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Auggie Doggie
11-06-2002, 10:13 AM
From reading so many posts around here, and responding in my typical long-head fashion, I find myself repeatedly making reference to 'harmonic function' and using Roman numerals to illustrate my points.

Being a little slow on the uptake due to illness and Comtrex, it finally dawned on me that the term 'harmonic function' may have little meaning to many users here. So, I will start this thread in an effort to explain the concept.

For this brief discourse, I will limit this particular post to functions within MAJOR KEYS ONLY (and in this instance, C major by virtue of its simplicity). If needed, future posts may delve into other areas.

_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_


Most players first get introduced to the Algebraic system of chord notation via the I IV V used in the 12-bar blues progression. The Roman numerals indicate the chords built from the scale degree of the same number:


C=1=I
D=2=ii
E=3=iii
F=4=IV
G=5=V
A=6=vi
B=7=(blank)*

* more on this shortly



I: I represents the TONIC chord. It is the harmony that is ultimately resolved to in a major key. Since it defined the "tonality", it is called the "tonic". (notice that the two words derive from the same root; etymology and nomenclature can be fun!) It is upper case, indicating a MAJOR chord. C E G


ii: The ii is called the SUPERTONIC; super meaning 'above' and the 'tonic' part was described above. The ii uses lower case, indicating a MINOR chord. It is also the relative minor of the IV chord. D F A


iii: The iii is called the MEDIANT. I have been given several explanations for that particular name choice, but I'll relay the one that makes the most sense. The word mediant essentially means 'middle', and the mediant tone happens to be in the middle of the tonic and dominant (more on this shortly) when ascending through a major scale. (C d E f G) The 'E' is the mediant in C major. The iii chord is MINOR. E G B


IV: The IV is called the SUBDOMINANT. This name, although it does make sense, can be a bit misleading. The reason for the confusion is that the dominant (again, more on this shortly) of any given tone is found a perfect fifth (7 half steps) above that note. In the key of C, the tonic (C) is the dominant of the 'subdominant' (F). So, the F chord here is not dominant; it is actually dominated by the tonic. The subdominant is one scale step below (aka "sub") the dominant tone (in this example, G is the dominant). So, you can think of 'subdominant' as simply being the scale tone below the dominant, or you can consider it as the tone that is dominated by the tonic. This chord is major. F A C

V: The V is called the DOMINANT (finally!). This tone is dominant because of the physics involved in the overtone series; it's the first (and therefore loudest) overtone apart from the tonic's octave overtone. Over the years, the word 'dominant' has been somewhat misused via convention. Since the dominant chord is so often a 7th chord, all major triads with a b7 are described as 'dominant 7ths'. However, the FUNCTION of a dominant can only be exerted by a major triad (7ths and other extensions may be added so long as the tones of the major triad are left intact; *EDIT* a rootless 9th chord substitution is also applicable*end edit*) that is 3 1/2 steps (a perfect fifth) above the tonic chord. "Secondary dominants" are major triads (again, extensions acceptable as per above) that resolve to a chord OTHER THAN the tonic. In other words, they temporarily 'tonicize' another tone/chord. The dominant chord is ripe with tension that resolves perfectly to the tonic. It is the simplest and most direct way to firmly establish the tonality of a piece of music. As mentioned above, the dominant chord is MAJOR. G B D (F)

vi: The vi is called the SUBMEDIANT. Recall for a moment the rationale for the naming of the iii (mediant). The submediant falls between the tonic and the dominant when DESCENDING. ('descending' implies going downward; 'sub' means below). The submediant is more commonly referred to as the relative minor (ie A minor is relative to C major). There is more to the relative minor concept which I shall adress shortly. As stated, the submediant is a MINOR chord. A C E

