diatonic functionality

[boobai]

i got some answers from a jazz teacher here and other forums.
the tonal tendencies are derived from the natural physical overtones/harmonics.
http://upload.wikimedia.org/wikipedia/e ... ervals.png
that's really connected to psychoacoustics and how our brain perceives tones.
the unstable tones (relative to C) tend to resolve toward the stable ones. (1-3-5-8).
perfect fourth is an exception cause it's half a tone from major third and a tone from perfect fifth. it's kinda 'loaded' with instability (maybe i got it wrongl).

here's a good answer i got from emusictheory forum:

A couple of things:

1. Some authors name the Tonic, Subdominant, and Dominant scale degrees as the "Tonal" degrees.
2. These same authors call the other degrees the "Modal" degrees (as they determine whether the mode is major or minor, or "come from" the major or minor mode as it were".
3. These same authors also say things like "double tonal degrees" when doubling notes in chords, however, these are broad generalities and rarely borne out in actual music.

A "more informed" but still broad generalization is the following:
1. The scale consists of "Tonic tones" and "Tendency tones" (or similar words). Tendency tones have a tendency to move toward a tonic tone.
2. Tonic tones are notes of the Tonic triad and considered stable. 1, 3, and 5, with 1 of course being the absolute most stable.
3. Tendency tones tend to (so maybe I guess there's an automatic disclaimer built in because it doesn't say they HAVE to go, they just have a "tendency" to!) move towards the Tonic degrees. Most specifically:

7-8 (1)
6-5
4-3
2-3
2-1 ("stronger" resolution)

The problem is, this is not necessarily borne out in actual music. That's because, aside from plainchant, most music IS written with harmony in mind (at least an obviously large body of music that people tend to be interested in writing, performing, etc.).

So it's difficult to list a "hierarchy" of tones because it really depends on what you're trying to point out about them.

Furthermore, a harmony can negate these aspects of a tone.

For example, theory students have it drilled into their heads - DO NOT DOUBLE THE LEADING TONE.

What they don't tell you is, the 7th scale degree isn't *always* functioning as a leading tone! It may be quite practical to double the 5th of a iii chord when it is in first inversion. Additionally, the 7th of a Imaj7 chord is the 7th scale degree, but as a chordal 7th it's supposed to go DOWN! (you still don't double an "active" note like this, but my point is it's negating the "normal" tendency of the tone).

So what we should probably say is, tones "often" go to certain places, unless they're found in the context of X, Y, and Z. In other words, there are a lot of exceptions!

I think it's a good idea not to get "locked in" to things like this. It's basically a "general observation" of music, rather than a "guide to writing good music".


edit:
also found this book:
http://www.khaldea.com/rudhyar/mt/mt_c8p2.shtml

very interesting!

[BertKoor]

Another thing you might like to read, is the BBCode guide on how to make pretty links and include pictures in your posts

[sammy24]

the rule, more accurately, is to not double the leading tone in a V or vii dim chord. but this does not necessarily apply in other instances, as you mentioned.
As far as the tendencies of where tones naturally want to go, tonally speaking:
1 and 3 are resting tones in major. 4 naturally wants to resolve down to 3, and 7 wants to go up to 8.
2 can go either direction because there is a whole step on either side, same with 6. And finally, 5 wants to resolve down a fifth to 1.
Yes obviously this does not mean that tones always move in these ways only. These are just the natural, tonal characteristics of these tones, and yes, context makes a difference. the most direct application is harmony, where for instance a dominant to tonic clearly reflects three of the above - mentioned motions, 4-3, 7-8, and 5-1.
The most important thing about this is to spend time listening to the tones in this fashion, and singing them. Knowing the tonal characteristics intellectually is not the point; the point is to HEAR these characteristics, and become more and more aware of them.

[JumpingJackFlash]

1 and 3 are resting tones in major...

1 is not a resting tone in a supertonic minor seventh chord, nor a Vsus4.
3 is not a resting tone in a subdominant major seventh chord....
There are many other exceptions to your generalisations too. The key thing is the context.

As jancivil said, it is an oversimplification.

