The Science of Partials – Mark Dresser:

Last week I fell off my bike and split my chin. Today the glue reopened, and to my dismay, tomorrow I will fly to New York for the first time with a huge bandage on my face. (And yes – definitely first world problems).

 

In other news, that tiny anecdote is completely irrelevant to the main subject of this post:

// Mark Dresser has written a wonderful resource to accompany his CD/DVD entitled ‘GUTS’, which superbly explains many of the extended techniques that have become known to the double bass. In contrast to the other articles and writings that have been reviewed and discussed in my research so far, this piece of Dresser’s writing was intended for a presentation in which he also provides accompanying scores and notations to solidify his points.

 

Before I continue to delve deeper into the many parts of this valuable resource, I have chosen to start by briefly summarising Dresser’s introductory paragraph in ‘GUTS’, which explains the meaning of the harmonic series in a refreshingly simplistic way. Read for my summation below:

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The harmonic series are ‘a natural phenomena of string vibration’ (2010, Dresser, P. 1), whereby the vibration of a string occurs in measured whole number multiples of the fundamental pitch; hence the string is divided into a certain number of equal subdivisions to produce different partials.

—> Adding to my current exploration in the world of partials, I have summarised a few of Dresser’s key points below:

1. The number of the partial indicates the number of subdivisions in which the string is vibrating.

—> For example – the 2nd partial on the G string directly divides the string into two, creating two equal distances of vibration. In this process, the frequency also doubles from 100Hz (G open string) to 200Hz.

—>Let’s take the 5th partial (‘B’ harmonic on the G string) as another example of this – it divides the string into five equal subdivisions.

2. Partial Number (minus) – 1 = The number of nodes

—> For example – Partial 4 indicates that there are 3 nodes on which to play this harmonic on any given open string. Partial 7 indicates that there are 6 nodes on which to play this harmonic on any given open string.

3. As a partial number doubles, the pitch moves up an octave

—> For example – Partial 1 = Open G String, Partial 2 = G harmonic an octave higher, Partial 4 = G harmonic an octave higher, Partial 8 = G harmonic an octave higher, Partial 16 = G harmonic an octave higher.

// In terms of the relevance of this science (however intimidating it may seem!), Dresser insists that the knowledge of the nodal locations is a key factor in improving intonation, bow placement, finger placement and a broader knowledge of timbral scope. To develop a solid comprehension of the harmonic series on the double bass is an invaluable tool in strengthening the understanding of the instrument as a whole.

This is only a fraction of information available from this resource, with much more to come. // 

The Overtone Series

// The Overtone Series (also referred to as Partial and Harmonic Series) of the double-bass is highly complex. To add clarity to my composition and performance, I have created my own diagram (see below) that outlines the different nodes on the neck on which the partials occur.

Note: The pitch indications on the diagram relate only to the naturally occurring harmonics on the G-STRING. It excludes the higher half of the bass neck, focusing only below the 12th fret. 

Partials

A brief overview of the workings of the overtone series (for each string):

  • The fundamental (Partial 1) is the open string i.e. E, A, D, or G
  • Partial 2 = the octave above i.e. the 12th fret harmonic for each respective string
  • Partial 3 = the fifth above the octave i.e. the 7th fret harmonic for each respective string
  • Partial 4 = two octaves about the fundamental i.e. the 5th fret harmonic for each respective string

As the partials grow higher, the distance decreases between them.

  • For each respective string, Partials 5-19 occur at multiple points on the neck. This creates a mirroring effect on the instrument.
  • Partials 12 and upwards are incredibly difficult (and nearly impossible) to execute due to their close proximity —- as seen in the diagram.
  • Notation of the higher partials becomes increasingly difficult, as they may occur in multiple places on the instrument, across each of the different strings.

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The complexity of the overtone series is fascinating when discovering the multitude of node-points that are available on the instrument. To understand it on a theoretical level is crucial at this point of my journey – both for specificity in performance and composition. So often, the stopped-tone is considered before anything else, but to delve deeper and further explore the underpinning partials that lie beneath each position is a surefire way to open more doors.

‘A Tree Tells’ – Notation V. 1

// My latest piece ‘A Tree Tells‘ holds a deeper meaning than the average artichoke.

