Wednesday, September 19, 2012

Aeolian Harps

‟MUSIC PLAYED WITHOUT human hands”: this is how the ancients described the sound of the aeolian harp — a musical instrument that sings its unearthly notes when the wind blows over its strings, making sounds that are melancholy, or soothing, or eerie, or distressing.

Here is an unusual aeolian harp from Italy:

Aeolian harps and the Romantics

The Aeolian harp is known for its influence on the Romantic poets. A popular home musical instrument by the turn of the 19th century, small wind harps were made to fit in windows; one such harp or lute is poetically described by Samuel Taylor Coleridge:
And that simplest Lute,
Placed length-ways in the clasping casement, hark!
How by the desultory breeze caressed,
Like some coy maid half yielding to her lover,
It pours such sweet upbraiding, as must needs
Tempt to repeat the wrong! And now, its strings
Boldlier swept, the long sequacious notes
Over delicious surges sink and rise,
Such a soft floating witchery of sound
As twilight Elfins make, when they at eve
Voyage on gentle gales from Fairy-Land,
Where Melodies round honey-dropping flowers,
Footless and wild, like birds of Paradise,
Nor pause, nor perch, hovering on untamed wing!
O! the one Life within us and abroad,
Which meets all motion and becomes its soul,
A light in sound, a sound-like power in light,
Rhythm in all thought, and joyance everywhere—
Methinks, it should have been impossible
Not to love all things in a world so filled;
Where the breeze warbles, and the mute still air
Is Music slumbering on her instrument.

— from The Eolian Harp, 1795.
The Romantic poets saw these instruments as playing nature's — or God's — own music, and so they thought that the harps were sources of natural or divine inspiration. These harps were first seen as being passive instruments, but the Romantics later understood that due to their design, they actively shape and transform the wind into music, and so became a symbol of the inspired poets themselves. ‟Make me thy lyre, even as the forest is,” wrote Percy Bysshe Shelley, in his poem Ode to the West Wind, where he is asking to become an instrument of the forces of societal change, as symbolized by a fierce west wind blowing through a forest. Shelley thought that the role of the poet, like a wind harp, is to shape and transform the tempestuous forces of nature, or mysterious spiritual impulses, into something more ordered and harmonious. Shelly explains in this manner:
We live and move and think; but we are not the creators of our own origin and existence. We are not the arbiters of every motion of our own complicated nature; we are not the masters of our own imaginations and moods of mental being. There is a Power by which we are surrounded, like the atmosphere in which some motionless lyre is suspended, which visits with its breath our silent chords at will.

Our most imperial and stupendous qualities — those on which the majesty and the power of humanity is erected — are, relatively to the inferior portion of its mechanism, active and imperial; but they are the passive slaves of some higher and more omnipotent Power. This Power is God; and those who have seen God have, in the period of their purer and more perfect nature, been harmonized by their own will to so exquisite consentaneity of power as to give forth divinest melody, when the breath of universal being sweeps over their frame. That those who are pure in heart shall see God, and that virtue is its own reward, may be considered as equivalent assertions.
Whereas the English saw the aeolian harp as a source of inspiration, the Germans found it a melancholy instrument, giving the listener a longing for heaven and the things beyond this world. Americans instead found themselves attracted for more practical and optimistic reasons. Henry David Thoreau wrote a poem where an aeolian harp itself speaks:
There is a vale which none hath seen,
Where foot of man has never been,
Such as here lives with toil and strife,
An anxious and a sinful life.

There every virtue has its birth,
Ere it descends upon the earth,
And thither every deed returns,
Which in the generous bosom burns.

There love is warm, and youth is young,
And poetry is yet unsung.
For Virtue still adventures there,
And freely breathes her native air.

And ever, if you hearken well,
You still may hear its vesper bell,
And tread of high-souled men go by,
Their thoughts conversing with the sky.
 The sound produced by a wind harp is mysterious, ethereal, disembodied, and otherwordly: it almost sounds composed, it almost has order, it almost has harmony, it is almost human music.

The Romantic composer Frédéric François Chopin composed a number of pieces which were partly inspired by the sound of the aeolian harp, including those here and here, as well as his Aeolian Harp Étude. The piano piece Aeolian Harp by Henry Cowell is unique in that the strings of the piano are plucked by hand, rather than sounded by striking the keys. Also of interest is Sergei Lyapunov's Harpes éoliennes (Op. 11 No. 9) which can be heard here.

