Group B, the common-tone approach: video materials, descriptions and observations.
I don't have the intention to transcribe the full content of the lessons here, but wish to select the most relevant parts of each class and discuss what happened in the light of the learning process.
Group B, 17 November 2014, teacher Karst (K=Karst, E=Eunike, Mc=Michelle, T=Tobias, Mk=Mekhi).
After a short introduction of the subject and goals of the class, I asked in this group also to which extent they have had any instruction on the subject of modulation so far. E: not really learned about it, except how to go from the major to the relative minor. (K: just a related question, which are the modulations always made in tonal musical structures? Of course from major key to it's dominant, and from minor to it's relative major key). Mc: last year we were taught about modulation, something with going from E major to E flat, but I don't remember. It was written on paper. T: we haven't learned yet with writing. Mk: I actually just started with music theory classes.
We will explore the so called common-tone approach, as described in the previous 'setup' chapter. The first exercise is to play random progressions of chords which have exactly one tone in common. The chords don't particularly have to be in one key. Watch the first attempt of E:
[VIDEO CT0760A (6:40)] Eunike
In the beginning E is not making the distinction between chords with one or two common tones. We evaluate and see that chords on a third distance such as I and VI have two common tones. Triads a fifth apart have just one. The dominant 7th chord in fundamental position with four different tones will not allow for a common tone with its resolution. In this case doubling the bass note (and leaving out the fifth) creates a common tone. Now we compare the progression C-major to a-minor with C-major to A flat-major. There is more surprise in the latter. This is a connection of two chords on a third distance with a single common tone.
Something else to consider is to consciously put the common tone in a certain voice. When put in the melody, it is particularly effective, while in the middle voice the connection is less obvious. It is clear that the students do not feel confident at this stage, there is simply too much thinking going on. This will undoubtedly improve with experience. As no one came up with the possibility yet, I showed some examples of creating the common tone in the bass:
[VIDEO CT0760B (14:32)] Karst
Next is T at the piano. Although he still needs a lot of time to think we can observe that he starts to feel more confident, and show more creativity in the choice of his chords and progressions. At some point he is even shocked by the 'unexpected' sound of an augmented chord. This is an important part of the exploratory character of the exercise. Even experienced improvisers are sometimes surprised by things that happen faster than what they expected with their imagination, and learn to deal with it:
[VIDEO CT0760C] Tobias
Group B, 24 November 2014, teacher Bert (B=Bert, E=Eunike, Mc=Michelle, T=Tobias, Mk=Mekhi).
Bert starts with an improvisation assignment: play a prelude where there is always one common tone when moving to the next chord. Try to always keep moving. If in doubt just repeat your chord before moving on. Enjoy the sound and the quality of the chords while playing. The first attempt is made by Tobias:
[VIDEO CT0032A (00:04)] Tobias
The common tone rule creates a natural connection between consecutive chords, where the improviser has the choice to create low or high contrast between them. It depends on the strength of the aural imagination to which extent there is control over this amount of contrast, as well as over the grouping of the chords into certain tonal area's. In Tobias's prelude there is a certain randomness which makes the listener get lost after a while. On the positive side there is good concentration, he plays without interruptions and makes a nice sound.
The next assignment is to take a similar approach but make a modulation. E is invited at the piano and makes modulations by sequence with a particularly nice contrasting connection of F minor to E major with the common tone in the melody. However, there is not much focus and it moves in many directions. Bert asks her to be more concrete and start in F major, then modulate to A major. Eunike does not really find a convincing way of doing this. Bert suggests that a more regular phrasing might help, and proposes to use a Scottish folk song as a starting point. This is Michelle's version:
[VIDEO CT0032B (22:48)] Michelle
Eventually the sequence moving each time a fifth up gets her there! However, the song gets lost as there is no material used, nor is much left of the original goal to use common tones to achieve the modulation. Bert ends the class by playing some of the modulation examples of Kalkbrenner's book, asking the students to prepare them as homework.
Group B, 1 December 2014, teacher Karst (K=Karst, E=Eunike, Mc=Michelle, T=Tobias, Mk=Mekhi).
