I have remarked before that music is a form of thinking.  It is a form of thinking for the composer and may also be for the listener.  If the performers are to transmit its essence effectively and well, it will be a form of thinking for them also. Listening recently to the music of Prokofiev,  I realize I don’t think in the way he does, and so I find his music alien.

But what is the nature of this musical thought?

In the case of late baroque fugue and 12-tone music, musical thinking takes the form of the group transformations that composers use for development  of a theme – repetition, transposition, reversion, inversion, and their combinations.   Composers use these transformations to develop the theme or tone-row, and writing or listening to such a development is a form of cognition, in the same way that following a sequence of deductions proving a mathematical claim is a form of cognition.   By analysis and careful listening, listeners can train themselves to hear these transformations, to anticipate them, to be delighted when one’s anticipations are proved correct or when surprised, and thus to gain pleasure from the thinking involved.  This mental pleasure is not the same pleasure one has in listening to beautiful or very pretty music, or the pleasure involved in hearing music which challenges the performers’ technical capabilities being played accurately, or the pleasure involved in hearing an interpretation coherently connecting notes, phrases, episodes and movements.  (Of relevance here is that the German word for musical movement is “satz”, meaning “sentence”.)

This mental pleasure, however, is very similar to that experienced by pure mathematicians in working through a proof or a counter-example.

In the case of the composers who followed the late Baroque – those of the so-called classical period – the development of a theme took a different course.  Here, some element or elements of the theme or themes – perhaps a rhythmic motif, or an interval pattern – would be transformed – altered, played-with, repeated, varied, presented in a different key or with a different rhythm, played by different instruments, or played over a different harmony or in a different mood – before returning to the theme(s) again.  Again, this act of transformation is a form of cognition for the composer, for the performer (who needs to make a coherent interpretation of the whole piece despite these transformations), and also for the listener.    The form of this act of cognition is different to that of the cognition in listening to fugal or 12-tone music, but no less pleasing to anyone trained in its conventions.

Even when working within a tradition, composers typically transform their material in idiosyncratic ways, ways peculiar to themselves; in other words, they think differently.   By listening carefully to a lot of music, listeners can come to recognize these idiolects.    And listeners can hear direct lines of influence – composers whose ways of musical thinking (their typical themes and their typical means of transforming their themes) are similar to those of other composers.    JS Bach, for instance, once walked 200 miles to Hamburg to listen to Dietrich Buxtehude, but Buxtehude is not the North German late baroque composer whose musical thinking I find closest to that of Bach.  The closest, and hence the one whose music I find most conducive to Bachian cognition, is Johann Adam Reincken (1643-1722). (Note that Bach may have visited Hamburg as much for the opera and the singing and music in churches of opera performers that the city was then famous for, as for Buxtehude.)

Likewise, Felix Mendelssohn influenced an entire generation of composers.  If you like Mendelssohn’s music – if you enjoy the act of cognition which close listening to his music enables – then you will likely also enjoy music that produces similar acts of cognition – for example, that of Luigi Cherubini (1760-1842), Johann Hummel (1778-1837), Franz Schubert (1797-1828), Louise Farrenc (1804-1875), Juan Chrisostomo Arriaga (1806-1826), William Sterndale Bennett (1816-1875), Johannes Verhulst (1816-1891), Neils Gade (1817-1890), Antoni Stolpe (1851-1872), the American George Whitefield Chadwick (1854-1931), and even the Australian composers Alfred Hill (1869-1960) and Frederick Kelly (1881-1916).  Mendelssohn was directly influenced by the music of some of these composers (eg, Hummel, Schubert) and taught others (Bennett, Gade, Verhulst).

He may also have met and been influenced by Arriaga and Farrenc on his visits to Paris as a teenager in the 1820s.   In the case of Cherubini, whom the young Felix did meet in Paris, Mendelsson both was influenced by him (eg, Cherubini’s first two String Quartets, 1814 and 1829, greatly influenced Mendelssohn’s early quartets), and influenced him in return (Cherubini’s later string quartets, from 1835 onwards).   You can hear the influences if you listen to the two composers’ quartets.  Similarly, Mendelssohn both influenced and was influenced by the music of his sister Fanny Mendelssohn-Hensel (1805-1847), as can be heard in her chamber music.

And, although an Antipodean, Hill studied at Mendelssohn’s Leipzig Conservatory and played with Mendelssohn’s old band, the Leipzig Gewandhaus Orchestra, before returning to Australia; his music also owes an audible debt to that of Schumann. Listening carefully to the music of these composers involves acts of musical cognition that are very similar, and closer to each other than to those acts involved in listening to other composers.

Other types of music also enable cognition, of different forms.  In minimalist music, for instance, musical material may be transformed not melodically or harmonically as in classical-era music, but rhythmically or with respect to emphasis and pulse.   Having parallel instrumental lines go in and out of phase, for example, leads a listener (and performers) to listen closely to the various musical lines and their relationships to one another, a form of musical cognition that is different again to that of classical or baroque or serialist music.   Detecting and tracking these phase progressions can also give great pleasure to listeners.  Not everyone finds this thinking task easy to do, particularly if they have received a western musical education which (until recently) emphasized listening to – and thus thinking about – harmonic transformations and progressions.   I am sure this inability to listen intelligently and to think appropriately is the root cause of the dislike of minimalism that many people have.

Listening, because it requires thinking, can be hard. But musical thinking, as with doing crossword puzzles or proving mathematical theorems, can be immensely rewarding.

Postscript (March 2023):

After the performance by Lucas Jussen and Arthur Jussen of Stravinsky’s two-piano version of his The Rite of Spring at Wigmore Hall in January 2023, Lucas Jussen commented that this music required intense concentration from the performers AND also from the audience. He praised the Wigmore Hall audience for concentrating so strongly, something which he and his brother could feel as they played. He could still recall that intensity of concentration from the Wigmore audience when I spoke with him in Paris in March 2023.