I've split it into three sections, the 1rst general theory. the 2nd how to apply to the fretboard, and the 3rd some fun things to do.
Recall, that we defined a chord as a group of distinct notes within an octave (and any octaves of those notes) usually played at the same time.
Recall also that in the last two lessons we discussed how to derive chords from scales by stacking thirds.
We first looked at triads built of stacked thirds. Specifically, we derived major, minor, and diminished chords from the major scale and its modes.
Recall that we discussed interval inversion, whereby the interval relationships between two named notes changes by moving one of them an octave to the other side of the other note.
We can also invert chords. Let's look at what we created by stacking 3rds. These are in the key of C, and the chords in order shown (from left to right) are C-Dm-Em-F-G-Am-Bo.
O |-------------------------O----- O O |-----------------O-------O----- O O O |---------O-------O-------O----- O O O |-O-------O-------O------------- O O |-O-------O--------------------- O -O-
Let us focus on the first chord C to discuss inversions. The discussion applies to all the above chords though.
The C major chord is made up of the notes C,E,and G. When the C (the 1) is in the bass we say it's in root position.
Now if we invert the chord, the letter names are the same, but the intervals from the lowest notes to the others has changed somewhere. So we start by going from root position and moving the C up an octave. We now have E in the bass with the G and the C above it. E to G is a m3, and E to C is a m6. We now say that this chord is a C major chord (triad) in 1rst inversion. Notice that E is the 3rd of the chord. We would typically write this as C/E. In general, if the 3rd is in the bass, we say the chord is in 1rst inversion (even if the notes above it are different from the specific intervals we just described).
|-------| |-------| O |-------| |-O---O-| |-O---O-| -O-
So here is C major (triad) in root position and 1rst inversion.
Ok. Now if we take the 1rst inversion and move the bottom note (E) up an octave, now the G (the 5) is on the bottom with the C and the E above it, this changes some of the internal intervals, but is still a C major chord. G to C is a P4, and G to E is a M6. We would write this as C/G, and say that it is a C major chord (triad) in 2nd inversion. In general if the 5th of the chord is in the bass, we say it's in 2nd inversion.
|-----------| O |-----------| O O |-----------| |-O---O---O-| |-O---O-----| -O-
So here is C major (triad) in root position, 1rst inversion, and 2nd inversion.
After we derived triads, then we derived 7th chords.
O -O- O O |-----------------O-------O-----| O O O |---------O-------O-------O-----| O O O O |-O-------O-------O-------O-----| O O O |-O-------O-------O-------------| O O |-O-------O---------------------| O -O-
The above is 7th chords in the key of C, derived from the major scale. These chords are Cmaj7-Dm7-Em7-Fmaj7-G7-Am7-Bm7b5. We can invert these too. looking at just the 1rst chord (Cmaj7) to use as an example.
O |---------------| O O |---------------| O O O |-O---O---O---O-| |-O---O---O-----| |-O---O---------| -O-
The above 4 chords are all Cmaj7. They are from left to right in root position, 1rst inversion (3rd in bass), 2nd inversion (5th in bass), and 3rd inversion (7th in bass), and could be written respectively as Cmaj7, Cmaj7/E, Cmaj7/G, and Cmaj7/B (or C/B).
So in general, a 3rd inversion is when the 7 is in the bass. Now, theoretically more inversions should exist for larger extensions, but I've yet to see this written in a theory text.
Although inversions of chords contain the same notes (same letter names), because the arrangement of these notes are different, their internal intervals are different, and thus have slightly different sounds. you may find that different contexts give rise to use of different inversions.
A common example of 1rst inversion used in a context would be a descending bass line over a progression like IV-I-ii-I.
In G, we could have C-G/B-Am-G. The G/B is in 1rst inversion, and the bass line is moving through the notes 4-3-2-1.
Here is one possible way to play this (in TAB):
|-----------| |--1-3-1-0--| |--0-0-2-0--| |--2-0-2-0--| |--3-2-0----| |--------3--|
note: that more than 3 notes were used per chord, and that not all strings were played per chord.
We could say that the particular chords above are particular voicings of these chords. A voicing is a bit more broad of a term than inversion. There might be several ways to play a particular inversion. those would be different voicings of the same inversion of the same chord. A voicing refers to the exact particular way the notes of a chord are arranged. Voicings do not have names, but they can be notated by drawing the chords out or by writing them down in TAB or standard notation.
