‘Brass’ instruments that can play the 7th harmonic
(and probably the 2nd , 3rd, 4th, 5th and 6th)
Here’s more of my exploration of harmonics and instruments played by vibrating the lips.
For the player of a standard brass instrument, knowledge of lower harmonics from early years comes through lip slurring practice although this is done primarily for muscle flexibility and strength building rather than tuning. Few give much attention to the odd numbered harmonics beyond 3 and 5. Some will play the 7th harmonic in arpeggios as part of a warm-up routine, yet usually consider it an out-of-tune version of a standard pitch.
Many authors of tutor books for the horn recommend practicing slurs between harmonics going as high as the 16th yet avoiding the 7th, 11th, 13th and even the 15th. They simply use standard arpeggio notes. Examples abound from Oscar Franz’s late nineteenth century volume (Franz 1942) to the well-known mid-twentieth century volume of Philip Farkas (1956) and Barry Tuckwell’s Playing the Horn (1978). Recently Jeffrey Agrell drew attention to this and suggested slurring with all the harmonics to allow the lip muscles to find their way around adjacent harmonics before learning to skip over particular ones (2008). Christopher Leuba, in his short 1962 work on intonation, advocates using the 7th harmonic for dominant seventh chords (2004: 13). Richard Merewether, horn player and instrument designer, argued for the use of the narrow minor third interval in doleful cadences such as the end of the Second Movement of Beethoven’s Eroica Symphony. In his pamphlet The Horn he referred to the ratio 7:6, the interval between the 6th and 7th harmonics (Merewether 1978: 39). Some unpublished warmups and teaching aids, such as Hector McDonald’s warmups (2005) and teaching aids produced by Dominic Harvey of the ANU School of Music (1999), include the 7th harmonic. Additionally I have heard a number of professionals slurring through to the 8th harmonic with no omissions. Also any player working through the publication by the Australian Music Examinations Board for Horn Grade Two and Three (Lawrance 1992) will have noticed that the slurring exercises are designed to use the natural harmonics including the 7th and Grade Four includes the 11th harmonic (Lawrance 1992). Interestingly, the early nineteenth century horn methods of Dauprat (1994/1824), Domnich (1985/1807) and Duvernoy (1802) do not place any emphasis on harmonics either in writing or in exercises. They simply refer to diatonic sequences and begin with exercises that require right hand technique to provide certain notes not available otherwise, in other words to fill the gaps between harmonics 2 to 3, 4 to 5, 5 to 6 and so on. It is clear that the tradition of horn playing has been that of tempering harmonics to fit with standard music practice. A few composers have used the natural 7th harmonic such as Randall E. Faust in his works Harmonielehre (1996) and Prelude (1977). Works by composers Britten and Ligeti are referred to in later sections (1.5, 1.6).
A similar situation is evident for other brass instruments: the 7th harmonic is included in slurring practice by some authors of tutor or exercise books. The few examples I have come across of trumpet music using the 7th harmonic are studies or slurring exercises. The recent book by John Foster includes some 7th and 14th harmonics in the section titled “Studies on the harmonic series” (2010: 21). A 1938 tutor book by Earl Irons includes the 7th harmonic in ten groups of slurring exercises (1966). Richard Hodges technical studies for treble clef brass instruments include the 7th harmonics in eleven exercises (2005: 57-62). I have not come across any compositions for trumpet that ask for the 7th harmonic to be played as it naturally occurs.
Trombonists do not shy away from using the 7th harmonic in slide positions other than first position though will adjust the slide a bit higher than usual to temper it. They use the 7th harmonic for pitching ease, articulation clarity and slide movement minimisation. Higher harmonics are generally more difficult to pitch than lower ones or articulate as clearly therefore selecting the 7th harmonic rather than the 9th or 10th can help. Additionally, minimising slide movement can make many passages more manageable.
An interesting effect called “slurring against the grain” is used in a few trombone solo works. The slide movement is identical to playing a descending chromatic scale, however the lips pitch a higher note with each shift. Example 1, below, shows the slide position, harmonic and the fundamental to which the harmonic belongs from a well-known trombone work. Players will temper the 7th harmonics and usually place a ‘#’ next to the relevant slide position as a reminder to raise the pitch. In this example the ‘#’ signs are placed above.
Example 1. Slurring across the grain in Frank Martin’s Ballade for Trombone and Piano.
An example of trombone playing that does not temper the 7th harmonic is found in Stuart Dempster’s recording Underground Overlays from the Cistern Chapel (1995) and in other compositions in live performances he has given. His piece for the MiniMax Festival 29 July 2002 in Brisbane was titled Twenty Tantalizing Titillating Trombones Tooting Turbine Tonics (2002).In the same concert a trombone quartet performed Robert Davidson’s Tibrogargan Round (2002) also using natural 7th harmonics.
Exploration by brass players of the many intervals and chords that can be associated with the 7th harmonic is extremely rare. Higher prime numbered harmonics receive even less examination. A musician wishing to use the 7th harmonic in musical situations, not only in exercises, requires an aural acceptance that the harmonic is completely valid without altering the tuning. Certainly pitching the 7th harmonic in new musical contexts requires additional practice.
