The Crystal Armonica

 An Instrument Designed for Hallifaxian Orchestal Settings

 

 Index

  Page 1 - Index

  Page 2 - Dedication

  Page 3 - Introduction

  Page 4 - Structure

  Page 5 - Theory

  Page 6 - Commentary

  Page 7 - Possible Modifications

  Page 8 - Final Notes

 

------------------------------------------------------------------------------

 

Dedication

 

This text is dedicated to the Symphonium of Hallifax in satisfaction of certain requirements and in appreciation for their efforts in ennobling the citizens and the State of the Commonwealth.  The Symphonium's continued championing of the Higher Emotions, which are among the greatest virtues of the Collective, is admirable and it is my pleasure to be able to apply my education at the Institute to the fabrication of a new crystalline instrument for their use.

 

------------------------------------------------------------------------------

 

Introduction

 

Musicians have long employed a wide variety of instruments for performance, with particular instruments tailored to fit the needs of specific occasions.  While bards have long preferred a number of compact stringed instruments for their size and ease of use on the move, a number of other instruments, such as the various of percussive drums and various wind instruments such as the flute are used in less functional but more evocative performances, particularly in orchestral settings with multiple performers.  While distinctly Hallifaxian musical styles, themes, and techniques have been developed there is no uniquely and definitively Hallifaxian instrument.  It is the author's intent to address this deficiency through the design of such an instrument, the crystal armonica, and by expounding on the technical theories governing the use of the same.

 

Much as a fine crystal wine-glass can be made to sing under one's wetted finger, so too does the armonica fill a room with perfect, crystalline tones at the hands of a skilled user.  While most instruments produce multiple tones, thus imparting a complex but invariant character to sound they produced, the crystal armonica emits only a single tone (or, if properly manipulated, a higher frequency overtone)  or secondary tones which allows a performer to construct a pure cord of any character they please. 

 

While the theory and design of the instrument was based on construction with leaded glass (Note well that untreated glass fails to resonate under standard usage conditions and so cannot be used in constructing an armonica) simple experimentation has shown that certain gemstones and even charged gems can be incorporated into the instrument's construction.

 

------------------------------------------------------------------------------

 

Structure

 

The crystal armonica functions on the same principle as a resonating wine glass.  While a glass can be tuned by adjusting the level or density of fluid within it, this is hardly feasible in the context of a live performance.  There are a few accounts of performances with so-called glass harps that utilize multiple glasses, each tuned in advance to produce a specific note, but such an arrangement is neither durable nor amenable to complex performance.  The armonica addresses these deficiencies by incorporating their tuning into their construction, with the pitch emitted by each glass dependant on the size of the glass and its thickness, as described in the section on instrument theory. 

 

The armonica as a whole consists of three-dozen carefully tuned bowls, covering three octaves.  Twelve bowls are required to reproduce an octave with sharp and flat notes.  The range must be selected prior to construction as physical alterations to retune a bowl are prohibitively difficult.  The context of use should determine the ideal range for a particular instrument.  Though the details necessary to craft tuned bowls are available in the section on theory, those without proficiency in glass blowing, mathematics, and musical theory may find it substantially easier to speak with the Arri Marks or another staff member of the Clarramore Gardens, as the craftsmen there have familiarity with the techniques and processes (if not the theory) as a result of their assistance of the author in constructing such instruments.  Bowls may be conveniently engraved or coloured to indicate their pitch to a performer.

 

The crystal bowls of the instrument are carefully drilled through at their base to allow them to rest snugly on a metal rod.  The bowls should be arranged by frequency on the rod.  The rod itself is best constructed of brass, though the resting point of each bowl must be silvered prior to securing the bowl.  The point of contact may then heated sufficiently to wet the crystal, at which point a strong bond between the silver and the crystal will form, preventing the anchored bowl from sliding.  The importance of a bonding ring of silver or another metal with high affinity for glass cannot be overstated, as the vibrations of the bowl can easily cause collisions between bowls if they are mechanically rather than fundamentally bonded.

 

A pulley wheel is next affixed to the end of the brass rod.  This wheel is to be driven by one of a number of processes, causing it to turn the rod at a rate between one-half and two rotations per second, as the volume requirements of a performance demand.  Mechanical foot-peddle mechanisms, a crank driven by an indentured assistant, or one of the gem-driven systems of the Matrix Research Institute (likely unavailable to the amateur practitioner) are all suitable so long as they provide a steady rate of revolution for the instrument.  The rod itself should be supported on by a stand with a low-friction bearing on each end to bring it to a comfortable height for the performer.  The stand should also have space for a shallow water trough for the convenience of the user.

