The double bass is the largest instrument in the strings family, therefore its proportionate scale and overall length has allowed for exploration of an extreme range of partials – both very high within the upper register and also allowing for the possibility of sub-harmonic frequencies within the undertone series. The deciphering of harmonics within different pieces often involves some earlier research and further explanation – particularly post-twentieth century. Many works involve different combinations of notation in the area of the complex partial sound-world. Whilst harmonics have been used over several centuries, the use of modern developments often require further research and examination from the performer. In addition to this, the use of extended harmonics is particularly difficult in terms of perfection and placement, which varies from instrument to instrument.
// Eric Daino has published a fantastic resource focused on the exploration of timbre – ‘The Double Bass: A Technical Study of Timbre’ (2010), with a chapter specifically focused on the application of harmonics as ‘technical and aural components of performance and composition’. Thus, this enquiry is based off his research and writings, which I have found to be useful for my own studies and compositional process. // As a bassist, I am gaining much from understanding the physics of my instrument, as this gives more meaning to certain techniques and where they may be best used.
Firstly, a general idea of the use of harmonics and how they work:
They provide clarity – upon the bowing of open strings/stopped notes on the double bass, the tone becomes rather complex due to the many overtones present above the fundamental pitch. However, the use of harmonics provides a ‘clear, glassy timbre’ (Daino, p. 2, 2010) which can be heard to blend more consistently with other instruments and with more clarity. Intonation is also guaranteed, and acts as a good reference point for difficult passages.
As the register of the harmonic increases (i.e. grows higher in pitch), the dynamic range decreases accordingly. This limits the use of these upper partials (i.e. above the tenth) to quieter or subtler parts of a piece. With this also comes more bow noise, which can sound scratchier the higher it gets.
Arco and pizz techniques are both used for the application of harmonics, however the use of the bow can often allow them to ‘speak more easily’ (Daino, p.2, 2010).
Bow placement can directly affect the production of harmonics. Quite often, the use of higher partials will be heard most easily when the bow is placed closer to the bridge. Expanding on this, the use of ponticello (sul pont.) can bring out some other unexpected overtones. Bow placement is often difficult to define, as each instrument has variances in this regard.
As partials grow higher, the more options there are for left-hand placement. As the partials grow higher, the pitch that is produced does not always correlate with the position used to activate the actual harmonic… this can mean more difficulty in defining the sounding pitch.
The ‘node’ = the point on a string where waveforms begin and end, and by touching, all lower partials are eliminated (Daino, p.2, 2010). Therefore, on the double bass, the node points are larger than that of a smaller scale instrument, which leaves more possibility for the string to vibrate accordingly.
Methods of Notation for Harmonics
||How does it appear?
|The ‘o’ symbol
||Indicated above a given pitch, indicating that the particular note should be played as a harmonic.
||In terms of which node to use, this is left ‘unspecified’ and determined by the bassist in terms of correct positioning. In lower passages (i.e. with the use of lower partials), this method of notation is often rather foolproof as the position become apparent in context of the piece.
|Indicated above a certain pitch, in which case there is a direct correlation with a harmonic node in the same position.
||Often used often by composers such as Bottesini, in which the stopped/notated pitch indicates the direct position of the harmonic itself.
|The diamond note-head
||Tablature style notation which is placed upon the direct position of the harmonic, however it doesn’t always relate to the designation of the sounding pitch itself.
||I.e. Stravinsky and Ravel used this system within passages of many harmonics, particularly ‘in conjunction with higher partials’. This system is workable in many cases, but can often cause confusion in terms of the desired sounding pitch…
|The combination of the two methods
||Used for the purpose of further clarity – can combine elements of different harmonic notations to improve clarity
||Composers such as Schoenberg was known to notate some harmonics with the ‘o’, diamond note-heads, smaller indications for the ‘flageolet tone’ and also gave the sounding pitch in brackets.
|Two separate staves
||Involves two staves: the primary staff indicates the position of the harmonic in tablature style notation, and a smaller ossia staff indicates the desired pitch.
||When communicating the use of more advanced upper partials, the use of two staves can prove to be helpful.
||Notated in tablature form: the stopped note is notated normally, with the position of the harmonic notated above with a diamond note-head.
||This method is considered common amongst most scores.
Types of harmonics:
||What are they?
||Harmonics sounded on any of the open strings – referred to also as open harmonics.
||The overtone series of just four fundamentals already allows a large variety of pitches within the open series. , however the ‘chromatic spectrum’ may also be completed with the use of artificial and stopped harmonics. (Daino)
||Unlike open harmonics, art. harmonics are produced via the stopping of an open string upon which the performer reaches for a new node that is formed from the shortened fundamental.
||Art. harmonics are determined by the reach of the instrumentalist, and most often used in the higher registers of the bass whereby the distance between the fundamental and partials is smaller. (Daino)
||The sounding pitch of the harmonic is raised by touching the node on the side of the string and pulling the string sideways towards the edge of the fingerboard (Daino)
||This involves an increase in the string tension, and the sounding pitch has the ability to sound up to a semitone higher. Nodes within the mid-range are often preferential with this technique, as the elasticity and range of pulling is larger than positions located closer to the nut or the bridge. This method is particularly useful when used intentionally, but also in adjustment to other instruments, often in compensation for flatter harmonics within the series.
||Glissando over a harmonic series: involves a clean break between each partial.
||Left hand touches any given node on the string and slides freely upwards or downwards. Most commonly used with the bow. Intonation remains within the open harmonic series.
