My 2 cents on harmony

[Soul Power]

Often when you think of chords you think vertically...and this is appropriate, but harmony is not vertical-harmony is linear, continuously moving forward.
You must be familiar with: The harmonic minor scale, how to construct chords, key signatures, and intervals to understand what I am about to dive into

In this lesson, I will explain how secondary dominant chords are used to modulate to different keys, and how to harmonize any scale.
When I refer to minor chords and scales, I am referring to harmonic minor; however, the formula can apply to any scale.

Let's use C major for the sake of familiarity, but be absolutely sure that you practice your weakest key the most often.

Let's dissect C major now:
C is the root, D is the major second, E is the major third, F is the perfect fourth, G is the perfect 5th or dominant, A is the major sixth, and B is the major seventh.

Each note of any scale can be harmonized in both triad and seventh chord form:

1: C,E,G or C,E,G,B
2: D,F,A or D,F,A,C
3. E,G,B or E,G,B,D
4: F,A,C or F,A,C,E
5: G,B,D or G,B,D,F
6: A,C,E or A,C,E,G
7: B,D,F or B,D,F,A

You will notice when harmonizing the major scale that the quality of the chords changes with each note:
The root chord of any major scale is ALWAYS a major chord
the second chord of any major scale is ALWAYS a minor chord
the third chord of any major scale is ALWAYS a minor chord
the fourth chord of any major scale is ALWAYS a major chord
the fifth chord of any major scale is ALWAYS a dominant seventh chord
the sixth chord of any major scale is ALWAYS a minor chord
the seventh chord of any major scale is ALWAYS a diminished chord.

I will now explain what secondary dominants are and what their purpose is:
Secondary dominants are dominant chords that are used to transition to a different key.
Usually, music only modulates down a half step or up a half step; but there are secondary dominants for every note.

If you see an A7 (dominant seventh) chord within the key of C, it is safe to assume that it is the secondary dominant of D minor and the key modulates to that through the use of accidentals.
Every secondary dominant uses accidentals to modulate to a different key; IT IS IMPORTANT TO KNOW THAT THE ACCIDENTALS USED WILL NOT BE WITHIN THE ORIGINAL KEY, BUT THE NEW KEY.

Let's dissect D harmonic minor, where the secondary dominant comes from, and the accidentals used to modulate.

D harmonic minor is spelled as follows:
D,E,F,G,A,Bb,C#.
Notice that A is the fifth of D harmonic minor; therefore it is a dominant 7th chord.
To construct the chord, let's spell out the scale in two octaves.
(Any note that is above the octave is counted up from 8, for example; F is the third of D harmonic minor but it is also the 10th)
D,E,F,G,A,Bb,C#,D,E,F,G,A,Bb,C#
If we construct a chord starting on A, then we will find the following notes within the secondary dominant:
A,C#,E,G,Bb

A, E and G are within the key of C, so they are NOT the accidentals used to transition.

Therefore, the third (C#) and 9th(Bb) are the accidentals necessary to tonicize the new key.


Notice that all of the notes, with the exception of Bb and C# are within the key of C major. NONE OF THESE NOTES ARE THE ACCIDENTALS USED TO TRANSITION TO D minor.
You must either use Bb or C#.

In this example, we will find the secondary dominant of, and modulate to E harmonic minor.

E,F#,G,A,B,C,D#.
The fifth is B, so the secondary dominant of E minor is B7.

Let's spell the scale in two octaves:
E,F#,G,A,B,C,D#,E,F#,G,A,B,C,D#,E

Starting on B, we count every other note as a part of the dominant seventh chord (usually, you will only need to know the four notes within a dominant seventh chord---only very rarely do you go above a 13th)

B,D#,F#,A,C,D#
I count until I begin repeating
B,A, and C are within the key of C major; therefore they are NOT the accidentals used to transition.
D# and F# are used to tonicize the key to E minor.