The aeoline, éolienne, or äoline stop on pipe organs was invented in Germany in the 1820s to imitate the sound of an aeolian harp, and these are usually the softest notes that can be produced by those otherwise magnificent instruments. These are either string stops, sounded with low pressure air, usually at an 8' pitch, or are reed stops which may lack a resonator. A harpe éolienne can be heard in the final chord of the piece here; also listen to this.

Aeolian harps fell out of favor sometime in the early 20th century, as music became less personal and more of an industry, but the 1970s saw a revival of interest in these instruments.

The error of the Romantics

The Romantics wrote during a period before the divorce between art and science (indeed, a virtuous person ought to be equally adept at both, and not simply a narrow specialist), but after the divorce between the passions and the intellect. As Christ tells us, divorce is due to the hardness of our hearts, and the Romantic movement was a heartfelt reaction to cold and heartless Enlightenment rationalism, which gave the world slavery, urban poverty, the absolutist State, and the “dark Satanic Mills” which blighted the formerly beautiful English countryside. The Romantics instead thought that feelings and passion ought to be of primary importance, and they took their main inspiration from nature. The Romantic music of the aeolian harp, discordant, unpredictable, and made by nature, is a fitting symbol of the movement, in contrast to the heavily composed and rational Classical music of the Enlightenment.

But are we to go by our feelings alone, without reason? The Romantic movement led to a mystical nationalism, unrestrained by reason, and which eventually led to the widespread slaughter of the Holocaust. Strains of Romanticism are still found today in horror films and in the irrational, nationalistic — and sometimes violent — reconstructed nature religions which are popular primarily with alienated young women.

A better way is orthodoxy: we let reason judge feelings, while understanding that the heart has its own reasons. Both rationalism and romanticism are half-true, they both have their proper place when joined to a well-formed human will. Likewise, the aeolian harp has its place alongside instruments played by human hands, although it sits not at the center, but at the fringe of art.

Aeolian harps in history

The aeolian harp extends much further back into history than the Romantic period. Aeolus [or in the Greek, Αἴολος, Aiolos] is a character in Greek mythology, whose harp was played by the spirits of the winds, and it is from Aeolus that wind harps are named.

Thomson's Aeolian Harp, 1809, by J.M.W. Turner, Manchester Art Gallery, shows Aeolus with his harp, played by the four winds.

This painting was inspired by James Thomson's poem, Ode on Æolus's Harp:
ETHEREAL race, inhabitants of air,
  Who hymn your God amid the secret grove ;
Ye unseen beings, to my harp repair,
  And raise majestic strains, or melt in love.

Those tender notes, how kindly they upbraid !
  With what soft woe they thrill the lover's heart !
Sure, from the hand of some unhappy maid,
  Who died of love, these sweet complainings part !

But hark ! that strain was of a graver tone :
  On the deep strings his hand some hermit throws ;
Or he, the sacred bard, who sat alone
  In the drear waste, and wept his people's woes.

Such was the song which Zion's children sung,
  When by Euphrates' stream they made their plaint ;
And to such sadly solemn notes are strung
  Angelic harps, to soothe a dying saint.

Methinks I hear the full celestial choir,
  Through heaven's high dome their awful anthem raise ;
Now chanting clear, and now they all conspire
  To swell the lofty hymn from praise to praise.

Let me, ye wandering spirits of the wind,
  Who, as wild Fancy, prompts you touch the string,
Smit with your theme be, in your chorus join'd ;
  For, till you cease, my Muse forgets to sing.

One of the Muses in Greek mythology, Terpsichore [Τερψιχόρη], is sometimes portrayed carrying an aeolian harp. Sculpture by John Walsh, 1771, Somerset County Museum in Taunton. [source]

According to the Talmud, the ancient rabbinical commentaries on sacred scripture, King David would hang his lyre in his bedroom window upon retiring for the night. The north wind, blowing across the harp and sounding the aeolian melodies, would wake David around midnight so that he could pray Matins.

The Psalms in the Bible are largely attributed to King David, who sang them while playing on his harp. The aeolian harp thereby can be seen as a symbol of divine inspiration, uniting David's harp with the wind, which is a symbol of the Holy Spirit.