 

The instrument is excited to sound by the application of a wet finger to the edge of a bowl.  Doing so will produce a pure tone as the bowl is excited to vibration, with the volume of the tone being modulated by the speed of rotation and the pressure applied by a finger.  A skilled performer can draw sound from three to four bowls with each hand, allowing for the construction of complex cords.  A bowl will continue to resonate for some time after being excited, but may be silenced by a light damping tap to any point besides its lip.  At the preference of the designer, a water trough may either allow the player to dip their fingers periodically or be situated in such that water in the trough just barely meets the edges of the bowls.  While the later method allows continuous playing with both hands, it dramatically reduces the ability of the bowls to resonate when released and will lower the volume of the instrument substantially.

 

For obvious reasons, a proper crystal armonica can only be played in a stationary position as the size of the instrument and complexity of its rotational mechanisms prohibit convenient motion.  Nonetheless, the author envisions a portable instrument spanning only a single octave and with a simple hand or charged gem mechanism for rotation might serve an extremely capable bard.

 

------------------------------------------------------------------------------

 

Theory

 

While playing the armonica is no more difficult and possibly easier than performing on a woodwind or a piano, precise construction is substantially more difficult and requires an understanding of harmonics and vibration.  All objects with crystalline character, be they true crystals or rigid metal or mineralized material, have modes of vibration.  Depending on the intensity and distribution of imparted energy, one or more such modes may be excited, causing the object to vibrationally flex in characteristic patterns.  While one may observe that a bowl is vibrating as a consequence of apparent blur of its edges, the unaided mortal eye cannot resolve the specific nature of such a vibration.  Such patterns can be elucidated with proper assistance.  Which the details of the experiments performed within the institute are beyond the scope of this work, techniques such as sand imaging, lens-assisted interferometry, and induced resonance were performed within the Matrix Research Institute and details on how to perform these experiments is available upon request.  By means of such techniques, the behaviour of vibrating bowls is well understood and can be produced to fit arbitrary construction requirements.

 

When a performer presses on the lip of a crystal bowl, they distort the crystalline structure by causing the edge to drag very slightly compared to the body of the bowl.  As the distorted region rotates out from under the pressure of the finger, it returns to its original position much like a spring might restore itself from having been stretched.  This restoration imparts energy into the bowl, exciting a particular vibration.  As previously mentioned, unlike most instruments which produce secondary vibrations at other frequencies, a singing bowl will produce only one tone under typical playing conditions.  In the primary vibrational mode of such a bowl, if one imagines the bowl divided into quadrants, two opposite sides of the bowl flex inward while the other two flex outward, after which this motion repeats in inverted form.  The bowl alternates between deformation into an ovalide elongated along the X and then Y axis relative to the reference of the rod.  Such deformations are not immediately visible but explain the nature of the tones produced under various circumstances.  This vibration is almost entirely isolated to the open side of the bowl, with virtually no deformation of the region connected to the rotating metal rod.

 

Experimental inquiry indicates that two properties dictate the tone of a crafted bowl.  The frequency produced is proportional to the thickness of the glass rim of the bowl and inversely proportional to the square of the radius.  We may consequently describe a singing crystal bowl's frequency (f) in relationship to the bowl's radius (r), thickness (t), and a proportional constant (k) by the expression f=kt/(r^2).  This should hardly come as surprise when one can see that the fundamental vibration necessarily requires the lip of the bowl to flex, a behaviour which will necessarily depend on the propagation distance of a vibration and the quantity of material displaced.  Knowing this, a bowl may be cast to a specific radius as suits the demands of an instrument for nesting the bowls, after which they may be tuned by grinding the lip until an appropriate pitch is achieved.

 

Under special conditions, unusual modes of vibration may be observed.  The application of two fingers to the same bowl at a distance of ninety degrees can produce not only the fundamental frequency but also its first harmonic, resulting in a pitch at twice the frequency.  Three fingers each sixty degrees apart, almost certainly requiring both hands and a very delicate touch, might excite a second harmonic at three times the fundamental frequency.  Two fingers at forty-five degrees from each other might conceivably be able to evoke a third harmonic, but no instrument thus far produced has been able to demonstrate this in the inventor's hands.  Finally, a sharp tap to the body of the bowl can excite diverse vibrational modes and result in a complex note containing secondary tones that are not harmonics of the lowest pitch.  The practicality of incorporating any of these techniques in performance by anyone but a very dedicated and practised player seems quite dubious.

