tag:thebrasswhisperer.com,2005:/blogs/blog-horn-harmonics-just-intonation-other-musical-interests?p=1BLOG - Horn harmonics, just intonation & other musical interests2023-10-17T01:55:31+11:00The Brass Whispererfalsetag:thebrasswhisperer.com,2005:Post/64052702020-08-09T00:47:09+10:002021-12-09T09:39:33+11:00Britten 'Prologue & Epilogue' in his Serenade for tenor, horn & strings<p>An excellent example of the way in which intervals of the harmonic series occur in music comes from the Prologue to Benjamin Britten’s Serenade for Tenor solo, Horn and Strings. Britten asked that the player use only natural harmonics, a simple enough task for the horn player who produces the overtones above a given fundamental by altering the vibrations of the lips. Britten exploits certain harmonics for their tonal effect in a most masterful way. </p>
<p>In bar 1 of the score we see the familiar interval of a perfect 5th establishing the tonality of F concert and in conjunction with the choice of rhythm creating a mood of openness and evocation. The horn player does this by producing the 8th harmonic then the 12th harmonic. This is the same interval as between harmonics 4 and 6, and also 2 and 3, also 6 and 9. This demonstrates an important aspect of Just Intonation (JI) language, the language of ratios. The interval of the perfect fifth when written as a ratio reads 3:2 or 6:4 or 12:8. Furthermore the convention when using ratios for JI represents an interval in the smallest possible terms, therefore 12:8 (or 6:4) becomes 3:2 showing that these three fifths have exactly the same ratio. </p>
<p>In bar four we hear the evocative and haunting sound of the 11th harmonic. Part of this inherent sound quality arises because it bears almost no relation to our accepted diatonic scale. Once we gain a familiarity with this pitch we can enjoy it for its own sake and not hear it as out of tune, for harmonics occur naturally. Here I echo Lou Harrison who chooses pitches because he ‘knows’ their evocative nature although he cannot describe what they evoke other than “certain emotional feelings” (Harrison 1987: 7). We could say that harmonics represent natural intonation and that human beings have constructed scales on the basis of the natural intervals of the harmonic series. From this point of view some pitches in our diatonic scale should sound odd such as the fourth and sixth degrees in the key of C because they do not naturally occur in the harmonic series. For instance one type of pentatonic scale appears naturally as harmonics 8, 9, 10, 12, and 15 giving notes C, D, E, G, B. However we have become so used to the sound of a major scale (C, D, E, F, G, A, B, C) that pitches like the 11th and 13th and even the 7th harmonics can sound ‘wrong’ as we tend to associate them with scale degrees 4, 6 and 7. Of course we can get used to the inherent qualities of these harmonics. </p>
<p>We still do not have a vocabulary to describe the emotional effect of the 11th harmonic and we rarely describe more common harmonic intervals, such as the 3:2 ratio (perfect 5th ); 5:4 (major 3rd); 6:5 (minor 3rd), in other than the simplistic terms of stable, happy and sad respectively. In bar four Britten moves from harmonic 8 to 11, back down in pitch through the 10th and 9th harmonics, with these leading to the last two notes of bar two followed by a repetition of bar three in the following bar. These notes in bar five seem different now for having made our strange journey to the non-diatonic interval of the 11th harmonic. Example</p>
<p>The more simplistic language of ratios unambiguously shows this group of intervals in bars four and five as: </p>
<p>8:11 11:10 10:9 9:6 (3:2) 6:10 (3:5) 10:8 (5:4) </p>
<p>However, staff notation becomes confused. The 11th harmonic could be written as an F or an F#. Obviously Britten chose F. The 11th harmonic sounds radically different to an F from Pythagoras’ scale. It sounds 53 cents higher (a 33:32 higher than 4:3) therefore 551 cents higher than the 8th harmonic (ratio 11:8). As Pythagoras’ whole tone has a distance of 204 cents and his semitone 90 cents this difference of 53 cents (considerably more than half his semitone) is quite radical. The Pythagorean F# sits 612 cents above C with ratio 729:512 therefore the 11th harmonic sits 59 cents lower than F#. The 11th harmonic is thereby six cents closer to F than to F# giving one reason to prefer F to F# for notation purposes.</p>The Brass Whisperertag:thebrasswhisperer.com,2005:Post/61951702020-01-30T00:44:08+11:002021-08-15T23:54:38+10:00Notating in DORICO<p><strong>Pitch and intervals are so interesting.</strong> (I won’t relegate rhythm to a lesser status, just musing with pitch as all good brass whisperers do.) </p>
<p>Many of the just intonation pieces I write have a different ‘tonic’ or reference pitch from each other. This makes preparing a large set up of pitches in the music software (Dorico) time consuming for each work. The issue with making a large set is deciding which pitch will be the reference and minimising the complexity of the calculation of notation symbols and divisions of the tones and semitones for microtonal playback. </p>
<p>Part of the idea is to minimise the number of combined accidentals (pitch modifiers) on the staff. </p>
<p>Another aspect is to make any reference pitch close to a standard Hertz reference (A=440, Bflat = ? etc). This is less of a problem since Dorico notation software can alter the pitch by Hertz. </p>
<p>Preparing for my work in 2020 I have set my reference pitch at G. This is not in deference to Harry Partch, but rather to help horns and strings have a good combined starting point. I did consider A, which is what Marc Sabat did for his work on microtonal horn writing in combination with strings, which has the advantage of the standard tuning note being the reference. His work 'Towards an Expanded Definition of Consonance: Tuneable Intervals on Horn, Tuba and Trombone (2006)' with Robin Hayward and '23-Limit Tuneable Intervals above and below A (2005)' show extensive possibilities.</p>
<p>For my purposes at the moment G is also a note that all standard orchestral strings use and is only 3 perfect 5ths in the chain from F and one more from Bflat. These are the easiest reference notes for tuning on the horn. After some experiments it seemed easier to work from a simple note name, one of these: A B C D E F G. The chain of 5ths sees these as F C G D A E B. Both G and D are in the centre. I chose G because it is one 5th closer to Bflat and Bflat is also an important note for other brass instruments as well as clarinet. By the way, the composition I am working on at present has a 'tonic' of D, the only adjustments I am making to the notation of the score is to show any tunings with cents with D as 0 cents and G as -2 cents even though the notation is based on G as 0 cents and D as +2.</p>The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727372019-09-09T10:00:00+10:002020-08-09T00:49:31+10:00'Brass' instruments that can play the 7th harmonic<p style="text-align: center;"><strong>‘Brass’ instruments that can play the 7th harmonic </strong></p>
<p style="text-align: center;"><strong>(and probably the 2<sup>nd</sup> , 3<sup>rd</sup>, 4<sup>th</sup>, 5<sup>th</sup> and 6<sup>th</sup>)</strong></p>
<p style="text-align: center;">Here’s more of my exploration of harmonics and instruments played by vibrating the lips.</p>
<p> </p>
<p>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 7<sup>th</sup> harmonic in arpeggios as part of a warm-up routine, yet usually consider it an out-of-tune version of a standard pitch. </p>
<p>Many authors of tutor books for the horn recommend practicing slurs between harmonics going as high as the 16<sup>th</sup> yet avoiding the 7<sup>th</sup>, 11<sup>th</sup>, 13<sup>th</sup> and even the 15<sup>th</sup>. 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 <em>Playing the Horn</em> (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 7<sup>th</sup> 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 <em>Eroica Symphony</em>. In his pamphlet <em>The Horn</em> he referred to the ratio 7:6, the interval between the 6<sup>th</sup> and 7<sup>th</sup> 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 7<sup>th</sup> harmonic. Additionally I have heard a number of professionals slurring through to the 8<sup>th</sup> 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 7<sup>th</sup> and Grade Four includes the 11<sup>th</sup> 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 7<sup>th</sup> harmonic such as Randall E. Faust in his works <em>Harmonielehre</em> (1996) and <em>Prelude</em> (1977). Works by composers Britten and Ligeti are referred to in later sections (1.5, 1.6).</p>
<p>A similar situation is evident for other brass instruments: the 7<sup>th</sup> 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 7<sup>th</sup> harmonic are studies or slurring exercises. The recent book by John Foster includes some 7<sup>th</sup> and 14<sup>th</sup> harmonics in the section titled “Studies on the harmonic series” (2010: 21). A 1938 tutor book by Earl Irons includes the 7<sup>th</sup> harmonic in ten groups of slurring exercises (1966). Richard Hodges technical studies for treble clef brass instruments include the 7<sup>th</sup> harmonics in eleven exercises (2005: 57-62). I have not come across any compositions for trumpet that ask for the 7<sup>th</sup> harmonic to be played as it naturally occurs.</p>
<p>Trombonists do not shy away from using the 7<sup>th</sup> harmonic in slide positions other than first position though will adjust the slide a bit higher than usual to temper it. They use the 7<sup>th</sup> 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 7<sup>th</sup> harmonic rather than the 9<sup>th</sup> or 10<sup>th</sup> can help. Additionally, minimising slide movement can make many passages more manageable. </p>