[sammy24]

Definitely context is the most important thing, I agree.
But actually, I kinda disagree about what happens to 1 in a Iimi7 chord that you gave as an example. I would say that 1 still retains its inherent character of being a resting tone, and tonic. Just there are other scale degrees occurring at the same time that are active, most importantly 4. 2 and 6 are also active. So when 3 out of the 4 tones are active, the overall sound is active. But 1 is not changing into an active tone, it is still a resting tone, but in an active chord. There is obviously one more factor, which is that in this chord, a dissonant interval is created between 2 and 1, a minor seventh. So THAT is what creates the desire for 1 to move down. But tonally, that 1 does not want or need to move anywhere.

So yes, context plays a role. And whether or not a tone wants to move somewhere else depends on additional factors, mostly harmonic intervals and dissonance. But there is an inherent quality within each scale degree in a key that does not change.

To bring it out a little more clearly: There are (at least) two major factors that make a tone "active". One is the inherent tonal character, which is what this thread is about. The other is dissonance created by harmonic intervals. Either one by itself is enough to create the tension that makes a tone want to resolve, or has an unstable feeling. For example, in a IImin chord, 4 is NOT dissonant as far as intervals go -- it is a consonant minor third above 2. So why does it sound so active? It's because of the inherent tonal character of 4, that is unstable (has tension) and wants to resolve to 3. (And it doesn't have to actually resolve, but the point is that it sounds like it wants to resolve, in other words you are expecting it to resolve).

So you might say it's a matter of semantics here, but I am of the opinion that it's important to understand the difference, i.e. what is causing the tension, because it sounds different! A tone that wants to resolve because of tonal reasons sounds different than a tone that wants to resolve because of harmonic dissonance. What do I mean? I mean that a listener can tell just by listening, with some experience, what is causing the tension. A person who spends $100,000 to repair their house after a natural disaster and someone who puts out $100,000 toward a new business venture are both spending $100,000 of their own money. That much is the same. But the two situations feel completely different, even in terms of how they feel about spending that $.
So to that end, I am using the terms resting and active to refer solely to the tonal characteristics. It is then possible for an inherently active tone to be in a context in which it doesn't really need to resolve (7 in a Imaj7 in jazz), or a resting tone to be in a context where it does need to resolve (like 1 in a Iimi7). A resting tone that needs to resolve because of harmonic dissonance sounds different than an inherently active tone that needs to resolve because of its inherent qualities. Yes they both want to resolve, but for very different reasons.

Same situation with a Vsus4, 1 is an inherently resting tone, 5 is active and wants to resolve to 1, 2 is active as well. Overall, therefore, the chord sounds active because of the 2 active tones. And furthermore, the dissonant interval between 5 and 1, as well as between 1 and 2, causes the 1 to want to resolve. But 1 still sounds like resting tonic from the tonal aspect of things; and when it resolves to 7, the situation now flips -- it is consonant from an interval standpoint, and sounds as though it has resolved, but on the other hand has now turned into an active leading tone from a tonal perspective. And THAT is why after it resolves to 7, the notes STILL want to resolve somewhere. Active 7 wants to go to 1, 5 to 1, and 2 to either 1 or 3. Even though all the harmonic intervals are consonant, the tones still want to move because of their tonal characters.

Same with IVmaj7 - 4 is active, 6 is active, 1 is restng, and 3 is resting. Overall it sounds active, mostly because of 4 which is so active. When multiple tones are played together, their tonal characteristics sort of fight with each other (when you have both restng and active together), and the end result either sounds basically resting, if the resting tones win out, or basically active. Most of the time, active wins out. This is the case on a IVmaj7, it sounds active overall, even though it contains some resting tones. Additionally, as far as dissonance goes, a dissonant interval is created between 4 and 3 that causes tension. So again, we find 3 wanting to resolve, but NOT because of tonal character, rather because of dissonance.

Tones do not lose their basic tonal qualities no matter the context. There may be other factors involved, obviously, that are very important. But the tonal qualities remain notwithstanding.

In a IIImin chord, for instance, there is no harmonic dissonance. 3 is inherently tonally resting, 5 is active, and 7 is active. But since 3 is so strongly and definitively resting, the overall effect is resting. 3 and 4 are the most important tones as far as active and resting is concerned. If a chord has 3, it will generally be resting no matter what, that is unless 4 is there too. 4 trumps even 3 and makes ithe overall chord sound active. So 3 and 7 together with no 4, 3 "wins out", in that overall it sounds resting.

