Borrowing functions

[rbarata]

I made some research trying to find a relationship between diatonic chord substitutions and Modal Interchange.

About chord substitutions, in both major and natural minor scale (for now), the reason why two chords can be substituted (keeping their harmonic function) is because both share (at least) two tones. Bellow, there's a chord study for major and natural minor scales that shows exactly that.

Major key
C D E F G A B

I - C E G
IIm - D F A
IIIm - E G B
IV - F A C
V - G B D
VIm - A C E
VIIº - B D F

Tonic: I, IIIm and VIm
C E G
E G B
A C E

Subdominant: IV and IIm
D F A
F A C

Dominant: V and VIIº
G B D
B D F

Minor key
C D Eb F G Ab Bb

Im - C Eb G
IIº - D F Ab
III - EB G Bb
IVm - F Ab C
Vm - G Bb D
VI - Ab C Eb
VII - Bb D F

Tonic: Im and bIII
C Eb G
Eb G Bb

Subdominant: IVm, IIº and bVI
D F Ab
F Ab C
Ab C Eb

Dominant: Vm and bVII
G Bb D
Bb D F

Now trying to find what's in common between two chords with the same function in two parallel scales (CMaj and C Nat. Minor), things are not so linear.
For example, considering the V chord in CMaj:

G B D

Comparing it with the V chord in C Nat. minor (G Bb D) we see the chord root is the same as well as the 5th is constructed by the same tones. The difference is in the 3rd, from Maj to minor by lowering the B.
This is more or less "intuitive" to me.

But a different case happens if, in CMaj, we borrow the bVII (Bb D F) to use it as dominant.

Instead of G B D we will use Bb D F. In CMaj, it's also intuitive that the VIIº root is half-step from the tonic so there's a tendency to be resolved. In this case we could think that the F has a tendency to move towards G (the true dominant) but it's a whole-step away from it.
The only possibility I see is that auraly the Bb D F is part of a bigger chord: G Bb D F (Gm7). Basically, the D and the F induces our ear to the missing G and the Bb is somewhat considered by our ears as "not so important" to determine the function (whie being important to add colour and variation through a change in the quality).

Another thing I've read is that what determines if a piece is minor or major is the quality of the I chord. No matter what is used after that, the quality will remain the same. This, together with the fact that the functions are the same for each chord of both parallel scales, is the essence of the modal interchange.

This makes me think that, like in modal jazz (where you use a I chord and another one that can be anything you want, as long as it contains the characteristic note of the mode), here you can also use anything you want in your progression, i.e., you can use any dominant chord from any scale you want (maj or min), any subdominant chord from any scale, etc. Basically, all the rules become irrelevant because both scales are so related that it doesn' make much sense to separate them.

Am I seeing thing where they don't exist?

[Malcolm]

.......... This makes me think that, like in modal jazz (where you use a I chord and another one that can be anything you want, as long as it contains the characteristic note of the mode),

Yes. Any mode is going to need a droning effect to sustain the modal sound. If you use a chord that has the mode's characteristic note in it that note will sustain the mode's sound, I like the word mood.
Lydian's characteristic note is the #4.
Mixolydian's characteristic note is the b7.
Dorian's note is the natural 6.
Phrygian's is the b2.
Locrian's is the b2 and the b5. Locrian's vamp works best with just the m7b5 chord, i.e. one chord droning.

......here you can also use anything you want in your progression, i.e., you can use any dominant chord from any scale you want (maj or min), any subdominant chord from any scale, etc. Basically, all the rules become irrelevant because both scales are so related that it doesn' make much sense to separate them.

No you are missing the point. For a mode to sustain the unique sound you only want one or two chords active under the mode notes. The tonic and the chord with the characteristic note - any more chords in play will not sustain the characteristic sound of the mode. For the mode's characteristic sound to develop you do not want a bunch of chords active. One or two at the most. Modes work with a pedal point (droning) not a tonal center found in a progression.

Scales use chord progression (V-I cadences) and with modes you do not want the V-I cadence. The V-I brings closure. You do not want resolution you want the characteristic sound to continue and sustain the mode's mood.

