Tamar Halperin

About Ground- Booklet Text

Does the key of a given composition by J. S. Bach reveal anything about the music itself?
This lecture offers a survey and an explanation of tuning and temperament systems, history of church modes, Key Characteristics, instrumental idioms, and Bach’s own (secret) tonal schemes. The result is a surprising and valuable insight into Bach’s compositional process.

What Can Performers of Classical Music Learn from Other Musical Genres?

Acquaintance and experience of non classical music — for example, Electronic music, Jazz, Folk, Pop, or “World” music — can influence and benefit the performance Western Classical music masterpieces.

How does Flamenco relate to Baroque music? And what does a classical recital program have to do with the set of Techno DJ’s  ?

This lectures covers practical aspects of interpretation & performance, with many musical examples, both recorded and live.

To my 8-year old daughter, Alma

Beloved Child,

You were born into a new century.
As I am writing this to you, technology, communication, politics, and climate are transforming at breathtaking speed. By the time you are an adult, our world and society will have changed in ways that no one can predict.

I was born and raised in the 20th century, you see, and it was in that time that I trained to be a classical pianist. I did it because classical music cast an irresistible spell on me. Works by old European masters, such as Mozart, Beethoven, Brahms, Debussy, and above all by J. S. Bach, captured not only my ear, but my whole being. This music moved my heart & my soul, stirred my imagination, challenged my intellect, and stimulated my body.
I was a child when I first experienced this. Deepening my knowledge of classical music has been my main pursuit since. Now— decades later— the spell of classical music is even a million times stronger.

You, too, love music with all your being. I see you singing to yourself the latest pop songs. You dance joyously, naturally, to the beats of popular hip hop tracks. Again and again you play your favourite rock songs in your earphones and find in it endless delight. There is such a directness, such an immediacy to the way you experience it!

I am not the one to preach to you that classical music is better than any of these genres which you enjoy so much.
When it comes to the practice of classical music —as manifested in concert halls in the west over the past 100 years— I myself am no longer convinced that it is all that better.
If time is the canvas of music, then the present is its frame.
For music to be relevant, I believe it must be alive, fresh, and resonant within current context of society and culture. I am no longer sure whether it is sensible to perform classical music masterpieces as if what happens outside the concert hall is of no relevance. I have a hard time justifying to myself a public musical performance of old music, if it is entirely detached from any context. These great classical masterpieces were conceived centuries ago within aesthetic norms that were well-known to historical audiences back then. These norms have meanwhile changed so much, that to the average young listener they are all but impenetrable, and arguably meaningless. It seems to me that in order for such old music to communicate and appeal to your contemporaries, certain stylistic bridges must be forged. Without them, I can see how the experience might be alienating to you.
But let us please separate the PRACTICE of classical music from the music itself.

Because, you see, classical composers have created some of the greatest musical masterpieces of our culture, which are nothing less than pinnacles of human achievement. These masterpieces are towers that changed our cultural landscape forever and which, from the moment of their creation, have become inevitable points of reference.

Not only in music, but indeed in all the arts, be it literature, the visual, or the performing arts: everywhere you turn, wherever you look, in anything you hear, you will find a reference to an older masterpiece.
How many current TV series are variations on biblical stories? How many contemporary films are modern adaptations of Greek myths or Shakespeare plays?
Of all the graphics that you see around you, how much is influenced by Da Vinci? By Van Gogh? By Mondrian?

In music, even the simplest pop song abides by musical rules and structures that were established centuries ago.
The Beatles quote Bach; Film music quotes Wagner; Telephone ringtones quote Beethoven.
No man is an island. We are part of an endless thread and all of us are entangled with it. Our culture is a complex construction of many parts, a fabric made of many layers, not one exists without the other.

With the passage of time many changes inevitably occur. Tastes, fashions, trends, styles, and languages evolve and transform. At any point you may consider some things old fashioned, while others things would appear to you trendy or forward looking. It is only natural, therefore, that the style of old works may seem foreign to you. The language of the bible, for example, is old Hebrew— a language no longer spoken, and unknown to most of our contemporaries. The same is true for Shakespeare’s English, and for Homer’s Greek. Most of us would need to use translation in order to understand the plots, let alone appreciate their poetry, creativity and wisdom.

Similarly, musical works from centuries ago are composed in a “language” that is no longer “spoken.” The language of Classical Music, too, requires either knowledge or “translation” in order for it to be understood and appreciated. And although today’s schools no longer make it a priority to provide this knowledge, nevertheless, it is not hard to come by. As long as your mind is curious and untamed by fear, you will be able to acquire any language, even if it is very different than your own.