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In the midst of the Bushfire crisis in my beloved Australian homeland, I felt a need to channel my sadness and angst into a song – told from the perspective of a tree (pictured) that I connected with during a recent movement workshop led by Sebastian Stert.

IMG_7769

It is easy to take nature’s magic for granted, but as our treasured planet continues to change ever so rapidly, this workshop was spent strengthening our connection to nature and reflecting upon the importance of self-grounding amidst our environment. It is so important to remain mindful of the need for greater action to preserve the stunning habitat in which we are harmoniously immersed within… It is so easy to lose touch… to forget to stop and listen to the trees. But perhaps the most valuable part of this adventure was a moment of connected energy between the trees and me. They have been there for many centuries, and will outlive all of us. The least we can do is to respect them and all that they give. // Needless to say, I went straight home and wrote A Tree Tells

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This composition is purposefully simple. In contrast to the other vegetable pieces, I felt that the lyrics were the foundation for this piece of music. Thus, I chose to use only partials to accompany the vocal melody; … to enhance the story, and to avoid distraction from the fundamental meaning of the lyrics.

———–

~~~ Notation ~~~

The notation of this piece has offered a great exercise in my continued enquiry into different methods of communicating my music to others on the score. As I have previously posted about the notational inconsistencies of harmonics across different scores, I have tried a particular method for this particular piece:

Click here for the full score: A Tree Tells 

——– > A numbering system was used to indicate which strings the partials are played on, accompanied by a diagram that I have made below:

Double Bass - String Numbering Diagram

——– > A second page is focused on the bass part, with a pitch indication on the line above. This allows for much closer detail in regards to particular string numbers, with a direct reference to the sounding pitch of each partial (see below).

Untitled~~~ Summary ~~~

Whilst I am currently experimenting with the complex world of notation, I am satisfied with the level of clarity that I have achieved in this particular score so far. In contrast to my other pieces, I chose to focus on this one due its simplicity and single-line accompaniment. The rare occurrence of double-stops has allowed for a cleaner appearance on the page, and perhaps with more work in this direction, it will become easier to translate the rest of my compositions into a more consistent form of notation.

 

 

The Textural Ricochet

// The Ricochet bow technique is one that I have started to use very frequently within my own playing. Often referred to as ‘the bouncing bow’ or also as ‘battuto’, Knut Guettler has written extensively about the use of this particular motion in his book A Guide to Advanced Modern Double Bass Technique. This post is related to his writings on this topic.

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What is it?

The ricocheted bow technique is useful in executing a clear articulation of a group of notes in ‘rapid succession’ – see fig. 1 below (Guettler, 1990, P. 28). Achieved with just one impulse of movement from the arm, the ricochet effect is subsequently achieved through the bouncing of the bow on the string/s.

Ricochet - Bow diagram

How does it work?

There are several factors of movement that influence the level of bounce, shown in the tables below (Guettler, P. 29):

Bow Grip Ricochet Speed
Loose Bow Grip Slower bounce
Tight Bow Grip Faster bounce
Bow Placement Ricochet Speed
Near to the tip

More rapidity in bounce

Nearer to the middle/frog Less rapidity in bounce

Naturally, with each ricochet of the bow, the level of bounce will decrease as shown in fig. 2 below (Guettler, 1990, P. 29):

Ricochet - Fig. 1

How is it notated?

The diagrams below indicate two particular forms of notation for the ricochet technique. The method in Fig 3. uses wedges to indicate a number of bow bounces within each triplet series, with a clear accent on the first note. Fig. 4 indicates an alternate form of ricochet notation, shown by the staccatos within the slurs. Fig. 5 has been derived from Ashley John Long’s themoderndoublebass.org.uk, which shows an excerpt from Scodanibbio’s Geografia Amorosa

fig. 3

fig. 4

 

fig. 5

 

 

Whilst each of these notational methods are widely used and also very effective in terms of communication, is important to note that this is in reference to a specific number of bounces to be executed by the performer. 

How can I apply this to my own pieces?