In this lesson we discuss the modulations to nearby keys. The first assignment is to go from C to G. Eunike plays the following:
[VIDEO CT0773A (01:42)] Eunike
She plays in fact a whole song, using first a Pachelbel pattern to confirm the key of C, then moving to G through VI6 with the common tone A between CVI6 and GV7. I remark at this moment that Kalkbrenner would probably look for the common tone between the Tonic of C and the Dominant seventh chord of G. This would have to be the C itself, which changes from a perfect consonance to the expressive seventh of the dominant for G. E quickly picks up this new information. We discuss how the same process would bring you from the key of c minor to the key of g minor.
The next assignment is to modulate from C major to A minor. Initially T is using the E as a common tone of the C major chord and the V7 in A. This works fine, although his attempts lack a convincing consolidation of the key. After some trying he comes up with another way which works quite nicely:
[VIDEO CT0773B (16:35)] Tobias
The next assignment is to modulate from C minor to E flat major. Mk tries but lacks so much basic experience with keyboard harmony that he can not find a convincing way. Looking for common tones between the tonic of C minor and the V7 of E flat he discovers that there are none. We discuss how in this case a common tone can be used from the IV or the V in C. F minor has two common tones with the V7 of E flat, so it is a good candidate for a fluid modulation. We practice both modulations to the relative minor and major starting from a few other keys.
Group B, 1 December 2014, teacher Bert (B=Bert, E=Eunike, T=Tobias).
Bert discusses a few examples of Kalkbrenner's book (Kalkbrenner, 1849). He asks T to play a few examples and comment at the same time on the things happening. The approach is very practical, just looking for common tones which will allow a fluid modulation to the new center.
Now they continue to improvise a consequence on a given antecedent in F major. First one that establishes the key of F, then a consequent that modulates to A major. T is at the piano and hesitates, looking intently at the keys. Bert remarks that it is not his intention to make T calculate and asks him to first play a cadence in A major. Next T makes a first attempt to modulate:
[VIDEO CT0232A (12:46)] Tobias
It is interesting to see that he gets there, but not with the common tone approach but rather a monte sequence which makes twice a step up from F to A. It may be that this kind of pattern is more intuitively accessible than the calculation that needs to be made. The real solution lies of course in the active imagination; varying on the melody in the antecedent one can for example play the motive up and choose the C# as a goal in the melody, thereby arriving easily in A. It is clear that we need more time with our students to achieve this.
With this fragment we arrive at the end of the report of group B. In the next chapter there is a summary of observations and conclusions of the study.
Group A, the directional approach: video materials, descriptions and observations.
I do not intend to transcribe the full content of the lessons here, but wish to select the most relevant parts of each class and discuss what happened in the light of the teaching and learning process. The descriptions follow roughly the time path and development of the lessons.
Group A, 17 November 2014, teacher Karst (K=Karst, N=Nastya, G=Gabriele, B=Bob).
The first question is in how far the students have had any instruction on the subject of modulation so far. N: We did it normally by hearing. There were rules, but I don't remember them. G: we learned a few types, the one with the dominant 2nd chord and with the diminished 7th chord. But it is all blurred now. B: I have had no lessons on this subject so far.
One copy of the grid (simplified Weber Space, see above) was put up on the piano, and each student received one to take home. The idea behind the directions in two dimensions was explained. Why perfect fifths and minor thirds? There appears to be a minor and a major side of one and the same selection of tones (diatonic scale), sharing the same circle of fifths. I played examples of this, showing the importance of the falling fifth, and the kinship of I and VI, the major and minor as related keys:
[VIDEO NTH0758A (5:40)] Demonstrating the relative major and minor on the circle of fifths.
