What do back-to-back crescendo-decrescendo ("<>") markings mean?

Question

Okay, So I understand the staccato and crescendo and diminuendo markings, and the accent mark...

But what does the less than and greater than mark that I highlighted mean?

This is Czerny, First Instruction in Piano Playing.

Answer 1

For the crescendo and descrescendo mark: small to large means crescendo; large to small means decrescendo. Sometimes the amount is indicated by a dynamics letter (f, ff, p, mp, etc.) and sometimes, one must use one's own judgment.

FOr single staff instruments, the marks are below the staff. For piano, the marks are between the staffs if applied to both staffs. (Else below the staff that's meant but I'm not always whether below the top staff is different from the middle; there are usually pairs of marks for each staff in that case.) Other instruments using the grand staff are treated similarly.

The short cases highlighted in the example are a bit unusual. These are common in voice or wind or string instrument parts but not so common on the piano (or organ but would work on an accordion or concertina or bandoneon). Apparently one is supposed to articulate things so as to give the impression that the single note is gently made louder than softer.

Answer 2

The notation can mean two slightly different things. In the Czerny case -- and generally in piano music -- it means to "lean into" the note. Outside of MuseScore, which calls it a "soft accent", I'm not aware of an official term for it. (I found no listing in The Oxford Companion to Music, among other sources.)

It can also indicate a swell, or messa di voce, which does mean an increase and decrease in volume on the same pitch. MuseScore includes this as a separate symbol, vertically wider than its "soft accent" symbol.

Dolmetsch online, which also uses the term "closed accent", gives only a single symbol, but with multiple meanings.

to increase volume and then die away in the duration of a single note or short phrase also called messa di voce (Italian) or mise de voix (French)

in Rossini, the typical markings of the 'closed accent' and the 'closed hairpins' appear frequently but they were also commonly used by his contemporaries. They signify, in the case of the 'closed accent', a more marked and longer accent than the norm; in the case of the 'closed crescendo', a crescendo that ends abruptly in a sforzato emphasis; in the case of the 'closed diminuendo', a sforzato that immediately trails off into a diminuendo

in nineteenth-century German non-vocal music the < > sign can represent a stress or accent as opposed to a crescendo followed by a decrescendo music. In such a case, the marking apparently indicates a kind of "warm", not too powerful, accent with implication of vibrato where appropriate. (emphasis mine)

Schumann, for example, uses this marking in "Melodie" from his Album für die Jungend (Op. 68, No. 1).

(Mm. 5-7, 2nd ed.: IMSLP.)