Yahoo Tuning Groups Ultimate Backup tuning Re: Explaining major 4:5:6 and minor 10:12:15 triads,Re:Beatings vs

"Marcel de Velde" wrote:

"That the minor 3rd is heard as a clouded major third sounds false to me."

Not the minor third, but the entire triad.

"And I'm not quite sure what you mean by that 10:12:15 takes more time to resolve
than 4:5:6. This sounds to me as if it implies that the consonance and character
difference of 10:12:15 and 4:5:6 is due to how long it takes our brain to
resolve it? (yet once it's resolved this information doesn't matter anymore
since it matters only how long it took to resolve it?)"

Take out the word consonance and this is basically right. The current neuroscience model — as I understand it from Martin Braun — is that we recognize tone complexes (vowel formants, chords) as harmonic structures by locking into a small set of intervals (3:2, 4:3, 5:4, 6:5, perhaps 7:6*). This is, ultimately, a missing fundamental model, in that, simple interval-by-simple interval it seeks to resolve a tone complex as a particular harmonic series fragment. Given a 10:12:15 triad, the mechanism would recognize the fifth first, which leads to an expectation of a 4:5:6 as the simplest harmonic series configuration of three tones bounded by a fifth. This expectation is not satisfied. Whether 10:12:15 is eventually recognized as a harmonic series segment or remains a collection of dyads is an open question. My guess is that there is amiguity here, and that context and register may play an important role, as well as all of the other psychoacoustic features in discussion.

"And that the 6:7:9 chord might take a bit longer to resolve than 4:5:6 and a
bit shorter to resolve than 10:12:15 and this gives it a character about
halfway between 4:5:6 and 10:12:15.
This makes no sense to me."

"Character" is this case is reduced to the length of time required to recognize, nothing more. 6:7:9 provides an interesting contrast to the other chords because the small minor third is within the critical band somewhat earlier than the 6:5, thus is more register dependent.

djw

_____
* I would add that I am personally more optimistic than this model. It seems entirely plausible to me that a wider variety of intervals can come into play, particularly when register is considered. e.g. tune up a pair of sine waves in 9:7s. You will find that the quality is highly depended upon register. With the lower tone above 660 Hz or so, thus entering in the typical range for 7th and 9th partials produced by male voices, it clearly becomes a consonance. But it is entirely possible that, with such intervals, other mechanisms are at exclusively work, especially combination tones. (The large sine-wave chords used by La Monte Young, for example, most plausibly depend on common difference tones.)

🔗Mike Battaglia <battaglia01@...>

On Thu, Jan 22, 2009 at 6:29 AM, Daniel Wolf <djwolf@...> wrote:
> "Marcel de Velde" wrote:
>
> "That the minor 3rd is heard as a clouded major third sounds false to me."
>
> Not the minor third, but the entire triad.
>
> "And I'm not quite sure what you mean by that 10:12:15 takes more time to
> resolve
> than 4:5:6. This sounds to me as if it implies that the consonance and
> character
> difference of 10:12:15 and 4:5:6 is due to how long it takes our brain to
> resolve it? (yet once it's resolved this information doesn't matter anymore
> since it matters only how long it took to resolve it?)"

I feel like this concept applies more to a 9/7 septimal major triad
than a minor triad. When I hear a supermajor triad, it definitely
sounds like a messed up major triad unless I'm REALLY listening
closely to it. A minor triad I tend to hear as a separate thing.

Also, if it's true that a minor chord sounds the way it does because
it's a "bastardized" major chord, then why don't sus4 chords sound
dissonant? They have a major second in them, which is probably more
dissonant than a major third, and the expectation of the third isn't
fulfilled in that chord either.

> Take out the word consonance and this is basically right. The current
> neuroscience model — as I understand it from Martin Braun — is that we
> recognize tone complexes (vowel formants, chords) as harmonic structures
> by locking into a small set of intervals (3:2, 4:3, 5:4, 6:5, perhaps
> 7:6*). This is, ultimately, a missing fundamental model, in that, simple
> interval-by-simple interval it seeks to resolve a tone complex as a
> particular harmonic series fragment.

I like this train of thought - where did you read about this? Can you
refer me to some literature on the subject?