Am I seeing thing where they don't exist?

You are trying to make it too complicated.

Of course all this is mute if the other members of the band do not also harmonize your modal melody notes with a modal vamp. If they continue using a chord progression your modal notes will never develop into a mood. The chord progression's tonal center will defeat your modal efforts.

[rbarata]

No you are missing the point. For a mode to sustain the unique sound you only want one or two chords active under the mode notes. The tonic and the chord with the characteristic note - any more chords in play will not sustain the characteristic sound of the mode. For the mode's characteristic sound to develop you do not want a bunch of chords active. One or two at the most. Modes work with a pedal point (droning) not a tonal center found in a progression.

Malcolm, I'm just making a comparison between modal jazz and the theory of modal interchange.

[rbarata]

I'm not sure if my thinking is valid or not. It can be complicated, like Malcolm said but...my view of these things is somehow correct?

[JonR]

I made some research trying to find a relationship between diatonic chord substitutions and Modal Interchange.

About chord substitutions, in both major and natural minor scale (for now), the reason why two chords can be substituted (keeping their harmonic function) is because both share (at least) two tones. Bellow, there's a chord study for major and natural minor scales that shows exactly that.

Major key
C D E F G A B

I - C E G
IIm - D F A
IIIm - E G B
IV - F A C
V - G B D
VIm - A C E
VIIº - B D F

Tonic: I, IIIm and VIm
C E G
E G B
A C E

Subdominant: IV and IIm
D F A
F A C

Dominant: V and VIIº
G B D
B D F

Correct.

Minor key
C D Eb F G Ab Bb

Im - C Eb G
IIº - D F Ab
III - Eb G Bb
IVm - F Ab C
Vm - G Bb D
VI - Ab C Eb
VII - Bb D F

Tonic: Im and bIII
C Eb G
Eb G Bb

I'm not sure about this. With an Eb root, the III chord is a lot stronger tonally than the i. Of course, you can have an Eb triad on a C bass, as Cm7. But I don't think the Eb triad alone will work as a sub for Cm.

Subdominant: IVm, IIº and bVI
D F Ab
F Ab C
Ab C Eb

Yes. (At least, I agree )

Dominant: Vm and bVII
G Bb D
Bb D F

The dominant in a minor key is a major chord: G B D in this key.
This shares a dominant function with the viidim chord, B D F. IOW, same two chords as in the parallel major.

You could view this as a traditional/conventional (historical) "borrowing" from the parallel major, although it's pretty much established as a proper part of the minor key.

The difference is that the 7th on the dim chord is a diminished 7th, B D F Ab.

Now trying to find what's in common between two chords with the same function in two parallel scales (CMaj and C Nat. Minor), things are not so linear.
For example, considering the V chord in CMaj:

G B D

Comparing it with the V chord in C Nat. minor (G Bb D) we see the chord root is the same as well as the 5th is constructed by the same tones. The difference is in the 3rd, from Maj to minor by lowering the B.
This is more or less "intuitive" to me.

The minor v chord in a major key will probably not have a dominant function. It's technically a "minor dominant", I guess, but it's more likely - IMO - to sound like a "secondary supertonic": ii of IV. Ie, a subdominant function relative to the F chord
IOW, if you use a Gm in key of C major, we'd probably expect it to be followed by a C7 (V/IV) and then F.

[see below, however]

But a different case happens if, in CMaj, we borrow the bVII (Bb D F) to use it as dominant.

Instead of G B D we will use Bb D F. In CMaj, it's also intuitive that the VIIº root is half-step from the tonic so there's a tendency to be resolved. In this case we could think that the F has a tendency to move towards G (the true dominant) but it's a whole-step away from it.
The only possibility I see is that auraly the Bb D F is part of a bigger chord: G Bb D F (Gm7). Basically, the D and the F induces our ear to the missing G and the Bb is somewhat considered by our ears as "not so important" to determine the function (whie being important to add colour and variation through a change in the quality).

