Progressive Complexity
In response to this comment on my post describing Lesson 005.1...
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All of your criticisms above make perfectly valid points. I have what I *think* are good reasons for structuring JiMS the way I am, but in the absence of hard scientific evidence as to the efficacy of one structure vs. another, there is very ample room for differences of opinion. I value, very highly, such critical feedback, because it forces me to revisit my assumptions and see if they have any rational basis. That said...Many of the concepts that I'm teaching in JiMS with specifics, could be taught with greater generality. Here's why I'm starting with narrow, concrete specifics, such as the assumption of the syntonic temperament in 12-TET tuning. I could design JiMS such that it did not assume the syntonic temperament (i.e., alpha = P8, beta = tempered "perfect" fifth, with first comma tempered to unison) or 12-TET tuning (i.e., P8=1200 cents and P5=700 cents). Instead, I could teach that alpha and beta could be any interval. This would be a temperament-neutral approach. So, why am I basing JiMS firmly on the syntonic temperament...and with a fixed octave, to boot? Firstly, because JiMS is based on the philosophy of "progressive complexity," which states that "the simplest approximations of the truth should be presented first, with increasingly complex approximations added later, only as necessary." (I'm quoting myself here, but some prominent educator somewhere must have said something similar.) So, JiMS starts with the diatonic scale in the syntonic scale, in 12-TET tuning, and will progress through the chromatic scale also in 12-TET. It's only when JiMS needs to introduce the enharmonic scale -- which I've decided to do WAY later -- that the concept of "tuning" needs to be introduced. After that, JiMS can introduce Dynamic Tonality. Somewhere right before the introduction of Dynamic Tonality, I'll introduce the notion that the octave's width can be tempered in the syntonic temperament, too. After Dynamic Tonality, I can introduce non-syntonic temperaments. Remember the immediate goal of JiMS: to dramatically increase the efficiency with which non-musicians gain sufficient musical knowledge to write their own pop/rock music. To achieve this goal, students do not need to learn about non-syntonic temperaments. That being said, JiMS' *ultimate* goal is to establish a new universal paradigm of music which expands the frontiers of tonality. I believe that this ultimate goal cannot be achieved without first achieving JiMS immediate goal. Therefore, the immediate goal must take precedence in all of JiMS' design decisions. Specifically, I can't allow JiMS early lessons to be made more complex in order to facilitate the later introduction of non-syntonic temperaments. My recent re-writing of Lessons 4 and 5 is a manifestation of this design trade-off. I have a tendency to want to introduce non-12-TET and non-syntonic ideas sooner than necessary, because I think that JiMS' ability to support those concepts distinguishes it from traditional approaches, and because I think that these concepts are WAY COOL. However, it's simply not efficient to introduce those concepts too early. Secondly, the musical invariances on which JiMS is based -- transpositional invariance, tuning invariance, and cardinality invariance -- are all invariant only within a single given temperament. None of them are invariant across temperaments. I can't teach these invariances in the abstract; I can only teach them in the concrete context of a given temperament. Combined with the doctrine of progressive complexity, the temperament-dependency of musical invariances requires me to teach them within a given temperament (and tuning) first, and only then to generalize those teachings across (tunings and) temperaments. For example, consider the syntonic and schismatic temperaments. Both have the same generators -- P8 and P5 -- so they can share the same note-names, note-layouts, and staff notation. However, their comma sequence differs, and hence so does their mapping of partials to notes. For example, from a fundamental on Do, the syntonic temperament maps the fifth partial to Mi, while the schismatic maps it to Fe. As a result, the "shape" of the major triad (for example) is different, on JiMS keyboard and the JiMS staff, even across temperaments as closely-related as the syntonic and the schismatic. Combined with the doctrine of progressive complexity, this variance-across-temperaments requires JiMS to start by assuming the use of a single (tuning and) temperament, introducing other (tunings and) temperaments only when necessary (and it isn't necessary until after Dynamic Tonality has been introduced, using the syntonic temperament). Thirdly, the music of human cultures in the real world seems to be strongly biased towards temperaments generated by the P8 and P5, including the syntonic and schismatic. The syntonic temperament's tuning continuum includes nearly all of the tunings ever used by human cultures; the exceptions are arguably schismatic, such as Turkish and arguably some Indian music. This bias may arise from the human ear/brain/mind's apparent use, for the detection and tracking of tonal relationships, of a "map of the regions" generated by P8's and P5's (as exposed by Petr Janata's brain-scans). Such a map of the regions is the dual graph of the Wicki/JiMS note-layout, and hence is topologically identical to it. Combined with the doctrine of progressive complexity, this human cultural bias towards the syntonic temperament leads me to choose it as the basis of JiMS, with the added complexity of other temperaments being added to JiMS only much later in the lesson sequence. Please note that all of this is "just talk," however. I don't have any scientific evidence that proves that these design choices lead to the most efficient and accurate acquisition of musical knowledge by musical novices, or that graduates of such an educational program are able to advance the state of the art faster and/or more creatively. But then, no contrary evidence exists to refute these claims, either. The efficacy of alternative paradigms in achieving such objectives is an under-studied area. I hope that, as JiMS becomes available, such rigorous studies can be carried out. In the meantime, you're not wrong, and I'm not right. We just disagree as to when, in the sequence of ideas, non-12-TET tunings and non-syntonic temperaments should be introduced. On the other hand, we agree that these concepts SHOULD be introduced as soon as possible -- an agreement that differentiates us from the vast majority of music educators and music theorists, who neither understand nor care about these concepts. I hope that you will find this response to be in the cooperative, exploratory spirit of give-and-take in which it is intended.
