Multiple Time Scales


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

2011oct29	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.

2011nov13	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.

2012feb26	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).

2012jul30	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.

2013apr07	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.

2013jul19	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.

2013sep07	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.

2013sep08 2013sep09	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.

2013oct19	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).

2013dec18	Bach, Diess sind die heil'gen zehn Gebot' (organ), BWV 678	Again, the canonic parts move at a different tempo from the accompaniment.

2014aug25	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.

2014sep27	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.

2016mar09 2016mar14 2016mar15	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).

2016apr28	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.

2016jun14	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.)

2016jun22	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).

2016jun26	Bach, Fugue in C-sharp minor, WTC I, BWV 849	In this, the horizontal scale gets smaller and smaller as the piece progresses.

2017may29	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.

2017jul20	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.

2017aug04	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).

2017sep21	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.

2017sep24	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.

2017sep25	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.

2017oct29	Bach, Contrapunctus 5, Art of Fugue	This one does something unusual at a little past : a stretto section at a faster tempo slides through.

2017nov03	Bach, Contrapunctus 6, Art of Fugue	A fugue with lots of augmentation/diminution.

2017nov07	Hunt, Prelude and Fugue in A major	Changes scrolling gradually to match changes in the tempo (fairly subtle).

2017nov08	Bach, Contrapunctus 7, Art of Fugue	Same techniques as the first version, but this time with Kimiko Ishizaka playing (and a nicer visualization).

2017nov11	Bach, Contrapunctus 9 Art of Fugue	This is another of the "theme floats by overhead" ones.

2017nov24	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.

2017dec17	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.

2017dec29	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.