Tone Generation and Tone Row of the Jew's Harp
+ Tone Generation
+ Scale of the Jew's Harp: The Natural Harmonic Row
+ Resonances: Sounds and Pitches, Melodies and Accompaniment

+ Open and Closed Vocal Tract
+ Literature

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This chapter presents some background knowledge: It starts with tone generation and the specific scale of each jew's harp, dependant on the tuning of the reed - the natural harmonic row. The sound of playing is formed in the mouth and throat. These are the resonating cavities also forming the sounds of speech. 

Tone Generation

It is difficult to place the jew's harp in the system of musical instruments. On the one hand it is classified as plucked idiophone, together with the musical clocks: The plucked part of the instrument sounds itself. On the other hand, the jew's harp belongs to the aerophones, together with the wind instruments and the instruments of the accordion type: In this class of instruments the sound is generated by a vibrating air column (flutes etc.) or by a stream of air stimulated to sound by a reed (harmonica, accordion). The affinity to the accordion instruments becomes clear when jew's harps, hold against the lips and teeth respectively, begin to sound without being plucked, just by breathing in or out. Clemens Voigt of Dan Moi (see links) told me how this effect works: The reed has to be shifted a little from the level of the frame, and the air flow has to pull it back towards the frame level (figure 1, cross section of a jew's harp).

figure 1

On bow-shaped jew's harps the effect works if the reed is pushed gently at the basis by the thumb of the hand holding the frame as in figure 1 to shift it a little. In this way the jew's harp works just like a harmonica. In sound example 14 (64 KB) the tone c is heard, first played on a harmonica, than plucked on the jew's harp, and finally stimulated by breathing in on the jew's harp.

Scale of the Jew's Harp: The Natural Harmonic Row

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In our common tonal system the octave consists of 12 equal half-tone steps (enharmonic temperament). This means, that the number of vibrations per second (frequency, unit: Hz) of one tone multiplied with 1,059463 equals the frequency of the following half tone. If any frequency is multiplied again and again with this factor, after 12 steps the frequency is just doubled, and the respective tone is transposed in an octave above. Thus, as the frequency of successive half tones always is altered by the same factor, the absolute difference of the frequencies is less at deep tones (low frequencies) and higher at high tones (high frequencies).

The tone row of the jew's harp (as well as that of any instrument with a natural harmonic row) is different: The reed of every harp has its specific fundamental frequency, e.g. 98 Hz (tone G) or 58.3 Hz (B1). The vibration that produces the fundamental note is always accompanied by its overtones. The overtones of a harmonic sound, like the one produced by the jew's harp reed, are called partials or harmonics. They have frequencies that are multiples of the fundamental frequency. Thus, the jew's harp tuned G plays the multiplication tables from 98 Hz, the one tuned B1 that from 58.3 Hz. This can be seen in figure 2: The sound of a jew's harp was recorded without contact to the mouth, that is, without resonances of the oral cavity (sound example 15a, 126 kB). The freeware programme Audacity was used to determine the frequency spectrum. Each peak of the green curve is one tone played by the jew's harp reed. They are situated at regular intervalls of 58 Hz. The first peak on the left under the first grey triangle is the fundamental note. The next, smaller peak to the right is the first overtone or partial, the following higher peak is the second partial and so on. The yellow curve shows a frequency spectrum of the same jew's harp as played normally with contact to the mouth (sound example 15b, 130 kB). 

Note: Without resonance (green curve) the peaks of odd-numbered overtones (no. 1, 3 and so on as counted from left to right) are lower than the even ones (no. 2, 4 and so on). This is the typical in terms of physics for springs that are fixed on one side and free on the other. For all vibrations forming the overtones the fixed end is a node. The free end is a strong antinode and a weak node, resulting in the stronger even-numbered overtones. Further explanations are given in the literature, see bottom of this page.

figure 2
frequency spectrum

Fundamental note and harmonics/partials form the natural harmonic row. The first partial vibrates with two times the frequency of the fundamental note, being its octave (tone B minor in figure 2, under the second grey triangle). No tone inside this octave can be played on the jew's harp. The next octave (tone b) again vibrates two times as fast (third triangle, fourth partial, 58,3 Hz x 4 = 233,2 Hz). Here we have one tone in between: 3 x 58.3 Hz = 174.9 Hz, which about corresponds to the tone f with an enharmonic frequency of 174.6 Hz. In the next octave until b1 (fourth triangle) there are already three partials. Thus, the higher we get in the scale, the more tones can be played with a natural harmonic row. In sound example 16 (109 KB) a jew's harp tuned G is plucked continuously, while the oral cavity is altered. The resonance of the 6 overtones from d1 to g2 can be heard.