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All of your criticisms above make perfectly valid points. I have what I *think* are good reasons for structuring JiMS the way I am, but in the absence of hard scientific evidence as to the efficacy of one structure vs. another, there is very ample room for differences of opinion. I value, very highly, such critical feedback, because it forces me to revisit my assumptions and see if they have any rational basis. That said...Many of the concepts that I'm teaching in JiMS with specifics, could be taught with greater generality. Here's why I'm starting with narrow, concrete specifics, such as the assumption of the syntonic temperament in 12-TET tuning. I could design JiMS such that it did not assume the syntonic temperament (i.e., alpha = P8, beta = tempered "perfect" fifth, with first comma tempered to unison) or 12-TET tuning (i.e., P8=1200 cents and P5=700 cents). Instead, I could teach that alpha and beta could be any interval. This would be a temperament-neutral approach. So, why am I basing JiMS firmly on the syntonic temperament...and with a fixed octave, to boot? Firstly, because JiMS is based on the philosophy of "progressive complexity," which states that "the simplest approximations of the truth should be presented first, with increasingly complex approximations added later, only as necessary." (I'm quoting myself here, but some prominent educator somewhere must have said something similar.) So, JiMS starts with the diatonic scale in the syntonic scale, in 12-TET tuning, and will progress through the chromatic scale also in 12-TET. It's only when JiMS needs to introduce the enharmonic scale -- which I've decided to do WAY later -- that the concept of "tuning" needs to be introduced. After that, JiMS can introduce Dynamic Tonality. Somewhere right before the introduction of Dynamic Tonality, I'll introduce the notion that the octave's width can be tempered in the syntonic temperament, too. After Dynamic Tonality, I can introduce non-syntonic temperaments. Remember the immediate goal of JiMS: to dramatically increase the efficiency with which non-musicians gain sufficient musical knowledge to write their own pop/rock music. To achieve this goal, students do not need to learn about non-syntonic temperaments. That being said, JiMS' *ultimate* goal is to establish a new universal paradigm of music which expands the frontiers of tonality. I believe that this ultimate goal cannot be achieved without first achieving JiMS immediate goal. Therefore, the immediate goal must take precedence in all of JiMS' design decisions. Specifically, I can't allow JiMS early lessons to be made more complex in order to facilitate the later introduction of non-syntonic temperaments. My recent re-writing of Lessons 4 and 5 is a manifestation of this design trade-off. I have a tendency to want to introduce non-12-TET and non-syntonic ideas sooner than necessary, because I think that JiMS' ability to support those concepts distinguishes it from traditional approaches, and because I think that these concepts are WAY COOL. However, it's simply not efficient to introduce those concepts too early. Secondly, the musical invariances on which JiMS is based -- transpositional invariance, tuning invariance, and cardinality invariance -- are all invariant only within a single given temperament. None of them are invariant across temperaments. I can't teach these invariances in the abstract; I can only teach them in the concrete context of a given temperament. Combined with the doctrine of progressive complexity, the temperament-dependency of musical invariances requires me to teach them within a given temperament (and tuning) first, and only then to generalize those teachings across (tunings and) temperaments. For example, consider the syntonic and schismatic temperaments. Both have the same generators -- P8 and P5 -- so they can share the same note-names, note-layouts, and staff notation. However, their comma sequence differs, and hence so does their mapping of partials to notes. For example, from a fundamental on Do, the syntonic temperament maps the fifth partial to Mi, while the schismatic maps it to Fe. As a result, the "shape" of the major triad (for example) is different, on JiMS keyboard and the JiMS staff, even across temperaments as closely-related as the syntonic and the schismatic. Combined with the doctrine of progressive complexity, this variance-across-temperaments requires JiMS to start by assuming the use of a single (tuning and) temperament, introducing other (tunings and) temperaments only when necessary (and it isn't necessary until after Dynamic Tonality has been introduced, using the syntonic temperament). Thirdly, the music of human cultures in the real world seems to be strongly biased towards temperaments generated by the P8 and P5, including the syntonic and schismatic. The syntonic temperament's tuning continuum includes nearly all of the tunings ever used by human cultures; the exceptions are arguably schismatic, such as Turkish and