> Given a 10:12:15 triad, the mechanism would recognize the fifth first, which leads to an expectation
> of a 4:5:6 as the simplest harmonic series configuration of three tones
> bounded by a fifth. This expectation is not satisfied. Whether 10:12:15
> is eventually recognized as a harmonic series segment or remains a
> collection of dyads is an open question. My guess is that there is
> amiguity here, and that context and register may play an important role,
> as well as all of the other psychoacoustic features in discussion.

I don't know if this idea has been substantially advanced, but I've
been throwing around the notion that there might be multiple
fundamentals in one chord that can be related to each other. Take a C
major 9 chord for example. That's kind of the same thing as a Gmaj
triad over a Cmaj triad (with an E minor in there somewhere) and I
somehow feel that I'm perceiving it as having fundamentals a fifth
apart or something. So in that context, a C minor would have a C
fundamental from the C and G, and then an Eb fundamental from the Eb
and the G. I think the two fundamentals interact and somehow give rise
to the full "character" of the chord. I could be wrong - from
rereading what I wrote, the idea has some holes in it, but I don't
think the Eb in a C minor chord is just discarded as "useless" - I
feel like the 5/4 between Eb and G is pretty strong and does something
to it. For a neutral triad in a low register, I could hear how the
third would completely jam up the works, but I feel like a minor triad
it runs a bit more smoothly.

-Mike

🔗Graham Breed <gbreed@...>

🔗caleb morgan <calebmrgn@...>

3/4, 1/1 4/3 16/9: say, in C: G,C,F,Bb?

that is, a simple chain of fairly consonant 4ths?

basically all jazz theory and early 20th century theory?

But Mike will answer for himself, no doubt, and with his own voice...

On Jan 23, 2009, at 7:10 AM, Graham Breed wrote:

> Mike Battaglia wrote:
>
>> Also, if it's true that a minor chord sounds the way it does because
>> it's a "bastardized" major chord, then why don't sus4 chords sound
>> dissonant? They have a major second in them, which is probably more
>> dissonant than a major third, and the expectation of the third isn't
>> fulfilled in that chord either.
>
> What theory are you working on where a sus4 isn't a dissonance?
>
>
>
> Graham
>
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🔗Mike Battaglia <battaglia01@...>

On Fri, Jan 23, 2009 at 7:10 AM, Graham Breed <gbreed@...> wrote:
> Mike Battaglia wrote:
>
>> Also, if it's true that a minor chord sounds the way it does because
>> it's a "bastardized" major chord, then why don't sus4 chords sound
>> dissonant? They have a major second in them, which is probably more
>> dissonant than a major third, and the expectation of the third isn't
>> fulfilled in that chord either.
>
> What theory are you working on where a sus4 isn't a dissonance?
>
> Graham

It doesn't sound all that dissonant. In certain common-practice
contexts, it is traditionally treated as a 'dissonance' in which the 4
resolves downward to the 3. However, even in those contexts, a minor
chord isn't treated as a 'dissonance' in which the minor 3 moves up to
a major 3 or something.

Even more so, sus chords can sound extremely consonant and in most
musical contexts outside of common practice harmony are treated that
way. Especially when upper extensions are added - Csus13 is often
voiced as a Bbmaj7 over C, and groups such as Earth, Wind and Fire
used those chords as consonances all of the time. You know that chord
- it's the "sun comes out and all of the birdies sing" chord. Far from
dissonant. That chord is often also used as a substitute for a V7 as
well, often sounding less dissonant than V7 in that context.

As caleb stated, modern modal theory, which is still developing but
uses nonetheless in a good amount of modern musical contexts,
generally acknowledges sus chords as having more functions than just a
delayed resolution to a major triad. The idea is that music can have
more than just 2 types of tonality to operate on: in addition to major
and minor, all of the modes in between and beyond can be used as
stable tonal centers that have their own functional harmonies and
expectations of how things will resolve. Rather than describing major
as "happy" and minor as "sad", or major as "consonant" and minor as
"dissonant", the modes are often treated in a spectrum ranging from
"brightest" to "darkest", or "most major" to "most minor", or
something like that. Lydian is the "brightest" diatonic mode, and
Locrian is the "darkest" (in basic modal theory, anyway).