But let's take a look at 7 in this context -- there is no dissonance, and the overall chord is resting. Yet composers of the tonal era do not end compositions on a III chord. Why not? Because yes, overall it is a resting chord, but it is not fully resting, and this is mostly because of 7, which still retains its active tonal quality even in this context. How else to explain why a IIImi does not sound completely at rest?

One more important example: Even in a tonic triad, the most resting chord known to man, there is an inherently active tone, 5. Overall, with 1 and 3 there too, the chord sounds resting. Also, all the harmonic intervals are consonant. But why do composers end compositions so often by omitting 5? Is this coincidence?
It is because 1 and 3 are inherently completely at rest, but 5 has active tonal qualities, and even though in this context there is not much tension, the tonal qualities of 5 are still present enough that keeping 5 in the final chord slightly undermines the completely resting feeling that the composer desired at the completion if the piece. You don't need to omit 5, but if you want a completely resting feeling, only 1 and 3 or just 1 alone will accomplish that.

When multiple scale degrees are mixed together, they don't transform each other into something new; 1 does not morph into an active tone in a IImi7 chord; f it did, you would no longer be able to tell it was 1. The way we can identify scale degrees is by their tonal characteristics (i.e. resting and active), and we can still pick up on these qualities no matter the overall context. Rather, the combination of active and resting can combine into an overall resting, or overall active sound, even though the chord at the same time contains tones whose inherent quality may contradict that of the overall chord sound. And finally, harmonic dissonance between the tones is yet a another major factor that may cause a desire for resolution. but that's like saying: inherently active tones do not need the assistance of other factors to want to resolve. 4 and 7, for example, have inherent tension. On the other hand, inherently resting tones like 1 and 3 need outside factors to force resolution. Being part of an active chord is one factor, but that alone won't make 1 and 3 themselves want to resolve. Dissonant harmonic intervals will, however, as we discussed. But you can tell that it is not 1 or 3 themselves that sound like they want to resolve, it is 1 or 3 being played against another note or notes that create a dissonance.

It is the dissonant interval that wants to resolve, not the scale degree.

[JumpingJackFlash]

Definitely context is the most important thing, I agree.

Glad we cleared that up.
Oh no, wait...

There are (at least) two major factors that make a tone "active". One is the inherent tonal character, which is what this thread is about. The other is dissonance created by harmonic intervals.

I don't agree with this notion of "inherent tonal character". The only note which I would say might fit into this category is the leading note which (in many but not all cases) "wants to" resolve to the tonic (but even this is dependant on context as discussed earlier).

The other notes however do not have any inherent tendencies of their own outside of a harmonic context. What determines "active" or "resting" notes is not their relationship to the key, but their relationship to the harmony. - The note C is completely at rest in a chord of C major, but active in a chord of D minor (for example) - that is, it has a definite "tendency".

Despite what the OP said, the note F (for example) simply does not have any inherent tendency to "want to" resolve down to E (or to any other note for that matter).

Well, I suppose you could argue that it does have a very, very small tendency to do so (mainly because of the semitone gap), but this is insignificant compared to the harmonic tendencies present.

F-E on its own does not sound like a resolution to me, nor does F to any other note sound like the avoidance of such. It could do in a certain context, but not in and of itself.

why do composers end compositions so often by omitting 5? Is this coincidence?

No. It's usually because of voice leading - the desire not to have parallel fifths when going from V7 to I for example. There are other reasons too of course, but the idea that the fifth is an active tone in a tonic chord is nonsense.

It is the dissonant interval that wants to resolve, not the scale degree.

Absolutely.

[boobai]

do these functions also work in a minor scale or in modal structures? cause 1 in major scale is 3 in the relative minor, and if we talk parallel (Cmaj and Cmin) then the whole interval structure is different...

[sammy24]

boobai- I will reply in a separate post.

Music has more than one thing going on a time. Just because harmony is very important in the kind of music we're talking about, so too is form, style, rhythm, counterpoint, and other factors as well. We are not disagreeing here about how important harmony is in making musical decisions.

As far as the idea of tonal character is concerned, may I make a few points:

1. If it is true regarding the leading tone, then it shows that the concept is real. The leading tone is just the easiest one to hear. You yourself agreed about 4 as well. But i definitely wouldn't agree that it is insignificant.