Again, that will enhance its sound as a subdominant of F. Gm7 or Bb(6).

Typically - at least in rock - that's how a Bb triad is used in key of C: as IV of IV. Hence the popular Bb-F-C chord sequence, sometimes known as a "double plagal cadence".

However, the other common rock cadence with borrowed chords is Ab-Bb-C; which could be viewed as an aeolian cadence, just with a major tonic. In that sense, Ab is certainly subdominant, so Bb is presumably dominant (?) - or at least apparently standing for something like a dominant; if we only have 3 possible functions, what else would it be? (I wouldn't swear to this, mind... Don't take my word for it.)

In jazz things are a little different, and Bb7 (including the b7, not used in rock) will typically be used to resolve straight to C. However, it's still (AFAIK) a kind of subdominant: but this time of C, being a sub for the minor iv chord (Fm).
Eg, a common jazz sequence is C-C7-F-Fm-C. That might be embellished to: C-Cmaj7-Gm7-C7-Fmaj7-Fm7-Bb7-Cmaj7.
The Bb7 will probably have a #11 extension.

I guess you could look again at that Ab-Bb-C and regard the Bb (in the light of the jazz Bb7) as some kind of sub for Fm... which is in turn the same function as Ab... but then it's totally counterintuitive (IMO), to regard two major triads a whole step apart as having the same function!

Another thing I've read is that what determines if a piece is minor or major is the quality of the I chord. No matter what is used after that, the quality will remain the same. This, together with the fact that the functions are the same for each chord of both parallel scales, is the essence of the modal interchange.

Well, that's the question: do all the borrowed chords have the same function?
With V, vii, ii and IV, yes.
With bIII, possibly not.
And as you've pointed out, the bVI chord from minor has a different function (subdominant) from the vi chord in major (tonic).

This makes me think that, like in modal jazz (where you use a I chord and another one that can be anything you want, as long as it contains the characteristic note of the mode), here you can also use anything you want in your progression, i.e., you can use any dominant chord from any scale you want (maj or min), any subdominant chord from any scale, etc. Basically, all the rules become irrelevant because both scales are so related that it doesn' make much sense to separate them.

Am I seeing thing where they don't exist?

I couldn't say!

You can certainly use any chord you want, anywhere you like. The interesting thing (to a theorist) is why and how do certain chords seem to sound right or logical, and others not. We tend to explain it by pointing to functional substitutions, or parallel scales. IOW, a "strange" chord can be explained by noting a similarity to some more familiar practice. What "sounds good", remember, is largely conditioned by what we're used to hearing. This is where conventional theory (the common practices of past music), is useful because it gives us the concepts that familiar music tends to follow.

When it comes to function, you have to consider the chords either side, usually the following chord. IOW, it's not about where the chord comes from (what is its function in the scale we think it derives from), but how does it relate to the chords either side, where it's actually being used? What job is it doing?
Eg, if you have a Gm (or Gm7) in key of C, where is it going? Is it going back to C, like a G or G7 would? If so, maybe we can talk of a "minor dominant" function. But probably not. Much more likely, it will go to C7 and then F. So its function is clearly revealed as a ii of F.

BTW, there is one case I can think of where we might want to think of a "minor dominant" chord. David Bowie's "Heroes" runs as follows:

|D - - - | - - - - |G - - - | - - - - |
|D - - - | - - - - |G - - - | - - - - |
|C - - - | - - - - |D - - - | - - - - |
|Am - - - |Em - - - |D - - - | - - - - |
|Am - - - |Em - - - |D - - - | - - - - |

What function does the Am have? In fact, this tune can be seen as a D mixolydian piece, rather than a D major key piece. There is no A major chord anywhere. So in that sense, the C and the Am are not "borrowed" at all; they're diatonic to the overall mode. (There is no "modal interchange"; everything comes from the same mode.)
Still, there is a sense that the Am-Em-D sequence resembles the common A-G-D sequence in D major. vi-ii-I replacing V-IV-I.

