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.
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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
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)*
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