Why use voicings? There are subtle variations in sound, that may not be obvious to your ears unless you've trained them, but it registers with your brain. when you repeat a common voicing, the brain identifies it with other times it has heard that voicing. So we could consider voicings to be archetypes. Or we could think of voicings as different hues of the same color. A bit more practical than contemplating the psychology of sound though is to realize that often these voicings are in a context. which brings us to the idea of voice leading.
Without going into the history of how and when evolved, just consider that when writing choral music, we could write out parts for various voices. Some simple systems would be SAB (soprano, alto, baritone), or SATB (soprano, alto, tenor, bass). These could quickly become more complicated but consider the first system as 3 voices, 1 high in pitch (soprano), 1 mid range (alto), and 1 low in pitch (baritone). And we could consider the 2nd system as 4 voices: 1 high (soprano), 1 high-mid range (alto), 1 mid-low range (tenor), and 1 low (bass).
Now looking back above at the 4 chords C-G/B-Am-G, we can see that they have 4 notes each. We could choose to consider all the lowest notes to be a voice (like the bass), and all the next lowest notes to be another voice (like the tenor), the 2nd highest notes as a third voice (like the alto), and the highest notes to be a 4th voice (like the soprano).
Small movements between the notes in a voice are considered to be smooth transitions, where large movements would be considered less smooth, or even jarring. So a note staying the same or moving by only a half-step or whole-step would be considered desireable to produce a smooth transition between chords. (this might be against what you're trying to do. for instance, if you're writing punk music, you might not want a smooth transition between chords)
Looking at the 4 chords above, we see that the bottom voice in these 4 chords is moving in a descending fashion through the notes C to B (1/2-step) to A (whole-step) to G (whole-step). All movements are relatively small and thus potentially smooth. The second lowest voice moves through the notes E down to D (whole step) up to E (whole step), down to D (whole step). The third voice (2nd highest) goes through the notes G to G (no movement) up to A (whole-step) down to G (whole-step). The top voice goes from C up to D (whole-step), down to C(whole-step) down to B (half-step).
All voices move in small intervals, so there is a good possibility that the progression will sound smooth. Just because there is smooth transitioning between chords does not imply that there is no tension. you can still create a good amount of tension (and release) using voice leading techniques. Understanding voice leading (what's taking place from chord to chord in each voice) will help us understand why we use different voicings, and give us a context to understand passing chords, substitution, and modulation, as well as ways to create chord progressions (that aren't necessarily based on any key).
Without going into great detail, i'll give an example of each of these (passing chords, substitution, modulation).
Here is an example of passing chords created by a chromatically ascending bass line (which is to say the bass line is moving up in pitch by half-steps).
Given the progression Cmaj7-D7-Em7, we can add passing chords between these chords. The chords I've chosen are created by moving one note of a chord twords the next chord, while keeping the other notes the same (specifically, the bass notes are moving. this is often encountered in samba/Bossa Nova musics.) Below is in TAB:
|-------------| |--5-5-7-7-8--| |--4-4-5-5-7--| |--5-5-7-7-9--| |--3-4-5-6-7--| |-------------|
So the 5 chords from left to right are: Cmaj7-C#m7b5-D7-D#o7-Em7. Here C3m7b5 and D#o7 are passing chords. We can see by considering each string to be a voice, all movements between any two chords are a half-step or a whole-step. We could also note there is parallel motion (all voices moving in same direction at same time). There is a smooth transition between chords, and yet the passing chords add tension (which is soon released) to the progression. Of course you could choose other notes to move, move more than one note, etc. I choose this example because it illustrates the principle of passing chords and it's a substitution commonly found in Bebop and samba/bossa musics.
So let's talk about substitution. Substitution is replacing one chord with another chord ( or several chords). Some substitutions work better than others. Let's start real basic, and consider that one way of looking at tonality (tonal centers, tonal progressions, etc.) is that the major tonal progression is I-I-I-I or i-i-i-i, that is of a static progression staying on the same chord. from here we could move a note in and out of the chord. For example: I-Isus4-I-Isus4-I (suspensions) or I-I(6)-I-I(6)-I (suspensions as heard in a blues shuffle). Put them together and you get I-Isus4(6)-I-Isus4(6)-I. Now, Isus4(6) happens to be the 2nd inversion of the IV chord, so the progression could be seen as I-IV-I-IV-I. This progression could be seen as V-I-V-I-V by changing perspective of what our 1 is. So we could create I-IV-V and i-iv-v progressions by means of substitutions. Now we can substitute other chords in their place to get even more possibilities of chords for progressions. let's take as a general rule that if a chord shares a majority of its notes with another chord that it may be a good candidate for substitution.
