Bach, Artwork of Fugue (animated graphical scores)

2023-01-27 02:22:39

This web page accommodates an index and descriptions for the animated graphical scores I’ve made for J. S. Bach’s The Artwork of Fugue.

The animations are based mostly on recordings by these performers (and myself) …

I purchased a rating of Bach’s Artwork of Fugue within the Seventies (once I was a young person),
and whereas it is displaying its age (as am I) …

… I am nonetheless simply as fascinated by it as I used to be then. (And, to the purists: sure, I’ve different editions with out Nineteenth-century expression marks.)

Between 2009 and 2015, I made animated graphical scores of a number of the Artwork of Fugue based mostly alone renditions
(or artificial renditions) …

In 2018, I revisited Contrapunctus 11 utilizing a recording by organist Martin Baker.

In 2020, Alberto Rasi gave me permission to make use of the recordings by his ensemble,
Accademia Strumentale Italiana (carried out on viols and organ).

Lastly, most not too long ago, in 2022, the Netherlands Bach Society revealed their performance,

and I re-did your entire set utilizing that recording (this is my YouTube playlist
for the person items,

and right here is a single video with all of them together—about 90 minutes).

The animations are largely the identical because the Ishizaka variations, with just a few issues tweaked.

Additionally, the reconstruction is one achieved by Leo van Doesellar and Kees van Houten.

As a result of I exploit a small set of visualization strategies and make use of them pretty persistently all through these animations,
I’ll concentrate on these strategies, and hope that when I’ve defined how my visible language works, will probably be straightforward
so that you can see how I am making use of it to the varied canons and fugues.

For every bit, the hyperlink from the identify (e.g. Contrapunctus 1) connects to the primary model
of the video I revealed; if I did follow-ups, they’re talked about within the dialogue.

The concept right here was that the topic moved slowly, ominously, inexorably, and was huge, architectural, like Greek columns.
This sense additionally appeared acceptable for the primary 5 half-notes of the enduring Artwork of Fugue topic,
however the next quarter-notes felt like they have been turning into much less solemn,
and “strolling away” freely. So, I simply put the primary 5 notes contained in the body,
and had the quarter notes stroll out of the body (utilizing the RollBox renderer).
The eighth-notes that adopted from there moved quicker than strolling,
so as a substitute of rolling, I simply had these operating notes gentle up (and made them strong to be extra distinct). The opening phrase, then,
appears to be like like this:

As you’ll be able to see, not like within the animation for the f-minor fugue, right here I solely present the primary notes of the topic after they’re sounding.
Why not? I wished the animation to replicate the truth that as a result of that is the primary fugue,
there’s the chance that you have not heard the topic but, and do not know what’s coming.
Additionally, I believed that if you happen to needed to do some work to comply with the topic,
it would make you extra inclined to recollect it in order that you may “plug it in” each time
you noticed that vacant body.

Apart from the topic and the strolling and operating notes, the opposite essential motivic materials is a two-note group, brief/lengthy.
I’ve proven these with a gliding-stretching ball form. The remainder of the notes are depicted as plain, stationary horizontal traces.

Oh, there’s one final thing that is value noting: the little 4-note motive within the soprano at 2:39;
this returns in later fugues.

What stands out on this fugue is the dotted (brief/lengthy) rhythm; I emphasised its angularity by placing every pair
of notes in a field, and having them stretch dramatically whereas they’re taking part in. Sadly, this meant that the strolling notes of the
topic appeared rather a lot just like the dotted notes, so within the second model I attempted
using just the stretching part of the effect (and never the containers) for the dotted notes.
That helped distinguish the 2, however made the dotted rhythm appear much less angular, so
it wasn’t apparent whether or not it was an enchancment. Once I made a third version with some corrections,
I went again to the containers.

Right here, I centered on the way in which Ishizaka performed the four-note determine (three brief, one lengthy) that dominates the piece.
To make it stand out, I put the remainder of the topic (that precedes it) contained in the body. When the four-note determine is rising,
Ishizaka performs it detachted, and when it’s falling, she performs it legato, and I match this distinction by various the way in which the circles depicting the notes transfer.
Different results:

… used connecting traces to focus on some factors of imitation.