vii: The seventh scale degree is called the LEADING TONE, as it is a half step below the tonic, and it pulls very strongly toward the tonic. In terms of harmonic function (and this may very easily become a point of contention for some of the guys here--bear in mind that there are conflicting views about this, and I am giving the perspective that I personally have), there IS NO "vii chord" in a major key. Why, you ask? Well, there is a certain 'pecking order' of harmonic tones in terms of their importance to the character and function of a particular chord (root, fifth, third, 7th, 9th, 11th, 13th). In this case, the 'vii chord' would be a diminished triad or a m7b5 (aka 'half diminished). A diminished chord lacks a perfect fifth, which makes it unstable. In the key of C, this chord is B D F (A). But remember the emphasis and power of the dominant chord, and consider its spelling (in C, it's G B D F).The 3rd, 5th, and 7th of the dominant chord are now the root, 3rd and 5th of this 'vii chord'. If you make this 'vii chord' a seventh chord (that sounds confusing, but if you think about it, it should make sense), then you add an A note. Going back to the dominant chord, adding an A note would simply be adding a 9th. So, this 'vii chord' is nothing more than the 3rd, 5th, 7th, and 9th of the dominant 9th chord, but without the root. With 4 harmonic tones of the dominant chord at play, the ear is pulled toward the dominant harmony, even though the root is missing (hell, it's still got 80% of the notes intact). Thus, from my point of view, the 'vii chord' in a major key is nothing more than a 'rootless dominant 9th chord'. Anyway, as mentioned above, if you want to label it as a 'vii chord', this chord will be diminished. B D F (A)





Still following? Good.


OK, back to this relative minor concept (as it ties in to related keys). If you recall, the vi chord (submediant) is the relative minor of the tonic (I) chord. It is located a minor third below the tonic, and the key signatures of a major key and its relative minor are identical.

There were two other minor chords above: the ii and the iii. The ii chord (supertonic) is actually the relative minor of the IV (subdominant), and the iii (mediant) is the relative minor of the V (dominant). In all cases, the relative minor is a minor third below its relative major, and shares its key signature.

If you are familiar with the circle of fifths (if anyone has a picture of it, posting it in this thread would be a welcomed act), you will know that the keys C and F have 6 of their 7 tones in common, and that C and G have 6 of their 7 tones in common. This large number of common tones makes them closely 'related' keys. In this case, the keys F and G are close relatives of the key of C. Also, since those two tones (F and G, IV and V respectively) each find their relative minors in the key of C (Dm and Em, ii and iii respectively), those minor keys are ALSO closely related to the key of C. While this may all seem like overkill for this post, it is vital information when it comes time to understand modulations, key changes, and 'borrowed' chords.

(The 'vii chord' is left out of this dichotomy, which is more support for my belief that the 'vii chord' does not exist as a harmony with its own function--it has no 'partner')



Sorry for the verbosity, but I wanted to be somewhat thorough.



I hope I didn't have any typos or other mindless mistakes...I'm either too lazy or too cocky to proofread this post.

:p

thamiam
11-06-2002, 10:21 AM
Originally posted by Auggie Doggie
If you are familiar with the circle of fifths (if anyone has a picture of it, posting it in this thread would be a welcomed act),

Ask and ye shall receive.

http://www.music-manuals.com/circle%20of%20fifths.gif

evan_02
11-06-2002, 10:25 AM
question:
say you play a song in a non-major tonality, for example, F lydian, do you still think of Fmaj7 as a subdominant or does it become the tonic? so does this mean that Cmaj7 would be the dominant?
it makes sense to me to call the Fmaj7 the tonic, because thats the "home base" of the lydian sound, if I still think of Cmaj7 as the tonic then I tend to resolve to it, which destroys my precious lydian.
can you clear this up for me, please?

thamiam
11-06-2002, 10:40 AM
This is exactly the kind of thing that was causing confusion over in the Modes & Scales thread.

Remember, the explanations Auggie Doggie gave above were specifically for the MAJOR scale. While it is true that the scale built on the fourth degree of the major scale has a Lydian tonality, it is still possible (and often desirable) to play a song in Lydian tonality.

The Fmaj7#4 is your tonic. The "dominant" of that scale would be the scale built on the fifth degree.
Tonic - F G A B C D E F
"Dominant" - C D E F G A B C

Dominant is in quotes because it is a bad word in non0major or minor tonalities. But the resolution from a Cmaj7 (the fifth degree) to the Tonic Fmaj7#4 will sound almost as strong as the resolution from G7 to Cmaj7 in a major tonality.

