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Johann Sebastian Bach wrote a couple of Trio Supers and Fantasia Supers, e.g.:

What does Super means in this context? A great trio?

Are there any other pieces called super?

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Super here means "on/based on" someone else's tune, as in the (English) title of Mozart's Twelve Variations on "Ah vous dirai-je, Maman" (known as "Twinkle, Twinkle" in English) for piano. In whatever language they are written (English, Latin, Italian, etc.), the different prepositions used indicate that the composer has based the composition on a musical kernel, usually a theme or melody, in someone else's work. So had he been writing in English, Bach might have named the piece Trio [based] on [the 1524 Lutheran chorale] "Nun komm der Heiden Heiland." There is nothing special about the fact that your examples are pieces for (solo) organ; the principle of using [genre name] + "on" + [a title] is generally applicable to any composition that borrows in this way. Sometimes the composer of the borrowed theme is named instead of the title of the piece it comes from. For example, Brahms wrote Variations on a Theme by Haydn for orchestra.

If you write a piece like variations on your own theme, you can simply leave this fact out of the title (in which case it will be assumed you wrote the theme too), or you can expressly state it. Elgar's "Enigma Variations," Op. 36 for orchestra is actually titled Variations on an Original Theme, and Brahms wrote a similarly titled set for piano. This practice probably started when it was common for one composer to write a set based on another composer's melody or a folk tune popular at the time. It's proper to acknowledge this rather than give the impression you are taking credit for the inspirational idea itself. An example is Chopin's early Op. 2, a set of Variations on "Là ci darem la mano", (a popular duet from Mozart's opera Don Giovanni) for piano and orchestra. Displaying the title of a well-known piece could also be a way of doing a little advertising and cashing in on an earworm people were whistling and humming, or a hymn they knew from church.

The theme for these types of works can also be a person's name. There are several works based on the motif B-A-C-H (H is the German letter for B natural; they use B for our B flat). See this Wiki article for a list of these composition. Schumann wrote Variations on the name "Abegg" for piano. (The big limitation here, of course, is that only the first seven or eight letters have corresponding notes.)

In works (especially variations) based on a theme, it's common practice to present the theme at the very beginning of the piece and in a fairly unadorned way, so that the "original" or starting material is immediately clear to the listeners. This lets them "fix" it mentally and subsequently pick it out as the variations become more elaborate and a lot is going on and also to appreciate the sometimes ingenious ways the theme is treated. Composers like building on a catchy tune or one that is inherently "malleable" as way of showing off their compositional prowess: "Hey word! Look what I can do!"

If you need a short-hand name, I would call pieces like those in your question by their respective genre: a Trio, a Fantasy (or Fantasia), Variations, or Trio on a Theme/Hymn, etc.. And while your examples may be great pieces, by using super in the titles, rest assured that Bach is neither congratulating himself nor supersizing his pieces :-)

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  • I'd add that “super” can mean both “over” and “on”. The English prefix super- relates to the “over” meaning whereas “on” or “about” are rather distinct. But in Latin, it can just as well describe simply something lying on the road – in English it would sound a bit silly to exclaim “the old newspaper was draped over the pavement”. — Also perhaps relevant: in German, “über” means both “about” and “over”. Dec 23, 2021 at 10:36
  • @leftaroundabout In general, prepositions rarely translate one-to-one between languages, leading to a lot of "false friends" where words that are clearly cognates have evolved entirely different usages. I'm sure linguists have theories about why that is; I'm tempted to ask on linguistics.stackexchange.com
    – IMSoP
    Dec 23, 2021 at 12:28
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    @IMSoP yes, this is driving me crazy in Norwegian. The language is in many ways very similar to English and German, but for example you “go on the cinema” to watch a movie and you're “empty for bread” when it's all been eaten. (Of course, German and English are hardly more logical with prepositions, only in different ways.) Dec 23, 2021 at 12:53
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    Prepositions and their use are highly idiomatic even within one language. You live and park on a street, but children are told not to play in the street. / You can learn a piece by heart, but you shouldn't take ignorant criticism of your playing to heart, etc. But of course Das Rheingold begins in the Rhine River--literally in the Rhine, not on it :-)
    – DjinTonic
    Dec 23, 2021 at 13:05
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    @IMSoP prepositions are among the more unstable elements even within one language. The UK lately seems to be rather different to the US, whereas the US is different from the UK. In the UK, you ring someone on a number, but in the US, you call someone at a number. Sometimes the instability is temporal or generational rather than spatial: younger people base their conclusions off something while older people base their conclusions on something. It seems to be similar with case (which of course has a similar function); I've heard of more than one language where case varies by region.
    – phoog
    Dec 23, 2021 at 22:47

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