The students were asked to play a free "path" on the grid. I explained that grid notes represent fundaments of the chords, so any major or minor chord on the root indicated in the grid is possible (to keep it simple for now). To avoid falling off the grid, one can jump to an equivalent fundament when nearing the border of the grid. Here is a video excerpt of Bob following a free path with a limited number of chords:
[VIDEO NTH0758B (11:43)] Bob
While trying this N remarked: "I have to think about major and minor". She is addressing a very important point, which has deliberately been left out in my research with Thomas Noll so far, but which is inevitable in relation to practical teaching. My initial answer is that a student needs to rely on musical intuition, and experiment with different possibilities (In my meeting with Peter Schubert at McGill, he stressed the importance of playing in the sandbox). It also helps to try to keep the chords compatible in the diatonic as far as possible. We should not forget that there is a great amount of freedom in the choice of chords, as most rules in this direction are based on the aesthetics of a certain style. One concrete thing one can do is to anticipate the upcoming harmonic direction. The chord types can be adapted to the situation: anticipating a falling fifth means that the chord chosen can be a dominant 7th, or the chord already chosen can be changed to a dominant 7th before making the falling fifth progression. Practicing this also greatly stimulates the active aural imagination: rather than playing chord by chord one imagines a sequence before actually playing it. Here is an example of G trying to do this:
[VIDEO NTH0758C (17:32)] Gabriele
In a Left progression followed by a Down, the voices can either stay (major goes to minor7th and minor goes to half-diminished 7th) or there can be a rising chromatic line when the Left becomes a dominant 7th.
Think about the possible paths within a diatonic situation. For example in C major one can go down a fifth to F, but not more than that, because Bb is out of the key. So a typical path is C-F-D-G-C. After the F comes a shift to the left rather than a falling fifth. The result is a typical classical cadence: I – IV – II – V - I.
Discovering simple patterns, N playing C-A-D-G-C and repeat. Confusion over bass note versus fundament (II65).
[VIDEO NTH0758D (20:23) Nastya
Group A, 24 November 2014, teacher Bert (B=Bert, N=Nastya, B=Bob, W=Wouter).
The lesson starts with playing free improvisations following paths on the grid. Bob is clearly more comfortable doing this than he was in the first lesson:
[VIDEO NTH0030A (0:02) ] Bob
Interesting to mention here is that Bob apparently said to Bert that this way of connecting chords matches what he already likes to do by himself while improvising. One can notice also that in this improvisation he has a preference for movements up and right, which gives the improvisation a distinct 'pop' like feel.
Regarding the grid on the piano A remarks "It is easier somehow when I don't look at this paper". This means the grid must be internalized, fundament connections need to be heard, seen and felt on the piano. Right now she finds it hard to keep playing while following the path on the grid. W finds it extremely difficult to do more than just playing single chords while moving about the grid. He lacks the ability to create movement and keep playing while anticipating chord changes. For this type of student we need to work on very basic patterns, like moving back and forth between tonic and dominant, before we can go further.
Bert asks now from the students a first try to play a modulation following the next steps: choose a starting key and consolidate the key, then follow a path towards new key, then consolidate this new key. The first assignment is to modulate from A major to B flat major. It sounds simpler than it is, as W is struggling to find a convincing way. Bert shows a possible solution in this short fragment, following the path A-C-F-Bb:
[VIDEO 0030B (18:09)] Bert
Just like I did in the previous lesson, Bert points out that changing a chord into a dominant enables the down progression, while changing from major to minor opens the way to the right movement. However to make a more convincing modulation, it works often better to make a II-V-I progression than to just play a chain of dominants.
Now to make it sound a little more musical Bert proposes to take a Scottish folk-song as input. Play the theme in F major and then make a modulation to A major. Two of the possible paths are: double-left and two times down, or monte sequence left, down, left, down. Bob uses the latter:
[VIDEO 0030C (23:23)] Bob
Group A, 1 December 2014, teacher Karst (K=Karst, B=Bob, W=Wouter).
We start discussing the relationship between fundament and bass note, as well as chords with "non-sounding" fundaments. The dominant 7th chord (on the fifth note) and the diminished 7th chord on the leading tone have the same fundament: their harmonic functioning is equivalent. Thus the diminished 7th chord can be regarded as having a non-sounding fundament which lies a major third lower. We recuperate some things from the previous lessons. W has a tendency of playing major chords on each and every fundament. We discuss why this does not work well. One has to try to make sensible upper structures that fit into the diatonic world above the fundaments. Trial and error is one of the strategies: this will train the aural imagination so that the right chords will be anticipated. This is an essential skill for improvisation. B is clearly ahead of W in this respect.
Next W is asked to play a modulation from C major to E minor. The following happens:
[VIDEO 0772A (18:40)] Wouter
He decides on the path C - A - F# - B - E. However, there is doubt about the exact voicing of the chords. It is interesting to see that with a little trial and error he finds a correct melody, after which he can think about adding the other notes of the chords. I think this is an important learning moment.