2. Here's why I think it may get overlooked, to the point that we could even be having this discussion about whether it exists. It's because it's just an intellectual explanation of the way we hear music. Most people ignore this, because they just never think about it. How is that as a child, you can hear a melody, and memorize it? Do you remember the actual pitches? Unless you have perfect pitch, then no. And you can sing it in any key, because you remember the actual melody, not the pitches.
Well maybe you are remembering the melodic intervals? If you spend some time thinking about it, you will realize that learning the distance of melodic intervals (i.e. being able to sing, say perfect fourths, in any context) is significantly harder than just learning to hear from a tonic. With some ear training, you can learn to immediately identify any note from a given tonic. When you do this, you are automatically recognizing the tonal character I'm talking about. That "sound" of, say, 4, that we are describing as an active sound, is just a verbal description of what 4 sounds like. If you already recognize 4, then you are recognizing this character, whether you know it or not. If you did not recognize this, at least subconsciously, then you would not hear it as 4 -- maybe it's 1? The whole concept of tonal music is based on the idea that some notes are more important than others, from a tonal perspective.

Let me be more clear -- this is simply a discussion of tonality. Tonality is an extremely powerful and significant factor in tonal music, hence the name tonal music. See the discussions on tonality in Bert Ligon's Jazz Theory Resources Part 1 ( I think Chapter 3) as well as in Ron Gorow's Hearng and Writing Music.

You can't have tonality without tonal character of each scale degree. The very definition of tonality is that one note is central, aka more resting, than all the others. The composition as a whole leads back to tonic, because it is the resting, central tone. Now, if all the tones were equally resting, then we wouldn't hear one as being the tonic. They would all be the tonic. And the leading tone is the most obvious example - even someone with no musical education will guess the next note.

I would make the case that tonality is the most significant aspect of tonal music. It is the basis for how the melodies go, how harmony works. Interval analysis, whether it be melodic or harmonic, and voice leading, is all tremendously important, but all secondary to tonality, in terms of the way the music sounds to us. If I write a classical piece filled with parallel fifths, bad voice leading, awkward rhythms, etc., it can still retain the basic sound of tonal music if the melodies and harmonies follow these natural tonal tendencies.

If you are someone who is able to immediately identify the notes he is heard, in any composition, improvisation, or context, then great, you are able to naturally hear this way, whether you are aware of it or not. But for most people who have to work at it, understanding how the ear works is the key to unlocking their musical potential. There is absolutely a character to every note from a tonic that can be heard and immediately identified, with practice. When I say character, I mean that you can literally feel this tonal tension of each note, it is not simply an intellectual process of determining melodic interval from tonic. b6 sounds a certain way, ( and #5 has its own character), as does 2, 6. Each tone has a certain quality about it in relation to a tonic that can become as obvious as whether you are listening to a saxophone or a string section. It is a "sound".

You can say, "no, that's just the distance from tonic you are recognizing". Well that's basically the same exact thing! It is the distance from tonic and its placement somewhere in the scale that gives it its own unique character.

Anyway, whether aware of it or not, it is THIS skill that professional jazz musicians excel at so much. There are many other skills like being amazing at rhythm, but at its heart, being "amazing" at tonality is the most fundamental skill required if you're going to play well off the top if your head.

l can tell you that Dick Grove, one of the most highly respected composers and arrangers in LA in the mid twentieth century, taught over 20,000 students and was a very influential music educator, uses this idea as the very cornerstone of his teachings, and considers it one of the biggest aspects lacking in many music education programs. You can study music for twenty years and still not know anything, if you can't hear it, in an intuitive and natural way.
He himself said the example I brought about composers omitting the fifth to prove that 5 is an active tone. Now, you can feel free to disagree with him if you'd like, but this was someone with over 55 years experience as a professional and an extremely well- respected educator on understanding music, so his opinion should not be summarily discarded.
On a personal note, I can say that everything about how I relate to music changed for me from the first day of his classes onward, and I learned to do things I never thought I'd be able to. And like I said, this is the cornerstone of his teaching method. The success thousands of his students saw in the areas ear training and improvisation based on this method would seem to in and of itself a strong indicator of the strength and validity of his musical conception.

[jancivil]

Definitely context is the most important thing, I agree.

Glad we cleared that up.
Oh no, wait...

There are (at least) two major factors that make a tone "active". One is the inherent tonal character, which is what this thread is about. The other is dissonance created by harmonic intervals.