The harmonics/partials of the fundamental note deviate from the tones of the enharmonic scale. The 10thharmonic is almost in the middle between two tones of the enharmonic scale (see below, figure 5, fourth peak from the left). These deviations are measured in hundredth of a half-tone, the so-called cent. As long as the fundamental note is a tone of the enharmonic scale, the harmonics allways show the same pattern: For any fundamental note the 10th harmonic will diverge by 49 cent from the enharmonic scale.

Table 1 shows how the tones of the natural harmonic scale (marked dark grey) fit into the normal (enharmonic) scale. This is a concise overview of the tones available for playing melodies. A more detailed overview of the specific scales of all tuned jew's harps is given in the overtone table (with explanations, pdf, 68 KB).

table 1

tone scale of the jew's harp

Explanations

The enharmonic scale is listed from top left to bottom right, starting from the fundamental note of the jew's harp. Each column represents the 12 tones of one octave and the first note of the following octave. Each row represents a tone and its octaves.  

The fundamental note and its overtones/harmonics are marked dark grey.

The bold figures show the number of the harmonic. The small numbers list the deviation of the respective harmonic from the enharminic note as cent. Negative numbers show that the harmonic is below the enharmonic note.

To the left and right of the list of tones circles indicate the mayor and minor scales respectively, starting from the fundamental note. Horizontal bars below the table indicate the tone range playable on different jew's harps. The broad part of the bar shows the main resonance (second formant, see below), the narrow part the accompanying lower resonance (first formant, see below).

On jew's harps with a lower fundamental note more different pitches can be played than on those with a higher fundamental note. E.g., a harp tuned A plays the multiplication tables from 55 Hz, wheras a harp tuned G plays that from 98 Hz. With the multiplication tables from 55 you will get more steps in the resonance range between 250 and 2000 Hz than with those from 98 Hz.

 Sounds and Pitches, Melodies and Accompaniment

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When playing the jew's harp, it is resonances that produce the sound: The jew's harp reed vibrates before the mouth. It excites vibrations of the air column enclosed in the cavities of mouth, throat and chest. Depending on the shape of the cavities the vibrating air column enhances certain tones of the natural harmonic row of the jew's harp. This is shown in figure 2: Played normally with contact to the mouth (yellow curve) the jew's harp has the same tones as played without contact to the mouth (green curve) - the peaks of both curves are at the same frequencies. But the yellow peaks are higher than the green ones, that is, the sound is amplified by resonance. Certain frequencies are pronounced, e.g. in the region around the seventh harmonic, below the fourth triangle. Such frequency regions that are especially amplified by resonance are called formants.

This is illustrated by a small sound experiment using a jew's harp tuned C (sound example 17, 70 KB): I pluck the reed regularly 12 times. The first four strokes I play the tone e3 and the accompanying lower tone g1 (figure 3, green curve). As this jew's harp is tuned C, g1 is the fifth harmonic (see table 1). At the following four strokes the tones e and g are switched: I play g3, accompanied by e1 (figure 3, red curve). e1 is the fourth harmonic of this jew's harp. The last four strokes I play 'openly', like forming the vowel a in "father" (not included in figure 3).  Figure 3 shows not the whole frequency spectrum, but only the peak tops. The amplified frequency regions, that is the formants, are again forming broad peaks with their summits near the pitches I intended to play. Again the primary peak tops of the two frequency specta, that is, the plotted dots of both curves, are at the same frequencies. 

Conclusion: The tones of a certain jew's harp are unalterable, yet the sounds are many and diverse, reacting on the slightest changes of resonance in the mouth, e.g. by movements of the tongue.  

figure 3

resonances, formants

The most pronounced resonance region is the second formant of the vocal tract, being somewhere in the range from 500 to 2000 Hz. The vocal tract is the sum of the cavities between the voice and the mouth that form the different linguistic sounds. The highest peaks of the curves in figure 3 show the second formant (blue background colour). On the jew's harp, tunes and melodies can be played using the second formant (see playing techniques: Pitches, how to play melodies). In addition, the deeper and less pronounced first formantof the vocal tract can be used to produce accompanying notes. The first formant can be anywhere in the range between 250 and 1000 Hz. In figure 3 the lower peak on the left side of both curves (red background colour) show the first formant. In the piece of music "Kein schöner Land" (see Music) the first verse is played without, the second one with accompanying notes.