However, this is in a sense a pointless analysis. It's not a piece of CPP classical music! It's rock. The song is what it is, and "D mixolydian mode" is a good enough summary. We needn't consider any parallel with the D major key; and it's doubtful whether a traditional functional analysis will tell us anything useful.

[rbarata]

It seems we have here two different things working at the same time.

We sharpen the 7th degree of the Natural Minor scale to increase its tendency to move to the tonic (hence, giving origin to the Harmonic Minor scale).
But when working on the Natural Minor scale we apply the same change so the the Dominant chords, Vm and bVII, get the same chord quality as in the major scale.

Are these two things working together or are they just different things that happen to have the same result, i.e., probably this has some historic background but when it has begun to be used it just happend to be a solution that solved two problems or were used initially used separately?

But in the case of the subdominant chords in the Natural Minor scale, we don't alter any note from the natural minor. Why?

Ultimately I could also ask why do we need a natural minor scale if we change it to be similar to the major scale.

[JonR]

It seems we have here two different things working at the same time.

We sharpen the 7th degree of the Natural Minor scale to increase its tendency to move to the tonic (hence, giving origin to the Harmonic Minor scale).
But when working on the Natural Minor scale we apply the same change so the the Dominant chords, Vm and bVII, get the same chord quality as in the major scale.

It's the exact same thing. Just two different perspectives on the same process. The second view is perhaps the best. because that's the reason for doing it.
The fact that it "gives origin to the harmonic minor scale" is a side issue. The harmonic minor scale is simply the apparent result of raising the 7th degree in order to get a leading tone, to give a stronger cadence. In classical convention the scale doesn't really exist as an entiity in its own right.
Of course, the raised 7th degree is harmonised by the V chord - or has a chord built on the 7th step itself - so you get the dominant harmonic function; essentially similar to that in the major key. The "harmonic" improvement is the reason for the name of the scale.

But in the case of the subdominant chords in the Natural Minor scale, we don't alter any note from the natural minor. Why?

Because there is no need. It does sometimes happen (you might find a major IV chord in a minor key), but normally we want to keep the "minor" quality of the key as much as possible, to distinguish it from major. That quality resides mostly in the b3, but also in the b6.
IOW, we want to keep our minor triads on I and IV (and dim triad on ii), otherwise we're getting too close to a major tonality.

Ultimately I could also ask why do we need a natural minor scale if we change it to be similar to the major scale.

It's only changed at certain points, namely cadences. That's the only time a raised 7th step is required.
Melodies may sometimes emply the melodic minor scale, but again only when ascending to the tonic. In descent, there is no need for the raised 7th degree,so the natural minor scale is used.
Outside of cadences, the natural minor scale is the basic minor key scale. All the chords except V and vii are harmonised from it.
This is a kind of crude simplification of common practices. After all, one does commonly find the raised 7th degree used in descending lines in modern minor key progressions, at least in the bass,
But it's certainly true that the harmonic and melodic minor scales are not generally used to compose whole pieces with. Natural is THE minor scale; harmonic and melodic minor are merely occasional alterations of it.
(It's arguable that they shouldn't really be defined as separate complete scales at all.)

[rbarata]

It's the exact same thing. Just two different perspectives on the same process. The second view is perhaps the best. because that's the reason for doing it.
The fact that it "gives origin to the harmonic minor scale" is a side issue. The harmonic minor scale is simply the apparent result of raising the 7th degree in order to get a leading tone, to give a stronger cadence. In classical convention the scale doesn't really exist as an entiity in its own right.

The basic effect of a dominant is to move toward the tonic. This happens in a melody aswell as in a chord progression. So, basically when we use a major dominant in a minor scale (raised 7th degree) we are "increasing" the tendency of the movement towards the tonic. It happens in the melody (B=>C) as well as in the V chord (because it contains a B instead of a Bb). Can we see it this way?

Historically, if I understood your post correctly, initially the 7th degree was raised with the above-mentioned intention but was not recognised as a different scale. It was simply a "trick" to get a stronger cadence. Only later it was considered as a scale per si.