Groups of instrumentalists that use the 7th harmonic unashamedly are the cors de chasse (trompes de chasse). Alphorn players also play the natural 7th harmonic and both groups of players will use harmonics as high as the 16th therefore these instruments will receive more attention in Section 1.6.
The bugle is a natural labrosone that has an available 7th harmonic. This conically shaped instrument is very well known in many western countries especially for its signalling and ceremonial use by the military. Most calls use harmonics 2 to 6 (Baines & Herbert 2007) though some rare older calls used harmonics 1 and 2 (Baines 1993: 27). The instrument has much less resonance higher in the harmonic series therefore the high written C, 8th harmonic, is never used. This is due to it having a larger bore than a trumpet (Bate 1966: 6-7).
It was bugle notation that was adopted by brass bands at their inception in the nineteenth century. The C just below the treble staff was and still is played on the 2nd harmonic (Baines 1993: 27). Orchestral trumpets and horns at that time equated this written note with the 4th harmonic, therefore their high written C was played on the 16th harmonic. Horn writing was not influenced by brass band conventions even after the almost universal adoption of the valved instrument. However, writers of trumpet music adopted the convention for the cornet (Tarr 2007). This occurred for a number of reasons. Trumpets and cornets often worked side by side in orchestras throughout much of the nineteenth century and once the valves for the trumpet became the standard setup there seemed little point in treating the notation differently. The introduction of the cornet also influenced trumpet players to change from using longer F instruments to the shorter B-flat and C instruments, a shift that occurred between 1850-1890 (Tarr 2007). Some musicians played all the orchestral trumpet repertoire on the cornet (Baines & Herbert 2007) though others used the keyed bugle or the keyed trumpet. The latter was used more for solo repertoire than ensembles, as was the slide trumpet in England (Dudgeon 1997: 131-9). Much orchestral music in the nineteenth century was written for a valve trumpet in F, mid-way in length between the natural trumpets and the modern trumpet or cornet. Players of this F trumpet would have needed to produce harmonics up to the 8th or 9th harmonic to cover standard repertoire.
As mentioned most orchestral trumpet players transferred to the short B-flat trumpet but now much orchestral repertoire is played on the C trumpet. For clarity and the security gained by greater pitching accuracy orchestral players began using even shorter trumpets. The D trumpet was first made in Brussels, 1861 and the piccolo G trumpet by Besson in France 1885 (Tarr 2001: 837). Stravinsky took advantage of both in his composition Le Sacre du Printemps (1965/1913). For orchestral playing the object has been to gain maximum clarity, cleanliness of articulation, accuracy and power. The pitch limits depend upon context but for some orchestral situations a C trumpet will be used up to the 10th harmonic for its fuller tone rather than a shorter trumpet.
The need to extend much higher than the 8th harmonic has not been a large part of trombone history. With the slide as its characteristic feature there have always been a significant number of notes available to fit in with standard western music writing. Even the very high passage in Schumann’s Symphony no.3 (n.d./1850) does not require higher than the 8th harmonic for the E-flatalto trombone though some players choose to use the tenor trombone for this work. This would require the 12th harmonic of the B-flat instrument. A few other examples of higher writing to the 12th harmonic are dealt with later. The range used in solo repertoire is not significantly different to large ensemble writing. In brass bands solo material usually goes to the cornet or euphonium therefore the pitch range for the trombone in this genre is more limited than in orchestral writing.
There is, or used to be, a certain psychological aspect to considering the 8th harmonic the upper limit of modern brass instruments other than the horn. The 8th harmonic on the open tube is the high written C above the staff for all brass instruments reading treble clef except the horn. This includes all the brass band instruments other than the bass trombone, which uses the bass clef. The notes leading up to high C from the G at the top of the staff all require 8th harmonics from the following sequence of gradually shortening tube lengths: valves 2 + 3; 1 + 2; 1; 2; 0 or slide positions 5, 4, 3, 2, 1. To go higher would seem to require a new sequence. However this is not the case as the C-sharp can be simply played as the 9th harmonic of valve 2 and the D as the 9th harmonic of the open tube, slide positions 2 and 1 respectively. Going higher still, playing the written D-sharp and E as 10th harmonics may result in intonation that sounds too low for many contexts. These notes could be played as 12th harmonics on longer tubes, making the tuning sharper. The disadvantage is that the 12th harmonics are more difficult to produce with as much pitching accuracy.
The vast body of western repertoire for standard brass other than the horn does not extend beyond the use of the 8th harmonic. Going higher is too demanding for a usable tessitura as the most comfortable range falls between harmonics 2 to 6 and 2 to 12 for the horn.
The serpent and the ophicleide had a part to play in European music history and they both have current exponents. The serpent was derived from the tenor version of the cornett at the end of the sixteenth century (Bevan 1978: 47). It was principally used in wind ensembles for its bass register (Bevan 1997: 144). Up to 8 harmonics are playable with all tone holes covered. However with the tone holes uncovered the tone deteriorates therefore the range is usually restricted to that between the 1st and 4th harmonics (Baines 1993: 49-50). The serpent also has considerable intonation issues with many a fingering choice being used for a number of adjacent pitches (Morley-Pegge, Bate & Weston 2001). In contrast the ophicleide has keys controlling the covering of holes which makes the “intonation much better than the serpent” as Bevan says (1978: 61). This gives it a large usable range up to the 8th harmonic.