Contrapunctus 4

Right here, the non-subject materials is sort of utterly composed of a four-note group (in circles) and a 2-note group (in squares).

Contrapunctus 5

Within the earlier fugue, the topic was inverted all through (did you discover?), and I did not do something to focus on that.
On this fugue, the topic is usually inverted and generally not, and I distinguish these by displaying solely the upper-left
or lower-left edges of the body.

About midway via the piece (simply previous 2:00), one thing uncommon occurs: there is a quick (double-speed) stretto (overlap) of the
starting of the topic, first inverted, then non-inverted. To make its timing relationship to the traditional velocity of the topic extra apparent,
I make the notes the identical width, and transfer them twice as quick.

Contrapunctus 6

This makes use of the inverted body and variable velocity strategies from Contrapunctus 5, and the dramatic stretching of the dotted notes
from Contrapunctus 2.

Contrapunctus 7

This makes use of the identical visible conventions as Contrapunctus 6.

Within the second version, I attempted a extra filled-in search for the background
(I do not suppose this works very properly).

Contrapunctus 8

This fugue has three topics, every of which is depicted with its personal renderer.
Additionally, when the non-subject passages use melodic movement that is much like one of many topics,
I exploit that topic’s renderer. As a result of it is generally onerous to maintain observe of the three topics,
within the second version of the animation, I attempted
one thing completely different: within the higher half the show, all of the notes are proven with the identical form,
and within the decrease half, the subject-related notes (and no different notes) are proven with their particular person shapes.

Contrapunctus 9

Right here, Bach will increase the distinction between the primary topic (from the primary fugue) and the second topic
(a operating passage that begins with a dramatic leap): the primary topic is so sluggish in comparison with the second that
the piece begins feeling like a chorale prelude, with the primary topic being off in its personal world.
To depict this, I put the primary topic within the background, transferring very slowly (utilizing the Voronoi renderer).
Within the second version of the animation, I made the primary topic
somewhat extra ominous-looking by making the background grey and surrounding the notes of the primary topic with pure black.

Contrapunctus 10

Right here, my focus was on articulation and phrasing. The opening topic begins with a really placing determine that begins on an off-beat
and contrasts a single indifferent notice with a pair of related notes; it does this twice. I’ve highlighted these six notes of the topic,
and for these notes, the remainder of the theme, and all of the non-subject materials in the remainder of the piece, I’ve used connecting traces to
present phrasing and articulation. In doing this, I’ve transcribed a facet of how I hear this piece: each time a kind of traces begins,
I discover it, and my consideration is continually bouncing round among the many voices.

Contrapunctus 11

This one makes use of the visualization strategies of Contrapunctus 10, however with extra combos of renderers (one for every of the three topics,
one for chromatic movement, and one for every part else).

Contrapunctus 12 / Contrapunctus 13

For the 2 invertible fugues, I present the piece within the higher a part of the show within the orientation that is being performed
and within the decrease half within the mirrored kind, as a way to take a look at the upside-down model and attempt to think about it when you’re
listening to the right-side-up model.


Compositionally, canons are very completely different from the fugues, as a result of the notes (no less than, the notes that represent the “canonic half” of canon)
should conform rigidly to a rule. In these animated graphical scores, I’ve tried to make this inflexible construction apparent.

Canon 1

The primary canon is per augmentationem in motu contrario, which means that the notes of the canon are performed at two speeds, one regular and one stretched out,
and with the melody transferring in reverse instructions. This can be a lot to maintain observe of,
so I’ve put the notes of the canon alongside a single line as a way to comply with the 2 voices of their various paths via it.
The entire set of notes of the canon associate with the the inverted model of the primary half of the notes being performed half as quick.
This leaves the second half of the inverted/sluggish notes with out an accompaniment, so Bach composes some additional materials
for that; I’ve proven this additional materials as “free”—not collaborating rigidly within the canon.
The colours appeared a bit garish, and I attempted a distinct palette within the second version.