Because there is no need. It does sometimes happen (you might find a major IV chord in a minor key), but normally we want to keep the "minor" quality of the key as much as possible, to distinguish it from major. That quality resides mostly in the b3, but also in the b6.
IOW, we want to keep our minor triads on I and IV (and dim triad on ii), otherwise we're getting too close to a major tonality.

I've read about something called Tonal and Modal scale degrees.
Tonal degrees (Tonic, Subdominant and Dominant) establish the tonality of a song.
Modal degrees (Mediant, Submediant and Leading tone) establish the modality.
The Supertonic (2nd scale degree) has characteristics of both, tonal and modal degrees.

Considering this, when you say that we want to use the IVm chord to establish a minot tonality, in fact we are using it not only with a tonal, but also with a modal function.
Considering that the IVm can be substituted by the IIº can I say that there is a relationship between the fact that the supertonic has modal and tonal characteristics and the fact that we are using a IVm to establish a tonality and also a modality?
Please note that I'm extending (correctly or not, I really don't know) a concept used in scales' degrees to chords' functions. If this is correct can I say that in the chords bellow (subdominants in the minor scale), the IIº and IVm have tonal and modal characteristics while the bVI is predominantly modal?

Subdominant: IVm, IIº and bVI
D F Ab
F Ab C
Ab C Eb

[JonR]

The basic effect of a dominant is to move toward the tonic. This happens in a melody aswell as in a chord progression. So, basically when we use a major dominant in a minor scale (raised 7th degree) we are "increasing" the tendency of the movement towards the tonic. It happens in the melody (B=>C) as well as in the V chord (because it contains a B instead of a Bb). Can we see it this way?

Exactly.

Historically, if I understood your post correctly, initially the 7th degree was raised with the above-mentioned intention but was not recognised as a different scale. It was simply a "trick" to get a stronger cadence. Only later it was considered as a scale per si.

I'm not sure of the history in detail, but IMO that's a good way of looking at it. The harmonic minor scale does play quite a strong role in some European folk and gypsy music (and interestingly in both Arabic and Jewish cultures), but is generally not used that way - melodically - in classical music, nor much in jazz or pop.
As you say, it was more like "trick" to make the V-Im cadence stronger, and it's only if you examine the music from a scale perspective that you would conclude "ah that must be a scale with a b6 and maj7". In a true sense it is, of course, but only fleetingly. After all, when melodies - ie real evidence of a "scale" - were involved (rising to the tonic) they would tend to employ melodic minor (with raised 6th as well).

Even so, this is still just the most common scenario in minor key music. (We're talking "common practice" remember ). It doesn't mean that harmonic minor would never be used melodically, nor that a V chord in a minor key would always be major. But I would suspect such examples would be rare - certainly in classical music.

I've read about something called Tonal and Modal scale degrees.
Tonal degrees (Tonic, Subdominant and Dominant) establish the tonality of a song.
Modal degrees (Mediant, Submediant and Leading tone) establish the modality.
The Supertonic (2nd scale degree) has characteristics of both, tonal and modal degrees.

Interesting. I wouldn't quite put it like that myself, because it seems to confuse scale degrees with chords built on those degrees.
Eg, the I, IV and V scale degrees alone communicate nothing about the tonality. Tonic, P4 and P5 are shared by major and minor keys, and by all modes except locrian.
It would be true that - with no other notes - they would suggest I as the "keynote", if that is what is meant by "tonal"; but that would include "modal" as well.
It is true that VI, III and VII (as scale degrees) do specify "modality" (in conjunction with I IV and V of course).

IOW, while I think it's interesting to distinguish between scale degrees in some such way, I don't think those terms help much.
I prefer to see I, IV and V as the primal octave divisions (defining the tetrachords of ancient Greece, and the fixed points of both the medieval modes and the major and minor keys). They are the "perfect" intervals and, as such, are fixed, in all the common western key and mode scales. It's the other notes that shift around (the other intervals coming in either "major" or "minor" form), to get various different key or mode effects.
IOW, rather than "tonal" as distinct from "modal", I-IV-V are the foundation of both systems.
I'm not saying the concept is wrong, only that the terms used are potentially misleading.

