A couple of days ago I stumbled across the Barry Harris system as taught by one of his students Shan Verma, who also runs https://www.jazzskills.com.
All of the practice is around learning the major 6th diminished scale, which has some very interesting properties, and sounds great.
These two videos show the two primary ideas for today’s practice.
Practice notes
C scale notes. I was playing through this one last night as well. In particular, I was attempting to get the ‘building up notes’ exercise fluid. If I played each step like a new chord it felt chunky. If I played each step like an ascending run in the right hand, and simultaneous descending run in the left hand it was fast. However, when I did those runs I was only playing single notes, and leaving out the internal notes that form the maj6 or dim7 chords. Then, I got into the swing of alternating my fingers properly.
The table shows the fingering for thumb to pinky (1-5), for the left and right hands. Start with both thumbs on the same note. Then, the index to pinky (2345) go on every note ascending on the right, and every note descending on the left.
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Took a little while, but once the symmetry hits the fingering locked in pretty easily.
In C, starting from the Ab has a particularly nice symmetrical viewpoint.
F scale notes. Practice went pretty well. This scale uses a different dim7 chord (GBbDdE). Felt like a little bit of interference from C. The Fmaj6 chord has the same shape and fingering as Cmaj6.
As I was playing the building up notes exercise through every note, I started to think more about how I could use the exercise. I started asking questions like, where does this movement want to go? For example, starting on the root, and “building up notes” seems to want to resolve on the V.
Bb scale notes. These observations would apply to any of the other scales, but I roughly had these thoughts around this time in practice. So, I’m going to stop organizing notes by scale.
More practice notes
When/Where to start building up?
Noodling around in CMaj6…lots of CEGA. I started building up on C.
step 1, playing a C is kind of redundant with the chord, but it sets the location
step 2. playing a BD is nice. It’s not part of CEGA, but it adds the maj7 and 9th. Easy to sprinkle in whenever, even if staying on CMaj6. sprinkles of possible movement.
step 3. ACE, restating the center, with minor vii feels
step 4. AbBDF, dominant chord, lots of possibilities, wants to go G
Still playing over a Cmaj6, I did a little bit of starting the building up notes on different notes, but not too much. Need to do that more, to get a better sense of the directions.
What a step in the building up exercise provides
The building up notes exercise starts by emphasizing some particular note in the scale. This could be where you are at, say in a melody. Then, it alternates between adding the next notes in a maj6 chord, or a dim7 chord. I should sit down and spell this out for myself at some point after I get the fingering down across keys.
- in general, the exercise provides a way to start on a note in the scale, transition between restating aspects of the root (through the maj6), or the diminshed 7th chord, with very harmonious sounding transitions. The transitions already have a bit of movement, and they set up off-ramps into other directions. Especially from a dim7th chord, which can easily end up as four different 7th chords.
Cognitive science notes: proactive interference
Proactive interference is a well-known phenomena in the learning and memory literature. The classic finding is from studies of free recall. Participants are given lists of items to study, like words, and then after a delay they are asked to recall as many as possible from the list. Pro-active interference occurs when your memory for items in the list is impaired by previous exposure and/or learning attempts to memorize other lists.
The figure shows some recall data from Underwood (1957). The x-axis is number of previous lists. Some subjects were new to these kinds of studies, and they had not tried to memorize lists of items before. Their recall was pretty high. Other subjects had participated in these kinds of studies before, and had tried to memorize many different lists (up to 20 different lists). The more lists one had previously tried to learn, the worse participants did when trying to learn and recall a new list.
As I try to learn the maj6th diminished scale across all of the keys I’m wondering about the role of pre-active interference, as well as other kinds of interference. If learning scales was like learning random lists of words, then it is possible that every time I learn one scale, the next scale becomes harder to learn because of this so-called pro-active interference. My general sense is that this isn’t how learning scales works in practice, and that prior experience generally helps with learning new things. Not to say that there isn’t sometimes interference.
Eb practice…got through it, thought a little more about pro-active interference, and “task-switching” or key-switching.
It’s not clear to me that findings showing pro-active interference in free recall should neatly generalize to learning scales. One reason is that the free-recall studies usually used arbitrary lists of items with no particular relationships to one another. Part of the pro-active interference is that one accidentally recalls words from a previous list, and those get counted as errors. Also, learning additional lists of random items is like trying to grow a vocabulary of random words with no particular meaning.