<p>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 7<sup>th</sup> 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.</p>
<p> </p>
<p><strong>Example 1. Slurring across the grain in Frank Martin’s Ballade for Trombone and Piano.</strong></p>
<p><img src="//d10j3mvrs1suex.cloudfront.net/u/399265/eb0e6c32c29c1928c8b62801ff9e04cfc8f8756d/original/ballade.jpg/!!/b%3AWyJyZXNpemU6MzYwM3gxMDU1Il0%3D.jpg" class="size_orig justify_inline border_" alt="" height="1055" width="3603" /></p>
<p> </p>
<p>An example of trombone playing that does not temper the 7<sup>th</sup> harmonic is found in Stuart Dempster’s recording <em>Underground Overlays from the Cistern Chapel</em> (1995) and in other compositions in live performances he has given. His piece for the MiniMax Festival 29 July 2002 in Brisbane was titled <em>Twenty Tantalizing Titillating Trombones Tooting Turbine Tonics </em>(2002).In the same concert a trombone quartet performed Robert Davidson’s <em>Tibrogargan Round</em> (2002) also using natural 7<sup>th</sup> harmonics.</p>
<p>Exploration by brass players of the many intervals and chords that can be associated with the 7<sup>th</sup> harmonic is extremely rare. Higher prime numbered harmonics receive even less examination. A musician wishing to use the 7<sup>th</sup> 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 7<sup>th</sup> harmonic in new musical contexts requires additional practice.</p>
<p>Groups of instrumentalists that use the 7<sup>th</sup> harmonic unashamedly are the <em>cors de chasse</em> (<em>trompes de chasse</em>)<em>. </em>Alphorn players also play the natural 7<sup>th</sup> harmonic and both groups of players will use harmonics as high as the 16<sup>th</sup> therefore these instruments will receive more attention in Section 1.6. </p>
<p>The bugle is a natural labrosone that has an available 7<sup>th</sup> 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, 8<sup>th</sup> harmonic, is never used. This is due to it having a larger bore than a trumpet (Bate 1966: 6-7). </p>
<p>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 2<sup>nd</sup> harmonic (Baines 1993: 27). Orchestral trumpets and horns at that time equated this written note with the 4<sup>th</sup> harmonic, therefore their high written C was played on the 16<sup>th</sup> 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 8<sup>th</sup> or 9<sup>th</sup> harmonic to cover standard repertoire. </p>
<p>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 <em>Le Sacre du Printemps</em> (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 10<sup>th</sup> harmonic for its fuller tone rather than a shorter trumpet. </p>
<p>The need to extend much higher than the 8<sup>th</sup> 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 <em>Symphony no.3 </em>(n.d./1850) does not require higher than the 8<sup>th</sup> harmonic for the E-flatalto trombone though some players choose to use the tenor trombone for this work. This would require the 12<sup>th</sup> harmonic of the B-flat instrument. A few other examples of higher writing to the 12<sup>th</sup> 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.</p>
<p>There is, or used to be, a certain psychological aspect to considering the 8<sup>th</sup> harmonic the upper limit of modern brass instruments other than the horn. The 8<sup>th</sup> 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 8<sup>th</sup> 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 9<sup>th</sup> harmonic of valve 2 and the D as the 9<sup>th</sup> harmonic of the open tube, slide positions 2 and 1 respectively. Going higher still, playing the written D-sharp and E as 10<sup>th</sup> harmonics may result in intonation that sounds too low for many contexts. These notes could be played as 12<sup>th</sup> harmonics on longer tubes, making the tuning sharper. The disadvantage is that the 12<sup>th</sup> harmonics are more difficult to produce with as much pitching accuracy.</p>
<p>The vast body of western repertoire for standard brass other than the horn does not extend beyond the use of the 8<sup>th</sup> 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. </p>
<p>The <em>serpent </em>and the <em>ophicleide</em> 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 1<sup>st</sup> and 4<sup>th</sup> 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 8<sup>th</sup> harmonic.</p>The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727362019-08-12T10:00:00+10:002022-05-11T09:42:47+10:0036 divisions played on the French Horn
<p>In a previous post I looked at playing 19 equal divisions of the octave on my horn with a modified stopping valve slide. My composition <em>Epictetus The Younger</em> uses a few pitches from the 36-division equal system. This piece is for standard B-flat trumpet and piano and can be played by French horn and piano.</p>
<p>The usefulness of this 36-division system is that there are 12 notes in common with a standard tuned piano. The usefulness of this for brass player is being able to play in duet with a pianist. This is also useful for students who may wish to begin exploring microtonality and have easily accessible reference pitches. Often students in their last year or two of high school find it musically rewarding to work with a pianist and ofter that pianist is a professional musician, and often of high calibre. Microtonality without easy reference pitches can be quite daunting. Of course, compositions can include computer generated music. Having another musician to work with can be a rich and wonderful experience, hence my interest in combining a pianist along with the microtone-producing musician.</p>
<p style="text-align: center;"><strong>It seems worthwhile to consider playing all 36 notes on the horn.</strong></p>
<p style="text-align: left;">I currently have two instruments with stopping valve. One is a B-flat single, the other a full double horn in F and B-flat. Both now have short slides attached to the stopping valve. The slides are short enough to produce reliable quartertones and can be easily extended to give the longer (63cent) semitone for 19 equal divisions. Neither slide can provide the 33cent step but can provide the 66 cent step. </p>
<p style="text-align: left;">The way to provide the 33 cent step is to sue the double horn and tune the entire F horn lower by 33 cents. The B-flat horn provides all the tones and semitones of the 12 equal divisions, and the short slide the steps that are 66 cents lower.</p>
<p style="text-align: left;"> <img src="//d10j3mvrs1suex.cloudfront.net/u/399265/c395ccbecc0c679e19e523234c43c8564e12b645/original/blog-36-edo-chart.jpg/!!/b%3AWyJyZXNpemU6MjA2MXg5NzEiXQ%3D%3D.jpg" class="size_orig justify_inline border_" alt="" height="971" width="2061" /></p>
<p style="text-align: left;">etc.</p>
<p style="text-align: left;"> </p>
<p style="text-align: left;"> </p>
<p style="text-align: left;"> </p>
The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727352019-02-25T11:00:00+11:002022-05-25T09:28:53+10:00‘Brass’ instruments that can play the 5th harmonic
<p> </p>
<p>The <em>la-pa</em> in China also known as the <em>tongjiao</em> has a range of harmonics 2 to 5 (Sachs 1964: 238). It is made of telescoped metal sections, like the Tibetan <em>dung-chen</em> yet is shorter. The same instrument in Taiwan is used in shadow play accompaniments. Harmonics 3 and 4 are most played, occasionally the 5<sup>th</sup> harmonic is added.<sup>1</sup></p>
<p> </p>
<p>Many labrosones are made of wood yet those previously discussed are played producing only one or two harmonics. Carved and fashioned from a manuka tree in New Zealand, the pūkāea can be as long as 2.5 metres with 5 or 6 harmonics available, the player “readily sliding between these to create a spine- chilling sound” (said Flintoff). This sliding technique seems to be unique, as far as this author knows.<sup>2</sup></p>
<p> </p>
<p>Field or military trumpets can be viewed as part of an evolutionary process in the use of brass instruments in Europe. Up to the eleventh century players went no higher than the 3<sup>rd</sup> harmonic. Between then and the thirteenth century players introduced the 4<sup>th</sup> harmonic. As higher harmonics continued to be introduced players began to specialise in particular registers. In trumpet ensemble music for five or ten players of the late 1500’s, the alto e basso part contained only the 3<sup>rd</sup>, 4<sup>th</sup> and 4<sup>th</sup> harmonics. Below this the players of the basso part provided the 2<sup>nd</sup> harmonic and the vulgano part the 3<sup>rd</sup> harmonic. Above these three the sonata part (quinta or principale) provided the main melody on harmonics 4 to 8 and the clarion part (soprano) was improvised using harmonics 8 to 13. The players of field or military trumpets in the 1500s used a combined range of the lower three parts of the ensembles just referred to, producing calls with harmonics from the 2<sup>nd</sup> to the 5<sup>th</sup>.<sup>3</sup></p>
<p> </p>
<p>An interesting example of the use of modern instruments being played like Field trumpets is in Ben Neill’s work <em>Antiphony</em>. Four trumpet parts each have notes equivalent to harmonics 3, 4 and 5. The lowest trumpet part is in the key of B-flat, the next in C, then D, then F. <em>Antiphony</em> can be viewed as a polytonal work or as a combination of tones all in the same key. The 4<sup>th</sup> harmonic from each trumpet part makes up a ratio of pitches that form harmonics 8, 9, 10 and 12 of the B-flat series.<sup>4</sup></p>
<p> </p>
<ol>
<li>
I gathered this information from authors Thrasher, Sachs, Baines.My thesis (2011, University of Wollongong) is available online and has all the sources cited appropriately.</li>
