In 1970, Disney released its twentieth animated movie
The Aristocats. (The children's book based on the movie was released thirty years ago this month.) Besides the title song, the only other song of the many songs written by the Sherman brothers that made it to the final cut of the movie was "Scales and Arpeggios." In this Mozartean tune, the cute kittens Marie and Berlioz practice their solfège ("do-mi-sol-do...") and piano playing together in their upscale
maison in Paris. (No cat on cornet at this point.) In the third verse, their mother, Duchess, joins Marie in song. On the third-verse line, "like a tree, ability will bloom and grow," Marie and Duchess sing the first vocal harmony in the song. The graphic below shows the two lines so that the syllables of the lyrics match up with the pitches of the tune. (C4 is middle C.) Duchess sings the orange notes, while Marie sings the green notes. The two-tone squares represent the two moments when Marie and Duchess sing the same pitch at the same time.
The notes inside the 7x7 square in the upper right display a special property. If one takes the Duchess's orange notes inside this square, plays them both backwards (retrograde, or R) and upside down (inversion, or I), fits the result as close to the same range while still achieving harmonic intervals that are all consonant, and uses the same syllables in the same order, one obtains Marie's green notes inside this square. The graphic below shows how reversing the Duchess's notes in both temporal space and pitch space, in either order, results in Marie's notes.
Another way to consider this, especially given the standard Western notation's assignment of a score's two spatial dimensions as temporal space and pitch space, is that the combination of a retrograde and inversion is the equivalent to a 180° rotation. Turn any score 180° and you will have performed a combination of a retrograde and an inversion on this score. Let me put this in drawing-tools terms:
This means that the two lines together, irrespective of who is singing which note, makes a pattern -- shown below in black squares -- that does not change when it is rotated 180° or, equivalently, when it is both retrograded and inverted.
Patterns like this one cry out for comparison to a crossword puzzle grid. Indeed, as varied as crossword puzzle grids can be, most use this standard form: each remains the same after being rotated 180°.
Not counting one-letter words, the grid above can be completed in exactly one way using only words from this month's blog post: four six-letter words, two four-letter words, et cetera. I'll get you started by including the word "Oy," which was the hardest to weave into the text above, although some of the other words didn't seamlessly blend in either. I'll show the answer next month.
This post begins a series of posts on using a combination of R and I to reveal structures in music.