I don't agree with this notion of "inherent tonal character". The only note which I would say might fit into this category is the leading note which (in many but not all cases) "wants to" resolve to the tonic (but even this is dependant on context as discussed earlier).

there is a terrific amount of verbiage here trying to justify this 'inherent tonal' business. The concept 'tonal' itself = context. it's all about context, and the long post about relating to a tonic as a foundation is in agreement here.

even 'if' that seventh has that tendency, in a 'scale', that might be cultural. there are ragas where it's a subdominant/plateau, we're happy to dwell here. musical principles out of context? it's problematic to assign very much meaning here.

I said before, 'a tone's tendency' gets confounded with harmonic context in the first place, in the OP. The whole notion of that C major scale is tied to convention.

I'm seeing phenomena extrapolated in order to form truisms, but they aren't true enough to be formulated as such.

[JumpingJackFlash]

I would make the case that tonality is the most significant aspect of tonal music.

Of course it is! - That's pretty much how it's defined.

But tonality comes from harmony based on the circle of fifths, with progressions of chords leading to the tonic. V is the most active, and I the most at rest. It is the chords we are talking about here, NOT the actual pitches (unless they're used in a way that implies a certain harmony).

It's true that (for example), in a tonal context, the subdominant note might have a certain "character" (if you like). What I am disagreeing with is the idea that it has an inherent tendency to move to the mediant.

So yes, all your lengthy paragraphs about people recognising a note in relation to the tonic is true. That's not what we're talking about. It's true regardless of what note comes after it.

[sammy24]

boobai-
Yes the concepts are still true in minor or modal music. We only talked about the major scale degree tonal qualities. There are also all the others-- b2, b3, b5, b6, b7, and their enharmonics, #1, #2, etc. Each has its own sound. We can generalize that the sound of all of them is active, and chromatic, meaning they sound "out of the key". By that I mean out of the major key. They might be diatonic to the scale they're in.

Remember-- to hear these, first you need to know and hear which note is tonic.
If you switch from c major to a minor, c is no longer tonic. A is. So 4 in C major, F, is not 4 in a minor, it is b6. F in context to an a tonic has the same sound as Ab in relation to a c tonic.

This concept really makes things simpler. C is tonic, 1, whether you're in C major or C minor or C lydian. And the note C has the same resting quality in each of them. So too, B the leading tone or 7 has same tonal quality whether in major or harmonic or melodic minor. So if you just learn the sound of the scale degrees, then you won't have trouble learning new modes like phrygian, etc.

The only tricky tone is b3. It sounds resting in the context of minor, in fact it replaces 3 as the most resting and definitive tone in the scale. Nevertheless, in a major scale context, b3 is a chromatic active tone just like the other chromatc tones like b6 etc. (an example: a b13 in a dominant chord, like Dmi9 - G7b9b13 - Cmaj9. That scale degree goes 3, b3, 2. In that context, b3 sounds active moving toward 2).

However, b3 is still inherently not really fully resting. Classical composers in the earlier days would finish even a minor piece with a major chord. Why? Because major is more fully resting, and free from tension, based on the overtone series. If you listen closely to a low C note, you can actually hear the 4th overtone (5th partial), 3. So when b3 is played above a tone, there is inherent contradiction, because the b3 tone is fighting/competing if you will, with 3, which is not actually being played but can be heard as an overtone. This fight between the overtone 3 and the note b3 causes the tension we know of as minor. If you practice, you can literally hear these two tones "going at it". So major is more free of tension than minor.

In a way, the sounds of modes and minor are even more obvious than major. The sound of b2 is an immediate effect. Once you know the sound of b2, you'll be able to hear it in phrygian, locrian, phrygian natural 6, mixolydianb9b13, mixolydianb9, and more. Those are other modes from other scales, btw, like modes of melodic minor or harmonic minor, etc.

There are many scales used in modern music. @30 that are used with frequency. So it'd be hard to learn every scale's sound from scratch. Instead, once you know the sound of all 17 scale degrees ( 7 major plus 5 chromatic and their enharmonics), you'll easily be able to learn whatever scale you desire.

Also - In minor or modes, certain things may slightly change-- for example, take 6. In major, it is surrounded by a whole step on both sides. In miixolydian, it is only a half step away from b7. So it has a bit more pull toward b7. But the note 6 still retains a certain quality that is the same regardless of scale.