In contrast to this form of notation seen above, my use of the ricochet technique is often used for sake of texture and with much more rapidity. Hence, whilst my own compositions are heard to use the ricochet effect within a specific pulse or time signature, the amount of bounces can vary from five to ten times; it never remains exactly the same. Thus, as I experiment with my own notation, I will consider using the wedge symbol on a singular basis (or in combination with a wavy line similar to that of Fig. 2) to leave the number of bounces open to the performer. With this, however, it is important to consider more instruction in terms of the textural effect that is needed i.e. ricochet on the tip of the bow with rapidity.

Summary

As Guettler has expertly documented, the ricochet technique is directly affected by a number of factors – the bow placement, the specificity of the execution, the grip of the hand, the position of the arm, and in my case, the desired effect of the bouncing motion. Future inquiry will need to be undertaken to determine a clearer way of communicating the use of a textural ricochet – something that is present across many of the vegetable-bass pieces already.

Take the time to listen to what you have just played….

// Yesterday I had a session in Cologne with Dieter Manderscheid, from which I took away some fantastic points of advice. The list below relates directly to solo performance and discovery – all of which I endeavour to implement further into my own practice:

  • Instead of beginning with the most difficult part of a piece, allow yourself to warm up towards that moment —> ground yourself with the instrument – tune in, resonate with the sounds and connect yourself to the intonation. For the double bass, the partial series is particularly useful in this regard – starting from subtlety and building further from this.
  • Start with a mood. As a soloist, it is both normal and useful to choose from a pool of ideas during performance. However, it is important to take time with this, and to build form gradually and mindfully in consideration of the listener. Development takes time.
  • Practice silence. Barre Phillips previously said that he would perform a solo concert for himself each and every week. And indeed, this is something that can often be overlooked as a soloist. With so much solitary time spent in a practice room, one can forget to see the bigger picture and to practice the moments that matter most – for example, silence and pause.
  • We don’t have to play all of the time. Instead, take breaks. —> Take the time to listen to what you just played.
  • What comes out during a solo performance is what we often do most in the practice room.
  • Experiment with rest and density.

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On a personal note, I particularly resonated with the idea of listening to what has just happened. This in itself can add a sense of mindfulness and relaxation to the pressures of solo performance, training one as an individual to feel comfortable within the moment and to be guided by the energy that is felt from within, and also from the room.

On a broader note of reflection, the aforementioned topics above can be made relatable to any musician who is embarking upon a journey of soloistic development. Irregardless of level, it takes a certain shift in mindset to embrace the vulnerability of individual discovery; thus, a deeper level of awareness is vital in preserving the beauty of spontaneous exploration and intuition (in combination with progressing technical discovery).

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// The Third Messiaen Mode

During my last session with Matthias Nowak, we spoke about the importance of different harmony with a particular focus on the third Messiaen Mode.

 

A brief overview:

Olivier Messiaen was known to utilise a series of 7 symmetrical scales of limited transposition, structured across a series of cyclic intervallic formations. Each of the scales can be utilised over a vast range of tonal centres, due to the many harmonic possibilities inherent within the combination of notes of each one.

^too many words (!!) – I know. But I’ll do my best to summarise it further below:

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The third Messiaen mode (also known as the Augmented Scale) features three sets of repeated material (each of which is spaced a major third apart) – forming a 9-note scale (fig. 1):

Messiaen Modes

In particular reference to the symmetrical harmony in mode 3, there are also three fundamental augmented triads that arise clearly from the notes (see fig. 2 above).

However, this is only the beginning of the many different chords that are hidden within this single 9 note scale; as the notes in this scale range from G A Bb, B C# D, Eb F Gb (fig. 1), this particular mode corresponds with a large range of other tonal origins. 

The list below details the many other options available within the third Messiaen mode (fig. 3):

Fig. 3 – Triads and 7th Chords within Messiaen Mode No. 3 (Root note = G)

Triads G major, G minor, G dim, G aug, A aug, Bb major, Bb minor, Bb aug, Bb sus 4

B major, B minor, B dim, C# aug, D major, D minor, D aug, D sus 4

Eb major, Eb minor, Eb dim, Eb aug, F aug, Gb major, Gb minor, Gb aug, Gb sus4

