Somehow in all these years of blogging, I've never written about my obsession with the first movement of Charles-Valentin Alkan's Concerto for Solo Piano. Actually, I did mention it in passing once here, and I've just added it to my otherwise rather static list of Favorite Music Works - a list which probably deserves a larger-scale re-visit. Leaving it off of that list was a big oversight, although I think my affection for this remarkable thirty-minute movement has only grown since then. I took a long walk this summer where I listened to the whole movement twice in a row, and I listened to it all on several other walks.
And yet, sadly I'm not here today to talk about that first movement, in part because I'm overwhelmed by the prospect of doing it justice. Just go listen here (recording includes all three movements), and I promise I'll make the time to tackle it some day. Alkan, a curious contemporary of Chopin and Liszt who was admired for his great virtuosity as a pianist, became something of a recluse who busied himself writing lots of piano music - some of it wildly ambitious and absurdly demanding. Perhaps most notoriously, his set of Twelve Etudes in All the Minor Keys (Op. 39) includes four etudes which form a symphony for piano solo and three more are the three movements of the Concerto for Solo Piano. [For reference, a typical etude would last about 3-5 minutes; these three together last about 50 minutes. Alkan was...different.]
And while I adore every bar of that first movement, the other two movements have more of the kinds of quirks I'd expect from such a mysterious, edge-of-history figure. In short, they don't appeal to me nearly as much. However, I've known for some time that near the end of the Finale, there is a wild passage which includes an F-triple-sharp (!). Yep, that's a pitch notated as an F but with a sign that means it sounds three half-steps higher - like a G-sharp. Most music students are bewildered enough by the concept of double-sharps and double-flats which seem useless since they point to notes with perfectly good, simpler names (F-double-sharp = G, etc.). Even notes like E-sharp can seem useless at first (E-sharp = F). So, I knew about this infamous F-triple-sharp, and had watched it fly by within a hailstorm of notes which you may witness for yourself here. That link should start at the 48:48 mark with the F-triple-sharp (notated as a sharp-double-sharp combo*) occurring just after the page turn. Don't blink!
The truth is, I'd never thought about why Alkan chose that exotic spelling. I just figured it was part of his legendary aura and perhaps a sign of insanity. But then, on a maddening but sometimes interesting Facebook group with the very generic name "Music Theory," someone proposed:
Generate a scenario, a tonal scenario, in which it is correct to write a triple flat or sharp. Go!!! 🙂
I include the poster's smiley face to reinforce that this challenge was pretty clearly posted in the spirit of fun and adventurous inquiry, though it's amazing how many inhabitants of this dumpster-fire group jumped in with inane comments about it being "nonsense," "impossible," "a waste of time," etc. Anyway, I happened to see the post soon after it went up, so was excited to be "first" in with the Alkan example. (Of course, given how social media most often 'works,' most commenters still didn't bother to read any of the comments before chiming in with great confidence about how no one would ever write such a thing.)
As discussion continued, I decided to look more closely into Alkan's maze to see what was actually going on - and though I'm not sure I'd ever be able to play that page, it didn't take so long to see the simple structure beneath, and to understand why he chose F-triple-sharp. I even made a little page on Noteflight which allows you to see and hear what's going on.
A few bits of background on this movement. Extreme solutions are often inspired by extreme conditions. In this case, a movement which began in the fairly standard key of F-sharp Minor (which has three sharps in its key signature) has arrived at a brilliant coda in F-sharp Major (which has six sharps in its key signature, making it one of the sharpest keys). While both hands are whirling away, the first two bars simply outline I, IV and V chords in the key - the three most common of chords in the most common progression! In this case, that means the following chords: F-sharp Major → B Major → C-sharp Major. The two bars end with a little six-note-figure in which the three pitches of a C-sharp Major triad are each preceded by a note one-half-step below: a series of lower chromatic neighbors.**
Because we're in a pretty far-out key and those neighbors are not even part of this key but from a world even further out, the addition of these raised notes in an already very sharp context gives rise to an unsightly trio of: B-sharp, D-double-sharp, and F-double-sharp. So things are already looking pretty wonky. But then Alkan does something else which, generally speaking, is super-normal. He sequences those two bars by essentially repeating them, but two steps higher. This means he's technically now working in the temporary key of A-sharp Minor, a very rarely used key which has ALL the possible sharps. (Well, all the possible normal sharps, that is.) The V chord in A-sharp Minor turns out to be a pretty pointy E-sharp Major triad, consisting of: E-sharp, G-double-sharp, and B-sharp. [If you care, the important note there is the G-double-sharp, which is not in the key signature for A-sharp Minor; but creating V chords in minor keys requires raising the leading tone, so the key signature G-sharp gets a bump upwards.)
