Scarlatti and dodecahedrons
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On May 9, M. Paul Shore sent this note to me:
A belated thank-you for the April 22nd Galuppi (1706-1785) link*. I’d never heard of him. That whole Baroque-to-Classical transition phase is a fascinating and enjoyable but underappreciated one. The composers from that phase who get the most attention (and deservedly so) are two of J.S. Bach’s sons, J.C. and C.P.E.
*"A bridge between Baroque & Classical"
To my mind, it’s always a sunny day in Scarlatti-land: even the moments of particular seriousness or slight gloom are just the result of swiftly passing clouds.
What blew my mind away about the Scarlatti-Ross album covers is that they prominently feature the dodecahedron. That made me wonder why the cover designer chose that particular complex, abstract figure to illustrate the Scarlatti albums. Was it because of the geometricity or cosmogonic nature of Scarlatti's sonatas?
When I mentioned the dodecahedron to M. Paul, he replied:
Ah, the dodecahedron! I’ve known that cover design for decades (I have the full Scott Ross CD box set of the sonatas), but never gave the dodecahedron in it any fully conscious thought, let alone relate it to the extensive discussion of the shape on Language Log.
I think we will never be done with the dodecahedron. There's something mathematical and ethereal about it.
Selected readings
- "New revelations and declarations about dodecahedrons" (3/17/26)
- "Dallas Dodecahedron Daze Days" (1/28/26) — with many references to previous posts on dodecahedra
David L said,
May 11, 2026 @ 3:34 pm
As far as I can tell, each of the series of Scarlatti albums has a different cover. The one you link to has a dodecahedron, but this one has an entirely different shape. Maybe the designer thought there was something geometrical in the nature of Scarlatti's sonatas and picked cover illustrations accordingly.
Peter Cyrus said,
May 11, 2026 @ 4:51 pm
The regular dodecahedron is nice, but my taste runs to the rhombic dodecahedron. It also has 12 identical faces, but two types of vertex. In addition, it's space-filling, and the dual of the cuboctahedron. If you don't know it, take a look – you'll be pleased.
Charles in Toronto said,
May 11, 2026 @ 5:53 pm
When I was in a children's choir we did Galuppi's Dixit Dominus and that melody has been etched in my brain ever since. Here is a rendition from Calgary with orchestra: https://www.youtube.com/watch?v=7EfGWk9tEQ4
M. Paul Shore said,
May 12, 2026 @ 5:37 am
Great catch, David L.! I’m now taking a careful look at the Scarlatti/Ross album cover images for the first time.
The original 555-sonata Erato box set consists of 34 incompletely filled CDs grouped into nine two- or four-CD “volumes”, these inefficient groupings apparently being done for no other reason than so that “DOMENICO SCARLATTI” could be spelled out across the volume spines—a flagrant abuse of consumers’ storage space even by the standards of the pre-downloading/pre-streaming era. Erato has now recognized its mistake and regrouped the sonatas into 27 single-CD-length “volumes” (even for downloading purposes).
Each of the nine original “volumes” had a different cover drawing depicting a sphere-approximating polyhedron or, in one case, what I’ll amateurly describe as a vertically asymmetrical icosahedron; and those nine drawings, with some coloring alterations, have been reused in subsequent repackagings of the recordings. Two of the drawings, those for original Volumes III and IV, depict dodecahedra, a closed and a latticework one respectively. Those dodecahedron drawings have now been reused for the new volumes 3, 4, 12, 13, 21, and 22.
Why did the cover artist create those images? As VHM and David L. have speculated, it may have been because he or she thought of the sonatas as possessing a geometrical quality, though based on my listening to all of them I’d have to disagree with such a view. Our thinking about Baroque music tends to be dominated by J.S. Bach, whose music, like that of his great Baroque and Renaissance polyphonist predecessors, does have a certain geometrical quality; but Bach was an unusual figure, both in his partially conservative stylistic proclivities and in his insistence on a hyperintellectual approach to composing. His coeval Scarlatti was more of a musical populist and humanist, as can be seen in his frequent use of elements of Iberian vernacular music. A few—just a few—of Scarlatti’s sonatas are even anti-geometric in their seemingly pointless, sometimes even deleterious alterations of key melodic and harmonic material from the exposition when they reappear in the recapitulation. (If only I could make a posthumous phone call to Scarlatti to ask him why he did that.) I’d also have to disagree with a perception on the part of the cover artist that there might be a cosmogonic quality in the sonatas: various composers have done cosmogony from time to time, but the Scarlatti sonatas exist comfortably (and brilliantly) in the terrene realm.
