Elements of Classical Music: Science, Methodology, and Story-telling

There are three sections in this blog post: (1) The science of pitch, and how a musical vocabulary is created. (2) The technical basics of classical music, how pitches are combined to create and release tension. (3) A retrospective of classical music in terms of this approach to tension and release. If you just want a listening guide, skip to Section 3! If you want to learn the theory, read Sections 1 and 2 as well.

Table of contents:

I. Introduction

Section 1: Building a musical vocabulary
II. The science of pitch
III. Creating pitches
IV. Scales

Section 2: Melody and harmony in classical music
V. The foundations of tension/release
VI. Constructing a melody
VII. Introducing chords and harmony

Section 3: The development of classical music
VIII. Classical music retrospective: extending tension and release
IX. Musical developments: pushing limits of the classical tradition

X. More resources

I. Introduction

The aim of this lecture is twofold: (1) to celebrate and teach the accomplishments of the classical music tradition; and (2), to give you, as listeners, some tools to help cultivate your enjoyment of classical music.

The great power of music all around the world comes from its ability to take you on deep, extended, emotional journeys. The various traditions through history and across cultures have developed different approaches to this art: some through rhythm, some through texture, some through harmony. Today we will discuss the fundamentals of Western classical music (i.e. European music, roughly between 1600 and 1900) which developed an approach to musical story-telling based on sequences of “tension and release” — achieved through combinations of melody and harmony — that can last seconds, minutes, and even hours.

Though this lecture will focus on a specific genre/era of music, we do want to recognize that music is and always will be a global phenomenon, core to the universal human experience — there are traditions and cultures all across the world, each with its own values, approaches, and techniques. We’ll refer to those global traditions a few times throughout the lecture. Let’s get started!

II. Building a musical vocabulary: the science of pitch

Before we discuss the methods by which tension is created and released in classical music, we need to establish some basics.

First, we will examine the concept of “pitch”: what is pitch, and how are pitches used to build emotional tension in a piece of music?

Scientifically, the “pitch” of any sound refers to the wavelength at which the tone vibrates. For example, the pitch which happens to vibrate at 440HZ is called “A”. The note “A” can be sung, or blown through a reed pipe, or plucked on any string found in nature. Just like we put syllables together to form a word, we can also put pitches together to begin telling a meaningful story. Different pitches played in sequence form the basis of what is called “melody.”

Here is a lovely video of the pitch “A”. (You don’t need to watch it for 10 hours before continuing on with this post.)

III. Building a musical vocabulary: multiple pitches

The next question for anyone who wants to express themselves through melody is: What other pitches can we put alongside “A” that make sense to the human ear?

Luckily, we are in the 21st century, and may have even studied some wave physics, so we can recommend an obvious contender: let’s try the pitch with double the frequency. Played together, these sound lovely! In fact, those wavelengths oscillate too nicely together… our ears are hardly able to distinguish the pitches. This “interval” (a set of two pitches) with double the frequency sadly won’t help us build any tension in our musical stories.

This file links to the sound of an octave. Don’t worry if you can’t distinguish the two pitches… that is sort of the point!

Our first guess (double the frequency) didn’t quite give us a new pitch to work with in our musical language. So, let’s try again… triple the frequency! This is equivalent to playing the pitch with 3/2 the frequency (because as we just learned: dividing or multiple by 2x the frequency is equivalent in our ears).

Now, our ears are definitely able to distinguish these pitches. And they still sound lovely together. So, we have our first success: two distinct pitches, like two distinct syllables, available for our musical language. The interval we’ve created is called “a perfect fifth”, commonly used in musical traditions all around the world.

This file links to the sound of a perfect fifth:

[Side note before moving on: Combining multiple pitches is not the only way to express oneself through music! For example, you could stick with the pitch “A” and begin to beat a rhythm. Building rhythms is a whole entire discussion in itself. In classical music, and in this lecture, we focus on melody and harmony.]

IV. Building a musical vocabulary: scales

So, we’ve learned how to create a second pitch. And in fact we can repeat this process of generating new pitches again and again. Given our original pitch, we can multiply its frequency by 3/2, then again to 9/4, then again to 27/8. We could theoretically define an infinite number of pitches. When we do we stop?

The open strings of a violin are four “perfect fifths” in a row.

