Multiple Time Scales

In my first animated graphical scores, time was represented in a completely fixed way, linearly; that is: a given horizontal distance represented a single, specific amount of time, with the center point of the display corresponding to the "now" point (the time of the music being heard at that instant). I used different time scales depending on how fast the notes were (so that they weren't too small or too large in the display), but for each piece, the scale did not change.

For music that changed tempo, however, this approach didn't work, and I started using multiple time scales in a single video. Since then, I've found other ways the time scale can be effectively altered, which I will describe here.

The videos I've made that use multiple time scales are collected in this playlist.

date YouTube link description


Saint-Saëns, Aquarium, from Carnival of the Animals The first way I modified the time scale was to warp it so that notes closer to the center of the display were wider than the ones at the edges—a kind of "fish-eye" effect. I've described that on this page about scrolling. For this Saint-Saëns piece, I used different amounts of warping for different instrumental layers, to give the effect of fish in an aquarium.


Brahms/Anon/ZRI Clarinet Quintet (Free But Lonely, Street Tune) In this piece, ZRI combined a slow movement of the Brahms Clarinet Quintet with fast gypsy music. To give the feeling of surprise, I had the gypsy music (which intrudes a little after 3:07 in this video) rush in from the right, like a band of street musicians interrupting a chamber music concert.


Malinowski, Fantasia Ostinato (white background) This piece is unusual in that the ostinato (which gets repeated several times) is played at various speeds, getting faster each time. To show that it was the same pattern being played at different speeds, I changed the scrolling speed of the ostinato so that it always had the same width; the result is that when it's played faster, it moves across the screen faster (against a background that moves at a constant speed).


Bach, Contrapunctus 7, Art of Fugue (Kunst der Fuge) A more typical way to use melodic material at different speeds in one piece is the one employed by composers of contrapuntal music: to play a subject in augmentation (slower than normal) or diminution (faster than usual). In this fugue, Bach combines the subject at three different speeds, shown in three colors in the foreground; the full score is shown in the background in blue.


Stravinsky, The Rite of Spring, Animated Graphical Score, 2/2 A a little past 7:50, Stravinsky ramps up the tempo dramatically. To match that drama, I tried ramping up the scrolling speed ramp continuously. The first time I watched this effect, the hair on the back of my neck stood up, and I knew I was on to something.


Ligeti, 6 Bagatelles, III. Allegro grazioso In this lovely piece, Ligeti passes a fast ostinato duet among the instruments, while the remaining instruments play a slow serene melody. Having two layers at different speeds was the obvious way to depict this.


Bach, Goldberg Variations, Variation 16, BWV 988 Here, I do something a little different: where the piece goes from slow to fast (a little past 1:30), the fast notes rush in from the right, but then slow down once they get to the center.


Bach, Goldberg Variations, Variation 15, BWV 988 (ver. 2)
Bach, Goldberg Variations, Variation 12, BWV 988 (ver. 2)
In these variations, there are not multiple time scales, but rather multiple "now" points, so that the inverted subject lines up visually with the non-inverted one.


Bach, Goldberg Variations, Variation 24, BWV 988 This variation also uses two "now" points for the canonic material, plus a third for the free bass part (which moves faster than the other two parts to make seem freer).


Bach, Diess sind die heil'gen zehn Gebot' (organ), BWV 678 Again, the canonic parts move at a different tempo from the accompaniment.


Beethoven, String Quartet No. 16 in F Major (opus 135), 4th mvt. The dramatic change from the slow, ponderous opening ("must it be?") to the joyous, affirming fast section ("it must be!") is matched with a change of scrolling speed.


Beethoven, String Quartet No. 14 in C-sharp Minor (opus 131) In the first four movements of this piece, I vary the tempo more gradually, to match the mood of the piece.


Mozart, Sonata for Two Pianos, K 448, first movement
Mozart, Sonata for Two Pianos, K 448, second movement
Mozart, Sonata for Two Pianos, K 448, third movement
In this piece, I use different time scales to provide a 3D effect: every note is drawn multiple times, with the scrolling speed (and thus width) increasing from back to front. These videos also use "Chromadepth" coloring so that the 3D effect is enhanced by wearing special glasses (which you can read more about here).


Chopin, Etude, opus 25 no. 11, A minor ("Winter Wind") In this one, there's a nice surprise: not only do the notes of the faster section scroll in from the right at a faster speed (which you would expect if you know the piece), but they "blow in" from the left as well.


Froberger, Ricercare XIV This one does the augmentation/diminution trick again: the full score is shown in the background, with the subject moving at different speeds in the foreground. (BTW, an earlier version of this video shows my hands playing the piece, but not the score.)


Bach, Prelude in D minor, WTC I, BWV 851 In this, the horizontal scale stays the same for the entire piece, but then scrunches up at the end (to go along with the ritardando).


Bach, Fugue in C-sharp minor, WTC I, BWV 849 In this, the horizontal scale gets smaller and smaller as the piece progresses.


Chopin, Grand Polonaise in A-flat Major, opus 53 The scrolling slows way down for the slow section in the middle, then speeds back up for the ending.


Mussorgsky/Rimsky-Korsakov, Night on Bald Mountain In this one, I really cut loose. Lots of different scrolling rates (and scrolling effects) for different layers and different sections.


Bach, Sonata for Viola da Gamba and Harpsichord BWV 1027, Adagio The slow harmonic background of this piece seemed worth emphasizing, so I depicted it separately in the background, and had that layer move more slowly (and fade out when the harmonies change more quickly).


Wick, Aero (from Piano Particles, 2017 version) The slow, high notes in the middle seemed like they were floating by like clouds, so I had them move more slowly.


Beethoven, String Quartet No. 13 in B-flat major (opus 130), 1st mvt. The harmonic background moves slowly, and the faster material moves quickly by in the foreground. The two-note "sigh" motive makes appearances at various speeds. In this piece, I felt as if I was really getting the hang of how to use multiple time scales as an expressive/explanatory device.


Beethoven, String Quartet No. 13 in B-flat major (opus 130), 2nd mvt. This does something new at a little past 1:00: the notes are not being shown in the future, and when they start moving at a slower rhythm, they suddenly slow down.


Bach, Contrapunctus 5, Art of Fugue This one does something unusual at a little past : a stretto section at a faster tempo slides through.


Bach, Contrapunctus 6, Art of Fugue A fugue with lots of augmentation/diminution.


Hunt, Prelude and Fugue in A major Changes scrolling gradually to match changes in the tempo (fairly subtle).


Bach, Contrapunctus 7, Art of Fugue Same techniques as the first version, but this time with Kimiko Ishizaka playing (and a nicer visualization).


Bach, Contrapunctus 9 Art of Fugue This is another of the "theme floats by overhead" ones.


Bach, Canone per Augmentationem in moto contrario, Art of Fugue Now for something complete different: no scrolling at all. Instead, the score is fixed. But there are still two time scales.


Bach, Fuga a 3 Soggetti, Art of Fugue This is mostly at a single scrolling rate, but near the beginning of Ishizaka's completion, there's a surprising passage in triplets which moves at a high rate of speed.


Holst, Suite No. 2 for Military Band, IV. Fantasia on the Dargason Holst combines two themes (the Dargason jig tune and Greensleeves) in meters that fit together but sound very distinct (3/4 combined with 6/8), which gives the feeling of them "passing through" each other; so, to mirror this, I had the 3/4 notes move at half speed, and be transparent so that they seemed to be in a different world.