Although styles and fashions change, once you’ve gotten past the language barrier you will find that there is one fundamental element at the core of everything which remains the same: it is the architecture of the human soul. Our experience of love and loss, abandonment and sorrow, grief and loneliness; our reverence for nature, for birth, for death; our falling in love, our quest for happiness, for safety, for a sense of belonging—
across generations and cultures, this has not changed: we are human, all of us.

Last night I had asked you: “do you think it is important to know the music of Bach? Do you think it is important to know the works of Shakespeare?”
-“Of course!” You said without hesitation. “It is a way to know more about the world!”
At your very young age you already know this much: that we can learn about the world from the art of great masters.

Because what is the purpose of art, ultimately, if not to crystallise some profound truth about the world, about human nature, to which we can relate? If not to present us with an insight, verbally or otherwise, about the human state?
When such truth reveals itself to us, it endows us not only its wisdom, but also an invaluable comfort and solace. Because in that moment— through the architecture of our souls— we are connected, not only to a specific artist or art, but indeed to all our fellow humans across all generations and cultures.

“Sapere Aude”:
dare to know; dare to be wise; dare to think for yourself.
This phrase, coined by Immanuel Kant in 1784, is perhaps the most famous motto for the age of the enlightenment. It stands for such ideals as liberty, tolerance, fraternity & knowledge; for placing reason over religious dogmas, and science over irrational beliefs.
It is thanks to this, that technology came as far as it did, so as to enables us in 2018 to carry in our pockets a gateway to practically all of human knowledge. Use your phone to ask Google, read on Wikipedia, listen on Spotify, watch on YouTube: no need to go far, everything you want to know is but a click away.
And yet, this very technology seems to act against the ideals that once enabled it: it often prompts an intellectual laziness, renders its users accustomed to instant gratification, and dims people’s sense of fraternity by masking them with the anonymity of computer screens.
Political tendencies in 2018 show the rise of extreme right in most countries. Religious differences threaten world stability, and the division between “us” and “them” (which often results from irrational beliefs and lack of knowledge) occurs on more levels than ever, in almost all cultures.

It is precisely for this reason that, in my opinion, the study of cultural treasures of the past is now essential. These works of art (music, literature, philosophy, etc.) place high demands on its consumers, but offer much more in return:
They demands knowledge— but educates us
They demands concentration— but augments the ability to concentrate
They require a purity of thought— but purify the mind in return.
This art requires actual involvement from its recipient, but in return offers the most profound insights, the deepest satisfaction, and a unique perspective that can purify and illuminate the human state.

Juilliard Journal, March 2009

https://journal.juilliard.edu/journal/ongoing-quest-bachs-temperament

In 1722, when Bach compiled his ingenious collection of preludes and fugues in all 24 keys, he gave it the title Das wohltemperirte Clavier (The Well-Tempered Clavier), a term that became as familiar as the music itself. But what does the name actually mean? And what led Bach to choose this peculiar title?

The term “well-tempered clavier” refers to keyboard temperament.
At the core of any discussion of temperament lies a mysterious acoustic phenomenon, which was discovered by Pythagoras in the sixth century B.C.: When a string is divided in half, the interval between the pitch of the full string and the pitch of its half-length is a pure octave; when a string is divided in the ratio 3:2, the interval between the pitch of the full string and the pitch of its two-thirds is a pure fifth.

As we know, a circle of 12 fifths begins and ends with the same note. Strangely, however, 12 pure fifths do not really “fit” within the octave, but actually exceed the octave, so that the final pitch is slightly different from the original one (it is lower than the original if the circle goes down, and higher if the circle goes up). The amount by which 12 fifths exceed the octave is called the “Pythagorean comma.” Therefore, to put it simply, temperament is the method of “compromising” the purity of the fifths in order to keep the octave pure. (Figure 1)

Figure 1: The circle of fifths (the rising fourths in this example are equivalent to descending fifths). If each interval is tuned to be pure, the last note will be lower than the first

In practice, singers and most instrumentalists solve the problem spontaneously by intuitively adjusting their intonation. But this cannot be done on instruments of fixed pitch, like harpsichord, piano, organ, harp, lute, or guitar. These instruments require a choice of temperament, which dictates the degree of “falseness” of the intervals, and therefore the “usability” of the various keys. (If one of the fifths is very false, the keys that include this fifth will be unplayable.)

