diatonic functionality

[JumpingJackFlash]

As discussed earlier, the tonic note in a supertonic minor seventh chord is definitely not stable.

WHAT? where must it turn in order to become stable? let's be concrete: the tonic pedal over which a series of harmonies pass over. it's not stable when 'ii' happens? Come on; 'definitely'? That's a reach, that isn't definining 'stable'.

If it's a pedal then yes, it's probably stable.
But otherwise, the minor seventh between root and seventh creates a dissonance which (in a tonal context) "wants to" resolve to a consonance (usually with the seventh moving down).

[sammy24]

jancivil-

I actually don't have a problem arguing semantics, as long as I know that's what I'm doing. But that wasn't the focus of the argument over here (at least I didn't think it was until it occurred to me that we had a major difference of opinion regarding the meaning of the words we were using.)

[jancivil]

well, the term 'semantics' has a pejorative sense that a lot of people take as its basic sense...

While I am in complete agreement here with JJF regarding 'tension belongs to context' it appears I don't agree with his definition of 'stable tone' as offered here, and as admitted to be no definition.
There is a context [eg., C in Dm7 moves to B in G or Em] but it's going to be hard to make the case of the seventh degree of a major or minor tonality as having that much pull or gravity itself, I think. At this point that seems to disagree some with the definition of 'tonality'.

He has objected strenuously to my use of 'tonal center' and 'tonic' before. If they are technically wrong, I think "the tonic is unstable _" is kind of a more salient technical point I don't acccept either.

[sammy24]

ha, well yes in this instance I meant it a bit pejoratively .

Regarding tension belonging to context, I wanted to mention that the idea of a central tone itself is obviously dependent upon context. The note B, for instance, can be any scale degree, only once a certain note is established as tonic will the B take on a role of one of the scale degrees. So that is what I meant way in the beginning that of course it depends on context.

In addition, IMO we could state that context plays a modifying role on the scale degree's expected movement, but not on its relative stability or instability. For example, Maj7 is relatively unstable, due to its half step distance from tonic. This instability is always there, and is the specific sound which allows the ear to identify maj7. Now, at its most basic (meaning, its most natural context), the ear would expect it to resolve to tonic. But a more complex context can modify this expectation, so that we no longer expect it to resolve at all, or so that we expect it to move elsewhere. But its unstable sound is still there, as that is what makes it maj7; I personally have yet to come across any context I can think of in which maj7 lacks that identifying quality that makes it maj7 (even as a descending chromatic passing tone from tonic to b7 in a mode that has b7 as its seventh degree). So long as I'm hearing the tonic in my head (as my central tone context), I hear maj7 in relation to it.

In a Dmi7 chord we expect the tonic to move down, because of the dissonant context. This context has modified our expectations regarding this most stable scale degree. But the sound is still the stable sound of tonic (to my ears).

Say I like the taste of vanilla ice cream better than chocolate. In the most basic context (all things being equal), the expectation would be for me to purchase vanilla rather than chocolate. However, in reality I may buy chocolate on occasion, say for variety, or because everyone else is buying chocolate. So the specific context has modified the expectation; nevertheless, it still tastes like chocolate.

But when it comes to learning the relative levels of stability and instability associated with the different scale degrees, I find it helpful for the student to have this most basic, "default", natural resolution in mind, in order to expedite the process of learning to hear the scale degree. Once attained, one can then hear the scale degrees in more complex contexts and still identify its relative stability and instability, which is the goal of relative pitch ear training (to identify the pitches). [and identifying pitches is not the be-all, end-all, the next step is analyzing the music, the contexts, etc., but first we must identify the pitches by ear correctly before we can embark upon analysis]

As far as "natural" or basic is concerned, we could argue from today till tomorrow what is basic or natural (some would say it's based on the overtone series as we discussed earlier], but I'd say that if we follow the development of Western music from simplicity to complexity, we can see what is most basic to the ear. It is logical to assume that the music developed in this fashion. (yes, there was music long before that; but this is an easily studied example of musical development where we can scientifically monitor the progression of development.) Similarly, children's music is so often a simple context in the major scale. Is this simply for the emotional effect, or because the music is less complex so it is easier for them to comprehend? I think it's the latter, mostly.