<li>Author Filntoff for info in this paragraph.</li>
<li>Author Tarr is the source for info in this paragraph.</li>
<li>Author Gann is the source here.</li>
</ol>
The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727342018-10-06T10:00:00+10:002021-07-12T11:39:45+10:00Third-tones (and 6th-tones) for trumpet to combine with a piano part
<p>I recently performed the compositions <em>to observe sea and sky</em> by Donald Bousted. He wrote it for the flute to play in 12 equal divisions of the octave (standard tuning) and the horn in 19 equal divisions of the octave. This combination worked well and I got to thinking about how close the divisions of 19 are to dividing a whole tone into 3 parts. This gives 18 divisions of the octave, basically a modified whole tone scale. I don't really want to write in whole tone scales, though of course there are only two required to provide a standard 12-tone chromatic scale. </p>
<p>One of the issues I deal with is writing for standard instruments and I am working on writing a piece for trumpet to be potentially performed in a high school final exam. Often in such exam situations a performer likes to work with piano in part for support both energetically and in sound, in part for the musical interaction and in part because the piano can give the other player a rest from time to time. My next thought about the possibilities a player could have when using a standard trumpet with movable 1st and 3rd valve slides. It seems to me that a trumpeter could play 1/6th tone variations of all chromatic notes in the middle octave reasonably easily. Donald Bousted and Stephen Altoft have shown how the standard trumpet can provide 1/4 tones, though not at great speed (https://donaldbousted.com/2015/08/22/the-4-valve-microtonal-trumpet/). So, I'll have to be careful how I write for a trumpet which is essentially playing 36 divisions of the octave.</p>
<p>The piano provides pitch stability over 12 tones each octave and the trumpet can provide additional pitches. So here is a computer generated audio extract (using Dorico notation program), from my first steps into this realm: the first 40 seconds of a piece called <em>Epictetus</em> (named after the great Greek philosopher.</p>
<p><a href="/files/539227/01-epictetus-first-40-seconds.mp3" data-imported="1">01_Epictetus_first_40_seconds.mp3</a></p>
<p>Here is the example in notation.</p>
<p><a href="/files/539228/epictetus-bars-1-9.jpg" data-imported="1">Epictetus_bars_1-9.jpg</a></p>
The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727332018-08-20T10:00:00+10:002022-05-11T09:42:22+10:00Knowing the chords in Just Intonation
<p>The contemporary music quartet LOCANA (Janine Grantham - flute; Rachel Westwood - violin; myself - horn; Matthew Farrell - cello rehearsed in Brisbane on Saturday August 18 and Sunday August 19 in preparation for the Sydney MicroFest 2 in Sydney September 22 and 23. We spent a lot of Sunday practising my composition <em>The Wound</em> even without the other 3 musicians who will take part (Wendy Dixon - soprano; Greg van der Struik - trombone; Edwin Diefes - tuba). Although the parts are without notation errors, the players wanted more help to understand the tuning and the way I have notated the tuning. To assist them I have prepared this chord chart today.</p>
<p><img src="//d10j3mvrs1suex.cloudfront.net/u/399265/c186318dc8552941255aa7474cb7124ebe6d4a2c/original/the-wound-chords-notation-full-score.jpg/!!/b%3AWyJyZXNpemU6NDk1OHg3MDE2Il0%3D.jpg" class="size_orig justify_inline border_" alt="" height="7016" width="4958" /></p>
<p>What I have found useful for the musicians I work with is to keep the symbols on the staff as standard as possible. To assist, I have indicated the number of cents by which each pitch has deviated from standard 12-division notation (7 white, 5 black on the piano - standard note names plus flats and sharps). I also indicate the position of each note in a chord through coloured note heads. </p>
<p>Black indicates the root of the chord. </p>
<p>Light blue indicates the perfect 5th or major 9th (3rd and 9th harmonics). </p>
<p>Red indicates the major 3rd (5th harmonic) and the rare times I used a minor 3rd from the root of a chord, also the major 7th (15th harmonic). </p>
<p>Dark blue indicates the minor 7th from the root (7th harmonic). </p>
<p>Orange indicates the harmonic series 11th from the root (a quartertone below the augmented fourth).</p>
<p>Purple indicates the harmonic series 13th from the root (a little more than a quartertone lower than the major 6th). I prefer the 11th and 13th to look like they are a minor 3rd apart, rather than an augmented 2nd as is the case when the 13th is notated as a minor 6th (13th) from the root and 41 cents higher. That's why I notate the 13th harmonic interval as a major 6th, -59c.</p>
<p></p>
The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727322018-07-31T10:00:00+10:002023-05-27T09:58:48+10:00Horn playing 19-division tuning
<p>In 2017 I worked out how to play 19-equal divisions of the octave on a standard french horn which is pitched in F and B-flat. My solution was to flatten the 1st note of the scale using the right hand. I started on written F (top of the treble staff), which is concert B-flat. Bending this pitch by 63 cents and all lower octave written Fs is easy, though there is a change of tone colour. </p>
<p>The 2nd valve slide is lengthened enough to produce the longer semitone, below written F, of 126 cents, which is not too far from its normal position for tuning a semitone at 100 cents. </p>
<p>The 1st valve slide is shortened slightly to produce a tone lower than written F, of 189 cents, which is 11 cents higher than the standard 200 cent whole tone.</p>
<p>I then tuned the next lower note by using the right hand. </p>
<p><strong>The whole scale of 19 notes can be done with 7 right hand adjustments or less with alternate fingerings (tube </strong><strong>length choices).</strong></p>
<p>Recently I purchased a second hand horn in B-flat with an extra valve and slide. The valve is operated with the thumb and my colleague Ed Diefes, who plays tuba and does brass repairs, shortened the slide so that it can provide good quartertones (50 cent intervals) and also good intervals of 63 cents for playing in 19-division tuning.</p>
<p>This means the tone quality of each note in the octave is a standard quality and other tonal qualities can be ascribed for reasons other than simply playing the required pitch. </p>
<p><img src="//d10j3mvrs1suex.cloudfront.net/u/399265/45b124e50139adccb2b5056e3a3da1bd4a891bb4/original/img-0014.jpg/!!/b%3AWyJyZXNpemU6NDAzMngzMDI0Il0%3D.jpg" class="size_orig justify_inline border_" alt="" height="3024" width="4032" /></p>
The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727312018-05-06T10:00:00+10:002020-08-09T00:48:55+10:00'Brass' Instruments that can play the 3rd harmonic<p style="text-align: center;"><strong>BLOG 11 </strong></p>
<p style="text-align: center;"><strong>‘Brass’ instruments that can play the 3</strong><strong>rd </strong><strong>harmonic </strong><strong>and probably the 2</strong><strong>nd</strong><strong> also</strong></p>
<p> </p>
<p>This blog presents some more exploration of the wide range of instruments that make a sound from the vibrating lips of the player. I found the research really interesting when I did it in 2010. I'm sure there is more to discover . . .</p>
<p> </p>
<p>Players of the kakaki of west Africa use a musical style with abrupt rhythms and pitch changes between the 2nd and 3rd harmonics. The interval between these harmonics is often wider than a perfect 5th. The kakaki are made of various metals from brass to the tin from petrol cans according to Anthony Baines in his 1993 publication <em>Brass Instruments: Their History and Development, </em>(see page 76). </p>
<p> </p>
<p>Many instruments in Asia would seem to be played in the same way as the kakaki such as the kombu from the Kerala district of India which is C-shaped and “is treated as a percussion instrument adding to the orchestral clamour” says Reck in his review of “Drumming and Chanting in God's Own Country: The Temple Music of Kerala in South India” 2003, <em>Yearbook for Traditional Music</em>, vol.37, pp181-182. </p>
<p> </p>
<p>There are other names for similar instruments throughout Asia such as karna, plural karnai, or karnāl. Baines suggests the tradition of the kakaki goes back at least to the fifteenth century and probably back to the eleventh century. Edward Tarr’s research shows us that trumpets were only the straight type in the eleventh century and it is assumed that players used one or two notes, the 2nd and 3rd harmonics .(I read this in the translation of his book <em>Die Trompete, </em>published in 1988 as <em>The Trumpet.</em>) In the eleventh century there was little difference between European and Moslem trumpets (see Baines again, pages 79-80), although the trumpet was perhaps better established in Moslem countries, providing music “on a grandiose scale” said Farmer in 1957 in his article ‘The Music of Islam’ from The New Oxford History of Music. It wasn’t until after the resurrection of the Roman tuba from the tenth to twelfth century in North Italy that trumpets in Europe began their long development and the range increased (again see Baines 1993: 73).</p>
<p> </p>
<p>Long trumpets had much the same function in the ancient world of the Mediterranean: they were used as signalling devices and to indicate military strength. Some of the trumpets we know of are the Egyptian šnb; a silver and a bronze trumpet from Tutankamen’s tomb; the Assyrian and Hebrew ḥaṣoṣerah and the Greek salpinx. All of these were straight trumpets between 47 and 58 centimetres long. This info I found in Sarkissian’s article in<em> The Cambridge Companion to Brass Instruments</em> 1997: 13. The salpinx was also used for musical contests, according to Scott in<em> The New Oxford History of Music </em>1986: 406-7. </p>