Considering this, when you say that we want to use the IVm chord to establish a minor tonality, in fact we are using it not only with a tonal, but also with a modal function.

Well, this kind of illustrates how the terms obfuscate rather than clarify!
We don't "use the IVm chord to establish a minor tonality" - not on its own. It suggests a minor key, because that's the context in which we normally hear it. But if the tonic chord is major, then the "established" key is major, and a IVm is heard as a "borrowing"; it doesn't suddenly make the key minor.
And it has nothing to do with modes! (except of course we can use the term "Modal interchange", to say it's borrowed from "parallel aeolian", rather than "parallel minor"; same thing, different word!)

Considering that the IVm can be substituted by the IIº can I say that there is a relationship between the fact that the supertonic has modal and tonal characteristics and the fact that we are using a IVm to establish a tonality and also a modality?

No - at least I don't think so. (Because I think this "tonal/modal" distinction is a misuse of terms in this context.)

Please note that I'm extending (correctly or not, I really don't know) a concept used in scales' degrees to chords' functions. If this is correct can I say that in the chords bellow (subdominants in the minor scale), the IIº and IVm have tonal and modal characteristics while the bVI is predominantly modal?

Subdominant: IVm, IIº and bVI
D F Ab
F Ab C
Ab C Eb

I see what you're getting at - there is a distinction there. But to me, it's down to the fact that bVI has (in relation to C major) two chromatic notes while the others only have one. That would explain why the bVI chord has a more dramatic effect when introduced in a major key. The IVm and IIº chords can be seen as just small alterations to diatonic chords, a more subtle effect.
But I don't think this (very real) effect is explained or even described very well using "tonal" and "modal" distinctions.

[rbarata]

After all, when melodies - ie real evidence of a "scale" - were involved (rising to the tonic) they would tend to employ melodic minor (with raised 6th as well).

Usually, melodic minor is used when ascending, right?

Tonic, P4 and P5 are shared by major and minor keys, and by all modes except locrian.

Right, if we consider only the major and minor scales (and their modes). But what about Lydian? Isn't the 4th degree an aug4th? Or am I missing something?

IOW, while I think it's interesting to distinguish between scale degrees in some such way, I don't think those terms help much.
I prefer to see I, IV and V as the primal octave divisions (defining the tetrachords of ancient Greece, and the fixed points of both the medieval modes and the major and minor keys). They are the "perfect" intervals and, as such, are fixed, in all the common western key and mode scales. It's the other notes that shift around (the other intervals coming in either "major" or "minor" form), to get various different key or mode effects.
IOW, rather than "tonal" as distinct from "modal", I-IV-V are the foundation of both systems.
I'm not saying the concept is wrong, only that the terms used are potentially misleading.

I believe, but said in a different way, that's the same that I've read.
I see it as the same "concept" that is used to explain modes, i.e., the III, VI and VII can be viewed as characteristic chords that establish the modality (just like the characteristic notes of a mode). The I, IV and V can be seen, again comparing with the modes, as the unalttered notes of the mode.
Obviously, as you've said, they will work together, the "tonal and modal chords", alone they don't mean nothing (or they mean a lot of different things).

We don't "use the IVm chord to establish a minor tonality" - not on its own. It suggests a minor key, because that's the context in which we normally hear it. But if the tonic chord is major, then the "established" key is major, and a IVm is heard as a "borrowing"; it doesn't suddenly make the key minor.

I never thought about that example.
So, this sugests thatt there's something much more simple that establishes the key. I have read that the tonic alone is the entity that's responsible for that. If we think about the key as the note on which a song starts and ends, we tend to take it as true. But there are a lot of examples that contradict, or at least, confirm that there are cases on which the tonic alone is not enough to establish a key.

I see what you're getting at - there is a distinction there. But to me, it's down to the fact that bVI has (in relation to C major) two chromatic notes while the others only have one.

Yes, I was looking to the chromatic notes in the chords.