Modes (and therefore, dominant, subdominant, median, etc... chords) can be built from any scale. In it's simplest form, it is a matter of building chords from every other note (in a 7 note +octave scale), from every degree in that scale. The V-I resolution will sound progressively less "inevitable" as you vary from the major scale, but will still exist.

Try mapping out the modes and chords for strange scales to get a better idea. Learn the modes for the harmonic minor, spanish scales, etc...

evan_02
11-06-2002, 10:45 AM
Originally posted by thamiam


Try mapping out the modes and chords for strange scales to get a better idea. Learn the modes for the harmonic minor, spanish scales, etc...
do the names tonic, supertonic, mediant, etc...always stick? it seems silly to call a b7 a leading tone, because based on Auggie Doggie's definition, it's not.

thamiam
11-06-2002, 10:49 AM
I know the names of the modes don't stick (the 2nd mode of the minor scale is not a Dorian), but I don't know about the degree names. I'll look around the web and see what I come up with.

evan_02
11-06-2002, 10:54 AM
Originally posted by Auggie Doggie

vii: The seventh scale degree is called the LEADING TONE, as it is a half step below the tonic, and it pulls very strongly toward the tonic. In terms of harmonic function (and this may very easily become a point of contention for some of the guys here--bear in mind that there are conflicting views about this, and I am giving the perspective that I personally have), there IS NO "vii chord" in a major key.
do you think the locrian mode exists? (i'm not being a wiseass, i'm just curious what you think)

Auggie Doggie
11-06-2002, 10:54 AM
Originally posted by evan_02

do the names tonic, supertonic, mediant, etc...always stick? it seems silly to call a b7 a leading tone, because based on Auggie Doggie's definition, it's not.


The b7 is NOT the 'leading tone'. The leading tone is the note a MAJOR 7th above the tonic, or one half step below.

The b7 is much more common in usage than the maj7, which is why "7" is typically used to designate the flat 7. If I screwed that up somewhere, I apologize. (guess I'm gonna half to proofread, damnit) But of course, that goes to show how some aspects of music theory have become a little ambiguous due to convention. Anyway, whenever the major 7th is used in a chord, it is always designated as "maj7", whereas a chord with the flat 7 is simply called a "7".


Also, the b7 DOES have a functional name: it's called the SUBtonic. But that goes beyond the bounds that I was trying to maintain. (it's common in minor keys)

thamiam
11-06-2002, 10:57 AM
OK, just found evidence from Outside Shore (Marc Sabatella) that the names dominant, subdominant, etc... are valid for major and minor scales. This leads me to believe that they are valid for all 7 note scales.

I have no idea what the conventions are for pentatonic, whole tone, or other non-7 note scales.

thamiam
11-06-2002, 11:01 AM
Originally posted by Auggie Doggie

Also, the b7 DOES have a functional name: it's called the SUBtonic. But that goes beyond the bounds that I was trying to maintain. (it's common in minor keys)

Hmmm...maybe the info I found was wrong. I for one would definitely be interested in going "beyond the bounds:, if you have that information.

Great posts, btw. Very valuable to have you contributing here. Thanks.

Auggie Doggie
11-06-2002, 11:04 AM
Originally posted by evan_02

do you think the locrian mode exists? (i'm not being a wiseass, i'm just curious what you think)


I do believe that the locrian mode exists; however, because of its lack of a perfect fifth as well as other potent chord tones in relation to the root, it's extremely unstable. To my ears, much like the 'vii chord', the locrian mode sounds like an extended dominant mode.