The great English saint, Saint Dunstan, was a harp player, and according to the Golden Legend, his harp once made music played without human hands:
And another time he was in his meditations, he had hanging on the wall in his chamber an harp, on which otherwhile he would harp anthems of our Lady, and of other saints, and holy hymns, and it was so that the harp sounded full melodiously without touching of any hand that he could see, this anthem was, Gaudent in celis animæ sanctorum, wherein this holy saint Dunstan had great joy.
Harps, lyres, zithers, and similar instruments have been found throughout antiquity, and the phenomenon of the wind playing them was well known — and ancient mythologies posit that these musical instruments themselves were inspired by the sounds made when the wind blew through strings found in nature: in one case, a cord attached to a tortoise shell, with the shell acting as resonator.  According to Giambattista Della Porta, from his book Magiae Naturalis, 1558, (a book of popular science, household tips, and practical jokes):
Do thus, when the wind is very tempestuous set your instruments just against it as Harps, Flutes, Dulcimers, Pipes. The wind will run violently into them, and play low upon them, and will run into the holes of the Reeds. Whence if you stand near and listen, you will hear most pleasant Music by consent of them all, and will rejoice.
Inspired by Della Porta's book, the first modern aeolian harp was invented by the remarkable Jesuit polymath, Athanasius Kircher, in about 1650. He was famed for his cabinet of curiosities — an early museum — including his collection of the artifacts sent by the Jesuits serving in Asia, as well as for his broad range of interests that is rarely found today. Kircher describes his invention in the book, Musurgia Universalis sive ars magna consoni et dissoni in X. libros digesta [volume 2]:
As the instrument is new, so it is also easy to construct and very pleasant. It is the admiration of every one. It is made exactly to fit a window, in which it is placed ; and the harp, while the window remains shut, is silent : but as soon as it is opened, an harmonious sound, though somewhat melancholy, coming from the passing wind, astonishes the hearers; for they are not able to perceive from whence the sound proceeds, nor yet what kind of instrument it is, for it resembles neither the sound of a stringed nor yet of pneumatic instrument, but partakes of both. The instrument should be made of pine wood, five palms long, two broad, and one deep ; It may contain fifteen or more chords, all equal and composed of the intestines of animals. It should be situated in a close place, yet so that the air may on either side have free access to it, in order which, it may be observed, that the wind may be collected by various methods; first, by canals, that are made the form of cones or shells, or else by valves; these valves should be placed on the out side, and parallel boards in the inside of the room ; its sound very much resembles that of pipes and flutes playing in unison. [source]
Here are illustrations of Kircher's harp from his book [images scanned by Google]:

The strings are attached to a sounding-box, which is placed in a box fitted with vanes to concentrate the wind:

Based on Kircher's invention, the anemocorde was an attempt to create a reliable aeolian harp that was played via a keyboard, with air blowing across the strings powered by bellows. I'm unaware if any such design was successful.

The Romantic interest in the aeolian harp, or even the Romantic movement itself, is said to have been inspired by Thomson's poem The Castle of Indolence of 1748:

Each Sound too here to Languishment inclin'd,
Lull'd the weak Bosom, and induced Ease.
Aereal Music in the warbling Wind,
At Distance rising oft, by small Degrees,
Nearer and nearer came, till o'er the Trees
It hung, and breath'd such Soul-dissolving Airs,
As did, alas! with soft Perdition please:
Entangled deep in its enchanting Snares,
The listening Heart forgot all Duties and all Cares.

A certain Music, never known before,
Here lull'd the pensive melancholy Mind;
Full easily obtain'd. Behoves no more,
But sidelong, to the gently-waving Wind,
To lay the well-tun'd Instrument reclin'd;
From which, with airy flying Fingers light,
Beyond each mortal Touch the most refin'd,
The God of Winds drew Sounds of deep Delight:
Whence, with just Cause, The Harp of Aeolus it hight.

Ah me! what Hand can touch the Strings so fine?
Who up the lofty Diapasan roll
Such sweet, such sad, such solemn Airs divine,
Then let them down again into the Soul?
Now rising Love they fan'd; now pleasing Dole
They breath'd, in tender Musings, through the Heart;
And now a graver sacred Strain they stole,
As when Seraphic Hands an Hymn impart:
Wild warbling Nature all, above the Reach of Art!
As implied by the poem, the aeolian harp was seen to be a plaything of the idle and indolent wealthy, but soon these instruments became commonplace. In a footnote to a poem, Thompson states that these kinds of harps were manufactured by James Oswald, a Scotsman living in London; Oswald later would achieve great fame, including his appointment as composer for King George III, and his Harp of Aeolus became popular.