W is still confused about the difference between bass and fundament. I offer a more elaborate explanation to clarify the situation, using an example from Beethoven:
As one can see, the underlying pattern is simple, initially just up and down prolonging the tonic, then moving to the dominant via left, down, down. Most of the chords are inverted to create a more melodic bass line. First and last chords of the phrase however are in fundamental position, clearly marking the main tonal functions. Gaining control over one's improvisation in this way is definitely a more advanced skill.
Group A, 8 December 2014, teacher Bert.
This class was a private class of Bert to Bob. At the beginning Bob received a copy of the modal charts, which looks like this:
It was explained how the cadential and the prolongational modes are two very common paths followed in the Classical and Romantic style. They can both be used to establish a key area. The fundaments are designated as Riemannian Tonic, Subdominant and Dominant functions. The altered Subdominant in the Cadential mode and the altered Tonic in the prolongational modes are optional. They can be used to intensify the harmony before the change to the next function (see also the more extended explanation in the chapter 'Sources I').
Bob initially explores the modes in various keys. Bert suggests to make a modulation by switching the #T in the second mode to the S in the first mode of the new key. It takes Bob a while to understand the concept. Eventually he plays in D major: I - VI and reinterprets the last chord as F#-minor IV, continuing with II - V - I. Translated to degrees of the functional modes this could read as: D: T, #T = F# S, #S, D, T. So far this works fine. Bert continues with presenting some 'beginnings', basically 4 bar antecedents that should be completed with a modulating consequence. Bob decides to modulate from C major to E flat major with this given beginning:
See and hear what happens the first time:
[VIDEO NTH0231A (00:00)] Bob
Here B starts the second half of the phrase with a Bb major chord, which is quite far from the C major chord at the end of the first phrase (up-left), as a result the phrases feel disconnected. Bert remarks that the B flat also is not a shared note in the modes of C and E flat. There has to be a better way. This is his second version:
[VIDEO NTH0231B (12:16)] Bob
Now the path is more elegant, the T at the end of the first half becomes the #T in the key of E flat major, and consequently moves to an f minor chord. In a more advanced stage one will be able to make fast choices about alternatives which share the same path, such as replacing the F minor chord with an F half-diminished, creating a chromatic passing bass note C flat (E flat: II43 moll-dur), or to change the C major chord first to C minor before moving on.
Bert rightfully stresses a few times the importance to be able to change color on the same fundament. Without this the upper structures will not fit into the new key area. The student must not only follow the path but also anticipate the new key with the choice of chords.
Group A, 15 December 2014, teacher Karst (K=Karst, N=Nastya, G=Gabriele, B=Bob, W=Wouter).
This week the group is complete. We began with discussing the chart with the modes and practicing to play elementary versions of these modes in various keys. It can be observed that the first mode of C coincides with the second mode of F. To the other direction the second mode of C coincides with the first mode in C. The only difference there would be is the type of chords one plays on these fundaments. One can modulate easily fifths up and down with these common fundaments. To illustrate this we try a few modulations on fifth distance:
[VIDEO NTH0813A (12:42)] Gabriele
The easiest path to follow when modulating a fifth up is: left, down, down. To modulate a fifth down one can follow: down, down, left, down, down. Of course there are many other paths possible. The students are still a bit confusion about the difference between the first and second mode. For now I try not to be too specific: the pattern is the same, and they are simply two different paths one can follow to stabilize a key area. The 'alteration' (black note in the graph) is optional. So for a second mode one can play: I - II - V - I, or I - VI - II - V - I. Inversions and secondary dominants are also possible, as long as they are based on the same fundaments of the modes (see also the examples in the chapter 'Choosing the chords).
We discuss some other common modulations such as the modulation to the relative minor key. The goal is to quickly imagine the patterns of the modes in relation to a key. Common fundaments can be the stepping stones between the key area's. We discuss this and Nastya plays a modulation from C major to A minor:
[VIDEO NTH0813B (25:18)] Nastya
With this class the series of 5 lessons ended. A further evaluation follows in the chapter after the lesson descriptions of group B.