In mixolydian mode, for example, a common chord progression would be
something like I / bVII IV / I. You can hear it as the bVII as a
IV/IV, and so it's sort of like a double plagal cadence if you want to
think of it that way. Functional harmonies like that exist in all 7 of
the diatonic modes (even Locrian, which is a bit harder to work with),
as well as all 7 of the modes of the melodic minor, harmonic minor,
and harmonic major scales. Often chords are "borrowed" from other
modes (just like borrowed chords work in the common practice system)
to create a more heightened emotional response. A sus13 chord, such as
Bbmaj7 over C, is often used to flesh out the Mixolydian mode in such
a fashion, and doesn't sound dissonant to my ears, but rather
"colorful".

-Mike

🔗Kalle Aho <kalleaho@...>

🔗Graham Breed <gbreed@...>

Mike Battaglia wrote:
> On Fri, Jan 23, 2009 at 7:10 AM, Graham Breed <gbreed@...> wrote:
>> Mike Battaglia wrote:
>>
>>> Also, if it's true that a minor chord sounds the way it does because
>>> it's a "bastardized" major chord, then why don't sus4 chords sound
>>> dissonant? They have a major second in them, which is probably more
>>> dissonant than a major third, and the expectation of the third isn't
>>> fulfilled in that chord either.
>> What theory are you working on where a sus4 isn't a dissonance?
> > It doesn't sound all that dissonant. In certain common-practice
> contexts, it is traditionally treated as a 'dissonance' in which the 4
> resolves downward to the 3. However, even in those contexts, a minor
> chord isn't treated as a 'dissonance' in which the minor 3 moves up to
> a major 3 or something.

Right, not "all that" dissonant, but ... dissonant. About what you'd expect for a 9-limit otonality in fact. What paradox were you seeing in that original paragraph?

In what context is a second not considered a dissonance in common practice harmony? The dissonance resolving down to the 3 is pretty much the definition of "suspension". But we know that the "sus" prefix is used outside of that context these days. The sus4 chord is one of the archetypal dissonances, and probably the reason fourths in general (in the bass) got classed as dissonant.

But yes, getting to the point, a minor chord isn't treated as a dissonance. It fails to be a major triad, and isn't an otonality, and so it wasn't used to end a piece in some styles. You could call this a weak requirement of resolution. But still, basically it's a consonance. So if a minor triad counts as a consonance why shouldn't the slightly more dissonant sus4 also be a consonance by analogy? Failing to be major obviously isn't enough to make something dissonant.

Here's a point that doesn't fit in anywhere so I'll mention it here: quartal harmony works well in (12 note) equal temperament. The fourths are much better tuned than the thirds. So for 20th Century music, with an equally tempered standard, it isn't so surprising to see the fourths asserting themselves. Do you have a near-JI context to compare 10:12:15 with 6:8:9?

> Even more so, sus chords can sound extremely consonant and in most
> musical contexts outside of common practice harmony are treated that
> way. Especially when upper extensions are added - Csus13 is often
> voiced as a Bbmaj7 over C, and groups such as Earth, Wind and Fire
> used those chords as consonances all of the time. You know that chord
> - it's the "sun comes out and all of the birdies sing" chord. Far from
> dissonant. That chord is often also used as a substitute for a V7 as
> well, often sounding less dissonant than V7 in that context.

You're being very liberal with your "most musical contexts" there. I may know this chord intuitively but I'm afraid I don't get the reference. I tried a Google search and an Oasis song came top, with no sus chords. But at least, this isn't a sus4 chord, so I don't know what it says about sus4 chords.

Less dissonant than a V7, maybe. But by small-ratio theories, a V7 (when tuned as extended 5-limit) is a dissonance. At least, clearly more dissonant than the 5-limit triads. It includes the same major second that makes a sus4 chord dissonant. It may not be treated as a dissonance, but in that sense what dissonances are there in equal temperament?

> As caleb stated, modern modal theory, which is still developing but
> uses nonetheless in a good amount of modern musical contexts,
> generally acknowledges sus chords as having more functions than just a
> delayed resolution to a major triad. The idea is that music can have
> more than just 2 types of tonality to operate on: in addition to major
> and minor, all of the modes in between and beyond can be used as
> stable tonal centers that have their own functional harmonies and
> expectations of how things will resolve. Rather than describing major
> as "happy" and minor as "sad", or major as "consonant" and minor as
> "dissonant", the modes are often treated in a spectrum ranging from
> "brightest" to "darkest", or "most major" to "most minor", or
> something like that. Lydian is the "brightest" diatonic mode, and
> Locrian is the "darkest" (in basic modal theory, anyway).

Who would describe minor as "dissonant"? Well, maybe you have.