The standard temperament nowadays is “equal temperament,” in which all 12 fifths are narrowed by the same amount (1/12th of the Pythagorean comma). In this temperament (which is used in all modern pianos, for example), all the keys are equally false, but the degree of their “falseness” is relatively small. However, “equal temperament” did not become the standard until late in the 18th century or later (and well after Bach’s death). Until then, a large variety of non-equal temperament systems were used, and it is probably to one of these systems that Bach referred in the title of his 1722 collection.

The terms “well-tempered” and “well-temperament” were first coined in 1691 by German theorist Andreas Werckmeister, referring to a sort of temperament in which the fifths are of different sizes, but none of the fifths is too false to use. In “well-temperament,” all the keys are playable, yet they vary in their purity and timbre. The concept of variety was an important part of Baroque aesthetics, and the different colors of the various keys (created by non-equal temperament) was considered an advantage. Perhaps this is what Bach meant to demonstrate in his collection of preludes and fugues. While Werckmeister gives clear instructions for his proposed temperament, there is no direct evidence of the exact kind of temperament that Bach himself used.

Over the years, attempts to reconstruct Bach’s temperament were made by a number of musicologists, from Kirnberger and Marpurg in the 18th century to 20th-century musicologists Herbert Kellner and John Barnes. But perhaps the most curious and unusual approach to the question of Bach’s temperament was presented in the February and May 2005 issues of Early Music by harpsichordist/mathematician Bradley Lehman. (The illustrations in Figures 2-5 in this article appeared in that publication.)

Examining the title page of the W.T.C. from 1722, Lehman noticed that the decorative scroll above the text features 11 loops of three different kinds (simple, double, and convoluted). (Figure 2) It occurred to him that 11 is the number that would describe the temperament of 12 fifths (if the first note is given, it would also be the last note of the circle, rendering the “12th loop” unnecessary). He noticed the letter C attached to the first loop from the right, and then decided to turn the loops upside down. (Figure 3)

Figure 2: The title page of Bach’s Well-Tempered Clavier from 1722, with labels added by the author of this article. D denotes double loops, S indicates a simple loop, and convoluted loops are marked C

Figure 3: Lehman’s interpretation of the scroll; the same graphic as in Figure 2, turned upside down, with note names above their respective loops

Lehman states that in the Baroque period the normal amount of tempering a fifth is 1/6th of a Pythagorean comma, which, he believes, is represented in the squiggle by the convoluted spiral. He interprets the double-spiraled loops to represent the tempering of 1/12th of a Pythagorean comma, and the simple loops to indicate pure fifths. He then devises a temperament he believes to be the one used by Bach, and which, according to Lehman, brings out qualities of Bach’s composition that are hidden in equal temperament.

Lehman’s theory received tremendous attention, being highly praised by some and severely criticized by others. The November 2006 issue of Early Music featured several responses to Lehman’s article on Bach’s temperament. One of them, written by John O’Donnell, challenges Lehman’s interpretation and offers an interesting alternative for the reading of the title-page scroll.

O’Donnell claims that, although tuning is done with fifths, its customary notation in the Baroque period was actually chromatic, rising from C. This is also the order chosen by Bach for the 24 preludes and fugues. Examining the scroll of the Well-Tempered title page once again, O’Donnell notices that the “D” of Das intersects with the third loop and that, to its left, there is a squiggle that looks like “Es,” the German notation for E flat, while to its right appears the German tablature symbol of “Dis” (D sharp). O’Donnell mentions the E-flat/D-sharp Prelude and Fugue, which, curiously, is the only piece in the collection that refers directly to the enharmonic phenomenon.

O’Donnell assigns pitch names to the scroll, starting from C on the left and ascending chromatically until reaching B on the right side. (Figure 4)

Figure 4: O’Donnell’s interpretation of the scroll

Based on his reading of the scroll, O’Donnell constructs a temperament system which, according to him, represents Bach’s own.

In 2007, in response to these articles, musicologist John Francis posted an article on the Internet that offered a systematic analysis of the scroll, considering the diagram’s orientation (left to right; right to left), tuning direction, starting position, and degree of temperament, so that, in total, 144 possibilities were mathematically analyzed. Francis compared his results with 52 existing tuning systems, and finally came up with a reading of the scroll, as seen in Figure 5.

Figure 5: Francis’s interpretation of the scroll

However, with all of this said and done, to this day no one knows what Bach’s temperament really was. Whether the decorative scroll of the Well-Tempered Clavier is indeed a temperament prescription or not, it now provides a subject for endless interpretation, almost like the music that follows the title page. The quest for Bach’s temperament will most likely continue to preoccupy musicians and theorists for generations to come.