Well, actually every culture has made its own decisions. The trade-off is between variety of pitches and our ear’s ability to distinguish separate pitches as they get closer and closer. If you stop at five pitches, you get a very famous set of notes: the pentatonic scale, a foundation for much of Asian music. If you stop at twelve pitches, you get the “chromatic scale:” the set of notes used by Western classical music. Arabic music uses twenty-four pitches, including “in-between” pitches that our (my) Western ears are not used to!

The pentatonic scale uses 5 pitches and avoids too much tension between notes.

Once a musical language picks the set of pitches it will use, the entirety of our musical repertoire is created from new patterns and insights discovered from arranging these pitches. The set of pitches that will be used for a given musical composition is called a “scale.”

V. The foundations of tension/release

Now that we have a set of pitches to use — in the Western classical tradition, the 12-tone chromatic scale — we are ready to discuss the first examples of tension and release. We will see that possibilities for tension and release arise naturally out of different combinations of these pitches. In fact, the entire history of classical music can be viewed as the exploration and development of those patterns and combinations.

We will start by exploring the sounds of the pitches when played in pairs. A pair of pitches is called an “interval”. From our discussions above, we may intuit that simple ratios of frequencies in pitches are nice to the human ear. It is hypothesized that our brains appreciate the ease with which it can distinguish the pitches, without being too similar.

The ratio of wavelengths 5/4 sounds pretty nice:

The ratio of wavelength with 15/8 is a little harder to enjoy:

Intervals which sound pleasant are called consonant, while intervals which sound harsher are called dissonant. With this knowledge, we can create our first example of tension and release: a dissonant interval followed by a consonant interval. We have begun to create a melody!

[An interesting question to ponder: though we’ve shown some scientific discussion behind the resonant nature of a “perfect fifth”, how much of our deeper interpretations of “pleasant” and “harsh” intervals is cultural?]

Here is a video showing some sequences of dissonance and release:

VI. Constructing a melody

We have learned that specific intervals of pitches cause tension and release by virtue of their wavelength ratios. With this knowledge, we can arrange pitches in sequence and distribute the experiences of tension and release across time. Our ears and minds are great at keeping these musical tensions in memory! When we construct an entire musical phrase of these sequences, we are writing a “melody.”

One of the great masters of melody was Mozart:

This melodic approach to musical composition works by (1) picking one single pitch to function as “home”, and (2) generating tension and release in relation to that pitch over the course of a melody. The single pitch that serves as home for a composition is called the “key” of a piece.

So, the composer of a melody must successfully orient their listener within the key of the piece, and then use that reference point to explore sequences of dissonance and consonance.

VII. Deeper structures: introducing chords and harmony

Western classical music was not content to stop at the construction of beautiful melodies. Composers wanted to deepen the emotional journeys their music communicated. One of the most important ways this is accomplished in Western classical music is via the concept of “harmony”: the exploration of tension and release that arises out of combinations of three or more pitches played simultaneously.

Just as the “interval” (2 pitches at once) is the building block of melody, the “chord” (3 pitches at once) is the building block of harmony. As an example, let’s attempt to create a chord that sounds reasonably “pleasant” using our previous ratio-of-wavelengths approach.

Given a single base note, we want to come up with two more notes that can be played simultaneously and all have simple ratios of wavelengths. First, let’s bring in our favorite “perfect fifth” — the interval of 3/2 the wavelength. Next, drawing from the notes available from our Western chromatic scale, there is only one other note that will create nice ratios with the first two. It is the tone in the major scale which forms a 5/4 ratio with the first note and 6/5 ratio with the second note. This grouping of three notes is called a “major triad”. Along with notes, and intervals, triads are the final foundational unit of the Western classical music language.

Here is the sound of that major triad:

Each triad in a given scale has an inherent potential for tension and release built into it, emerging from the “meta-relationship” between its constitute pitches and the home key of a musical composition. This means that if we learn how triads work, we can now employ two layers of tension and release at once.

Here is the sound of the most basic sequence of triads in classic music, the perfect cadence:

A defining feature of the Western classical tradition is that it combines melody (single-note sequences) and harmonic progression (triad sequences) in its approach to the creation and release of tension. In the next sections, we’ll explore the history of classical music through the lens of evolution in melody, harmony, tension and release.

VIII. Classical music retrospective: the development of tension and release

The “classical era” of the Western music tradition begins roughly towards the end of the European Renaissance. Over the next three hundred years, composers in this tradition would explore and push the limits of tension/release within the context of tonality and harmonic sequencing described above. Composers began to ask themselves — how far can we push the listening experience?