Can also be used with art. harmonics, which allows for more possibilities chromatically as the gaps are filled between the open nodes.
|Even sliding of a pitch, within the timbral sphere of the harmonic: applied through the use of art. harmonics.
||Involves much precision and a careful adjustment of the stopped pitch and the above fundamental, as the distance changes (decreasing as one climbs higher, and increasing as one descends lower on the neck).
||Two or more nodes on a string may be isolated at the same time, during which the multiple of their partials will sound (Daino).
||Eg. If the respective nodes of the third and fourth partials are activated simultaneously, the pitch of the twelfth partial will be heard. Often used to reach upper partials in positions on the fingerboard that do not approach the extremes near the bridge or nut. (Daino). In correlation with the upper partial series, the use of multi-nodal harmonics is limited to a softer dynamic range and special attention is needed in regards to bow placement. As one continues to delve deeper into the upper partial series (i.e. above the twelfth), more practice is needed to be consistent with the positioning of the left hand.
||Flautando bowing: sul tasto, drawn lightly – imitates the timbre of a flute.
||Harmonic flautando bowing utilises the same principle as traditional, but activates a partial above the fundamental, allowing for a highly accurate imitation of the flute. This technique is particularly useful when accentuating harmonics out of a textural sound series (without altering the left hand). I.e. Mark Dresser is known to do this, with much vibrato to emphasise the flautistic qualities.
Application: While harmonic flautando has not been used prominently in current repertoire, it may be used as a substitute for passages marked with traditional flautando. One must simply use left hand positioning an octave lower than written and bow at the fourth partial to produce the correct pitch. (Daino)
||Sub-harmonics exist in the undertone series, allowing for a sounding note that is lower in pitch than the fundamental.
*Due to the unspecificity of the pitch that is produced, these sub-harmonics have also been referred as Anomalous Low Frequencies (ALFs) (Strings magazine – June 2009).
|The undertone series is the inverse of the overtone series – this series is produced by locating the existing harmonic nodes on the string and applying increased pressure with the bow. The resulting ‘groan/scratch’ of the bow stroke can be further controlled and manipulated to voice a lower pitch – this depends directly on the exact bow pressure and the position of the bow. ALFs require a specialised technique for accurate execution. It is possible to extend the range beyond the lower limit of the piano and even beyond the lower limit of human hearing. The overpressure from the bow creates beating/clicking from the vibration of the strings.
*Mari Kimura – Japanese violinist at the forefront in the use of ALFs.
*Due to the differences in string instruments, it has been difficult to refine a method for the use of ALFs – therefore, on the bass, it is recommended to focus on the sub-octave frequencies and for players to refine their own relationship between bow pressure, positioning and speed.
Mark Dresser refined a method for the use of the subharmonic octave (1988) – when producing a pitch an octave lower than the stopped tone, the bow should be placed on the node of the 6th partial. A clear, even bow stroke can be applied to ‘catch’ the lower octave with added bow pressure and also added ‘stopped’ pressure from the left hand. (Daino, Dresser).
||The production of combined partials in the harmonic series – achieved through activating two partials together, often between two closely positioned nodes. (Daino).
||When two or more partials sound together, the ‘dead’ spot between nodes is no longer present and the string continues to vibrate. The aforementioned areas of the neck can be found by sliding the left hand across the nodal series (whilst bowing) until two partials are heard simultaneously. The more partials that are heard together, the less defined the chordal nature of the multi phonic will be. Application of harmonic partials requires less than normal pressure in the left hand. They should be notated with an additional staff that indicates the sounding pitch-set.
*The application of bass multi phonics is more delicate than that of wind instruments i.e. saxophone.
|Double stopped harmonics:
||Two harmonics are played simultaneously on different strings
||This can be difficult to execute due to the specific nature of harmonic resonance – thus, the control and bow placement needed for a single harmonic on a single string may not correlate with the other. I.e. certain combinations are much more possible than others. Some combinations that work particularly well include the use of subharmonic octaves and traditionally bowed notes/open strings.
Multiphonics are used both in conjunction with a certain pitch-set, and often distinctly for textural/timbral quality.
Whilst this is only the beginning of the world of bass harmonics, Daino has provided a wealth of information in regards to the technicalities of each type, through which I will aim to approach my intuition with more scientific knowledge.
***Resource: The Double Bass: A Technical Study of Timbre’ (2010) – Eric Daino
*** Web link: http://udspace.udel.edu/bitstream/handle/19716/5505/Daino,%20Eric.pdf?sequence=1