<p> </p>
<p>The interchangeable names lituus and bucina stood for a bronze hooked instrument that came to Rome from the Etruscans before the first century BC, later the name referred to an animal horn instrument. There were two other types of Roman trumpets, the tuba and cornu, also originating from the Etruscans. Thecylindrical tuba was up to 1.3 metres long and sounded the attack and retreat; the bronze, curved cornu sounded the relief for sentries. (Meucci has more on this in the article ‘Roman Military Instruments and the Lituus’, The Galpin Society Journal.) A surviving bronze lituus in the Vatican is 1.4 metres long. Experiments with replicas show that 6 harmonics can be produced on it as shown by McKinnon (see ‘Lituus’, The New Grove Dictionary of Music and Musicians 2001: 11).In the Middle East sometimes a name appears in more than one context and applies to distinctly different instruments. This contrasts with a prior example in which the same instrument has a number of names. Meucci and Ibsen al Faruqi commented that “many Arabic words at various times indicated a straight trumpet” this quote from Sarkissian and Tarr in <em>Grove Music Online, </em>who also provide the next bit of research:. Other names include anfar and būq, the latter more likely to refer to a horn from an animal.</p>
<p> </p>
<p>Some African instruments made from the horns of animal such as the sable antelope, the kudu or the gemsbok have an available 1st harmonic as well as the 2nd and 3rd harmonics. Just as the metal or wood instruments have a stretched interval between the 2nd and 3rd harmonics, these animal horn instruments have a stretched octave between the 1st and 2nd harmonics (Baines 1993: 45). </p>
<p> </p>
<p>Shofar is the name for the instrument fashioned from an animal horn by Jewish groups</p>
<p>such as the Yemenites and Ashkenazim. The Yemenites use the horn from the kudu whilst other Jewish groups use the shorter horn from a goat or ram. Many groups play them at any time of rejoicing though the Ashkenazim use them only for ceremonial events. In such cases the shofar player presents the four main calls using two pitches: harmonics 2 and 3.</p>
<p>Montagu acknowledges the interval between the two pitches on any particular horn may be as narrow as a fourth or as wide as a sixth “yet they are always regarded as the 2nd and 3rd harmonics” (<em>The New Grove Dictionary of Music and Musicians Grove</em> 2001).</p>
<p> </p>
<p>There is no evidence to suggest that players of long trumpets in Europe ventured higher than the 3rd harmonic before the eleventh century. Sometime after that the first four</p>
<p>harmonics were used. Indications come from current experts’ understanding of the earliest written music and a clear statement to that effect made by Johannes de Grocheo c1300 (Sarkissian 2007 <em>The Cambridge Companion to Brass Instruments</em>). In the late fourteenth century instrument makers developed the skill of bending and folding metal. The earliest</p>
<p>depiction of an ‘S’ shaped trumpet is thought to be 1379 (Sarkissian 2007). This allowed important changes to trumpet design. Up till then players were confined to holding up straight trumpets with a useable length of around 150 centimetres (see Steele-Perkins’s book T<em>he Trumpet</em> 2001: 5-7). With the new craft of metal bending the overall tube length could be greatly extended and players experimented with a larger number of available harmonics. The twice-folded ‘natural’ trumpet was produced early in the fifteenth century</p>
<p>(see Smithers <em>The Music and History of the Baroque Trumpet before 1721</em>, page 35) scarcely changing through to its ‘golden age’ in the baroque period. Also of interest are the trumpets with slides which were being built no later than 1411 (Sarkissian and Tarr) and perhaps as early as 1379 (see Polk’s chapter in <em>The Cambridge Companion to Brass Instruments</em> 1989: 395).</p>
<p> </p>
<p>There seems little doubt that the early Renaissance slide trumpet was the direct ancestor of the trombone and no doubt it was used as a bass instrument in ensembles with two shawms (Steele-Perkins 2001: 26; Polk 1997: 42). Late in the fourteen hundreds the more practical trombone with its U-shaped slide took over the bass role in such ensembles. The trombone was closely associated with the cornett for a couple of centuries although the trombone's role was not restricted to one consort (see the Glossary in <em>The Cambridge Companion to Brass Instruments</em>).</p>
<p> </p>
<p>From the eleventh century in Europe the cornett has been played with fingering</p>
<p>holes like a recorder yet blown as a brass instrument. It evolved from a basic animal horn, is conical in bore and made of wood or ivory. Virtuosi of the cornett appeared from 1450 and would have needed at least harmonics 1 to 3 to cover a range of two octaves, whilst production of the 4th harmonic would allow for almost three octaves (see Dickey’s chapter in <em>The Cambridge Companion to Brass Instruments</em>). The curved, treble cornett is about 60 centimetres in length and its lowest note, an A just below middle C, is produced with all finger holes closed and can be lipped lower to a G (Baines & Dickey in <em>Grove Music Online</em>).</p>
<p> </p>
<p>The final example in this category is the conch as used in Japan. There it is called the hora by the Buddhist priests who traditionally use harmonics 2, 3 and 4 as well as a falset below the 2nd. This bit of info is in the book by Clark: <em>Sound of the Silk Road: Musical Instruments of Asia</em>.</p>The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727302018-03-21T11:00:00+11:002021-12-27T11:46:15+11:00Nexus of pitch matching between brass and strings
<p><strong>BLOG </strong></p>
<p><strong>Nexus between brass and strings in just intonation</strong></p>
<p> </p>
<p><strong>Temporary conclusion: the best nexus pitch is a C.</strong></p>
<p> </p>
<p>I’ve been composing a just intonation piece for 6 horns and decided to re-write some of it for a mixed ensemble of flute, 2 horns, violin, cello, double bass and soprano. In this blog I’ll show some of the tuning detail and the issues of working with strings and brass. Most of the tuning issues will be the same when composing in equal divisions.</p>
<p> </p>
<ul>
<li>2 main tuning issues</li>
</ul>
<p> </p>
<p><strong>1.</strong>Brass players and wind players determine how to achieve a pitch ratio by calculating the distance below a pitch played without using valves or keys. String players determine how to achieve a pitch ratio by calculating the distance above pitch played on an open string. Brass players and other wind instruments players <strong>do </strong>something additional to using the open tube resulting in the pitch lowering, ie. put down a finger onto a valve or key and the pitch goes down. String players <strong>do </strong>something additional to using the open string resulting in the pitch raising, ie.put down a finger onto a string and the pitch goes up.</p>
<p> </p>
<p><strong>2.</strong>Tuning issues arose in this particular composition due to conceiving the original work for horns.</p>
<p> </p>
<p><strong>1. </strong>Brass: establish a relationship between the main tube length and a pitch in the composition. Tune the valve slides to other pitches in the composition.</p>
<p>Strings: establishing a starting pitch with at least one open string matching a particular pitch in the composition.</p>
<p>Find a nexus between the two.</p>
<p> </p>
<p><em>Example: tune strings to brass: </em></p>
<p>Starting pitch B<sup>♭</sup> (central reference pitch or perhaps the tonic) for trumpets, trombones, B<sup>♭</sup> side of the standard double (french) horn, some tubas, euphoniums, baritones. </p>
<p>Call this pitch the ratio 1:1 and tune it in ‘normal’ relation to A=440Hz. </p>
<p>Match the D string of orchestral strings (violins, violas, cellos, double basses) to the 5:4 ratio. This would mean the D string would be tuned lower than usual. The other strings if tuned normally would also need to be lower than usual.</p>
<p><em>Example: tune brass to strings: </em></p>
<p>Starting pitch D (central reference pitch or perhaps the tonic) for orchestral strings. </p>
<p>Call this pitch the ratio 1:1 and tune it in ‘normal’ relation to A=440Hz. </p>
<p>Match brass B<sup>♭</sup>to the 8:5 ratio. This would mean the B<sup>♭</sup> would be tuned higher than usual.</p>
<p> </p>
<p>A more straightforward nexus comes with tuning brass to the C string of the cello and viola.</p>
<p> </p>
The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727292018-01-13T11:00:00+11:002018-01-15T06:03:47+11:00THIS INSTANT chords
<p style="text-align: center;"><img src="//d10j3mvrs1suex.cloudfront.net/u/399265/bca2aec70341eee205d4c20a0cd4b4b712a96016/original/this-instant-blog-chords.jpg/!!/b%3AWyJyZXNpemU6MzMwNXg0Njc3Il0%3D.jpg" class="size_orig justify_inline border_" alt="" height="4677" width="3305" /></p>
<p style="text-align: center;"> </p>
The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727282017-12-03T11:00:00+11:002023-10-17T01:55:31+11:00'Brass' instruments, fundamentals and 2nd harmonics - Part 2<p style="text-align: center;"><strong>This blog further explores lip vibrated instruments (labrosones) that mostly use only one harmonic</strong></p>
<p> </p>