In order for you to truly learn this, I will not reveal the accidentals used to modulate to all the other keys that are within C major.

I will say this though, sometimes there are 2 accidentals used to modulate, and sometimes one.

This can be applied to walking bass lines and soloing over chord progressions.

[ericw]

Correct me if I'm wrong: An A7 chord could just as easily transition to D major.

So the Bb is what suggests D harmonic minor. But when you spell a chord A(1), C#(3), E(5), G(b7), Bb(b9), what do you call it? A-dominant seven-flat nine?

[Soul Power]

Originally Posted by ericw

Correct me if I'm wrong: An A7 chord could just as easily transition to D major.

So the Bb is what suggests D harmonic minor. But when you spell a chord A(1), C#(3), E(5), G(b7), Bb(b9), what do you call it? A-dominant seven-flat nine?

Yes, or a dominant 9 chord.

[ericw]

I think a dominant 9 chord has a major 9th in it. Which is why I asked what it's named with the flat 9th.

Appreciate the info. I had to read it a few times due to my cubicle coma (almost 4!) but I think I see what you're getting at - bassically, in layman's terms, if you want to change keys, find the difference-makers in the target key and apply them to the chord on the fifth degree of the target key? Errr.. just play the fifth of your target key?... Never mind I think I'm getting stupider.

[Soul Power]

You CAN play the fifth of your target key but that sounds monotonous, you want to go for those accidentals for it to have a bebop/jazzy sound

[esoomssab]

It seems to me you may be pigeon holing secondary dominants into one specific possible function. Modulation is by no means the only use for secondary dominants, in fact, I'd say that's far from their main use.

For instance, in your first example, you say an A7 pops up in the key of C major, and that means we're modulating to d minor. The secondary dominant (V/ii in C), if used for modulation, could just as easily be pointing to D major - it seems you're pointing to D minor because of the diatonic triad in C? As a pivot chord (C:V/ii, d or D:V7), yes it could work as a modulation. But it could also just go to a normal old d minor chord in the key of C.

Anyway - just wanted to say that this seems an incomplete, maybe slightly inaccurate introduction to secondary dominants.

[ericw]

Originally Posted by esoomssab

But it could also just go to a normal old d minor chord in the key of C.

Could you explain this more? So you're saying the D7 could/would resolve to a d minor chord? Wouldn't the V/ii in C be an A7 not a D7?

Secondary dominants and pivot chords (if that's what V/V or V/ii and all that stuff refers to) is not something I have learned about yet. But am interested if anyone has a link to share or just wants to take another stab at explaining it.

[JimmyM]

i wouldn't call going from a D7 to a Dm "resolving," but sure, you can make your chords go from whatever chord to whatever other chord you think is appropriate. it's all allowed these are just some common uses you'll run into a lot.

[esoomssab]

I wasn't saying that a D7 would resolve to a d minor - I was making reference to the A7 mentioned previously - sorry that was unclear.

In a modulation, pivot chords are chords that can be analyzed in both keys, and precedes the point of modulation. I may be incorrect (it's been quite some time since my last classical theory course) about using secondary dominants as pivot chords, so hopefully someone who knows more will correct me if that is wrong. Anyway - as an example, in the key of C you could use the G chord as a V in C, but analyze it in D major, using the G triad as a IV chord in D. So the chord works as the go between between the two keys. The pivot chord isn't the actual modulation though, because nothing has actually occurred at that point - if there's nothing to indicate we've switched to D major, the G major triad is still just a V chord in C. So in this situation (key of C going to key of D), the G major would probably be followed by an A triad or A7 chord with the C# to indicate the switch to D.

That's the reference I was making earlier - an A7 in the key of C is analyzed as a V/ii. But it's also just a normal V7 in D major and d minor.