I was listening to some Mozart the other day on my commute, and then switched to the Wayne Shorter Quartet, and I wondered to myself what Mozart would have
thought if he heard that music. I think he possibly would have been incredibly intrigued, and kind of blown away. Certainly no one back then was playing that sort of music, nor could. Music has just gotten more and more sophisticated as time goes on.

[jancivil]

I'll try once more to show you exactly where you lose me:

Maj7 is relatively unstable, due to its half step distance from tonic. This instability is always there, and is the specific sound which allows the ear to identify maj7. Now, at its most basic (meaning, its most natural context), the ear would expect it to resolve to tonic.

this seeks to make a conditioned, contextual and cultural affect into 'natural' and 'basic'.

There is all sort of music that just sits on a major seventh chord as the most relaxed thing in the world. Pop music contexts. The demand from this idea, of its resolution is more complex, I think.

There is no "nature" at work here, there is conditioning. I agree with a number of things you say, but this is not a good line of argument. It's begging the question, if you understand that term, it's a form of circular argument.

[jancivil]

In a Dmi7 chord we expect the tonic to move down, because of the dissonant context. This context has modified our expectations regarding this most stable scale degree. But the sound is still the stable sound of tonic (to my ears).

so speak for yourself, there is no 'we' here. I do not find this true. The very word "dissonant" here is a sign of a received view, as though to make objective something that isn't.

Before I had this lingo to deal with, I never thought a Dm7 was a tense chord that had to do any such thing! I could sit there and dig it. There are a number of these things, intervals that are dissonant, vs others. Why is the minor third sounded at the same time more consonant than a minor seventh? Objectively, tell me about some physics! No, this is bullshit that is received out of the authority of a style asserted as superior, in a thrust towards cultural hegemony. Another 'perfect fourth needs to resolve'. No, there is a style that carries a certain expectation; this is not dealing with things objectively.

You're actually using the object 'D minor seventh' chord as it resides in a context as if it means something outside the context. As if its function as ii7 in C is its reality. That's just error-prone. You have these beliefs, and it's clear enough to me they are received and you're too ready to appeal to your sources for it as authority.

this illustrates the problem perfectly:

I'd say that if we follow the development of Western music from simplicity to complexity, we can see what is most basic to the ear.

That is a non-sequitur. You need to follow 'development of Western music to a point of complexity' to find 'what is most basic'. You wind up with utter nonsense.

[jancivil]

physically, the 'major seventh' is the third partial of the major third. it's not that complex if you look at it a certain way. it's the fifth partial of the perfect fifth. It seems to sort of vibrate nicely, all of this. take a good low fundamental and give it energy enough to generate the series: where is this need to resolve, really?

in this view, a major third is consonant. a 12 EDO major third on a piano. But it's 13.69¢ sharper than a fifth harmonic in the overtone series. What's so consonant about it now, objectively?


think of these intervals unbound by this restriction, which is at a certain point not a lot more than an artifice of language - "dissonance" - and find new 'consonances'. Conventions have their place, but subjective is not the new objective.

[sammy24]

I do hear what you are saying. But you could make the following case: continuing to sit on major 7, without resolving, is itself a context that changes the ear's expectation. When you first hear the maj7, maybe your ear does indeed expect it to resolve, but when it doesn't, then it no longer is so sure.

Certainly for a long time in classical music they made sure it resolved, consistently. You could say it was a matter of their conditioning. But maybe it's the other way around -- maybe conditioning is required to overcome the initial expectation, and in other cultures this conditioning was better developed.

As European music developed, you can literally map the loosening of dissonance rules, etc. ninths started to pop up, Imaj7 chords, and so on. The mere fact that they couldn't handle I major 7 chords (as a stable I chord) is surprising. Now we're quite fine with it .

Upon reflection, natural isn't a great choice of word. But I do think lack of tension is more "basic". I would say that from the human side of things, we love resolved tension, not just in music. So I think that's what makes stability more "basic" to most people.