A word about the Ross performances: Despite their occasional imperfections, which would have been easy to fix practically or digitally while Ross was still alive and needless to say could still easily be fixed digitally (if Erato hasn’t done so already), they’re by far the best available introduction to the Scarlatti sonatas as performed on the harpsichord. (Piano is a separate and equally important matter.) I’d give them an A-minus.
MA Khan said,
May 12, 2026 @ 6:52 am
Beautiful reflection — “sunny days in Scarlatti-land” is such a perfect description. The connection between Scarlatti’s intricate sonatas and the mysterious geometry of the dodecahedron feels strangely fitting and fascinating.
Jeffrey Kallberg said,
May 12, 2026 @ 8:18 am
It's not always sunny in Scarlatti-land:
https://www.youtube.com/watch?v=7jdn_SC9QTg&list=RD7jdn_SC9QTg&start_radio=1
Ross at least keeps the tempo up. There's a Russian (and Russian-influenced) tradition of pianists playing this particular sonata very slowly – to great effect, if not particularly informed from a historical point of view.
Ross Presser said,
May 12, 2026 @ 9:11 am
@David L: The solid depicted in the video you linked is very appealing but does not have a formal name. The best description would be something like "Quadrilateral-faced sphere approximation with triangular caps" or "subdivided octahedron". (disclosure: Microsoft Copilot helped me with this.)
Michael Robertson said,
May 12, 2026 @ 11:22 am
Is it possible that the dodecahedron on the Scarlatti covers might be a reference to the twelve pitch classes in the circle of fifths in music theory?
M. Paul Shore said,
May 13, 2026 @ 1:57 am
Michael Robertson: Scarlatti wrote keyboard sonatas set in ten of the twelve possible major keys (the missing ones being D-flat major and G-flat/F# major) and in ten of the twelve possible minor keys (the missing ones being G# minor and E-flat/D# minor); and furthermore, transient modulations to the missing keys would be easy to find in the interiors of various of the sonatas. Given that, and given the simple fact of there being twelve notes in the scale (ignoring the peculiarities of pre-equal-temperament tuning systems), if all nine of the CD cover images (discussed in my comment above) contained drawings of dodecahedra, or even just of geometric figures whose number of faces was divisible by twelve, then I’d say yes, it’s fairly likely that a connection was intended by the artist. Since only two of the nine images depict dodecahedra, though, and since only two of the remaining seven depict geometric figures whose number of faces is divisible by twelve, I’ll say there’s probably no connection intended.
M. Paul Shore said,
May 13, 2026 @ 2:13 am
Ross Presser: Or you could say “72-faced latitude-and-longitude-divided sphere approximation”. Generically, a 72-faced solid of whatever shape is known as a hebdomicontadissaedron; or, taking a more colloquial tone, a heptacontadihedron. See https://www.polyhedra.net/en/model.php?name-en=hebdomicontadissaedron.
Ross Presser said,
May 13, 2026 @ 11:48 am
@M. Pal Shore:
Thank you! today I learned.
And it's quite appropriate to learn a new long Greek-derived word on Language Log. It helps hold back my hippopotomonstrosesquipedaliophobia.
M. Paul Shore said,
May 14, 2026 @ 4:53 am
It occurs to me, belatedly, that I should explain why I brought up the subject of Scarlatti in the second paragraph of my May 9th email as quoted above by VHM. It’s not that I particularly think of him as a Baroque-to-Classical transitional figure, certain tendencies of his in that direction notwithstanding. Rather, in bringing him up I was harking back to, and illustrating with the links, my April 19th and April 20th Language Log comments about the usefulness of Scarlatti’s and other eighteenth-century harpsichord music in enduring MRI scans, those comments being what prompted VHM to email me the Galuppi link as an item of more general interest. My comments were under VHM’s April 19th post “Somatic sounds in the hospital”, about the din of MRI machines.
The reason I brought up the subject of Scarlatti’s life and work locations in my subsequent May 11th email, also quoted above, was to make the point that he never lived in areas where ancient dodecahedra have been found.
M. Paul Shore said,
May 14, 2026 @ 1:04 pm
Looking at “Selected readings” above, I can’t help but notice that the “many references to previous posts on dodecahedra” in the (in turn) “Selected readings” section of the referenced 1/28/26 “Dallas Dodecahedron Daze Days” post include the following: "Wheat and word: astronomy and the origins of the alphabet" (3/15/24) — with references to seven substantial papers on this subject by Brian [R.] Pellar”. Insofar as that subject is concerned, could those papers be considered the Seven Wisdoms of Pellar?