[Richard Lindsey]

There's some good stuff in the original post, but also a fair bit of misunderstanding. For one thing, you do NOT modulate every time you use a secondary dominant. Typically, what you've done is at most a tonicization. The main use of secondary dominants is not in fact to modulate but generally to provide a nondiatonic approach to a diatonic chord (or sometimes to another secondary dominant that then goes to a diatonic chord--eg, C A7 D7 G7 C).

For instance, if you play C A7 Dm G7, even though A7 is a secondary dominant, you are at no point going to the key of D minor in any real sense. You are temporarily treating Dm as if it's a tonic, but that Dm then goes on to fulfill its function as a ii in the key of C major. More often than not, a secondary dominant is a nondiatonic way of approaching a diatonic chord.

[Richard Lindsey]

Originally Posted by Soul Power

You will notice when harmonizing the major scale that the quality of the chords changes with each note:
The root chord of any major scale is ALWAYS a major chord
the second chord of any major scale is ALWAYS a minor chord
the third chord of any major scale is ALWAYS a minor chord
the fourth chord of any major scale is ALWAYS a major chord
the fifth chord of any major scale is ALWAYS a dominant seventh chord
the sixth chord of any major scale is ALWAYS a minor chord
the seventh chord of any major scale is ALWAYS a diminished chord.

This is a little confused, because sometimes you seem to be talking about triads, and sometimes about 7th chords. For example in strictly triadic terms, the chord built on the 5th degree of a major scale is always a MAJOR chord, not any kind of 7th chord.

If you're talking about 7th chords, the order would be

1: maj7
2: m7
3: m7
4: maj7
5: 7 (ie, dominant 7)
6: m7
7: m7b5 (ie, half-diminished)

[nothumb]

free music theory instruction: you get what you pay for. thanks OP

[Chris K]

Originally Posted by ericw

I think a dominant 9 chord has a major 9th in it. Which is why I asked what it's named with the flat 9th.

Seems your question was overlooked.

A chord with a flat 9 is called a minor ninth chord.

http://en.wikipedia.org/wiki/Ninth

The correct naming of chords is subject to discussion. Differences may occur between common chord names (used in regular band work) and theoretically correct names.

Pretty much of what the OP says (the parts without the misconceptions pointed out by Richard) is at everybody's free disposal on Wikipedia. Type a chord name in your search engine and off you go.

[JimmyM]

Originally Posted by Chris K

Seems your question was overlooked.

A chord with a flat 9 is called a minor ninth chord.

http://en.wikipedia.org/wiki/Ninth

sorry, chris. from the article you linked:

"The minor ninth chord is played with the third and seventh both flattened. The formula is 1, ♭3, 5, ♭7, 9. This chord is written as Cm9. This chord has a more "bluesy" sound and fits very well with the dominant 9th."

[HaVIC5]

Jeez...I have a feeling this will end up becoming one of those threads where musical misinformation is thrown around all over the place confusing and misinforming all of the less theory-inclined.

Take it with a grain of salt, people.

[JimmyM]

Originally Posted by HaVIC5

Jeez...I have a feeling this will end up becoming one of those threads where musical misinformation is thrown around all over the place confusing and misinforming all of the less theory-inclined.

Take it with a grain of salt, people.

right on. and for god's sakes, don't let it stop you from making music! you can do anything you want with music. you can play any note in any key, and if you do it in the right context, it will sound good.

also, on the gig, if you get a chart that has some of this stuff on it, just roll with it and don't get wrapped up in making it fit the key. if you're in C and you get an A7 to Dm, just play the damn thing and shut up!

[dtiii]

Often when you think of chords you think vertically...and this is appropriate, but harmony is not vertical-harmony is linear, continuously moving forward.

You seem to be contradicting yourself in your opening statement. Harmony is made up of vertical structures that can

1) move forward in a harmonic progression;
2) remain static, meaning that there is no motion; and
3) proceed as a regression, meaning that there is no motion in a progressive manner (wandering).

Regardless of how the harmony is laid out, we can follow the path, or linear perspective, of each individual note. This is called voice-leading.

