This article is part of a series on Baroque Music. See also:

What is music, and how does it assume beauty and structure? The question is difficult, yet awesome – and its answers appear, to me, above all else in the baroque music of Johann Sebastian Bach (1) (2) (3). Bach’s music attains a virtually geometric perfection, dividing time into cascading blocks which each, within themselves, convey struggles, twists, and resolutions – all in perfect harmony. The result evokes a series of late-Renaissance paintings unfolding in real-time.

Music, then, has structure, and it’s of a unique kind. Notes take on meaning in short sequences; these phrases then, in turn, build more complex and nuanced passages. The product is the creation and development of a theme; this theme is introduced and progressively accumulates additional flavor, conflict, and subtlety. In Baroque tradition, it will always end in resolvement.

I will explore a couple themes intimately related to structure in music.

Memory

Your humble author has retained, in memory, large segments of almost every piece he has played throughout his lifetime. (At age 7, I played the entirety of Bach’s “Jesu Joy of Man’s Desiring” (4) by memory on the recorder in front of my first grade music class.) How is music memorized? It seems clear that randomized sequences of notes would be much more difficult to memorize than “real music”; this result is indeed confirmed in studies (5). Our answer lies here: the brain, in memorizing music, is not merely memorizing the individual tones in succession. The brain memorizes macro-scale themes and structures. We’ve made progress.

We might draw an analogy to general psychological tests of memory, which demonstrate that “sensory” memory (i.e., segments of purely sensory input such as sound or image) persists only in the short term, while “semantic” memory (i.e. memory of meaning) lasts much longer. It seems that we can conclude that musical memory is semantic in character.

In the same way that the brain finds meaning in places such as literature and language, the brain too identifies meaning in music. Though the nature of this meaning seems unique to music, it’s (apparently) similar enough – at a deep level, that is – for our brains to encode it into semantic memory. Music has strong structure and our brain employs this during memorization.

Music Theory

Why do our brains like music? Music theory describes chords – more precisely, progressions of them and relationships between them – which, in implementation, form music which strikes us as ideal. I claim that classical music, and Baroque music in particular, has “mastered” these chord progressions: composers like Bach create music which is, almost literally, mathematically perfect.

These chords strike our brain as beautiful. Why? Clues might be found in the ratios between pitches: common musical intervals feature mathematically salient ratios between their frequencies. Two notes an “octave” apart are typically said to be the same; more precisely, the muscial scale operates on a “cycle” which repeats every octave. The ratio between octaves? Exactly double. The “perfect fifth”, meanwhile, features a ratio of 3:2. Even more interesting: the ubiquitous major and minor thirds feature ratios of 4:5 and 5:6, respectively. The perfect ratios of these intervals undoubtedly influence our brains’ subjective enjoyment of them.

But why subjective enjoyment – why do we convert these perfect intervals into emotion? This question is even more difficult, and carries significant philosophical depth. I only offer one striking fact: Bharucha (2010) showed that the minor third is replicated in sad speech, mimicking its use in music! (6) The emotional power of music is truly deeply ingrained.

As a closing word, I urge the reader to listen to the links below – and to work to detect the structure. Listen not to each note, but to each phrase, and to each sequence of phrases; broaden your scope, as it were, to the extent that you can. I hope you enjoy.

A playlist containing Bach’s outstanding Brandenburg Concertos. https://www.youtube.com/watch?v=Zpf38dQpMzk&list=PL7CF3989F048B5211 Bach’s unaccompanied Sonatas and Partitas performed Rachel Podger CD1 CD2 The famous “Concerto for Two Violins” or “Bach Double”. https://www.youtube.com/watch?v=vesrqFeq9rU Jesu Joy of Man’s Desiring https://www.youtube.com/watch?v=FwWL8Y-qsJg Sloboda, J. A. (1985). The musical mind: The cognitive psychology of music. Oxford, England: Oxford University Press. Curtis ME, Bharucha JJ (June 2010). “The minor third communicates sadness in speech, mirroring its use in music”. Emotion 10 (3): 335–48.