Just consider the small number of pieces written in locrian. There's a reason that it's rare: it's practicially devoid of any tonality of its own. After all, how exactly does one resolve to a diminished chord? Without resolution, the piece can never come to rest (aka 'unstable!!!!!!'). It's certainly an effective 'effect', but it lacks many of the basic qualities that establish a tonality. (since this thread is geared toward tonal music, I hesitate to introduce concepts of atonality or serial music in order to harmonically 'justify' this bizarre residue of the 12-tone system we are dealing with)

Good question though. I hope my evasion of a decent answer suffices. :D

thamiam
11-06-2002, 11:13 AM
Originally posted by Auggie Doggie
(since this thread is geared toward tonal music, I hesitate to introduce concepts of atonality or serial music in order to harmonically 'justify' this bizarre residue of the 12-tone system we are dealing with)


Yes please, for heaven's sake leave Schoenberg out of this before we all go mad!!! ;)

Auggie Doggie
11-06-2002, 11:17 AM
Originally posted by thamiam


I have no idea what the conventions are for pentatonic, whole tone, or other non-7 note scales.


Well, since we're dealing with harmonic function in tonal music (currently with a focus on major keys), those other scales don't quite fit in.

Let's take C major pentatonic for instance...



You can certainly (and most likely would) retain the labels for the same notes.

C=I
D=ii
E=iii
G=V
A=vi

The other harmonies (IV and 'vii') would be implicit.

However, if you were to COMPLETELY limit yourself to ONLY the notes in that scale, and attempt to construct harmonies by stacking thirds, the results are unusual.


I=C E A (A minor?!?!)

ii=D G C (Gsus?!?! not really a 'chord', it's a suspension)

iii= E A C (A minor again?!?! can't have 2 functions for the same chord in the same setting!)

V= G C E (C major?!?! the old 'tonic' harmony as the 'dominant'?)

vi= A D G (Dsus?!?! again, not a 'chord')

So, you can't stack thirds, and the entire system is out the window.




Whole tone:

C D E F# G# A#

all chords would be augmented, and wouldn't make much sense




So, in order for the basic concepts of harmonic function to apply, you need to adhere to major/minor/modal scales. Outside of that, you need to construct your harmonies in a non-tertial way.

There are clusters (harmonies built by stacking seconds), and there is quartal harmony (stacked 4ths---quintal harmony is really quartal harmony inverted). But again, those venture far outside the 'box'. Fun stuff to play around with, though!

Auggie Doggie
11-06-2002, 11:18 AM
Originally posted by thamiam


Yes please, for heaven's sake leave Schoenberg out of this before we all go mad!!! ;)


What do you mean "before"?


:D

Dave Regio
11-06-2002, 11:24 AM
Originally posted by evan_02
question:
say you play a song in a non-major tonality, for example, F lydian, do you still think of Fmaj7 as a subdominant or does it become the tonic? so does this mean that Cmaj7 would be the dominant?
it makes sense to me to call the Fmaj7 the tonic, because thats the "home base" of the lydian sound, if I still think of Cmaj7 as the tonic then I tend to resolve to it, which destroys my precious lydian.
can you clear this up for me, please?

I would just see it as a Fmaj7 chord, treat it as a I chord and play Lydian over that. As I am learning to improvise, I find myself playing the #11 to lead into the 5th, whether the "correct" scale is major or lydian.

even if it was a IV chord, you'd still assume the C7 as your V chord (as a secondary dominant). You can then put a iimin7 before the V7, which is your Gmin7.

After all that babble, I just convinced myself to assume the Fmaj7 as a I chord even if you're playing a Lydian scale.

thamiam
11-06-2002, 11:33 AM
One thing Dave just pointed out, I wanted to highlight.

Although the dominant chord in Lydian tonality would naturally by a major 7 chord, it is common usage to make just about all dominant chords resolving to the tonic a dominant 7th, regardless of tonality.

Auggie Doggie
11-06-2002, 11:45 AM
Originally posted by evan_02
question:
say you play a song in a non-major tonality, for example, F lydian, do you still think of Fmaj7 as a subdominant or does it become the tonic? so does this mean that Cmaj7 would be the dominant?