<p>The <em>dung-chen </em>in Tibet are made of telescoped metal sections and would seem to have a potentially large range due to their length of up to five metres. However, the very wide and flat mouthpiece inhibits this.2 In ritualistic settings two notes are played in a powerful manner, an octave apart. There is info about this in <em>Sound of the Silk Road: Musical Instruments of Asia</em> by M Clark page 123. Precision with pitch does not seem to be a significant issue since dung-chen, customarily played in pairs, are often not in tune with each other. Just as the monk’s vocalisations are part of a meditative and mantric practice wherein each individual sings his lowest note with no direct relation to others, the low note of the dung-chen does not need to have a direct relation to musical surroundings. The importance of the sound is the metaphorical relation to the “terror deities”. It does not matter if the 1st harmonic is not a perfect octave below the 2nd or in tune with the rest of the natural notes. Non- conical trumpets generally do not have a good 1st harmonic due to a lack of optimal resonance, which also does not matter in this context. One source on Tibetan music notation discussed in Grove suggests that three pitches are played. However, Kaufmann states that two of the sounds are dynamic/timbral qualities of one pitch. The lowest note is played either as a distant, mellow sound or a rough roaring sound. The other, higher pitched note is only used in instrumental pieces. This implies the use of the 1st and 2nd harmonics. Most of information I sourced from page 16 of the book Kaufmann's 1975 <em>Tibetan Buddhist Chant: Musical Notations and Interpretations of a Song Book by </em><em>the Bkah Brgyud Pa and Sa Skya Pa Sects</em> and Helffer's Grove entry on Tibetan Musical Notation.</p>
<p><em>Didjeridu </em>players produce a continuous drone through the technique of circular breathing. The main pitch is the fundamental. In addition to a tremendous rhythmic variety provided by players a wonderful repertoire of sounds is made through the interactions of vocalisations with a drone. Generally cylindrical instruments have only the odd numbered harmonics available. The interval between the 1st and 3rd harmonics will be anywhere between a stretched octave and a narrow twelfth. I found some information on this in Knopoff's entry in Grove Online. Also Joe Wolfe has a lot to say about didjeridu acoustics [ <a data-imported="1" href="Wolfe,%20J%20n.d.b,%20Didjeridu%20harmonics,%20accessed%2015%20July%202009,%20http://www.phys.unsw.edu.au/jw/???harmonics.html" target="_blank">http://www.phys.unsw.edu.au/jw/???harmonics.html</a> ]. The 3rd harmonic is most often played at the end of a composition. The next harmonic playable on the didjeridu is the 5th, which will not conform to harmonic series ratios either, and is rarely heard. </p>
<p>Finger holes have been applied to animal horns or short wooden labrosones for at least a millennium. A twenty-two centimetre long ox horn instrument from Sweden is dated to the tenth century. More on this can be found in <em>Grove Online, </em>the entry 'Cornett' by A Baines and B Dickey. Finger hole labrosones when used in folk music are often played without overblowing, requiring only the 1st harmonic. They include the <em>ožragis </em>of Lithuania with two to six finger holes, this from Karaška's 1984 entry in <em>The New Grove Dictionary of Musical Instruments</em>, the <em>sarv </em>of Finland, see Dournon in <em>Handbook for the Collection of Traditional Music and Musical Instruments</em>, the <em>bans </em>or <em>b</em><em>!</em><em>s </em>or <em>bugīr </em>of India (Arnold 1998: 916) whilst the <em>aza rag </em>of Latvia and the <em>rozhok</em><em>3 </em>of Russia may have added mouthpieces. The last information from Marcuse in the 1975 book <em>A Survey of Musical Instruments</em>.</p>
<p>The more well known cornett or cornetto will be examined in a later blog as it can use more than one harmonic. </p>
<p> </p>The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727272017-11-22T11:00:00+11:002017-11-22T15:48:13+11:00SKOLION - a sketch
<p><strong>The workings of a new composition: SKOLION for 6 horns in 13-limit just intonation.</strong></p>
<p>This sketch starts with muted horns playing a concert F chord (written C): root as 2nd harmonic plus 3rd harmonic, 5th harmonic, 7th harmonic and 11th harmonic. This 11th harmonic becomes the 14th harmonic of a new root, the ratio 13:7. the original chord is then repeated with an 8th harmonic rather than a 7th harmonic. This 8th harmonic (written C) becomes the 11th harmonic of a new root, the ratio 16:11. Chords change in the same way throughout the excerpt. Different unmuted horn parts take turns in playing short melodies. Each section and melody is successively longer than the previous.</p>
<p>The recording is a bit scratchy, as it is a homespun one.</p>
<p><iframe frameborder="no" height="300" scrolling="no" src="https://w.soundcloud.com/player/?url=https%3A//api.soundcloud.com/tracks/359352803&color=%23ff5500&auto_play=false&hide_related=false&show_comments=true&show_user=true&show_reposts=false&show_teaser=true&visual=true" width="100%"></iframe></p>
<p>Here is the first segment in notation.</p>
<p>The colours help to identify the position of notes in the chord, relative to a root (or fundamental in a harmonic series). Light blue shows 3-limit intervals, such as the 3rd harmonic or 9th harmonic (perfect 5ths, 12ths and major 2nds and 9ths in chords); red shows 5-limit intervals such as the 5th harmonic (major 3rds and 10ths in chords); dark blue shows 7-limit intervals such as the 7th harmonic (minor 7ths in chords); orange shows 11-limit intervals such as the 11th harmonic (neutral 4ths and 11ths in chords); purple shows 13-limit intervals such as the 13th harmonic (neutral 6ths and 13ths in chords). [These colours are the ones Robin Hayward uses in his Tuning Vine <a href="http://www.tuningvine.com" target="_blank" data-imported="1">http://www.tuningvine.com</a>.]</p>
<p><img src="//d10j3mvrs1suex.cloudfront.net/u/399265/d0ac888a97024ef3d8537dd4aeba2e6b13f0c912/original/skolion-sketch.jpg/!!/b%3AWyJyZXNpemU6MjIzNngzMTQ4Il0%3D.jpg" class="size_orig justify_inline border_" alt="" height="3148" width="2236" /></p>
<p> </p>
The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727262017-11-07T11:00:00+11:002017-11-08T02:54:11+11:00'Brass' instruments, fundamentals and 2nd harmonics
<p style="text-align: center;"><strong>Welcome to a blog about 'brass' instruments that use one harmonic</strong></p>
<p style="text-align: left;">It would be just as accurate to call a trumpet a metal didjeridu as to call a didjeridu a wooden trumpet! Therefore a conch is a shell trumpet and so on. A few blogs entries ago I used the word labrosone to refer to all instruments that require the buzzing of the lips (8th October 2017). The blog also included a chart of a large number of instruments and the harmonics they use, classified by the upper prime numbered harmonic. This blog with explore a few of the labrosones that use the fundamental or the 2nd harmonic.</p>
<p><em>Conchs </em>and <em>tritons </em>are of interest. Anthony Baines, in his book <em>Brass Instruments: Their History and Development</em> states that it is the fundamental of a conch that is most likely to be sounded, due to its resonance (page 42). Sometimes a second, non-harmonic note is played up to a fourth lower than the main note. This is achieved by allowing the embouchure to vibrate below the optimal resonance of the harmonic. The technique is called playing in falset by Baines and the pitch is referred to as a factitious note (page 36). The same technique is used on standard brass instruments. Another technique of conch players involves placing the hand, or an object, in the bell to change the pitch and tone colour as done in traditional Maori conch playing. You can read more about this in the beautiful book <em>Taonga Puoro: Singing Treasures </em>by Brain Flintoff 2004. Players throughout the world use this technique, some adding wooden or bamboo mouthpieces to provide lower pitches (Baines 1993: 43). Larger conchs may be sixty centimetres long due to the spiral shape inside and therefore have three or four harmonics available (Baines 1993: 42). Examples of such extended use can be heard in Japan and will be explored in a later blog.</p>
<p>Many other instruments are traditionally played sounding one pitch only such as the wooden <em>kul </em>of Papua New Guinea (Sentā & Hakubutsukan 1989) and the <em>mabu </em>of the Solomon Islands, both being used to instil a fighting spirit. I found info about the <em>kul</em> in The JVC/Simthsonian Folkways Video Anthology of World Music and Dance and the <em>mabu </em>in Baines' book.</p>
<p>Players of longer instruments may be able to produce a number of pitches yet be bound by tradition to sound but one. This is the case for players of the <em>titiru </em>trumpets in Wayana, South America. Playing more than one pitch is considered bad taste! This info is in The Garland Encyclopedia of World Music, vol.2, an article called ‘The Distribution, Symbolism, and Use of Musical Instruments’.</p>
<p>In some parts of Africa melodies are produced through the combination of a number of instruments, each player producing one pitch. In the Alur region of Uganda <em>agwara </em>can be as long as three metres though only one pitch is played on each. A pentatonic scale is created from the combined pitches, melodies arising in a hocket fashion. An excerpt from the <em>JVC/Smithsonian Folkways Video Anthology </em>shows all this clearly and more info can be found in the article ‘Side-blown Trumpet’, <em>The New Grove Dictionary of Music and Musicians Grove.</em> Similar types of ensembles are present in other parts of Africa. A complete ensemble of <em>waza </em>has ten, sometimes twelve instruments in Sudan. I found this info in the article ‘Music in Sudan’, Garland Encyclopedia of World Music. Bands using the ivory horns in Congo, also present melodies in hocket fashion (Baines 45-6), as do the ensembles in Ghana playing the <em>ntahera </em>(info in ‘The Hocket-Technique in African Music’, Journal of the International Folk Music Council and ‘West Africa: An Introduction’, Garland Encyclopedia of World Music.</p>