As a result of I go away all of the notes seen, when the piece is full, you see the whole rating, with each notice of the canon being proven 4 instances
(and the free materials proven twice):

Canon 2

The second canon is far easier, each conceptually and perceptually: there is no augmentation or diminution,
no inversion, and the second voice (comes) follows quickly sufficient after the primary (dux)
that it was doable to see them each shut up, two sprites dashing via the identical notes.

The beginning of the canon is predicated on the notes of the primary Artwork of Fugue topic,
nevertheless it’s very extremely ornamented; I’ve put the unique kind within the background as a way to see how the 2 relate:

Canon 3 / Canon 4

The third and fourth canons are “two-way” canons—that’s, there’s a couple of manner the notes of the comes can match with the notes of the dux.
The best way these items are constructed is uncommon sufficient that I made a number of makes an attempt and was nonetheless undecided I would made it clear.

In these animations, nearly all the fabric is performed many instances,
and I’ve organized the notes in layers round a circle (or ellipse) in order that any time a selected sample is being performed,
it occurs on the similar place across the circle.

In Canon 3, a lot of the melodic materials (fundamental Artwork of Fugue [S]ubject and passages A/B/C)) is used at two or three pitch ranges (unison, main third, excellent fifth):

Passages D/E/F seem at just one degree.

See Also

The first version
of Canon 3 was achieved with very plain circles of two colours (one for every voice),
and the second version is considerably the identical:

The spiral within the middle is the “progress bar/compass” for the piece; it exhibits the place within the piece every voice is taking part in
(and, by the bars getting wider, exhibits what’s been performed up to now).

These variations appeared very complicated to me, so I attempted a very completely different method within the
third version—I organized the notes linearly,
and confirmed them in on the correct pitch degree:

Not as fairly, however clearer (n.b., on this diagram, the unison degree is inexperienced, main third is brown, and ideal fifth is blue).

A good friend from faculty prompt it would work to point out the pitch ranges with 3D,
and within the fourth version I attempted that
(utilizing the Chromadepth 3D system):

Indicating the pitch degree with shade and 3D place, may need made it a bit clearer than the primary model,
however what struck me was that it appeared cooler, and within the subsequent few variations (5,
I performed round with methods of creating the “mandala” extra dramatic
(in some, I clearly went overboard):

Canon 4 is inbuilt sections, and every sections begins with a flashy rising triplet determine.
I made a decision that these figures stood out sufficient from the remainder of the canon that they need to be
depicted otherwise. As a result of they functioned form of like “joints” or “glue” between the
sections, I made a decision to have them rise away from the middle on the factors of division
(and I delineated the sections by shading the background):

A good friend stated that the rotation of the mandala made him dizzy (and made it onerous to recollect which part was which),
so within the second version I attempted making the
notes stationary. Higher? I am unable to inform; possibly it is only a matter of particular person desire.

Within the third version of Canon 4, I added some black
holes within the background so point out the relationsh between the primary Artwork of Fugue topic
and the primary part of the canon (seen between 12 o’clock and a couple of:30 right here):

[A few days after making this elliptical version, while watching it in a daydreamy reverie,
I found the animation suggesting a fanciful narrative: the five (or six, if you count the little sliver) gray
panels were the earth’s tectonic plates, and the black circles were a constellation in the sky.
In the beginning, nobody knew what the constellation meant, but then one day there was an earthquake,
and after the initial triplet tremors at the fault line, what emerged
matched the pattern of the constellation—it wasn’t just a bunch of stars—it was a prophecy!
After that day, there was seismic activity at regular intervals, and each time,
the message of the prophecy was reinforced and elaborated at sites of seismic activity around the world.]

Fuga a tre soggetti (with completion by Kimiko Ishizaka)

For this fugue, I added some issues to focus on the truth that Bach’s unfinished fugue was being accomplished.
As we method the place within the piece the place Bach’s manuscript ends,
the animated rating exhibits nothing sooner or later—simply the void:

However, when the taking part in arrives on the fringe of the abyss, the long run begins writing itself,
first notice by notice, after which bringing in larger chunks (the themes that Bach had already composed).

Statements of the topic (composed by Bach) are given their colours all through,
however the newly-composed materials is proven in grey till it’s performed.

On this fugue, every topic seems in each its regular orientation and inverted, and for every,
the traditional and inverted statements are distinguished otherwise:

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