You must be familiar with: The harmonic minor scale, how to construct chords, key signatures, and intervals to understand what I am about to dive into

In this lesson, I will explain how secondary dominant chords are used to modulate to different keys, and how to harmonize any scale.
When I refer to minor chords and scales, I am referring to harmonic minor; however, the formula can apply to any scale.

Let's use C major for the sake of familiarity, but be absolutely sure that you practice your weakest key the most often.

Let's dissect C major now:
C is the root, D is the major second, E is the major third, F is the perfect fourth, G is the perfect 5th or dominant, A is the major sixth, and B is the major seventh.

If you are referring to the interval of each scale degree in relation to tonic than you should be consistent by saying “C is a perfect unison.” More importantly, the terminology is misused here. I think the following is more appropriate:

C is tonic or scale degree 1
D is supertonic or scale degree 2
E is mediant or scale degree 3
F is subdominant or scale degree 4
G is dominant or scale degree 5
A is submediant or scale degree 6
B is the leading tone or scale degree 7

Each note of any scale can be harmonized in both triad and seventh chord form:

1: C,E,G or C,E,G,B
2: D,F,A or D,F,A,C
3. E,G,B or E,G,B,D
4: F,A,C or F,A,C,E
5: G,B,D or G,B,D,F
6: A,C,E or A,C,E,G
7: B,D,F or B,D,F,A

You will notice when harmonizing the major scale that the quality of the chords changes with each note:
The root chord of any major scale is ALWAYS a major chord
the second chord of any major scale is ALWAYS a minor chord
the third chord of any major scale is ALWAYS a minor chord
the fourth chord of any major scale is ALWAYS a major chord
the fifth chord of any major scale is ALWAYS a dominant seventh chord
the sixth chord of any major scale is ALWAYS a minor chord
the seventh chord of any major scale is ALWAYS a diminished chord.

The term root chord is incorrect. The root is the note after which the chord is named. It is best to refer to each chord by scale degree number, name, or Roman numeral label. For example:

The chord built on scale degree 1, the tonic chord, or the I chord (stated ‘the one chord’). All of these refer to the same thing – a C major chord in the key of C major. This follows for all the chords stated above.

I will now explain what secondary dominants are and what their purpose is:
Secondary dominants are dominant chords that are used to transition to a different key.

As stated earlier by esoomsab, secondary dominants, and I will add secondary leading-tone chords, can be used for both modulation and tonicization.

Usually, music only modulates down a half step or up a half step; but there are secondary dominants for every note.

A chord progression can modulate to anywhere.

If you see an A7 (dominant seventh) chord within the key of C, it is safe to assume that it is the secondary dominant of D minor and the key modulates to that through the use of accidentals.

It’s never safe to assume anything when analyzing a piece of music. A7 can be functioning as a respell for either an Italian or German augmented sixth chord if it proceeds to G# (Ab) with the goal being C# (Db). This is a wonderful way to modulate up a half step from C. It can also be a Neopolitan chord if it proceeds to Eb when modulating to Ab, bVI in the key of C. If it proceeds directly to Ab then it can be analyzed as a b5 sub for Eb7.

Every secondary dominant uses accidentals to modulate to a different key; IT IS IMPORTANT TO KNOW THAT THE ACCIDENTALS USED WILL NOT BE WITHIN THE ORIGINAL KEY, BUT THE NEW KEY.

This is true most of the time. It’s not true when modulating from a minor key to its relative major. VII7 in minor is also V7 in the relative major. In this situation the key signature will not change.

Let's dissect D harmonic minor, where the secondary dominant comes from, and the accidentals used to modulate.

“Let’s examine the D harmonic minor scale” better states your intent.

D harmonic minor is spelled as follows:
D,E,F,G,A,Bb,C#.

Notice that A is the fifth (again, dominant or scale degree 5 is better) of D harmonic minor; therefore it is a dominant 7th chord.

The chord built on A in D minor is A7 because of the chromatic alteration of scale degree 7 of the natural minor scale.

