Re: The Center of All Things

In JiMS iGetIt! Music System, the notes of the diatonic scale (in any key) are named "Do Re Mi Fa So La Ti." What are the names of the notes of other scales?

I am not aware of any standard mapping of these other scales' notes to tonic solfa names, nor of any standard rules for defining such a mapping, nor of any standard criteria for comparing one mapping-rule to another. One possible mapping-rule might be to "maximize the correspondence between one scale and another."

For example, when mapping the notes of the a given scale to tonic solfa, one might reasonably choose to map them to that set of tonic solfa names that maximzed the given scale's correspondence with the Diatonic scale. Using this mapping-rule, the Harmonic Major and Harmonic Minor scales would be mapped to a set of note-names that differed from the Diatonic by only one note. The Harmonic Minor would have Si instead of So, while the Harmonic Major would have Le instead of La. Those are perfectly cromulent mappings, which usefully expose the similarity of these scales to the Diatonic.

However, that's note the mapping-rule that I used in the just-posted online version of JiMS iGetIt! keyboard, however.

Instead, I chose to use a different mapping-rule: maximize the extent to which the scale is centered on Re. Using this rule, it is obvious that all of the Prime Scales

• include the notes So, Re, and La
• are either
• symmetrical around Re (Diatonic, Melodic, Neapolitan, Double Harmonic), or
• are not symmetrical (Harmonic Major and Harmonic Minor), but are reflections of each other around the Re axis.

I don't know that this mapping-rule is any better, and it may be much worse. By what criteria should different mapping-rules be judged? In the development of JiMS, I had only one criterion throughout: maximizing the efficiency of learning. However, I'm not sure that this criterion delivers a clear answer on this mapping-rule question. Exposing the consistency of the Prime Scales' So-Re-La core is a good thing, but is it better (i.e., more efficiency-increasing) than exposing the near-identicality of the Diatonic and Harmonic scales? I don't know.

Certainly the "Diatonic maximization" rule hews most closely to music-ed tradition, which sees all scales in terms of their difference from the "major scale" (including the other modes of the diatonic scale, which is just bizarre). I happily admit to having a knee-jerk reaction against traditional musical thinking. This reaction forces me to ask "why?" about absolutely everything, which has proven to be a very useful habit. However, if I can't find an efficiency-increasing alternative to a traditional practice, then I'll go with the traditional practice, to meet the secondary criterion of "maximizing compatibility."

For example, I would *love* to change the tonic solfa names to something more meaningful, so that the vowels of the names in the diatonic scale meant something, instead of actively conflicting with meaning as the diatonic vowels currently do. ('i' means 'sharp,' except for Mi and Ti; 'e' means 'flat,' except for Re. This is exactly the kind of inconsistency that makes music so hard.) One alternative set of names would be "Do Ra Ma Fo So La Te", with 'u' meaning flat and 'i' meaning sharp, 'o' meaning the root of a major triad, 'a' meaning the root of a minor triad, and 'e' meaning the root of a diminished triad. There are two problems with this alternative naming: it is meaningful only for the diatonic scale, and it would irritate everyone who had already learned the traditional solfa names. The first concern eliminates any efficiency benefit; the second imposes an efficiency cost. Hence, JiMS uses the traditional solfa names, despite their irritating lack of meaning.

What note-name mapping-rule should JiMS use for non-diatonic scales?

Your comments welcome. :-)

The Prime Scales

On a piano keyboard, the notes of the C Major scale have one shape and color (the "white keys"), while the notes that are chromatic to C Major have a different shape and color (the "black keys"). This seems awfully arbitrary. Why C? Why not A, B, or Bb?

On a digital piano, one can easily transpose the keyboard so that any given diatonic scale's notes fall on the white keys. That's cool. But what about other scales? There's more to music than the diatonic scale.

One of the nice things about a "virtual" on-screen keyboard is that one can change the way individual buttons are drawn "on the fly." That allows us to draw the notes/buttons that are in "the current scale" one way, while drawing those that are out of the scale a different way.

The latest version of my Flex iGetIt! keyboard, shown below, allows the user to select one of the Prime Scales from a ComboBox, with the coloration of the keyboard's notes/buttons changing accordingly. The notes of the current scale are the "white keys," whereas the out-of-scale notes are the "black keys."


Why is this a "good thing"?

There are scads of "scale books" that describe scads of "scales." I don't understand this.

As far as I can tell, there are really only a half-dozen scales that are relevant to tonal music -- the previously-mentioned Prime Scales. The scale books are fat with "scales" because

• they confuse scale and mode, treating different modes of the same scale as if they were different scales, and
• they confuse scale and key, treating different keys of the same scale as if they were different scales.

This conceptual confusion can lead to a combinatorial explosion of "scales." Do the math: six Prime Scales times seven modes per scale times fifteen possible keys is 6 * 7 * 15 = 630 possible "scales." Six hundred and thirty! From an educational perspective, that might as well be "infinity." No wonder people hate learning scales! Using the traditional instruments, notation, and theory, there is no end to it. You could study and practice your whole life and never master them all.

I don't see the point. This explosion of "scales" is an artifact of traditional music technology (i.e., traditional instruments and notation). They are not meaningfully distict, except that -- using traditional technology -- they require different notation and different performance gestures. The explosion is not a theory problem; it's a technology problem. Using JiMS, you only have to master the six Prime Scales. Six! That's less than 1/100'th of the traditional number. Two orders of magnitude!

More importantly, by clarifying the relationships between scales, modes, and keys (and chords, and melodies, and tunings, and so on), JiMS inter-relates these important musical concepts, thereby providing a strong theoretical foundation for understanding music.

First Flash control: PitchSlider

To develop my forthcoming music education courseware using Adobe's Flash/Flex/AIR, I'm developing a suite of components that display and control musical information.  This is going well, considering. Although I have a Computer Science degree, I haven't written a line of code since 1992...17 years ago.  Climbing up the Flash/Flex/AIR/ActionScript/Eclipse/XML learning curve is fun but challenging.

My first Flash control is a slider that allows the user to choose a frequency (it works best if you drag the thumb slowly):

No big deal, but writing it helped me understand a lot of stuff, including Flash 10's new sound synthesis API SampleDataEvent. 

I've seen other posts in which the source code to such controls is easily available (by right-clicking on the control and choosing "View Source" from a pop-up menu), but I don't know how to support that feature. I can't find any documentation for it; apparently it's so "obvious" that it is never described. If a reader could please tell me how to add support for Flash's "View Source" feature -- in full newbie-tutorial detail -- I'd be happy to make the code available for this and subsequent iGetIt! controls.  (iGetIt!'s proprietary value is in the patent-pending iGetIt! Music System and the lessons based on it, not in its Flash controls.)

I expect to use the PitchSlider control (or something like it) to show the student that musical pitch (frequency) is continuous, varying in a smooth and unbroken manner. Some frequencies have names (such as 440Hz, which is named A4), and some do not, but all are musically equal. The structure of music is the same for all frequencies.  Obviously, this ignores a ton of psychoacoustic issues like the human ear's range of hearing and critical band, but... close enough, as a first approximation.