Conditioning plays a role in music and everything else. But sometimes if certain themes keep occurring, it points to the fact that there are other forces pulling toward it than just conditioning. Look at how instability/stability plays a role in musical form, among other things. The types of melodies and harmonic progressions that most people think "sound good" generally seem to move from stable to unstable back to stable. So does a good story. Is happy ever after a conditioning, or would humans gravitate toward that naturally?

Do children love ice cream and candy because of conditioning, or because they just naturally love it? My personal experience would tell me it's the latter. I'm willing to bet a child on a deserted island with no one around will prefer ice cream to brussel sprouts.

And I think you can't take the humanity out of it, because so much of music (all?) is our perception and not the physical frequencies.

Then with conditioning, we can learn to accept horror movies, unresolved maj7's, and even brussel sprouts. And we may even learn to enjoy it.

I similarly think it is natural to be selfish, as babies are born basically completely selfish. Then with conditioning they can learn to become selfless. But there is a basic starting point.

[sammy24]

sorry I only saw your last two posts after I had already posted mine.

That is a non-sequitur. You need to follow 'development of Western music to a point of complexity' to find 'what is most basic'

You misunderstood me. I meant that we find a clear progression of increased complexity, you can therefore go back to the earlier music to see what is simple. Not to the complex music. sorry it wasn't written well, but let's not jump to accusations of making up nonsense.

As far as dissonance vs. consonance, I had no idea of your opinions on these matters. If I could only mix you and JJF we'd be in complete agreement!

But honestly I can't say I agree, at all. Yes, we were taught things, but like everything else I learned, I didn't just accept it without question.

You don't think a minor 9th sounds more dissonant than a major third?

Forget about the overtone series here. Just in listening to music, I don't need to read a book to hear the difference between a triad and a quartal or cluster voicing.
Let me ask you a question: it has been an accepted idea that ascending melody generally increases tension, descending releases (generally speaking, a million factors aside, all things being equal). Is this scientific? Maybe you disagree altogether. But so much of music is subjective!! Fact is, most people agree about these factors. If you hear it differently, then that's fine.
Maybe I should get upset when someone describes the sound of a tuba as a low brassy sound. I hear it as a high-pitched, squeaky flute-like sound. It's about perception, not science.

Btw I quote people whom I think know what they're talking about, and esp. when I myself agree with what they were saying.

[JumpingJackFlash]

I'm going to address several points in the one post:

There is a context [eg., C in Dm7 moves to B in G or Em] but it's going to be hard to make the case of the seventh degree of a major or minor tonality as having that much pull or gravity itself, I think.

This is another example of the influences of culture. People in the 18th century would have almost certainly regarded it as "needing to resolve", but in modern times, we accept such things as "stable" in their own right.

The note B, for instance, can be any scale degree, only once a certain note is established as tonic will the B take on a role of one of the scale degrees.

But this is the problem; just what exactly do you mean by "role of one of the scale degrees"?

Yes, in C major, the note B is often called the "leading note" or "leading tone", but that's just a name. It only functions as a leading note in certain contexts.

This instability is always there, and is the specific sound which allows the ear to identify maj7....
But the sound is still the stable sound of tonic (to my ears).

There seems to be a contradiction here. You first say that the sound is unstable because of tension between root and seventh (which is correct), but then you say that the sound of the tonic is stable? - So does it sound stable or unstable? - It can't be both because that's meaningless.

I don't think stable is the best word to use here.

I find it helpful for the student to have this most basic, "default", natural resolution in mind

I think we'll have to agree to disagree on this point.

if we follow the development of Western music from simplicity to complexity, we can see what is most basic to the ear. It is logical to assume that the music developed in this fashion.

I don't agree with this at all.
"what is basic to the ear" is entirely dependant on culture, it is not an absolute otherwise all music from all over the word and all throughout history would sound the same. But people at different times and in different countries hear things very differently.

Music has just gotten more and more sophisticated as time goes on.

I don't agree with this either, not without some sort of qualifier.
Firstly "sophisticated" is a subjective term. I don't find most of the music produced today to be sophisticated, quite the opposite in fact. It is also a loaded term that has connotations of being superior, but music today is not "better" than music from the past, it is just different.