In contrast to random lists of words, musical scales have many shared elements across keys. There is lots of opportunity for facilitation and interference. For example, learning to play the dim7 in the C major 6th diminished scale could facilitate learning the Eb, Gb, and A versions of that scale, because they use the same dim7 chord. At the same time, there could be associative interference at play based on prior learning attempts. For example, learning to interleave CEGA with DFAbB(dim7) could reinforce those interchord assocations, such as C6-Ddim7-E6. Then, consider moving to learn Eb major 6th diminshed. There is a C6-Ddim7-Eb6, and perhaps here the E6 will interfere with the Eb6? I wonder what a MINERVA process would do here…
Cogsci notes: Key-switching costs
Another classic finding in cognition is called the task-switching cost. This has been demonstrated in diverse task situations. The basic finding is that there are usually costs, in terms of time and accuracy, when switching from one task to another.
I’ve been practicing the build up exercise in C, F, Bb, and Eb. The fingerings are all different, but similar enough that my fluency is getting better, even as I switch to new keys.
These four keys share some notes. For example, C appears in all of C, F, Bb, and Eb scales. I did practice the build up for all four, across all notes of the scale, which means that I did start on C and do the build up for each key. However, I practiced the build up ascending and descending within each scale.
I am 100% experiencing pretty strong key-switching costs if I start on C alone, and try to then produce a build in the key of F, Bb, or Eb. It’s much easier to start on C major. Need to break out of the switch cost by practicing these more.
A musical benefit is that a build-up exercise starting say on C, can take you in lots of places, by building up into different keys from that one note. Opening so much opportunity for movement. Wow.
Cogsci notes: Spacing and repetition during practice
Another well-known set of phenomena in learning and memory are spacing and repetition effects. I have been thinking about these phenomena as I’ve been practicing, and I was probably thinking more about these than what I was trying to accomplish in Ab as I was learning the maj6 diminished scale in that key.
Spacing effects seem to be a common export of cognitive psychology, especially in various apps for ‘optimizing’ learning. For example, flashcard apps and language learning apps will build in a spacing algorithm. The purpose of the algorithm is to space out repetitions during practice, which can facilitate learning and memory (whether or not spacing effects have positive or negative benefits, or no effect can depend).
Repetition effects are another commonly studied phenomena. In general, repeatedly practicing an action, movement pattern, or series of movements, increases the fluency and “automaticity” of the action. Musician’s know this very well. If you haven’t practiced a Gb scale before, or in a while, your performance will be slow and error-prone. If you repeatedly play the scale up and down and up and down, over and over, it get’s easier, and your performance will become faster and more accurate. Repetitions can also make performance worse sometimes (but I’ll skip over those cogsci things for now).
Studies of practicing motor skills, like learning scales, typically show that performance gains follow a power or exponential functions (both are very similar looking), like the one below.
The general outcome is that measures of fluency, like scale speed, increase with more practice. However, the gains that are made with practice decrease. The biggest gains in performance are seen early on in practice, afterwards, it takes a lot of practice to make very tiny gains. There are lots of reasons for this basic curve. On a piano, one issue is that people can only move their fingers up to some limit, so there are hard limits to the floor of the function. And, it may take loads of practice to approach those near floor limits.
A related concept with repetitive practice is the idea of diminished returns. Repetitive practice will increase fluency for sure, but at some point in practice one becomes fluent enough, and further practice isn’t going to do much. So, the question becomes when to stop repeating and move onto something else? Which leads back to the spacing of repetitions question.
Let’s say you are trying to practice major scales in all of the keys. What kind of practice schedule should one adopt? There are lots of options, and depending on how you arrange things, the repeated attempts can be massed together or spread out. I’ve got more to say about this kind of stuff, but will get back to practicing Gb. Although, it would be possible to get fancy and use concepts from cognition, I’m just going through the circle of fifths. This has musical benefits, and moving in that direction involves going from one key to another that share many notes. As a result, I think I get a little bit of facilitation from learning one scale to another, and also a little of bit of a discriminative challenge to make sure I’m not playing the previous one. Seems like a productive level of difficulty.
Lunch break
Turning up the interference
All the above being said, over lunch I was wondering about maximum interference practice schedules. For example, consider this build-up note exercise. I could write a computer program to tell me what note to start on, and what key to build on, and have this be totally random. That would be a great little practice tool (note to self to make some midi javascript stuff later). But, it would be hard. Especially for me right now because I don’t know the build-up patterns in most keys yet.