Remeber that the function of a dominant (or secondary dominant) is only exerted by a MAJOR TRIAD (extensions allowable, and of course the 'rootless 9th' substitution works too) located a perfect fifth above the tonic (or temporary tonic, however you want to look at it). So, a simple C major chord would serve just fine as your dominant. If you want to use 7ths, you could choose the b7 or the maj7 variety. In the b7 case (your garden variety 7th chord), the 7th will fall a half step to the 3rd of your tonic (Bb->A). This is a strong resolution, even though it would detract briefly from your established modal sound (this is neither good nor bad; it just 'is'), but it would be restored the instant you resolved to that #11. If you use Cmaj7, the maj7 note (B) can remain unchanged and serve as the #11 of your tonic, or it can rise a half step to the fifth of the tonic (depending on your voice-leading and how your ear perceives the movement of the notes)


it makes sense to me to call the Fmaj7 the tonic, because thats the "home base" of the lydian sound, if I still think of Cmaj7 as the tonic then I tend to resolve to it, which destroys my precious lydian.
can you clear this up for me, please?


If you think of the Cmaj7 as the tonic, then to establish and reinforce its status as such, you would need to register that harmony as tonic via a cadence that uses all 7 notes of your parent scale and none others (F-G-C(maj7), Fmaj7-G7-C(maj7), etc). Doing so would leave no doubt as to what your tonic was.

But that is what you DON'T want to do, so you would simply have to avoid any cadence that resolves to C. Of course, this is where modes get tricky, because they lack the 'pull' of the harmonies toward the tonic that the major/minor system has. Keep in mind that 'borrowed chords' become quite useful in modal settings, and substituting a few harmonies from the key of F or D minor(while always using a #11 voicing for your F chords instead of simple triads) can make your modality much more apparent.

So, in short, if you want to preserve your lydian sound, don't resolve to the C (the tonic of the parent major scale); instead, use the C chord(s) as dominants and avoid the G7 like the plague.

J the D
11-06-2002, 12:07 PM
Originally posted by Auggie Doggie


Just consider the small number of pieces written in locrian. There's a reason that it's rare: it's practicially devoid of any tonality of its own.

Now how come you say this in this particular thread but when I said pretty much the same thing in another thread you started throwing songs out to demonstrate the use of this mode?

Auggie Doggie
11-06-2002, 12:14 PM
Originally posted by J the D


Now how come you say this in this particular thread but when I said pretty much the same thing in another thread you started throwing songs out to demonstrate the use of this mode?


In the other thread we were discussing the phrygian mode in particular. In this thread (at this point in time) the discussion concerns the locrian mode. They both share the b2, but the locrian lacks a perfect fifth, which is what sparked several posts in this thread. The phrygian mode, however, not only contains the perfect fifth, it also has a long and rich history of usage in many types of music. (Can't say that about locrian, though-use of it is about as common as hen's teeth)

J the D
11-06-2002, 03:13 PM
Originally posted by Auggie Doggie



In the other thread we were discussing the phrygian mode in particular. In this thread (at this point in time) the discussion concerns the locrian mode. They both share the b2, but the locrian lacks a perfect fifth, which is what sparked several posts in this thread. The phrygian mode, however, not only contains the perfect fifth, it also has a long and rich history of usage in many types of music. (Can't say that about locrian, though-use of it is about as common as hen's teeth)

What I said was, "Modes starting on the other notes (3 or E natural and 7 or B natural) have an initial half step from 1 to 2 in them which does not sound good to our Western Ear and are rarely used."

I was talking about both modes even if you weren't. Maybe that's part of the miscommunication we had.

WattsUrizen
11-07-2002, 07:12 PM
The Phrygian is a strange one. Because of the flattened second degree, the sixth degree can tend to function as a dominant.

Auggie Doggie
11-08-2002, 02:39 PM
Originally posted by Anomandaris
The Phrygian is a strange one. Because of the flattened second degree, the sixth degree can tend to function as a dominant.



Oh sure...bring THAT up, why don't you?


;) :p :D :) :cool:

StratKat
11-09-2002, 12:51 AM
Ya know?

Its threads like these that make me smile!!

Its proof that no matter how good ya thing you are there are always folks out there a mile above ya....