arguably some Indian music. This bias may arise from the human ear/brain/mind's apparent use, for the detection and tracking of tonal relationships, of a "map of the regions" generated by P8's and P5's (as exposed by Petr Janata's brain-scans). Such a map of the regions is the dual graph of the Wicki/JiMS note-layout, and hence is topologically identical to it. Combined with the doctrine of progressive complexity, this human cultural bias towards the syntonic temperament leads me to choose it as the basis of JiMS, with the added complexity of other temperaments being added to JiMS only much later in the lesson sequence. Please note that all of this is "just talk," however. I don't have any scientific evidence that proves that these design choices lead to the most efficient and accurate acquisition of musical knowledge by musical novices, or that graduates of such an educational program are able to advance the state of the art faster and/or more creatively. But then, no contrary evidence exists to refute these claims, either. The efficacy of alternative paradigms in achieving such objectives is an under-studied area. I hope that, as JiMS becomes available, such rigorous studies can be carried out. In the meantime, you're not wrong, and I'm not right. We just disagree as to when, in the sequence of ideas, non-12-TET tunings and non-syntonic temperaments should be introduced. On the other hand, we agree that these concepts SHOULD be introduced as soon as possible -- an agreement that differentiates us from the vast majority of music educators and music theorists, who neither understand nor care about these concepts. I hope that you will find this response to be in the cooperative, exploratory spirit of give-and-take in which it is intended.
Labels: JiMS
posted by JimPlamondon | 12:39 PM
3 Comments:
I guess what I was most worried about was depriving the learner of the whole truth in the beginning to the point where it almost seems like lying to me =P
I have to agree with your decisions of using progressive complexity. Because all of the concepts you are going to teach will transfer over to the rest of the syntonic temperament, and because some of them will even transfer over to other temperaments, I can not argue that you are setting up a learner for any hardship down the road. You are also probably saving time while maintaining a larger audience by keeping things somewhat traditional (tuning wise) and not introducing too much out there stuff just yet.
All I can argue is that when you define explicitly the stack and fill method with fifths and octaves, I would feel a little betrayed when I learned the bigger picture. Maybe there is a quick fix in wording for neurotics like me, or maybe the fix is unnecessary because we are such a low percentage of the population ;-p
Either way, I can't wait for your lessons to come out, and I'm glad my often ineloquently worded criticisms are taken as what they are meant to be: constructive. Thanks for the post Jim =)
On the other hand, I've been toying with the idea of numbering my definitions, in the form "Definition (1 of N) of Term X," thus making it clear from the outset that Definition 1 is a "first approximation," which will be refined in later lessons.
For example, the definition of "note" as being "a point on a note-grid" would be labeled "Definition (1 of 1)," indicating that it not going to be refined in future -- it's "the whole truth."
On the other hand, the definition of "the fifth" that occurs in lesson 4 would be Definition (1 of N," where N would be a pretty big number, indicating that it is a very rough first approximation, which the student can expect to see refined many times in future.
The problem with this numbering scheme is that one must know N from the outset. I don't know N yet for most of the terms I'm defining. How many tims will I need to refine the definition of "the fifth" over the full course of all JiMS' lessons?
- defining diatonic (major & minor) fifths
- defining chromatic (augmented and diminished) fifths
- defining the valid tuning range of "the fifth" in the syntonic temperament
- defining the difference between "the fifth" and the third partial
- defining the more general relationship between alpha and beta in rank-2 regular tuning systems
- defining the variation among fifth-widths in irregular tuning systems
...and so on.
Being able to provide some kind of "progress bar" for each term, indicating its progress towards final definition, would be very helpful, I suspect. I just don't know how to do it yet.
That does sound like a really cool way to handle things, though I can't think of a solution for the number of definitions problem. Maybe just have use a symbol like a star that is defined early on as the "not the whole truth" star, and put it next to these definitions? It wouldn't provide as much a feeling of progress (as opposed to a progress bar) but it would be effective, and you could still have a completion symbol when something is defined for the last time.
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