<p>A similar technique was used over a period of sixty to seventy years from 1757 in Russia, bands of hunting horns were used to present standard western music in a similar manner to the ensembles mentioned above. The players were instructed to produce only one harmonic. Later each player learnt to provided two harmonics an octave apart. Additionally they inserted the hand in the bell to produce pitches a semitone below each harmonic. Thus each player could provide four pitches. One band had thirty-two players, giving the arranger a pitch range of several octaves (Baines, 1993: 176-7). This tradition has been reinvigorated in recent times by Sergey Peschansky and the group Russian Horn Cappella. Checkout their Facebook page: [<a href="https://www.facebook.com/horncapella.spb/" target="_blank" data-imported="1">https://www.facebook.com/horncapella.spb/</a>]. A similar tradition exists in Lithuania with the ensemble members playing the wooden <em>ragai </em>and forming a scale by the pitches of the various sized instruments. Info on this is in the article ‘Ožragis’, The New Grove Dictionary of Musical Instruments and ‘Lithuania’, Garland Encyclopedia of World Music.</p>
<p>There are more instruments in this category to explore, however I like to keep each blog reasonably short so will do a post on Tibetan, Australian and finger hole instruments later.</p>
<p> </p>
<p style="text-align: left;"> </p>
<p style="text-align: left;"> </p>
The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727252017-11-01T11:00:00+11:002022-04-26T22:37:59+10:00Grady and Brass
<p><strong>Welcome to the 1st Guest Blog - Kraig Grady</strong></p>
<p style="text-align: center;"><em>I've known Kraig for a few years now, since he came to live in Australia. </em><em>Kraig composes using just intonation, designs and builds instruments, redesigns existing instruments, retunes instruments, designs and builds shadow theatre characters and props, writes stories for them, and plays mallet instruments. Kraig has composed a couple of pieces that I've been involved in and we've done a couple of improvisation sessions. It's a great delight to bring you some of his thoughts on writing for horn. </em></p>
<p>This is probably more a testimonial of the wonderful opportunity that has been opened by Dixon’s own development of the French horn as an extended microtonal instrument.</p>
<p>My use of brass instruments have been somewhat limited. It has been a rewarding one especially with this blog’s host. I’ve also had a rewarding interaction with trumpet player Kris Tiner. Compositionally, in both cases, I approached it more like Duke Ellington in writing for the player as much as the instrument. In both cases, it is the player’s excellent ears that have made music possible, allowing for the passing from notation to sounding the desired note. </p>
<p>This last feature was used with both Tiner and Dixon playing against a tuner to play specific pitches. These were then cut and pasted into compositions that only exist as recordings. A strange form of ‘acoustic’ electronic music. While not to the liking of many purists, such work serves the purpose of allowing the players to hear the tuning in a musical setting making it much easier to play live. Something I have even witnessed players using some of these intervals in their own improvised music. </p>
<p><em>Relentless Tangents </em>was instead a piece to be played live using the horn with flute, violin and cello. Having worked with Dixon in the past, I could think about composing the music as opposed to being concerned about how he was to get the pitches. This I left up to him and the other players. </p>
<p><em>A Weathered Petroglyph </em>(<a href="https://silentrecords.bandcamp.com/track/a-weathered-petroglyph" target="_blank" data-imported="1">https://silentrecords.bandcamp.com/track/a-weathered-petroglyph</a>) and still to be released <em>A Molten Wind </em>involved a quite extreme challenge. The scale called Copan involves superhuman harmonics in the hundred of thousands. A technical page on the tuning can be found here [<a href="http://anaphoria.com/copan.html" target="_blank" data-imported="1">http://anaphoria.com/copan.html</a>] for those interested in such things. Both these required the Horn player to match the tones of a 19-tone scale that clustered around 8 tones with small deviations as small as 13 cents (that is about a 7<sup>th</sup> or 8<sup>th</sup> of the smallest note of a piano). Thus it is scale that at this point would be hard to do live. While working with the recordings of especially Dixon’s tones, I explored extending the range of the horn downward that quite unintentionally resembled a didgeridoo. Again this might offend the purist of the instrument but it serves a purpose in extending the range as something for instrument designers and creators to think of. It seems the use of electronics has stopped the further development of acoustic instruments when it should encourage it, so that was the purpose. Perhaps it points to the possibilities of new instruments too. The process is more than sampling because one is working with a very specific person and the small gestures that a player makes becomes an integral part of the composition.</p>
The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727242017-10-23T11:00:00+11:002022-05-20T18:32:38+10:00Horn Harmonics (to the 7th) and simple chords<p><strong>Welcome to BLOG 6 on using horn harmonics (including the 7th) to play simple chord progressions with 7th chords.</strong></p>
<p>Good tuning is possible by players of even modest ability. The harmonics of the horn can be used to help hear and play simple chords nicely in tune. A good, steady, well focused tone is the main requirement, then the natural resource of the horn can do most of the subtle tuning. A standard double horn provides, easy to play major triads in the middle range in 11 keys. These can all be played with harmonics 4, 5 & 6. The key of B major (concert pitch) on harmonics 4, 5 & 6 is awkward as it naturally sits a quartertone sharp and some of that good, well focused tone can be lost when bending them lower. Much of this is detailed in the Blog (October 1), <strong>Horn harmonics and simple chords.</strong></p>
<p>Also in the mid range of the horn are many 7th harmonics. These, too, can be accessed by players of modest ability. Students having played for less than a couple of years may not have the strength and steadiness of tone to do this well, but many students beyond that can.</p>
<p>Here is a short sound file of a standard chord progression played by four horns (multitracked at home for convenience). The progression is I-IV-II-V-I. In the music notation example below this is the first one. I used the 5th harmonic of the E horn (2nd valve) to get close to the written Eb which is the 7th of F in chord IV. Otherwise I used 7th harmonics to achieve the 7th of the chord. These achieve a smooth sound; pretty much what good barbershop quartet achieves.</p>
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<p><iframe frameborder="no" height="300" scrolling="no" src="https://w.soundcloud.com/player/?url=https%3A//api.soundcloud.com/tracks/348342303&color=%23ff5500&auto_play=false&hide_related=false&show_comments=true&show_user=true&show_reposts=false&show_teaser=true&visual=true" width="100%"></iframe></p>
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<p>Here is another example, slightly higher in the range for the 1st horn part. This also has a chord with 2 notes tuned as 7 ratios: the root with a narrow minor 3rd and a narrow minor 7th, along with the pure 5th. This is chord two in the second notated example.</p>
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<p><iframe frameborder="no" height="300" scrolling="no" src="https://w.soundcloud.com/player/?url=https%3A//api.soundcloud.com/tracks/348342156&color=%23ff5500&auto_play=false&hide_related=false&show_comments=true&show_user=true&show_reposts=false&show_teaser=true&visual=true" width="100%"></iframe></p>
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<p>Here is the notation of the 2 chord progressions:</p>
<p><img src="//d10j3mvrs1suex.cloudfront.net/u/399265/c13ac1ed8ff22e4da06bb4ef6ed01093d325f3ee/original/blog-6-tetrads.jpg/!!/b%3AWyJyZXNpemU6MjA2NXgyMDQ1Il0%3D.jpg" class="size_orig justify_inline border_" alt="" height="2045" width="2065" /></p>
<p>Enjoy.</p>The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727232017-10-16T11:00:00+11:002017-10-16T16:51:48+11:00Piano, Horn and Microtonality
<p><strong>Welcome to Blog 5 exploring some ways of writing microtonal music that includes the piano, with an example from a new song for soprano, horn and piano. </strong></p>
<p> Here are there basic ways of including the piano in microtonal music with piano: </p>
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<li>Retune the piano <br>
</li>
<li>Exploit 'beatings' between piano pitches and microtones from other instruments </li>
<li>Use piano fixed pitches within a larger pitch universe </li>
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<div>1. When retuning a piano, there needs to be time to do so, money for the piano tuner to do the deed and return the piano to 'standard' tuning afterwards, along with logistical management along with other items on the program.</div>
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There are many examples of retuning pianos and here is a beaut video on YouTube of Alexei Lubimov, Piano. Pierre-Laurent Aimard, Piano. playing the 1st of Charles Ive's <em>Three </em><em>Quarter-tone Piano Pieces. </em>These are now classics, written in 1925.