Something more approachable, but still hard, would be for me to do much less repetition as I practice the remaining keys (I think I have about 8 left). Up until this point, I have been doing a lot of varied practice within each key. Something like this for each key:
play the all the notes of the scale up and down, and all around
play them all at the same time to “see the notes all together”
play them in sets of 4 or 5, starting on different notes
play them up and down starting on different notes
play the maj6 inversions as chords, then as arpeggios
play the dim7 inversions as chords, then as arpeggios
put the alternating chords together, play through the scale up and down in chords
play through the scale up an down in arpeggios
Start playing the build-up exercise on each note of the scale. Do this up and down and all around
That’s a lot of different kinds of repetition, and it seems to work pretty well. My fingers get used to the pattern of notes in the key, and then I’m on my way. Still, playing the scale in terms of chords is slow at first, and I’m not getting very fast, but it does become comfortably slow fairly quickly.
A different sort of practice schedule would be more painful. For example, I could go immediately to playing the chords of the maj6 diminished scaled in Db, which is the next key I need to practice. This will be new for me, and I know it will take sometimes a few seconds or more of staring and thinking, and getting a bit lost, to press the first chord, and then the second and so on. I will be working it out on the fly. After going up the scale one time, I could decide to stop Db, and switch to Gb (the next one in my anti-clockwise circle of fifths practice cycle). That would be new and somewhat painful too. In other words, the harder, less repetitive, more spaced out practice schedule could be: once up then switch to new key.
Maybe I will try this next I’m not sure if I have the patience for it…as I like to feel the progress. However, I can imagine some potentially interesting side effects (benefits? or at least potential consequences) of this switchy schedule. One possibility is that this schedule may increase associative linkages between a current musical goal and an intended outcome. One reason this might happen is that when attempting new patterns, the goal may be clear (e.g., play the third chord of the maj6 dim scale in Gb), but the action and corresponding pattern may not be clear. So, one is keeping the goal in mind as an instruction, and trying to work out the pattern, and then execute. As a result, this constitutes a processing episode where the goal was in mind at the same time as a puzzling out process, as well as an action being executed. According some theories of learning and memory the things that happen during an episode of learning are preserved in memory, and later retrieved when similar circumstance are re-encountered. Not sure what the practical consequences would be for learning scales in this manner…maybe I should go try this.
Alright…not as bad as I thought that would feel. Here’s a practice table with some scale completion time data:
| Db |
1:23 |
| Gb |
1:00 |
| B |
1:44 |
| E |
1:30 |
| A |
:49 |
| D |
1:17 |
| G |
:56 |
| Well-practiced (C) |
:12 |
This was pretty slow going, and fairly cognitively taxing. Was constantly reminding myself what I was trying to do, while puzzling out what to play. Not too bad though. Perhaps this caused me to make some more deliberate connections than I otherwise would have, not sure. My times were generally getting faster as I moved anti-clockwise, but that could reflect my overall fluency in those keys in general. I hadn’t tried the major 6 dim scale in any of these keys before and all the completion times (to play the chord for each note ascending) are about a minute or longer. By comparison, I went back to the piano and played through the C scale in 12 seconds…still pretty slow. For another comparison, I went back and played a regular C major scale in 7th chords in less than 3 seconds. Presumably with enough practice I get the above scales down under 3 seconds too. In C, I’ve already got down to 12 seconds. Not bad.
I had the worst time on B. I’m also curious on what kind of fluency gains I would make by just repeating this over and over. I think I should practice this a bunch of times in a row and see what the learning curve looks like. I’m using anything fancy, just the stopwatch on my iphone. I will play the scale in chords ascending, and press the lap button every time I’m finished. Let’s put in 10 minutes of repetitive practice and see where that gets me.
Done. And, time plot the data in R!
── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr 1.1.4 ✔ readr 2.1.5
✔ forcats 1.0.0 ✔ stringr 1.5.1
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── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
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ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
It’s not a pretty power curve, but at least it is generally decreasing. I was hovering around a minute per ascending attempt for the first 7 attempts. Then, a few things started to get easier, and I started speeding up. I cut my time by more than half, yah! Still a long way to go to get faster than 3 seconds. And, I suppose this gives me some perspective on what I got out 10 minutes of this kind of practice.
I’m going to try one more 10 minute burst for fun. This time I’ll do the scale in E, which was my second slowest time. However, instead of playing the scale ascending over and over for 10 minutes. I’m going to do whatever I want for 10 minutes, and see what happens. More specifically, I’ll take the list of things I mentioned earlier that I was doing, that helped me get my fingers into the key, and all that kind of stuff. Then, in the 9th minute, I’ll start timing my ascending runs. Maybe my more varied practice version of 10 minutes would get that scale into shape faster than just focusing on ascending runs…Or maybe not?
Did that. At the end I did a run of chords in E in about 20 seconds. But, my second attempt ended around 30 seconds with lots of errors. I was probably getting a bit better at all of the other things I was practicing, rather than being able to specifically do the ascending chords.
Also, starting to experience brain melt from too much piano practice. Maybe I should call it a day :)