I taught music in stores and gave lessons to probably a thousand people over time. But im nowhere as educated as these guys!

Yes my friends, here at HC even pros can be taught something about anything (including humility).

:D

brings a tear to mah eye....

Auggie Doggie
07-22-2003, 08:48 AM
*bump*

vote4dicktaid
07-22-2003, 09:21 AM
[QUOTE]Originally posted by Auggie Doggie
[B]

"Our" functions in any major key:
I= tonic
II= subdomiant-relative
III=dominant-relative
IV=subdominant
V= dominant
VI= tonic-relative
VII= leading tone

I think these names are bit more logical, as they tell a little more about the functions of the minor chords, 2nd, 3rd and 6th step. How come these aren't the generally accepted names?

Auggie Doggie
07-22-2003, 09:52 AM
Originally posted by vote4dicktaid


I think this is a bit interesting. In Denmark (and probably all of the Scandinavian countries) we have different names for some of the functions than the above mentioned.

"Our" functions in any major key:
I= tonic
II= subdomiant-parallel
III=dominant-parallel
IV=subdominant
V= dominant
VI= tonic-parallel
VII= leading tone

I think these names are bit more logical, as they tell a little more about the functions of the minor chords, 2nd, 3rd and 6th step. How come these aren't the generally accepted names?

I actually find those names to be a bit misleading due to the word 'parallel'. If 'relative' was used instead, then it would make perfect sense to me.

ii is the relative minor of IV (subdominant). However, the parallel minor of IV would be iv (in the key of C, the parallel minor of F is F minor). The subdominant minor chord (iv) is not at all uncommon, and resolves beautifully to I.

iii is the relative minor of V (dominant)....the parallel minor of the dominant, v (Gm in the key of C) is called the five-minor, as the name 'dominant minor' is illogical since a dominant chord is a mjaor one.

And as I mentioned in the original post, vi is the relative minor of the tonic. (Am in the key of C). The parallel minor of the tonic would be Cm in the key of C (i).

Remember, a 'parallel' minor shares the tonic with its major counterpart (C major/C minor are parallel....A/Am are parallel). All the names you gave would make sense if 'parallel' was replaced by 'relative', since those two terms (in English anyway) have very different meanings.

Further, just the fact that only tonic, subdominant, and dominant names are chosen for I ii iii IV V and vi indicate the concept of chord families, which is a concept I am not fond of; it blurs the distinct function of, say, the supertonic region by lumping it in with IV (the subdominant). While they are closely related, they are not, in my opinion, substitutes for each other. In other words, if a piece is in C, and an F chord comes up, I don't play a Dm in its place; to my ears, that is a distinct harmony. Of course, from that statement you can probably infer that I am not keen on using 6th chords in that context (IV6 is not in my toolbox :D)

As a firm proponent of keeping functions distinct, if I was to modulate (or at least deviate) to Dm while in the key of C, my harmonic choices would likely come from borrowing from Dm (Bb's and C#'s would come into the picture). If I was to think of Dm as a member of the 'subdominant family', only the Bb would be used (the C# leading tone for D would not present, and the Dm would not be established strongly).

Excellent question, though. :) And I'm sure there are people on both sides of that fence. :D

vote4dicktaid
07-22-2003, 12:13 PM
Originally posted by Auggie Doggie


I actually find those names to be a bit misleading due to the word 'parallel'. If 'relative' was used instead, then it would make perfect sense to me.

And as I mentioned in the original post, vi is the relative minor of the tonic. (Am in the key of C). The parallel minor of the tonic would be Cm in the key of C (i).

Remember, a 'parallel' minor shares the tonic with its major counterpart (C major/C minor are parallel....A/Am are parallel). All the names you gave would make sense if 'parallel' was replaced by 'relative', since those two terms (in English anyway) have very different meanings.



OK, it seems the Dansih music vocabulary is quite different from the English. What I meant by "parallel" was indeed "relative", and I'll edit my original post now. What's interesting is that what you call the "parallel" (Cmaj/min and so on...) would be refered to in Denmark as the "variant"!

So actually we seem to agree on this one!