonance". I believe Margo Schulter was the one who dubbed this "asonance".

On Wed, Jan 25, 2012 at 10:28 PM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Alright, but do you see what I'm saying? The first is made up of three
> > 900 cent dyads, and the second is made up of seven 450 cent dyads. The
> > second, in other words, is made up of two copies of the first, placed
> > 450 cents apart. And that makes the "annoyingness", at least for you,
> > go down.
> >
> > -Mike
> >
>
> It's been mentioned a number of times on this list that increasing noise and ambiguity does not always equal increasing dissonance, but can actually create an alternative "consonance". I believe Margo Schulter was the one who dubbed this "asonance".

In what sense do you mean "ambiguity" above? Ambiguity of what?

Can you link me to some posts on asonance?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Jan 25, 2012 at 10:28 PM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > Alright, but do you see what I'm saying? The first is made up of three
> > > 900 cent dyads, and the second is made up of seven 450 cent dyads. The
> > > second, in other words, is made up of two copies of the first, placed
> > > 450 cents apart. And that makes the "annoyingness", at least for you,
> > > go down.
> > >
> > > -Mike
> > >
> >
> > It's been mentioned a number of times on this list that increasing noise and ambiguity does not always equal increasing dissonance, but can actually create an alternative "consonance". I believe Margo Schulter was the one who dubbed this "asonance".
>
> In what sense do you mean "ambiguity" above? Ambiguity of what?
>
> Can you link me to some posts on asonance?
>
> -Mike
>

Assonance and isonance were both proposed by Margo Schulter- look for her posts on "metastable intervals".

"Ambiguity" can only refer to those elements of a sonority which can be clearly perceived or not, of course. The intervals constituting the sonority, in both relative size and sheer number; root tones (i.e. finding a tone to which to even subjectively attach "root" can be difficult with an ambiguous sonority); perceived tendencies of resolution.

Personally I think it is more sensible to speak of assonant, metastable, however you'd like to call it, structures rather than intervals (dyads).

The 12-tET tritone is considered a dissonance in isolation, but its use in jazz is clearly more "assonant", as part of vertical structures.