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<div>There are also many examples of pianos tuned in various forms of Just Intonation, from La Monte Young's <em>Well Tuned Piano</em> and Michael Harrison's <em>Revelation</em> to Ben Johnston's <em>Suite for Microtonal Piano. </em>Here is the 'Blues' movement played by Aron Kallay.</div>
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<div>Another possibility is to use an electronic keyboard that is programmable if the pianist is comfortable using such an instrument. </div>
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2. In this sonic realm the piano retains its standard 12-equal semitones and other instruments or singers provide microtones that 'beat' producing some gorgeous sounds. I was part of a perfomance of Erkki Veltheim's <em>Seance for Orchestra: Prelude and Coda </em>with the Sydney Syphony Orchestra on October 15, where the oboist had to play 'out-of-tune' with the piano far enough to produce audible pitch beats. My piece <em>Five Tastes</em> for clarinet, cello and piano also uses this musical technique. I was about to include a segment of this here, then discovered I don't have a recording of it even though the trio <em>Charisma</em> has performed it three times. The clarinet and cello provide microtonal variations of some piano pitches. In some musical portions, the ear is deceived and it sometimes seems like the piano is 'bent'.</div>
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<div>3. In this compositional method the piano retains its standard tuning yet provides some of the pitches in a larger, microtonal universe. In my trio for soprano, horn and piano <em>You Were Never My Country</em> the piano provides harmonics 3, 9, 17 and 19 of fundamentals A and D, which function as chords I and IV. </div>
<div>The horn and soprano provide harmonics 5, 7, 11, 13 of the same fundamentals and the horn also provides harmonics from B, C sharp, and E flat. </div>
<div>The A is the reference pitch (tonic). A is also the 14th harmonic of a sharp B (231 cents, ratio 8:7);the 13th harmonic of a flat C sharp (359 cents, ratio 16:13; the 12th harmonic of D (498 cents, ratio 4:3); the 11th harmonic of a flat E (649 cents, ratio 16:11); the 10th harmonic of a slightly sharp F (814 cents, ratio 8:5); and the 8th harmonic of A (0 cents, ratio 1:1). </div>
<div>Grevillea Ensemble (Wendy Dixon and David Miller) and I perform this work on October 22. I hope to upload a recording in the near future. </div>
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The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727222017-10-08T11:00:00+11:002021-12-27T11:46:42+11:00Brass Instruments, Harmonics & Prime Limits
<p><strong>Hi and welcome to BLOG 4 which begins an exploration of instruments that are played by buzzing the lips and their modes of vibration, the harmonics. </strong>Such instruments are usually called brass instruments though they don't have to be made of brass. Some are made of wood, conch shell and so on. </p>
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<p>A convenient label is labrosone, a term used in the landmark book <em>Brass Instruments: Their History and Development</em> by musicologist and instrument researcher Anthony Baines (page 40), though I haven't seen it used elsewhere!</p>
<p>I have grouped each instrument by the harmonics a player can produce. This grouping is a new classification of labrosones using the tuning theory of musical pioneer Harry Partch. His book <em>Genesis of a Music</em>, published in 1974, has details of his theories. A prime numbered harmonic is the limit for each category. The reason for this only becomes clear when dealing with the larger context of just intonation. (See my thesis if you are keen: <a href="http://ro.uow.edu.au/theses/3419/" target="_blank" data-imported="1">http://ro.uow.edu.au/theses/3419/</a>.)</p>
Briefly,</div>
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<ol>
<li>each even numbered harmonic is less significant than each odd numbered harmonic</li>
<li>each odd numbered harmonic is less significant than each prime numbered harmonic </li>
<li>each prime numbered harmonic establishes a pitch limit. (Just intonation deals with pitches observed as ratios and have been considered such for millennia, whereas the understanding of harmonics has only been known for a few hundred years.)</li>
</ol>1. Every harmonic that sounds an octave higher than a lower harmonic is also known as doubling the harmonic series number. Harmonic 2 is an octave above harmonic 1, ratio 2:1. Harmonic 4 is an octave above harmonic 2, ratio 4:2. This is invariable. 6:3, 10:5, 14:7 etc. In other words the only new pitch information is the octave which is not so musically significant as music is not made up of only octaves and unisons. </div>
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<div class="column">2. Every odd numbered harmonic provides a new pitch quality though some odd numbers can be observed as multiples of other odd numbers therefore they don't provide as much pitch information as prime numbered harmonics.</div>
<div class="column">Harmonic 3 when played after or at the same time as harmonic 2 produces the wonderful and familiar sound usually called the perfect 5th, and perfect it is indeed when played steadily and with well focused tone. This is shown as the ratio 3:2. Ratio 3:1 is the perfect 12th.</div>
<div class="column">Harmonic 6 is an octave above harmonic 3, so is not a distinctly new sound/interval. </div>
<div class="column">Harmonic 9 gives the sound of adjacent perfect 5ths, such as A to E to B. It also gives the sound of the whole tone (ratio 9:8). Yes, this is a new interval but is a product of 3:2. Chains of 3:2s can provide wondrous music, indeed and large chains can give the sound of any other desired interval, however many unique intervals are discovered easily by exploring other prime numbered harmonics.</div>
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<div class="column">3. Every prime numbered harmonic provides a unique pitch quality. Prime numbered harmonics 2, 3, 5, 7, 11, 13 are easily played on the (French) horn and are achievable on a number of other labrosones. </div>
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<div class="column">One blog each month will look at some instruments that can be classified by each prime numbered harmonic. Later blogs will explore writing music for each instrument type. To start this process the table below shows a number of instruments, many of which may appear unfamiliar, the prime limit they mainly belong to and the length of the instrument.</div>
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The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727212017-10-01T11:00:00+11:002017-10-02T16:05:05+11:00Horn harmonics and simple chords
<p><strong>Hi, and welcome to the third blog.</strong></p>
<p>It is easy to play simple chords, beautifully in tune, in the middle register and higher using the harmonics of the horn. This can be done on any of the 16 tube lengths of the standard double horn. A few are only subtly different from their nearest neighbour and one is a quartertone different from the nearest neighbour. The longest tube length is a quartertone sharper than a long horn in B and is produced on the F horn with all valves pressed. However, it is quite difficult to produce a tone that is not stuffy. The shortest tube length is the B♭ horn. The usual setting of the valve slides then provides the descending chromatic scale, very closely tuned to match an equal tempered chromatic scale. These are shown at the end of this blog.</p>
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<p><strong>Harmonics 4, 5, 6</strong> on each of the horn's tube lengths will usually give a very nicely tuned <strong>major</strong> <strong>triad</strong>. The tuning is even simpler to make true by playing the 5th harmonic slightly softer than harmonics 4 and 6. (Some horns are not as well focused on all tube lengths and some horns are not well focused on any tube length.) Good tuning by playing each harmonic with a well focused tone and no adjustment is possible on many well made horns. </p>
<p>The interval between harmonics 4 and 6 (ratio 6:4 & 3:2) is tiny bit wider than the same interval played on, say a nicely tuned keyboard. Harmonics give 702 cents, keyboard gives 700 cents. This is just enough to eliminate the 'beating' sound. (I can go into this more in a blog, otherwise I recommend the book <em style="font-size: 10px;">Just Intonation Primer</em> by David Doty for a clear explanation of the acoustical reasons for this.) </p>
<p>The interval between harmonics 4 and 5 (ratio 5:4) is quite a bit narrower than the same interval played on a standard keyboard with standard tuning, 14 cents narrower. The harmonics give a beautifully peaceful major 3rd without beats. The wider major 3rd might be considered more shimmering by some. However, the triad from the harmonics sounds strong and vibrant, especially when payed for longer than 1 second.</p>
<p>Here is a sound file of harmonics 4, 5, 6, (ratio 4:5:6) on all 16 tube lengths starting with the shortest.</p>
<p><iframe frameborder="no" height="300" scrolling="no" src="https://w.soundcloud.com/player/?url=https%3A//api.soundcloud.com/tracks/344384151&color=%23ff5500&auto_play=false&hide_related=false&show_comments=true&show_user=true&show_reposts=false&visual=true" width="100%"></iframe></p>
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<p>The interval between harmonics 5 and 6 (ratio 6:5) is quite a bit wider than the same interval played on a standard keyboard with standard tuning. 16 cents wider, where the higher note is 316 cents above the lower note. This minor 3rd is the most vibrant just intonation minor 3rd, yet not the only good one. Interval ratio 32:27 is also good and very useful. It is easy to achieve: Go down a 5th from written C to F (ratio 4:3), down another 5th to B♭ (ratio 16:9), then another 5th to E♭ (ratio 32:27). Change the octave so the E♭ is higher than the original C. The higher note is 294 cents above the lower note, rather than 316 cents.</p>