7th chords Gmaj7, Gmaj7(b5), Gmaj7(#5), G7, G7(b5), G7(#5), Gmin7, Gmin7(b5), GmMaj7

Bmaj7, Bmaj7(b5), Bmaj7(#5), B7, B7(b5), B7(#5), Bmin7, Bmin7(b5), BmMaj7

Ebmaj7, Ebmaj7(b5), Ebmaj7(#5), Eb7, Eb7(b5), Eb7(#5), Ebmin7, Ebmin7(b5), EbmMaj7

A7(b5), A7(#5), C#7(b5), C#7(#5), F7(b5), F7(#5)

Bbmaj7, Bbmaj7(#5), BbmMaj7, Bbmin6

Dmaj7, Dmaj7(#5), DmMaj7, Dmin6

Gbmaj7, Gbmaj7(#5), GbmMaj7, Gbmin6

Undoubtedly, the options within this particular scale are abundant. Interestingly though, due to its symmetrical structure the third Messiaen mode is limited to only four different tonal combinations in total (*note: each single mode already covers three variants within itself when each repetition/grouping is ordered differently i.e. starting on ‘G’, starting on ‘B’, starting on ‘Eb) – just as augmented triads are also limited to only four transpositional variants.

And whilst this is all highly theoretical, a later post will follow this week in which I have actively limited myself compositionally to only the notes within the third Messiaen mode (fig. 1). In regards to composition, the active choice to set parameters within a modal framework has allowed for different musical choices to arise as a result, with a refreshing ambiguity to the harmony as the root notes can freely be shifted below.

More to come on this, but in the meantime, ——

… thank you Olivier Messiaen for your paramount musical influence!

// A recount of Eric Daino’s article – ‘Harmonics on the Double Bass’

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

Type: How does it appear? Further explanation
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.
Artificial Harmonics 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.

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Types of harmonics:

Type: What are they? Further explanation
Natural harmonics: 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)
Artificial Harmonics: 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)
Pulled harmonics: 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.
Harmonic Glissandi: 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).
Multi-nodal harmonics: 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.
Harmonic Flautando: 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 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.

How?:

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).

Multiphonics: 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

 

 

// H-Moll/D-Dur – Håkon Thelin

This week I travelled to Finland, during which I was fortunate enough to be gifted hours upon hours of train travel. Naturally, this seemed like the perfect opportunity to sit back, look at the snow (it was -18 degrees outside) and listen to solo-bass works by a variety of my favourite musicians.

Thinking Of: a tribute to virtuoso bassist Stefano Scodanibbio, is an album that I have listened to several times during this week. It is a compilation of short pieces, performed by different bassists from around the world (includes Mark Dresser, Sebastian Gramms, Barre Phillips, to name a few). // However, one track in particular – H Moll/D Dur (performed by Håkon Thelin), kept jumping out at me upon each listen.

Håkon Thelin is a Norwegian double-bassist, having performed with ensembles including Olso Sinfonietta and musickFabrik. ‘At present, his main interest lies in the combination of contemporary music and folk music, in microtonality and in the sonic exploration of harmonics and multiphonics on the double bass.’ (quoted via his website: http://haakonthelin.com/index.html).

// As a result of my own current exploration of bass composition and new sounds, my music has similarly adopted a folky characteristic to its style. In this light, it is easy to see why Thelin’s piece H Moll/D Dur is so resonant with my current journey. As the title suggests, there is a clear tonality throughout, through which Thelin uses a variety of different pedal points to underpin extensive use of harmonics and multi-phonics as the ‘upper voice’.

A rather challenging task is to transcribe the entire work. So far, I have started with the introductory section (see here): H Moll:D Dur – Hakon Thelin PDF

// As I am fairly unacquainted with advanced new-music notation, I have encountered some difficulty in notating the higher harmonics in a legible manner. My Masters research aims to develop a system in which I can communicate these sounds to other players in a more readable format. As seen in the score above, I have done this (temporarily) by indicating the sounding pitch in brackets above the higher harmonic melody line. Therefore, my ability to read such a score (with each harmonic pitch indicated individually) will effectively focus my practice when first learning this piece.

There will be more to come on the actual execution of this excerpt. No doubt, the listening aspect is far more effective than the notation, in which one can hear the musicality and melody – without the square-eyed effect of deciphering the notation!