This is an interesting point, so I'll digress. Jazz and blues aren't very hot on minor -- chords or keys. You can interpret this as saying jazz doesn't like otonalities. So if I put my "jazz ears" on I can hear a sus4 chord as consonant, along with the well-tuned 4:5:6 and the other 9-limit otonal triad 6:7:9. In this context that 10:12:15 minor triad is a muddy interloper. The 6:8:9 sus4 is brighter and more forceful. It likes to resolve down to major, but it certainly doesn't want to resolve to minor.

Then I put my "baroque ears" on and find the 5-limit triads to be different shades of the same smooth harmony. The minor's a bit weaker but still a point of rest. In this context the sus4 is plainly dissonant because it's rougher and wants to resolve (still by preference to major rather than minor).

I think this does support two kinds of consonance -- one about minimizing roughness and the other about finding simple otonal ratios.

> In mixolydian mode, for example, a common chord progression would be
> something like I / bVII IV / I. You can hear it as the bVII as a
> IV/IV, and so it's sort of like a double plagal cadence if you want to
> think of it that way. Functional harmonies like that exist in all 7 of
> the diatonic modes (even Locrian, which is a bit harder to work with),
> as well as all 7 of the modes of the melodic minor, harmonic minor,
> and harmonic major scales. Often chords are "borrowed" from other
> modes (just like borrowed chords work in the common practice system)
> to create a more heightened emotional response. A sus13 chord, such as
> Bbmaj7 over C, is often used to flesh out the Mixolydian mode in such
> a fashion, and doesn't sound dissonant to my ears, but rather
> "colorful".

Isn't "colorful" the new word for "dissonant"?

Graham

🔗Chris Vaisvil <chrisvaisvil@...>

for what it is worth I use and hear sus chords as inversions of quintal
harmony.

I find that stacked 4ths and 5ths are "mood neutral" - they deny either
major or minor.
As an extension then - you have this beginning of a cluster of major 2nds -
and quite frankly I find stacked major 2nds acceptable in some contexts as
well. Stacked minor 2nds are pretty rough though.

On Fri, Jan 23, 2009 at 10:42 PM, Graham Breed <gbreed@...> wrote:

> Mike Battaglia wrote:
> > On Fri, Jan 23, 2009 at 7:10 AM, Graham Breed <gbreed@...<gbreed%40gmail.com>>
> wrote:
> >> Mike Battaglia wrote:
> >>
> >>> Also, if it's true that a minor chord sounds the way it does because
> >>> it's a "bastardized" major chord, then why don't sus4 chords sound
> >>> dissonant? They have a major second in them, which is probably more
> >>> dissonant than a major third, and the expectation of the third isn't
> >>> fulfilled in that chord either.
> >> What theory are you working on where a sus4 isn't a dissonance?
> >
> > It doesn't sound all that dissonant. In certain common-practice
> > contexts, it is traditionally treated as a 'dissonance' in which the 4
> > resolves downward to the 3. However, even in those contexts, a minor
> > chord isn't treated as a 'dissonance' in which the minor 3 moves up to
> > a major 3 or something.
>
> Right, not "all that" dissonant, but ... dissonant. About
> what you'd expect for a 9-limit otonality in fact. What
> paradox were you seeing in that original paragraph?
>
> In what context is a second not considered a dissonance in
> common practice harmony? The dissonance resolving down to
> the 3 is pretty much the definition of "suspension". But we
> know that the "sus" prefix is used outside of that context
> these days. The sus4 chord is one of the archetypal
> dissonances, and probably the reason fourths in general (in
> the bass) got classed as dissonant.
>
> But yes, getting to the point, a minor chord isn't treated
> as a dissonance. It fails to be a major triad, and isn't an
> otonality, and so it wasn't used to end a piece in some
> styles. You could call this a weak requirement of
> resolution. But still, basically it's a consonance. So if
> a minor triad counts as a consonance why shouldn't the
> slightly more dissonant sus4 also be a consonance by
> analogy? Failing to be major obviously isn't enough to make
> something dissonant.
>
> Here's a point that doesn't fit in anywhere so I'll mention
> it here: quartal harmony works well in (12 note) equal
> temperament. The fourths are much better tuned than the
> thirds. So for 20th Century music, with an equally tempered
> standard, it isn't so surprising to see the fourths
> asserting themselves. Do you have a near-JI context to
> compare 10:12:15 with 6:8:9?
>
> > Even more so, sus chords can sound extremely consonant and in most
> > musical contexts outside of common practice harmony are treated that
> > way. Especially when upper extensions are added - Csus13 is often
> > voiced as a Bbmaj7 over C, and groups such as Earth, Wind and Fire
> > used those chords as consonances all of the time. You know that chord
> > - it's the "sun comes out and all of the birdies sing" chord. Far from
> > dissonant. That chord is often also used as a substitute for a V7 as
> > well, often sounding less dissonant than V7 in that context.
>
> You're being very liberal with your "most musical contexts"
> there. I may know this chord intuitively but I'm afraid I
> don't get the reference. I tried a Google search and an
> Oasis song came top, with no sus chords. But at least, this
> isn't a sus4 chord, so I don't know what it says about sus4
> chords.
>
> Less dissonant than a V7, maybe. But by small-ratio
> theories, a V7 (when tuned as extended 5-limit) is a
> dissonance. At least, clearly more dissonant than the
> 5-limit triads. It includes the same major second that
> makes a sus4 chord dissonant. It may not be treated as a
> dissonance, but in that sense what dissonances are there in
> equal temperament?
>
> > As caleb stated, modern modal theory, which is still developing but
> > uses nonetheless in a good amount of modern musical contexts,
> > generally acknowledges sus chords as having more functions than just a
> > delayed resolution to a major triad. The idea is that music can have
> > more than just 2 types of tonality to operate on: in addition to major
> > and minor, all of the modes in between and beyond can be used as
> > stable tonal centers that have their own functional harmonies and
> > expectations of how things will resolve. Rather than describing major
> > as "happy" and minor as "sad", or major as "consonant" and minor as
> > "dissonant", the modes are often treated in a spectrum ranging from
> > "brightest" to "darkest", or "most major" to "most minor", or
> > something like that. Lydian is the "brightest" diatonic mode, and
> > Locrian is the "darkest" (in basic modal theory, anyway).
>
> Who would describe minor as "dissonant"? Well, maybe you have.
>
> This is an interesting point, so I'll digress. Jazz and
> blues aren't very hot on minor -- chords or keys. You can
> interpret this as saying jazz doesn't like otonalities. So
> if I put my "jazz ears" on I can hear a sus4 chord as
> consonant, along with the well-tuned 4:5:6 and the other
> 9-limit otonal triad 6:7:9. In this context that 10:12:15
> minor triad is a muddy interloper. The 6:8:9 sus4 is
> brighter and more forceful. It likes to resolve down to
> major, but it certainly doesn't want to resolve to minor.
>
> Then I put my "baroque ears" on and find the 5-limit triads
> to be different shades of the same smooth harmony. The
> minor's a bit weaker but still a point of rest. In this
> context the sus4 is plainly dissonant because it's rougher
> and wants to resolve (still by preference to major rather
> than minor).
>
> I think this does support two kinds of consonance -- one
> about minimizing roughness and the other about finding
> simple otonal ratios.
>
> > In mixolydian mode, for example, a common chord progression would be
> > something like I / bVII IV / I. You can hear it as the bVII as a
> > IV/IV, and so it's sort of like a double plagal cadence if you want to
> > think of it that way. Functional harmonies like that exist in all 7 of
> > the diatonic modes (even Locrian, which is a bit harder to work with),
> > as well as all 7 of the modes of the melodic minor, harmonic minor,
> > and harmonic major scales. Often chords are "borrowed" from other
> > modes (just like borrowed chords work in the common practice system)
> > to create a more heightened emotional response. A sus13 chord, such as
> > Bbmaj7 over C, is often used to flesh out the Mixolydian mode in such
> > a fashion, and doesn't sound dissonant to my ears, but rather
> > "colorful".
>
> Isn't "colorful" the new word for "dissonant"?
>
> Graham
>
>

Re: Explaining major 4:5:6 and minor 10:12:15 triads,Re:Beatings vs

🔗Kraig Grady <kraiggrady@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Daniel Wolf <djwolf@...>

🔗Daniel Wolf <djwolf@...>

🔗Mike Battaglia <battaglia01@...>

🔗Graham Breed <gbreed@...>

🔗caleb morgan <calebmrgn@...>

🔗Mike Battaglia <battaglia01@...>

🔗Kalle Aho <kalleaho@...>

🔗Graham Breed <gbreed@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Kraig Grady <kraiggrady@...>