This popularity led prominent scientists to investigate how the notes were sounded, since the aeolian harp's tones did not correspond well to human-played music. This research on the fringes of music led to the science of acoustics and well as contributing to fluid mechanics. An unfortunate side-effect of this was the divorce between music and mathematics into unrelated disciplines, which were long joined together in the quadrivium of the classical liberal arts.

Designing an aeolian harp

Constructing an aeolian harp is simple, for all you need is a strong wind and a string. Nylon strings work well, as does steel. However, the sound made will be extremely weak (even more so for steel strings), and for the purpose of amplifying the sound, you need to construct a sound-board for the strings. That is a complicated art: please consider the complexity and effort that goes into constructing and tuning the body of a violin, as well as the great expense that a fine instrument can demand. Modern harp-builders, however, can use magnetic transducers, commonly used in electric guitars, to capture the sound which then can be electronically amplified. Designing a good electrical pickup is an art in itself, and there are many variations and room for improvement.

To design a musical instrument well, you need to have a Pythagorean or Platonic understanding of mathematics, the understanding that was found in the Middle Ages but which fell out of favor in modern times. According to this understanding, mathematics is poetic and harmonious, with its own truth and beauty, and it is at the center of all art. Modernity, however, killed the beauty and the joy of mathematics, and even sometimes its truth, and made it a dreadfully dull subject, perhaps only interesting to specialists. Mathematics has now become the enemy of artists, although it was not yet so in the days of the Romantics. But I ask my dear readers to try to understand the mathematical discourse following, and try to see the beauty in the numbers and their harmonies.

The sound that an aeolian harp makes is caused by a phenomenon called the von Kármán vortex street effect. A fluid flowing over a cylinder (such as a string), under certain conditions, will lead to an alternating series of vortexes that periodically shed from the cylinder, forcing it sideways in one direction and then the other. The equation governing this motion is:
Re = V × d / ν
Where Re is the Reynolds number, V is the velocity of the wind, d is the diameter of the cylinder or string, and ν [Greek letter nu] is the kinematic viscosity of the air. Generally speaking, we can get string vibrations if the Reynolds number is greater than about 90. From the equation we can see that double the diameter of a harp string gives us the same Reynolds number in half the wind speed. The kinematic viscosity of dry air at sea level and 70° F. is about 0.000164 ft2/second, and it gets smaller as the temperature drops, which tells us that these instruments ought to perform better in colder air; also lower altitudes are better.

The Reynolds number is important because it tells us something about the quality of flow:
  • Less than 5, the flow of air around a string is smooth, and no vibration is possible.
  • Between 5 and 44, stable vortices form behind the string, but strings do not vibrate.
  • Between 44 and 49, a transition range, von Kármán vortices may or may not occur.
  • Between 49 and 90, von Kármán vortices occur, but supposedly, this range does not seem to activate aeolian harps.
  • At 90, there is a slight change in the quality of the vortices.
  • Between 90 and 150, aeolian harps start to sing, and the vortices are very regular.
  • Between 150 and 300, transition range where flow becomes unsteady.
  • At 300, flow beyond the string is turbulent. 
  • At 400, flow is completely turbulent, higher overtones become much more prominent.
  • As the Reynolds number increases, the aeolian harp makes sounds that are increasingly screeching and distressful.
Would-be aeolian harp makers are often disappointed that their creations don't work at all except under strong winds. An examination of the Reynolds numbers indicate that thicker strings may be needed.

By the way, von Kármán was inspired to develop his theory upon viewing a Gothic painting of Saint Christopher carrying the Christ child across a river. He was fascinated that the 14th century painting showed alternating swirls of water in the flow behind the Saint's legs, and he wanted to know why.