Baroque Era: The Baroque Era composers of the 1600s learned how to create intricate harmonic sequences, often repeating short moments of tension and release in complicated and textured work. The famous composer J.S. Bach was particularly talented at uncovering harmonies that arose out of melodies and melodies that arose out of harmonies. Here is a section from his incredible work, The Art of Fugue:

Classical Era: The Classical Era composers of the 1700s explored tension and release through beautiful melodies layered on top of harmonic sequences. In general, they removed the more complicated, dense textures of the Baroque era and also began to explore longer-form journeys and varieties of emotion. Let’s take a moment to enjoy the musical bliss uncovered by Classical composers like Mozart.

Romantic Era: After Mozart came the emotionally-packed Romantic era. Composers like Beethoven introduced harmonic techniques that were unexpected and jarring. Chords full of tension were played loudly, and did not resolve as expected. Compositions began to shift frequently between keys — just when we thought we had built tension/release around a home key, a work would shift into a new home key and force us to recalibrate. New chords were introduced as the music became more layered and dynamic, four notes at a time and sometimes even five notes at time, pushing the limits of the “tonal” basis for tension and release that emerge from the basic major and minor scales.

Late Romantic Era: Composers like Mahler pushed the temporal limits of the listening experience. Listeners were used to tension and release within a period of seconds. But what if we held a moment of tension for minutes? What if the most basic pairing of “tension” and “release” lasted 10-minutes long instead of just seconds? Symphonies grew to multiple hours — asking for more extreme concentration and commitment from their listeners. Wagner famously created operas in which entire acts were built to present a single, unresolved moment of tension… until resolving in the final moments of the opera.

These compositions of the 1800s reflect the fundamental techniques introduced in the 1600s pushed to their limits. Though still based around the basic foundational element of tension and release caused by playing a “dissonant” interval followed by a “perfect” interval, composers had (a) introduced more complicated harmonic sequences, and (b) stretched out the progressions to last hours long.

IX. Beyond tonality: the end of the classical tradition

All good things must end, and the tradition explored by these composers between 1600–1900 seemed to reach its limit in the early 20th century. It was at this point that composers began to fundamentally reject the postulates around which classical music was based: that tension and release should arise out of the natural consonance and dissonance inherent in the major and minor scales.

Impressionism: Composers like Debussy began to move beyond traditional tonality — he wrote music which no longer felt tethered to a single key, or “home”, around which intervals would create tension and release. His compositions create “impressionistic” soundscapes, with notes and chords shifting in and out.

Modernism: Composers like Stravinsky began to move beyond traditional harmony — he wrote music which rejected the hypothesis that music should build and release tension. Pieces like The Rite of Spring do not assume that “release” is the state a piece should be aiming for, and embrace tension as a state of the music.

Atonality: Finally, composers like Schoenberg began to move beyond melody — he wrote music that rejected emphasis on any single note, rejecting the basis of tension and release itself. At this point, classical music had moved past many of the assumptions that hold together our entire discussion so far: that music should follow clear sequences of tension and release following the natural ratios of wavelengths of pitches.

And so, bit by bit, the postulates of Western classical music were unwound and musical development took place along other paths. In the year 2020, we are about 100 years beyond the “end” of the classical era. It is a great time to reflect on the achievements of the tradition, take the time to explore musical traditions and cultures around the globe, and imagine what will come next!

X. More resources

If you enjoyed this blog post, I’d like to offer a few resources for further reading and learning!

  • A series of lectures given by the conductor and composer Leonard Bernstein at Harvard in 1973: https://www.youtube.com/watch?v=8fHi36dvTdE. These lectures cover many of the topics discussed here, with additional discussion and performances!
  • A YouTube channel by Richard Atkinson: https://www.youtube.com/user/richardatkinson2108. This YouTube channel takes favorite selections from classical music and explains how and why they work so well. Some of the discussions are a little more technically advanced, but I think they are still approachable!
  • An organization to donate: http://www.sphinxmusic.org/. If you are reading this far, then you probably value arts education and appreciate the wonder and beauty it brings to our lives. The world is in the midst of a great movement around Black Lives Matter, so please take a minute to learn about this organization which brings classical arts education to diverse communities.

I love music and literature. This is my app: https://itunes.apple.com/app/id1332841582.

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