One more important point-- in minor, 4 is NOT a half step from b3, it is surrounded by a whole step on both sides. Nevertheless, it STILL retains the active quality we talked about. G dominant chords resolve to C minor all the time--- that's 4 going to b3. 4 and 7 still want to resolve, whether in major or minor.

Btw, in terms of resting and active, downward motion is associated with releasing tension, upward increases, all things being equal. So that may account for 2 often going to 1 rather than up to 3.

My advice-- learn solfege!! Associate these tonal characters with the solfege syllables, and then start singing what you hear, what you play. The more you sing, the better you will hear, and the better musician you will become.

[sammy24]

Recognizing the notes in relation to tonic is what is most significant.

But In terms of where notes want to move, that is just a result of these inherent qualities. Since 4 is active, and it's right next to 3 (halfstep), that's why it has a tendency to move to 3.

Since 3 is inherently resting, it has no desire or tendency to move anywhere. Obviously it still moves forward toward the next part of the music.

Since 7 is active, and a halfstep from tonic, it has a strong tendency to move to tonic.

2 and 6 are both inherently active sounding/ they have tension, but being surrounded by whole steps in the major scale (which is closely cnnected to the overtone series), they don't give you a hint where they're gonna move. But they do sound like they want to move someplace.

5 also inherently has some tension, and because of the relationships in the overtone series, wants to resolve to tonic. So-Do. It is the most basic sound in tonal music, and is one of the primary ways that a specific tonality is defined ( what makes you hear a certain tone as tonic).

So in these instances, the inherent quality of each scale degree and where they sound like they want to move can be thought of as one and the same.

As far as where a tone will actually move, yes that is based on context. But just because a G7 moves to A min (most basic deceptive progression) or Ab, at the time the G7 was played it still sounded like it wanted to go to C.

Also, chords are nothing more than multiple pitches or scale degrees played at once. So when chords "want" to resolve someplace, that is always because of the pitches themselves that make up the chord.

G7b13#11b9#9 = nothing more than each pitch wanting to move in the most natural way. the root (scale degree 5), wants to go to 1, the third (7) wants to go to 1, the seventh (4), wants to go to 3, the b13, (b3) wants to go to 2, the #11 (#1) wants to go to 2, the b9 (b6) wants to go to 5, and the #9 (#6) wants to go to 7. So the chord resolves to a Cmaj9 and all the pitches are happy. Chords are not truly things in and of themselves,even though sometimes we think of them that way, they are just more than one pitch at a time. Each pitch wants to resolve naturally, and by naturally we mean based on the inherent characteristics associated with tonality and the overtone series.

[sammy24]

It is the chords we are talking about here, NOT the actual pitches

This is the notion I'm disagreeing with, in a nutshell.

[JumpingJackFlash]

Since 3 is inherently resting, it has no desire or tendency to move anywhere.

This is only true in certain contexts.
It is false just as many times as it is true.

2 and 6 are both inherently active sounding/ they have tension,

Nonsense. Notes do not have tension by themselves. It depends on the intervals that they create with other notes.

Also, chords are nothing more than multiple pitches or scale degrees played at once. So when chords "want" to resolve someplace, that is always because of the pitches themselves that make up the chord.

Again no, it's all about the intervals involved.
Probably the most obvious example is F-B, the augmented 4th naturally found in V7 that wants to resolve outwards to E-C. The tension comes from the interval, and the resolution occurs because you're moving from a dissonance to a consonance. By themselves (out of context), the individual notes of F and B do not have anywhere near the same tendency.

G7b13#11b9#9 = nothing more than each pitch wanting to move in the most natural way. the root (scale degree 5), wants to go to 1, the third (7) wants to go to 1, the seventh (4), wants to go to 3, the b13, (b3) wants to go to 2, the #11 (#1) wants to go to 2, the b9 (b6) wants to go to 5, and the #9 (#6) wants to go to 7. So the chord resolves to a Cmaj9 and all the pitches are happy.

This might be good voice leading, but it's got nothing to do with the "inherent desire" of each note (which doesn't exist).

Chords are not truly things in and of themselves

Neither are individual pitches.

Each pitch wants to resolve naturally, and by naturally we mean based on the inherent characteristics associated with tonality and the overtone series.

Sorry, but this is just nonsense.

[Tricky-Loops]

Each pitch wants to resolve naturally, and by naturally we mean based on the inherent characteristics associated with tonality and the overtone series.

No, that isn't true. You always need some heat or a solvent to resolve the pitch...