Different resonance cavities and organs are shown in figure 4, left. Especially the tongue influences the vocal tract and the jew's harp sound. The second formant is influenced by movements in the throat (figure 4, right, blue region), the first formant by movements in the oral cavity (figure 4, right, red region).  

figure 4
Resonanzräume   Formanten

The resonance chambers of mouth and chest of the player can amplifie a certain range of frequencies, irrespective of the fundamental note of the jew's harp. This range of tones that can be played is certainly different for each individual player. In her book on the jew's harp, Regina Plate states that the pitches that can be played range from 500 to 2000 Hz, corresponding to two octaves. In my experience tones with a frequency of up to about. 2300 Hz can be played. The notes of the first formant can be as deep as about 250 Hz. On the basis of the fundamental note, the tones that can be played on a certain jew's harp can be looked up in the overtone table (with explanations, pdf, 68 KB).


 

Open and Closed Vocal Tract

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When playing the jew's harp with some breathing, the vocal tract is open at both sides, to the mouth and to the lungs. But when the voice chink (or glottis) is closed (see Playing Techniques, Sound Effects), and also when the tongue closes the oral cavity at the soft palate like when speaking "ng" in the suffix "-ing", the resonance chamber is open only at the mouth and closed at the other end. With a "closed" resonance chamber the jew's harp sound is different and shows the following peculiarity: The even-numbered overtones (that is, the tones with even numbers in table 1, see above) are amplified and can be played especially clearly, but the odd-numbered overtones are not. With "open" resonance chambers, also tones with odd numberes can be played clearly. For example, in traditional Norwegian jew's harp playing, musicians most often open and close the vocal tract for the respective tones of the scale.

To examine this effect, I played and recorded odd and even numbered overtones on a jew's harp tuned G. The tones were played with open vocal tract and some gentle breathing (figure 5, blue curves), and with closed vocal tract, either by expressing "ng" (closed at the palate, red curves) or with closed voice chink/glottis (yellow curves). Freqency analysis was done with Audacity, seperately for the different tones and modes of playing. As an example of the results, in figure 5 the spectra for the playing of the 10th and 11th overtones are plotted.  As a reference, the sound of the same jew's harp without any resonance of the oral cavities was analysed. For this, one side of the jew's harp frame was fixed in a vice and the reed plucked and recorded (lower diagramm in figure 5, "vice").


figure 5

resonance with open and closed vocal tract

Without resonance (vice), the even numbered overtones are louder than the odd ones, which is normal for the vibrations of a spring fixed at one end. When holding the jew's harp to the mouth and intentionally playing the 10th overtone (about tone cis) the respective peak of the frequency spectrum is clearly pronounced (figure 4, upper diagramm), with open as well as closed ("palate", "glottis") modes of playing. With closed playing, the peak even seems to be a little higher than with open playing, pronouncing the tone more clearly.
Without resonance, the peak of the11th overtone (tone d) is smaller than the adjacent 10th and the 12th (lower diagramm, "vice"). When playing this tone, the respective peak only with open playing is sufficiently elevated to be at least a little louder than the adjacent ones. Closed playing pronounces the same frequency region, but the 11th peak is not elevated over the adjacent ones. Thus, tone d will only be heared with open playing.

So, the frequency analysis confirms the idea that even-numbered overtones are played most clearly with open vocal tract, and odd-numbered with closed. The reason for this is not clear to me so far.


That is all . At the end some Music (339 KB).

Write down jew's harp music? Sound example "Music" in music notation (27 KB)

Literature
Anonymus: Physics 1, Fundamentals: Module 3 Oscillations & Waves. Standing Waves, Doppler Effect. The University of Sydney, School of Physics, www.physics.usyd.edu.au/teach_res/jp/waves/waves111011.doc (March 2009)
B.J. Kröger: Artikulatorische und akustische Phonetik - Ein Kurzüberblick. http://www.speechtrainer.eu/ (Dezember 2008)
U. Michels: dtv-Atlas zur Musik. Band 1. Deutscher Taschenbuch Verlag, München, 1994

B. Myer: Vocal Basics. Der Weg vom Sprechen zum Singen. AMA Verlag, Brühl, 1998

R. Nave: Forming the Vowel Sounds. http://hyperphysics.phy-astr.gsu.edu/hbase/music/vowel.html (Dezember 2008)
R. Plate: Kulturgeschichte der Maultrommel. Verlag für systematische Musikwissenschaft, Bonn, 1992
P. Rennert & H. Schmiedel (Hrsg): Physik. BI Wissenschaftsverlag, Mannheim, 1995

H.G. Tillmann & F. Schiel: Akustische Phonetik - Kapitel II: Was ist Sprachschall? http://www.phonetik.uni-muenchen.de/studium/skripten/AP/APKap2.html (Dezember 2008)

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