To construct the chord, let's spell out the scale in two octaves.
(Any note that is above the octave is counted up from 8, for example; F is the third of D harmonic minor but it is also the 10th)
D,E,F,G,A,Bb,C#,D,E,F,G,A,Bb,C#
If we construct a chord starting on A, then we will find the following notes within the secondary dominant:
A,C#,E,G,Bb

I’m not sure why Bb made it in here. It’s an extension of A7. It does not have any bearing on the quality of A7.

A, E and G are within the key of C, so they are NOT the accidentals used to transition.

Therefore, the third (C#) and 9th(Bb) are the accidentals necessary to tonicize the new key.

The Bb is better identified as the 5th of E half-dim7, which serves as a predominant to A7. The Bb is important with the presence of this chord, but not necessary.


Notice that all of the notes, with the exception of Bb and C# are within the key of C major. NONE OF THESE NOTES ARE THE ACCIDENTALS USED TO TRANSITION TO D minor.
You must either use Bb or C#.

In this example, we will find the secondary dominant of, and modulate to E harmonic minor.

It now sounds as if you are speaking in the context that there are ‘harmonic minor’ keys. There are minor keys. The natural minor scale is the structural representation of a minor key. Scale degree 7 is often raised in order to create a leading tone, which the natural minor scale lacks. This alteration creates a harmonic minor scale.

E,F#,G,A,B,C,D#.
The fifth is B, so the secondary dominant of E minor is B7.

Let's spell the scale in two octaves:
E,F#,G,A,B,C,D#,E,F#,G,A,B,C,D#,E

Starting on B, we count every other note as a part of the dominant seventh chord (usually, you will only need to know the four notes within a dominant seventh chord---only very rarely do you go above a 13th)

B,D#,F#,A,C,D#
I count until I begin repeating
B,A, and C are within the key of C major; therefore they are NOT the accidentals used to transition.
D# and F# are used to tonicize the key to E minor.

There is a distinction between modulation and tonicization.

In order for you to truly learn this, I will not reveal the accidentals used to modulate to all the other keys that are within C major.

I will say this though, sometimes there are 2 accidentals used to modulate, and sometimes one.

This can be applied to walking bass lines and soloing over chord progressions.

There are times that you are speaking specifically in regard to your topic and times when you are making generalizations in regard to music. Try to be more focused when writing. Sometimes if we hold on too tightly to the point that we are trying to make our scope becomes too narrow and we miss the alternatives. A past professor said it was like stacking the cards in the favor of your analysis.

Secondary function in music is an established theory. In order to speak rightfully about it one must survey the existing scholarship. A thorough investigation is ambitious for this forum. Chapters are dedicated to the topic, usually two – Secondary Dominants and Secondary Leading-Tone Chords. I highly recommend either of these two texts (ideally both):

TONAL HARMONY Kostka/Payne (better for high school and undergrad)
HARMONY AND VOICE LEADING Aldwell/Schachter (better for grad)

Like I said, this is an ambitious topic. I do commend you on trying to tackle it. Good luck in your studies.

d

[Chris K]

Originally Posted by JimmyM

sorry, chris. from the article you linked:

"The minor ninth chord is played with the third and seventh both flattened. The formula is 1, ♭3, 5, ♭7, 9. This chord is written as Cm9. This chord has a more "bluesy" sound and fits very well with the dominant 9th."

Thanks, Jimmy... I should have been more careful... Made a translation form Dutch (dominant 7th chord with added minor ninth as we say).

So... how do YOU guys call 1, 3, 5, b7, b9?

[dtiii]

dominant 7 b9

[Richard Lindsey]

Originally Posted by Chris K

Thanks, Jimmy... I should have been more careful... Made a translation form Dutch (dominant 7th chord with added minor ninth as we say).

So... how do YOU guys call 1, 3, 5, b7, b9?

7b9, as in A7b9.