Music is "sophisticated" in different ways. J. S. Bach for example was writing music that was much more sophisticated in terms of harmony and counterpoint that a lot of later composers did. There are some would even argue that nobody has yet equalled his mastery in this regard.

Later composers were concerned with different things. Classical composers with form, Romantic composers with emotion, and 20th Century composers with timbre (to use simplistic generalisations).

maybe conditioning is required to overcome the initial expectation

No, this is nonsense. Notes do not have an "initial expectation", the expectations are all dependant on culture.

The types of melodies and harmonic progressions that most people think "sound good"...

... is again dependant on culture.

Yes, we were taught things, but like everything else I learned, I didn't just accept it without question.

Culture isn't something you're actively "taught" though, it's much more subtle that that. You are exposed to it from birth (some would argue even before) - it becomes part of you without you even knowing it. It's not even conscious. Most people don't even realise there is any alternative (until much later in life).

[jancivil]

When you first hear the maj7, maybe your ear does indeed expect it to resolve, but when it doesn't, then it no longer is so sure.

Certainly for a long time in classical music they made sure it resolved, consistently. You could say it was a matter of their conditioning. But maybe it's the other way around -- maybe conditioning is required to overcome the initial expectation, and in other cultures this conditioning was better developed.

I'm going back to when I started playing with musical concepts, on my own. Probably the first thing I thought about a 'Major Seventh Chord' was 'this is that pretty chord', one I recognized from a kind of pop music context. In jazz, I noticed a lot of songs actually end with it that weren't really exploiting it. In fact it was a sign of finality!

I heard a lot of jazz in the home and not classical music. By the time I was learning anything on a [chordal instrument] guitar I was 14. I don't remember things with terrific fidelity of course, this is over forty years ago, but I can't get a sense of any time I thought of a Major/Major 7th as a particularly tense object that needed to do something, through its own tension. (Singing the interval, sure, it likes to go up, but it likes to go down to the fifth of the chord. You may not have time for it but that Raga Kalyan is instructive here. Both the tonic and the P5 are present throughout in the drone. The ^7 is the dominant tone of the raga. It does not mean 'go now to the tonic'. More typically the note above it is a grace to it.)

So, when you tell me it does, I have to say, that's you; I don't recognize it, it must not be true per se. Reading this, you could say I had different conditioning, but I don't think that changes your notion being a product of conditioning (and reinforced by language). I don't accept that "initial expectation", there isn't anything to be overcome.

I had not received views from books, or tutelage about this. I made things up by ear based on my experience with other people's songs. That whole classical world view, it hadn't any hold on me. By the time I got very involved with the theory, I had my own ideas of things.

[jancivil]

As far as dissonance vs. consonance, I had no idea of your opinions on these matters.

You don't think a minor 9th sounds more dissonant than a major third?

I don't need to read a book to hear the difference between a triad and a quartal or cluster voicing.

so, why is a perfect fourth, through itself, more dissonant than a major third? what you are consistently doing here is confounding the thing, through itself, with the thing in context of other things. if you require the latter: G as a perfect fourth below the C which is the root of the chord - Dissonant? Where is the dissonance in this, a major chord? What does it need to resolve to? Now perhaps you can begin to see the absurdity of your position.

I remember reading Frank Zappa say that one day he played a pop record he was excited about to his high school music teacher 'what is going on here that I like, that's different?' and the man showed him it was stacked perfect fourths. I remember my first theory class where the teacher illustrated the same thing. Past one octave. I like it. It doesn't occur to me to judge it as 'dissonant', it sounded and I liked it a lot as it is. You have a preconception, the P4 wants to resolve. You want it to out of your expectation, which is received and you accept that. It isn't true though. Yes, there is a difference between a quartal 'harmony' and tertial. You accept that the latter is more normal. This is prejudice. I think at the back of your mind you are tethered to these ideas, at least you are arguing their necessity.

the major seventh or minor ninth vertically has a certain tension, similar in quality as two notes a semitone apart sounding at the same time. physically it's going to oscillate a certain way. objectively 'dissonant' has a certain meaning. however the need to do anything with that is an artifice, an idea a person has, subjective.

[jancivil]

Certainly for a long time in classical music they made sure it resolved, consistently.