 

------------------------------------------------------------------------------

 

Commentary

 

The author regretfully has many obligations that prohibit the dedication of his full time to mastering the performance of the armonica.  It is hoped that other members of the the Collective will find the pure sound of the armonica appealing and find opportunity to develop techniques, variations, and performances niches for the instrument.  The uncomplicated nature of the sound produced by the instrument may leave it well suited to accompany vocal performances, whether by the singer or speaker themselves or at the hands of another performer. 

 

The instrument may also have some use as a meditative aide. Many test audiences report that the crystalline tones of are quite soothing.  It may be appropriate to include instruments in contemplative areas such as public gardens and libraries for the purpose of improving the experience these locations provide.  While a talented musician is required for true performance, even an indentured servant could be trained to produce the slow, soothing tunes appropriate to this end.  Such use may also be of aide to citizens in mentally strenuous occupations and may be suited to environs such as medical or psychological facilities.  Such duties would have an added benefit of provided lower caste citizens the opportunity to develop skills that may make elevation to a higher caste feasible for them or for their children.  The armonica is particularly well suited for use by the lower classes owing to its entirely crystal and glass construction.  Unlike like the wood, leather, and gut string composition of most instruments, the armonica is extremely resistant to the passage of time and largely unaffected by abuse by water or organics which would ruin a less sturdy instrument.

 

Finally, the instrument may have strategic use.  Large, thin-lipped bowls produce low frequency sounds which carry for considerable distances through the open air.  When carefully prepared, these can even induce vibration at a distance in bowls with identical tuning or other tuned receivers.  Properly arranged, these devices could be used to transmit encoded messages without the benefit of aetheric transmission from armonica to armonica at a pitch below mortal perception.  Particularly interesting applications may arise if such techniques are implemented with certain modifications in the final section.

 

------------------------------------------------------------------------------

 

Possible Modifications

 

As previously mentioned, the crystal armonica is a stationary instrument.  With modification, a compact form might be suitable for easy transport and performance on the move.  While such an instrument would necessarily have smaller bowls to render it compact, the bowls would also necessarily be thinner to reduce the weight of the instrument.  It might therefore have a similar, though shorter, range of tones.  While such a device would doubtless strain the weak of frame, it may remain possible for sufficiently strong bards to perform with such an instrument while on the move, evoking similar powers as those they do with various stringed instruments.  While this is a niche application, it would bring this author joy to see Symphonists armed with instruments of pure crystal,

 

The performance of many instruments can be modified by the application or incorporation of charged gems.  The author has had neither the time nor the resources to safely test the affect of charged gemstones into the construction of the instrument.  One can imagine that, having various densities and rigidities dissimilar to leaded glass, the aural properties of bowls formed from carved gemstones would be substantially changed.  At the very least, this may affect the acoustic properties of the instrument, allowing higher or lower pitch ranges for a given size of instrument.

 

It is possible that using charged gems may do more than modify the acoustic behaviour of the instrument.  It is well known that the vibrations of charged gems are capable of inducing physical and psychological harm or aid and it may be that in the hands of a talented musician capable of utilizing the powers of a Divine voice, such effects could be expressed on a wider field by using charged gem bowls in an armonica.  It may also be that the affinity charged gems have for the plane of Continuum might allow resonance between two glass bowls that are proximate but on separate planes, potentially allowing for the creation of a cross-planar relay.

 

------------------------------------------------------------------------------

 

Final Notes

 

The author extends his gratitude to all readers who have taken the time to read, in part or full, the details of this novel instrument.  Readers are reminded that additional supplemental information is available upon request.  The use of the crystal armonica for commercial purposes outside of the Symphonium or Institute is prohibited. 

 

The author would like to thank the following:

 

The Institutional Society of Hallifax for the Improvement of Temporal Knowledge

  for contributed resources and technical support

The Symphonium of Hallifax

  for their consideration and for the inspiration behind this design

The Clarramore Gardens

  for expertise in the working of metal and glass