Now, if you're following this - first of all, thank you! - when lower chromatic neighbors are added to these, we now need a note only one half-step away from that G-double-sharp. You guessed it! We need an F-triple-sharp. Here's the context, more or less.
Doesn't that look simple? But seriously, if this is too confusing to follow, the basic point is that what Alkan is doing is not that unusual harmonically. It's just that by starting in a VERY sharp key, the normal need for raising a couple of pitches leads to this unusual situation. If he were to re-write the whole passage (or just part of it) in the enharmonically equivalent key of G-flat Major, this problem would not arise. However, many musicians will tell you there's an important psychological difference between music in sharp keys vs. flats, aside from historical associations caused by less equal-tempered tuning methods. (I wrote about this in a post where I was intentionally re-writing a sharp-key Bach Prelude & Fugue into a "simpler" flat key, and my pianist friend Erica found the transformation disorienting.)
For what it's worth, if you go and view/listen to the Noteflight page I made, you may see also how this progression and then Alkan's actual music would look if he briefly diverted to a flat-heavy key signature. If you've never used Noteflight, be sure your mobile device is not in "do not disturb mode," to hear the content. Also, you may slow down (or speed up!) the music using the little lightning slider.
As far as I can tell, there's one other prominent example by an established composer which uses an F-triple-sharp. In his second Clarinet Sonata, the German composer Max Reger (known especially for this dense counterpoint) has a passage which, like Alkan's, has modulated from F-sharp Minor to the parallel F-sharp Major. In this case, writing for A Clarinet, if Reger had chosen the enharmonic G-flat Major, that would have put the A Clarinet part in the ungainly key of B-double-flat Major. Yes, he could have written the piano part in a different key than the clarinet, but that likely went against Reger's sense of contrapuntal honor - not to mention that he also might have felt that the psychological and implied coloristic different of F-sharp Major is worth preserving. So, in a thorny little part of the piano part, a G-double-sharp has arisen as part of a chromatic passing function in the left hand. This means that a little neighbor-note figure in the right hand also begins with a G-double-sharp, and its lower neighbor is again an F-triple-sharp.
Unlike the Alkan, this is a gentle, innocent-sounding passage which you may hear starting around the 21:00 mark of this video. The clarinet begins this new F-sharp Major coda at that point and the F### comes at the end of the page as shown above.
If you'd like to hear an even more innocent-sounding F-triple Sharp, a Facebook group contributor named August Rex proposed a very simple little modulation from F Major to its mediant A Minor featuring a lower chromatic neighbor and then showed how if that music was in the - you guessed it - key of F-Sharp Major, one would get the very same situation as Alkan's. I also made a little "listen and learn" version of this on Noteflight.
I know this is all pretty esoteric and "edge of reason" - which, of course, is why it's interesting. It was also a fun challenge to hack Noteflight, which doesn't actually acknowledge triple-sharps, to make these demonstrations. Noteflight is not great for creating polished looking notation, but it's useful for creating little online notational excerpts which play back easily for anyone.
But wait, there's more! What about triple-flats? Well, a composer from New Zealand (don't you love the Internet?) submitted this passage from a duet for violin and cello. Here, the cellist is basically ascending by half-steps chromatically, but the composer Craig Utting decided the consistent use of flats paints a clearer picture of what the cellist is doing.
There were two aspects of this example which intrigued me. One is that by not re-spelling the C-flat as a B-natural (which would've invited use of C-natural and negated the need even for double-flats), Uttig's solution uses a minimal number of accidentals displayed - the tradeoff being that the performer has to live with those extreme accidentals. I also thought it was interesting to see how many letter names in row could be included in a chromatic scale without resorting to quadruple accidentals. So, I submitted the following in response to Mr. Uttig.
There are other situations in which triple-flats might arise (or descend?), but I think perhaps we've seen enough for one post. Stay tuned for another new post on Tuesday!
* Notice that the triple-sharp is so rare that it doesn't even have a standard sign.
**In general, notational practice prefers that such neighbor relationships be spelled out by using note names with adjacent letters. C-sharp to D is much preferable to notating as D-flat to D. The morning after this topic had invaded my brain, I woke up thinking about the "Kangaroo" music from Camille Saint-Saëns's Carnival of the Animals, in which a long series of grace-notes are all lower chromatic neighbors. You may see that demonstrated here - and also see how converting to A-sharp Minor would create the need for many double-sharps. Another friend pointed out the passage at 2:30 from this Chopin waltz with upper chromatic neighbors (see all those double-flats), and another friend pointed out the series of lower chromatic neighbors in the famous Handel-Halvorsen Passacaglia (5:07 here), although the tame key of G Minor means we don't get any super-exotic spellings. I have awesome friends!
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