Let's breifly go into the key of C, as looking at letter names is often a good way to examine substitution possibilities.
So I = C, IV= F, V= G.
From the previous lesson on harmonizing chords we recall these triads from C major scales.
C = C,E,G = I
Dm= D,F,A = ii
Em= E,G,B = iii
F = F,A,C = IV
G = G,B,D = V
Am= A,C,E = vi
Bo= B,D,F = viio
Given the progression I-IV-I-IV-I, we could substitute in some of these (or other) chords.
For the IV chord (F), I could substitute Dm or Am, both of the chords share two of the same notes with F. (this would be equivalent to saying that we could substitute the ii or vi for the IV).
For the I chord (C), we could substitute Em (iii) or Am (vi), since they share 2 of the 3 notes with the I chord (C).
For the V chord (G), we could substitute the iii (Em), or the viio (Bo).
We could find substitutions for the other 4 chords.
For the vi, try substituting the IV or I.
For the ii, try substituting the viio or IV.
For the iii, try substituting the I or V.
For the viio, try substituting the V or ii.
Of course the possibilities for substitution are rather large, and we are not constrained to notes found in a key. for example for the viio (Bo= B,D,F) I could substitute Bb (Bb= Bb,D,F). This would be a major sound rather than a diminished sound, and because the two chords share most of their notes, it would be a good substitution to try. we could look back at the chords from th epassing chords example, and find a substitution rule for various seventh chords ( one can replace a major seventh chord with a half-diminished seventh chord whose root note is a half-step higher and vis-versa, etc.) Substitutions can be analyzed on a note per note basis between the chord that was substituted and the one it was usbstituted for.
A basic definition of modulation would be a change of keys. We can say that within a key, that the chord with the strongest resolution to the I is the V. This is often used as the basis for modulation between keys.
So say that we are in the key of C (chords given above), and that we want to switch to the key of Eb. We could just stop playing progressions in one key and start in another. That might sound too abrupt. So we might want to smoothly move from one key to another. Probably the most common way to do this is to put the V of the new key before the I of the new key. So to get from C to Eb, we could have C-Bb7-Eb (often the dom.7 chord is used on the V as the resolution is even stronger). that might not sound so great, maybe we could use a ii-V-I progression to change: C-Fm-Bb7-Eb. Fm is one note different from f which is the IV of the first key (C). So we could try C-F-Fm-Bb7-Eb. And we could substitute chords for other chords, etc.
Consider the movement of notes from chord to chord in the last possibility C=C,E,G ; F=F,A,C ; Fm=F,Ab,C ; Bb7 = Bb,D,F,Ab ; Eb=Eb,G,Bb. There exists the possibility in moving from chord to chord that each note would only have to move a half-step or whole-step.
Above we saw that Csus4(6) and F/C are in fact two different ways of describing the same notes. We call any two such chords, chord synonyms.
Why would we entertain more than one possible way to name a structure? Often to emphasize the functionality of the chord. in the first chord (Csus4(6)) I am emphasizing that it is a C chord that has some notes suspended from their normal positions. in the second chord (F/C), I am emphasizing that it is an F chord though with the 5th in the bass.
Is their likewise another name for the first inversion of a chord? yes, probably. By looking at it we can come up with a strategy to attack chord synonyms. So C major is (C=C,E,G), and we can Look at C major 1rst inversion as (C/E= E,G,C). Now instead of considering it a C chord, we shall consider the same notes as some kind of E chord (E?=E,G,C). The E is the 1, G would be a b3, and C would be a b6 (or #5). So we could write the chord synonym as Em(b6) or Em+ (Em+5).
Seventh chords have 3 inversions . So let's use a minor seventh chordas an example to find chord synonyms with.
Am7 = A,C,E,G
Am7/C = C,E,G,A = C6 (6=1,3,5,6)
Am7/E = E,G,A,C = Emb6
Am7/G = G,A,C,E = G6/9sus4 or G6sus2(4) or Am/G
So you would re-analyze all the notes in the chord with respect to the new root note, and find the best fit to the intervals.
Again we would use different names depending on what we wanted to emaphasize. Although C6 and Am7 share the same notes, they do have different sounds (one has a major sound, one has a minor sound). Of course you can manipulate your voicing to accentuate or diminish these differences.
The more distinct notes a chord has, the more inversions and synonyms it can have.
Next part of the lesson is on creating your own voicings.
How do I change all those numbers to letters (for notes, chords, etc.)? Here's a transposition chart simianmoon.com/snglstringtheory/guitar/8theory3.html
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