The Major-Minor Axis

I've written a little Flash application to show how the modes of the diatonic scale relate to one another, using JIMS' Keyboard.  It's not intended to be courseware, but rather to answer some questions that have come up in a different forum (which is why I didn't clean up its bugs).

To run the app, click here.

There are two button on the lower-right corner of the screen:
- Minor-ward: Moves the mode one degree towards the minor end of the major-minor axis (Ti).
- Major-ward: Moves the mode one degree towards the major end of the major-minor axis (Fa).

Initially, the app just shows JIMS Keyboard.

1. Click once on the "Minor-ward" button. The simple diatonic intervals (henceforth, "intervals") of Fa-mode (Lydian) will be revealed. All of its intervals are major, because Fa-mode is the major endpoint of the major-minor axis.  Note that this discussion uses the renaming of "perfect" intervals discussed here.
2. Click again on Minor-Ward button. Fa-mode's pattern of (major) intervals will be slid up-and-right to Do, the next note minor-ward along the diatonic major-minor axis. Fa-mode's pattern of intervals fits Do-mode just fine, except for one interval: the major fourth. In the previous mode, it ended on Ti, but in this mode, it ends off the diatonic scale, on Fi. Therefore, we must replace the previous mode's major 4th with a minor 4th. By shifting the interval's endpoint to Fa, we get Do-mode's minor 4th.
3. Click on Minor-ward again. Do-mode's pattern of intervals, including the m4, will be slid along the major-minor axis to So. Do-mode's pattern of intervals fits So-mode just fine, except for one interval: the major 7th. In the previous mode, it ended on Ti, but in this mode, it ends off the diatonic scale, on Fi. Therefore, we must replace the previous mode's major 7th with a minor 7th. By shifting the interval's endpoint to Fa, we get So-mode's minor 7th.
4. Click on Minor-ward again, shifting the previous mode's pattern of intervals to Re-mode. Again, the previous mode's intervals all fit Re-mode just fine, except for the major third, which ends off the diatonic scale, on Fi. Replacing the major 3rd (ending on Fi) with a major third (ending on Fa), we get the intervals of Re-mode (half major, half minor).

• By now, the pattern should be clear: at each step minor-ward along the major-minor axis, the only interval changed in width is the (major) interval ending on Ti, which is replaced by a (minor) interval ending on Fa.

1. Click on Minor-ward again to see the Ti-ending major 6th change to a Fa-ending minor 6th.
2. Click on Minor-ward again to see the Ti-ending major 2nd change to a Fa-ending minor 2nd. 
3. Click on Minor-ward again to see the Ti-ending major 5th change to a Fa-ending minor 5th.

Now, we've arrived at Ti-mode, at the minor end of the major-minor axis.  All of its intervals are minor.

1. To go back down the axis in the other direction, click on Major-ward. All of Ti-mode's intervals will fit Mi-mode just fine, except for Ti-mode's minor 5th. In Ti-mode, this 5th ended on Fa, but now it falls off the diatonic scale onto Te -- so it must be switched to end on Ti, instead, giving Mi-mode its major 5th.
2. Before clicking on Major-ward again, identify the interval that ends on Fa. It's Mi-mode's minor 2nd. That's the interval that will be changed when moving down the major-minor axis to La-mode.
3. Click on Major-ward, and watch Mi-mode's Fa-ending minor 2nd be replaced by a Ti-ending major 2nd in La-mode. Which interval will be replaced next? The one that ends on Fa. Which one is that? La-mode's minor 6th.
4. Click on Major-ward again to see La-mode's Fa-ending minor 6th be replaced with Re-mode's Ti-ending major 6th.
5. Click on Major-ward again to se Re-mode's Fa-ending minor 3rd be replaced by So-mode's Ti-ending major 3rd.
6. Again, and So-mode's Fa-ending minor 7th is replaced by Do-mode's Ti-ending major 7th.
7. Again, and Do-mode's Fa-ending minor 4th is replaced by Fa-mode's Ti-ending major 4th.

Unfortunately, code bugs prevent you from going back up the axis, or from reversing course mid-way along the axis.

Nonetheless, this simple app usefully exposes some of music's patterns:

1. Fa-mode (Lydian) is "the most major" mode, and Ti-mode (Locrian) the "most minor," each being at extreme ends of the major-minor axis, which runs along an axis of major fifths.
2. Moving up the axis towards minor, the (major) interval ending on Ti will be swapped for the (minor) interval ending on Fa.
3. Moving down the axis towards major, the (minor) interval ending on Fa will be swapped for the (major) interval ending on Ti.
4. Re-mode (Dorian) is half-major and half-minor, giving it a uniquely-ambiguous position along the axis.
5. Stepping from Do-mode to So-mode changes an odd-numbered degree (7th), and so does the adjacent step from So-mode to Re-mode (3rd).  These are the ONLY two adjacent steps along the major-minor axis which both change odd-numbered intervals. This is significant, because tonal harmony is based on stacking odd-numbered degrees (that is, 3rds) in the mode of a given chord's root. (Similarly, the steps Re-to-La-to-Mi change the 6th and 2nd degrees, which might matter more to stack-of-4ths [quartian] harmony, as found in some jazz, than to stack-of-thirds [tertian] harmony).
6. The traditional names for the 4ths and 5ths obscure the consistency of these patterns. These intervals' names should follow the same pattern as the other two-value diatonic intervals, that is, the larger size (traditionally "augmented 4th" and "perfect 5th") should both be called "major," and the smaller size (traditionally "perfect 4th" and "diminished 5th") should be called "minor." The only intervals that should be called "perfect" are unison and its octaves, because they alone are distinguished by having only one size in the diatonic scale.
7. The The traditional names for the 4ths and 5ths also obscure the potential consistency of the "diminished" and "augmented" names. Once the names of the 4ths and 5ths are regularized, then "augmented" and "diminished" intervals can be recognized as referring consistently to chromatic alterations of diatonic intervals.

Much more betterish.  ;-)