La-based minor revisited

I have gotten a lot of feedback on my earlier post, Why La-based Minor?

 

In brief,

• my understanding of Do-based minor was wrong.
• I am now considering a different scheme, which seems to me to combine the best of both La-based and Do-based minor.

My new thinking, which is still somewhat half-baked, goes like this.

Do-based minor emphasizes the parallel minor, while La-based minor emphasizes the relative minor. Why emphasize one over the other?  Why not clearly distinguish between the two?

Case 1: Starting in Major
Let’s assume that you’re going to notate/play a piece starts in major (diatonic Do-mode), so you transpose the pitches under the keyboard to move the desired tonic pitch to Do. Let’s say that you’re playing in C Major, so Do is C, La is A, Mi is E, and Me is Eb.

When the piece begins, in Do-mode, all is well. The tonic is on Do (C), and that mode’s third degree is Mi (E), which is where we pegged the keyboard, so those notes have those pitches.

1a) If the piece wanders from Do-mode into its parallel minor (C minor), all is well. The tonic stays on Do (C), and Do-mode’s third degree is Me (Eb), but no new transposition of the keyboard/notation is necessary, because those notes already have those pitches.

1b) If the piece wanders from Do-mode into its relative minor (A minor), all is well. The tonic moves from Do (C) to La (A), and La-mode’s third degree is Do (C), but no new transposition of the keyboard/notation is necessary, because those notes already have those pitches.

The next question is, “where do the scale dots and tonic indicator go?”

We're starting in diatonic Do-major, so the scale dots are on the usual diatonic notes, Do, Re, Mi, Fa, So, La, and Ti, with the tonic indicator on Do.

1a) Moving from Do-major to Do-minor, the scale dots change to Do, Re, Me, Fa, So, Le, and Te, with the tonic indicator staying on Do.

1b) Moving from Do-major to La-minor, the scale dots stay the same (i.e., on Do, Re, Mi, Fa, So, La, and Ti), but the tonic indicator moves to La.

The interplay of the scale dots and the tonic indicator show, in JIMS staff notation, what is happening.

• If the scale dots change, but the tonic indicator stays on the same note, then the music has moved to a parallel mode.
• If the scale dots stay the same, but the tonic indicator moves to a different note, then the music has moved to a relative mode.

This is not a factoid to be memorized, per se, but rather something which can be observed from the note-patterns on JIMS keyboard as one plays.

This system usefully distinguishes Do-major's relative minor (La-minor) from its parallel minor (Do-minor). The two would be notated using different notes on JIMS staff, and played using different buttons on JIMS keyboard.

When used strictly by “La-based minor” singers, the notation and keyboard could be transposed such that both the parallel and relative minors always used La as their tonic. However, that would NOT be the general case. the main difference between my previous proposal and this one.

Case 2: Starting in Minor
Now, let’s assume that you’re going to notate/play a piece which starts, and remains primarily, in A minor, so we map A to La.

2a) If the piece wanders from minor into its relative major (C Major), all is well. The tonic moves from La (A) to Do (C), and Do-mode’s third degree is Mi (E), but no new transposition of the keyboard is necessary, because those notes already have those pitches.

2b) If the piece wanders from minor into its parallel major (A Major), all is well. The tonic stays on La (A), and La-mode’s third degree is Do (C)…wait a minute. That’s not right. We’re talking La-MAJOR now, not La-MINOR.

Case 2b above is (I suspect) at the heart of the conflict between the La-based minorists and the Do-based minorists. Who would ever expect to find a major scale with La as its tonic?

If Case 2b's minor-to-parallel-major-and-back movement dominated a given piece, then it would make sense to start the piece in Do-minor. Then, when the mode changed from the primary minor key to its parallel major, the major mode’s tonic would be Do, as one would normally expect. Using D-minor in this way would emphasize that the core relationship in this piece was parallel, not relative.

Let's look at the scale dots and tonic indicator in Case 2.

2a) Starting in La-minor, the scale dots are on the usual diatonic Do, Re, Mi, Fa, So, La, and Ti, with the tonic indicator on La. Moving to the relative major, the scale dots remain the same, but the tonic indicator moves to Do.

2b) Starting in Do-minor, the scale dots are on Do, Re, Me, Fa, So, Le, and Te, with the tonic indicator on Do. Moving to the parallel minor, the scale dots change to Do, Re, Me, Fa, So, La, and Ti, with the tonic remaining on Do.

If the music moves farther than one relative or parallel step away from the tonic, in either direction, then it has modulated (hasn't it?). One could either keep shifting the stack of scale dots to reflect the changing set notes in the current diatonic scale (much like introducing more sharps and flats into a key signature, with all of the disadvantages thereof), or simply transpose JIMS staff and keyboard (using a transposition indicator and user-interface gesture, respectively).

Limitations
If a piece's tonal center is ambiguous, then no tonally-focused notation (like JIMS) is going to offer significant advantages over less-tonally-focused notations (like traditional notation).

However, most music played and listened to by the majority of the people in the First World is strongly tonal (and even strongly modal, if one considers the major scale to be the Ionian mode), which plays to JIMS' strengths, so I don't think that this limitation counts for much.

Advantages
The above-described approach seems to me to combine the best of both Do-based minor and La-based minor, by distinguishing unambiguously between the relative and parallel relationships. The person notating a song would need to do a significant amount of work to analyze what’s happening in a given piece, in order to notate it correctly -- but that's a GOOD thing, because once this analysis is done by the notator, it is very easily accessible by the student and/or performer.

 

Having a clear distinction, in JIMS notation, between parallel and relative intervals helps distinguish between notes that have the same name but are a comma or two apart (in Just Intonation), thereby helping singers it the right notes. Nonetheless, for purely vocal music in the La-based minor tradition, one could transpose JIMS notation (and perhaps an accompanying JIMS keyboard) to keep the scale dots constant, i.e., to use a La-based minor whether that minor was relative or parallel. But this would not be *required* under the above-proposed revisions to the JIMS system.

 

I think that this refinement is a considerable improvement to JIMS. It exposes a meaningful difference—the difference between relative and parallel keys—in a clear and unambiguous manner. This is in line with JIMS' neo-Riemannian roots.

 

Perhaps this refinement is sufficient to make JIMS useful to those who teach music using a Do-based minor system. I hope so. In my wildest dream, I imagine that JIMS, with this refinement, might be sufficient to heal the centuries-long rift between the La-minorists and the Do-minorists.

Comments and corrections welcome!  :-)

Modulation

If JIMS'staff notates music using "Moveable Do with a La-based minor," how does it notate modulations? How does one execute such modulations on a JIMS-compatible keyboard?

Here's a link to a forum post on that topic. It refers to a hand-written document that I whipped up for the purpose, which I probably shoud have taken more time to draw up carefully.

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. :-)