I have to admit I have little experience analyzing the music of the classical period, but JS Bach did not seem to require that per se.



in case you have any trouble identifying it, early on at ~6 seconds in... a feature, not a bug as they say

[jancivil]

Let me ask you a question: it has been an accepted idea that ascending melody generally increases tension, descending releases (generally speaking, a million factors aside, all things being equal). Is this scientific? Maybe you disagree altogether.

Why do you agree with that? Since you asked, I don't. There are ideas about certain ways to proceed owing to the intervals, I've seen that, but I never saw anyone say this. I don't know what's good about this idea. I'm not sure what's supposed to be meaningful. A B C D E, and E has to resolve up rather than down? Show me what's so compelling it pushes a million factors aside. I think I need context.

Fact is, most people agree about these factors.

THE SURVEY SAYS!

[sammy24]

You're totally missing my position here.

I don't think dissonance necessarily equates with a desire to resolve. Dissonance just as a certain sound to it. As I discuss later, it is humans who sometimes want or expect it to resolve.

You seemed to be arguing with the very notion that certain intervals are more dissonant than others. The greatest minds in music over the last few centuries beg to differ. Maybe that was not what you meant, but that's sure what it sounded like.

the major seventh or minor ninth vertically has a certain tension, similar in quality as two notes a semitone apart sounding at the same time.

Why is the minor third sounded at the same time more consonant than a minor seventh? Objectively, tell me about some physics!

Whatever, I hear your physics-based argument, but in all honesty, like I said earlier, music comes down to human perception. Amplitude isn't the ear factor in music, it's loudness that matters. Frequency isn't the factor that matters, it's pitch perception. When differences arise between the physics and the perception, perception is what wins out from the standpoint of making musical decisions.

I dunno about the physics of it, but I can tell you that just like a maj7 has, to quote you, a cerain tension, as does a m9 and a m2, I perceive a very similar effect frm a m7, just to a significantly lesser degree, as do two notes a M2 apart. There must be some ear-based reason why jazz orchestrators do not put the 2nd voice a whole step below the melody except for special effect. I mean, you don't hear that? And If physics doesn't seem to support it, who cares? Music is about human reaction and perception.

From a physics standpoint, OF COURSE a tone has no desire to resolve. The very connection of two or more consecutive tones into a meaningful whole is based upon human perception! Scientifically, it is just two unrelated frequencies.

One therefore cannot separate the human element. So yes, I absolutely agree with you - when I spoke of a scale degree having inherent characteristics, I certainly did not mean inherent literally. I mean from a human perspective.

Besides, M7 as a scale degree is not necessarily the same as M7 the harmonic interval. The concept of a central tone in muic means that the human listener can perceive the other tones in relation to a specific tone EVEN when the tonic is not currently being played, or sometimes without the tonic ever being played. So that means the listener has that central tone basis in his/her mind. That is man-made dissonance then. A flute playing the note G, unaccompanied, and heard by a listener based on context and perception as M7 of Ab, has no physical dissonance. But a human can perceive it as though the Ab were sounded against it.

Take away memory and perception, and you basically do not have music as we know it. Scale degrees, and scales themselves, are human-based and not scientific-based.

Since we are all humans here (I'm assuming), this doesn't pose a problem. And we can have a discussion about what is natural perception to humans.

I maintain that humans have certain natural perceptions regarding music that they are born with, and that has perhaps been strengthened by conditioning. Biologically, and possibly caused at least in part by our perceptions of the OT series. Not that it correlates 100% with the series, but that the OT series which pervades every musical note plays some role in our perception of central tones, consonance vs. dissonance, and more. (And these perceptions also can be eradicated through conditioning.) Our friend JJF believes it is all based purely on conditioning. Either way, though, we're conditioned to it, so if we want to make music typical of these styles, we had best resign ourselves to it. If we don't, that's another story.

I didn't get a chance to hear the Bach piece yet, but obviously I was talking in a general sense, there are exceptions to every rule. But resolving leading tone is a major component of the art of voice leading, and classical harmony. And for every exception I could find you a hundred examples where it does resolve, either directly or indirectly.