If the frequency of the vortex shedding is harmonious with the tuning of a string, then resonance develops and the string sings. The vortex shedding frequency has the equation:
f = St × V / d
Where f is the frequency of vortex shedding, V is the velocity of the air, d is the diameter of the string, and St is the Strouhal number, a dimensionless factor which characterizes the air flow. The Strouhal number has a complicated nonlinear relationship with the Reynolds number, as is seen here. But as it so happens, the Strouhal number does not vary much at all in the range of the Reynolds numbers associated with typical aeolian harps — those that use guitar strings in moderate breezes — at say, a range of Reynolds numbers of 400 and higher, and so faster winds will give us proportionally higher notes. At these Reynolds numbers, the Strouhal number is about 0.21.

However, the Strouhal number gets smaller for the Reynolds numbers associated with slow winds and large string diameters, and so we would expect that aeolian harps strings meant to operate under these conditions would require special tuning. It is from a Reynolds number range of between 90 and 400 that we would get the lower, more soothing notes from the instrument, which are often the notes most preferred by listeners. This sound might be compared to the sound of a bagpipe drone.

The fundamental tone or frequency of a string is given by the equation:
f = (1/2L) × √(T/μ)
where f is the frequency of vibration, L is the length of the sting, T is the tension in the string, and μ [Greek letter mu] is the linear density of the string — the mass per unit length of string. The string can also vibrate with frequencies that are integer multiples of the fundamental frequency given by this equation: 2, 3, 4, 5 times and so forth; these frequencies are called overtones or harmonics. If you pluck a stretched string, the tone you get will be the fundamental frequency along with a combination of the various overtones, and similarly, an aeolian harp will intone a rather different combination of these harmonics.

We see how the Strouhal number in the second equation above causes a vibration in the air around a string at a particular frequency: whenever this frequency comes close to one of the harmonic frequencies of an aeolian harp string, the string will resonate strongly at that frequency, giving us an audible tone. Since wind velocities fluctuate, the particular tone voiced on a string will change frequently, gliding from one overtone though silence to another overtone.

All aeolian harps more or less sound the same, although a good amplifier design — either a sounding board or electronic pickup — can increase the quantity of sound, as well as perhaps its quality. For this reason, there is little point in attempting to tune an aeolian harp much beyond tuning the strings to resonate with their sounding board. These harps always sound dissonant, and builders will typically tune all of the strings to the same pitch, although they will typically use various diameters of string within the same instrument to allow it to work under a range of wind speeds.

An important property of aeolian harps is that the fundamental harmonics of the strings is not heard: instead we only hear overtones, with the predominant frequency (according to various authorities) being as high as the fifth, eleventh, or 22nd overtone. Faster winds excite higher overtones, while suppressing the fundamental and lower overtones. Because of this phenomenon, slight mistunings of the fundamental note of a string become highly mistuned at high overtones, contributing to the dissonant sound of the instrument.

To achieve singing, it is noted that laminar winds — such as those found blowing off a large lake or the ocean — are preferred to turbulent ones, as is found in cities. Kircher installed his harp in a  box in order to smooth, direct, and amplify the wind. Authorities state that solid strings are preferable to wound ones, as these respond better to the vortex effect.


You can purchase your own monumental aeolian harp here. Although I don't care for the overall design, I do like the concept. Here is an audio recording of this harp:

The creator of this aeolian harp writes that some architecture of the past — on purpose or by happenstance — would create music-like sound in the wind. Would this be a good thing for new architecture, I wonder? Consider the old Catholic tradition of integrating all of the senses into her architecture and liturgy. Would something like this be good for a cloister or church garden? Many people do think that these sounds can be soothing and inspire meditation.

But judging from the reviews of this harp, as well as comments on audio recordings of aeolian harps, I find that many people either ignore or reject the sounds they make, calling the whole endeavor ‘stupid,’ or an intrusion because it doesn't fit their taste in music. Others find them irritating or depressing or a waste of money better spent elsewhere. Considering the types of people who were drawn to aeolian harp in the first place, clearly they would not appeal to those who don't share those traits. On the other hand, other kinds of people may read too much into the sounds that the harps make, turning them into a false mystical experience; clearly there is a New Agey feel to aeolian harps, and this is often due to eccentric design.

I think they could be more successful if their wild and romantic qualities could be rationalized a bit, bringing the emotions and the intellect closer together. Better design of the harps, with significantly better control over the higher harmonics, perhaps through clever damping, could retain the soothing qualities of its sound while eliminating the harsh irritating sounds. A certain classical or medieval influence would help, especially in the designs of the sculptures in which these harps usually reside.

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