<p>This can be useful in chord progressions. An example is the use of chord II in a major key.</p>
<p>Here is a simple progression, in triads, of chord I - IV - II - V - I, played four times. </p>
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<p><iframe frameborder="no" height="300" scrolling="no" src="https://w.soundcloud.com/player/?url=https%3A//api.soundcloud.com/tracks/344384151&color=%23ff5500&auto_play=false&hide_related=false&show_comments=true&show_user=true&show_reposts=false&visual=true" width="100%"></iframe></p>
<p>In the first example the 1st part moves between two written As: notes 2 & 3. The small pitch shift is the interval called a syntonic comma. The second example puts the comma into the low horn between notes 3 & 4. The third example avoided the comma shift by dropping all parts down a 3rd between notes 2 & 3. This does result in consecutive 5ths. The fourth example avoids those by making the 3rd chord a II7. A chord progression that avoids IV-II-V will not need any comma shifts, but maybe they are okay!</p>
<p>Here is a pic of the examples for easy study.</p>
<p><img src="//d10j3mvrs1suex.cloudfront.net/u/399265/10c5a7ae5a4ab146cdf9019bff70ef1a021c7063/original/horn-triads-for-blog-3.jpg/!!/b%3AWyJyZXNpemU6MTIzOXgxNzU0Il0%3D.jpg" class="size_orig justify_inline border_" alt="" height="1754" width="1239" /></p>
<p>A later blog will give examples of 7th chords using <strong>7th harmonics</strong> as well as the discordant 7th. Harmonics 8 & 7 together (ratio 8:7) sounds more like a barbershop quartet use of the 7th chord. Harmonics 9 & 8 together (ratio 9:8) gives a biting and exciting discordant sound, such as in Beethoven's <em>Symphony 8,</em> Mov. 1, bar 157 a II7 chord. Interestingly, two bars earlier the horns are also a tone apart (this time played on harmonics 10 & 9, though 1st horn best play a lightly sharper than the harmonic sits) in a diminished7 chord, which looks like a c minor chord in all other instruments except for 1st horn with the concert A. The whole tone can be a powerful sound.</p>
<p>The 16 tube lengths of the standard horn are: </p>
<p>B♭ horn, no valves<br>+Valve 2 = concert A<br>+Valve 1 = concert A♭<br>+Valves 1 & 2 = concert G, slightly sharp (+10 cents, or so)<br>+Valve 3 = concert G, slightly flat (-15 cents, or so, when set for the 2 & 3 combination)<br>+Valves 2 & 3 = concert G♭ (0 cents or +15 cents if the valve slide 3 is set for concert G)<br>+Valves 1 & 3 = concert F, quite sharp (+30 cents or so)<br>+Valves 1, 2 & 3 = concert E, quartertone sharp (+50 cents or so)<br>F horn = concert F, no deviation 0 cents<br>+Valve 2 = concert E<br>+Valve 1 = concert E♭<br>+Valves 1 & 2 = concert D, slightly sharp (+10 cents, or so)<br>+Valve 3 = concert D, slightly flat (-15 cents, or so, when set for the 2 & 3 combination)<br>+Valves 2 & 3 = concert D♭ (0 cents or +15 cents sharp if the valve slide 3 is set for concert D)<br>+Valves 1 & 3 = concert C, quite sharp (+30 cents or so)<br>+Valves 1, 2 & 3 = concert B, quartertone sharp (+50 cents or so)</p>
<p>The cent value is a useful measuring tool to quickly see relative intervals. A semitone has 100 cents and an octave has 1200.</p>
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The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727202017-09-23T10:00:00+10:002017-09-26T15:25:41+10:00Horn Harmonic Series
<p>Last week I looked at using the harmonics of the horn when playing Nielsen's <em>Wind Quintet</em>.<strong> This week I'll pay attention to the number of harmonics playable on the horn and start showing how pitches from the different lengths of tube in the horn can interact with each other.</strong></p>
<p><strong>Here's a short paragraph about the instrument.</strong> Horn parts are almost always written a perfect 5th higher than they sound. The standard instrument from the middle of the 19th century was the F horn with valves so most music for valve horn is written for horn in F. Nowadays a large portion of players use a double horn in B♭and F with 3 valves plus thumb valve yet the music is still written in F. Each valve allows air to vibrate through another length of tube. The second valve slide lowers the pitch of either B♭or F horn by a semitone, 1st valve by a tone, 3rd (or 2 & 1) by a tone and a semitone, 2 & 3 together by two tones, 1 & 3 together by somewhat short of two tones and one semitone, all three by a quartertone short of 3 tones.</p>
<p><strong>Harmonics. </strong>The easiest harmonics to play on the F horn are harmonics 3-12 (written G below the treble staff to the G at the top of the treble staff. The easiest harmonics to play on the B♭ horn are harmonics 2-9 (written F below the treble staff to the G at the top of the treble staff. In the same pitch range the low C horn (F horn plays valves 1 & 3) uses harmonics 4-16. These are not so easy to play as the overall tube length is long and narrow and the sound often a bit stuffy.</p>
<p>The short video here shows these harmonics. Horn in F, Horn in B♭ (high; short), horn in C (low; long). At the end of the video you can hear the F horn harmonics 1-19 to show how the extended range of the horn and the smaller and smaller intervals, progressively through the higher range.</p>
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<p><strong>Matching harmonics</strong></p>
<p>It's easy to achieve a scale of just intonation intervals by matching the tuning of 2 harmonic series. The most obvious is to match the written Cs between the F and Bb horns. The middle C is F horn harmonic 4 and B♭horn harmonic 3. A nice F major scale can be played with just these two horns and is shown in staff notation below. The 4th degree is flatter than normal, for sure.</p>
<p><img src="//d10j3mvrs1suex.cloudfront.net/u/399265/0f519fb78555776aece23c8f4570c5194421f276/original/blog-f-m-scale.jpg/!!/b%3AWyJyZXNpemU6MTA2M3gyMTMiXQ%3D%3D.jpg" class="size_orig justify_inline border_" alt="" height="213" width="1063" /></p>
<p> This is how it sounds:</p>
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<p>Other simple scales can be achieved by slightly adjusting a valve slide. For example, pushing the F horn 1st valve slide slightly in matches so that its harmonic 10 matches the F horn harmonic 9.</p>
<p>(For those interested the ratios of the written C scale are C=1:1, 0 cents D=9:8, 204 cents E=5:4, 386 cents F=27:20, 520 cents G=3:2, 702 cents A♭=63:40, 787 cents B♭=9:5, 1018 cents.)</p>
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<p>Extending the F horn 1st valve slide slightly, so that its harmonic 9 matches the F horn harmonic 8.</p>
<p>(For those interested the ratios of the written C scale are C=1:1, 0 cents D=10:9, 182 cents E=5:4, 386 cents F=4:3, 498 cents G=3:2, 702 cents, A♭=14:9, 765 cents B♭=16:9, 996 cents.)</p>
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<p>In an upcoming blog, I'll show the harmonic series matching of 5 tube lengths to the pitch concert A, as used in my trio <em>You Were Never My Country</em> for soprano, horn and piano. Greviilea Ensemble will perform this on October 22.</p>
The Brass Whisperertag:thebrasswhisperer.com,2005:Post/60727192017-09-17T10:00:00+10:002020-01-09T14:33:35+11:00Horn harmonics, Intonation, Nielsen Wind Quintet.
<p><strong>Hi and welcome to the very first blog of The Brass Whisperer.</strong></p>
<p>I want to share some of the music that has inspired me and fuelled me over the decades: the genre of chamber music. As a performer I love the responsibility, the intimacy and the sheer necessity to be constantly musical. It’s a great joy to have a truly vital role in the recreation of each piece of music. One’s perceptions must be alertly attuned to what every other musician is doing.</p>
<p>I’m not going to rave on for paragraphs about this marvellous collaborative process, rather I want to delve into the <em>Wind Quintet</em> by Carl Nielsen. In particular I want to engage with the variation for horn in the last movement. This brings into play the two main areas of what this blog is all about: playing and writing music for brass music instruments and fine intonation skills including just intonation.</p>
<p>Here is a brief video of myself playing the horn variation. </p>
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<p>Nielsen wrote for Horn in F. Certainly, in Variation IX, using the F horn as much as possible brings out the flavour of the music and sets up the intonation really simply. In the video I used a Richard Seraphinoff horn with an F crook and three piston valves. The music notation shows the pitches with the harmonics played and the tube length used (no valves, each valve or the combination of valves 1 & 2). The colours are similar to what Robin Hayward used in his Tuning Vine. Light blue for all harmonics (3), 6, 9, 12; red for harmonics 5, 10. Light blue harmonics are a little bit sharper than pitches played on a standard keyboard. Red harmonics are significantly flatter than those on a standard keyboard. These small differences add a lot to the flavour, and when played in chords make a wonderful difference.</p>
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<p><img src="//d10j3mvrs1suex.cloudfront.net/u/399265/d495aaae28e882313aa558e8b460ab8abfcd7308/original/blog-1-nielsen-horn-variation.jpg/!!/b%3AWyJyZXNpemU6MTA3NHg3MTYiXQ%3D%3D.jpg" class="size_orig justify_inline border_" alt="" height="716" width="1074" /> </p>
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<p>Playing the horn is all about working with harmonics and subtle tunings.</p>
The Brass Whisperer