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A Study of French Horn Harmonics

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A Study of French Horn Harmonics DIPLOMA IN ACOUSTICS AND NOISE CONTROL A Study of French Horn Harmonics Andy Thompson Submitted for the Institute of Acoustics Diploma in Acoustics and Noise Control 2010 A STUDY OF FRENCH HORN HARMONICS PAGE 1 OF 78 Q: How do you make a trombone sound like a French horn? A: Put your hand in the bell and play all the wrong notes. A STUDY OF FRENCH HORN HARMONICS PAGE 2 OF 78 ABSTRACT • The acoustic theory of sound production and the harmonic series of the French horn are examined. • A summary of how brass instruments function acoustically is presented and related to the theory of resonance in closed-open cylindrical pipes. • The harmonic series produced by a horn is measured and analysed with an FFT analyser. • The horn is modified with various lengths of cylindrical hosepipe to study the effect of the conical mouthpiece and mouthpipe and the flaring bell separately. • The experiments indicate that the mouthpiece, mouthpipe and bell modify the tuning of harmonics of the simple cylindrical pipe in a frequency-dependent manner. • The lowest note playable on the horn is found not to be a natural resonance of the instrument, but a heterodyne tone produced by interaction between the upper harmonics. This note is called the ‘pedal note’. • The mouthpiece and mouthpipe have a relatively small effect on the tuning. The bell significantly changes the tuning of the lower harmonics so that the horn appears to play a full set of odd and even harmonics from the pedal note upwards. A STUDY OF FRENCH HORN HARMONICS PAGE 3 OF 78 ACKNOWLEDGEMENTS I would like to thank the following people: Dr Bob Peters and Hansa Parmar at the IoA for a very enjoyable year studying the IoA Diploma. My colleagues at AJA for general encouragement, their (apparent!) interest, and putting up with the dreadful noises required to produce this project! Particular thanks to Andy Pearce for proofreading. Stephen Cox for the loan of textbooks. Andy Taylor of Taylor Trumpets for a very interesting discussion on the subject of instrument building. Last, but not least, Sarah, Anna and Emily for their love and support. A STUDY OF FRENCH HORN HARMONICS PAGE 4 OF 78 CONTENTS 1 INTRODUCTION.......................................................................................................................... 7 1.1 SCOPE ............................................................................................................................................... 7 1.2 STRUCTURE OF THIS PROJECT ............................................................................................................ 7 1.3 A NOTE ON NOMENCLATURE............................................................................................................. 8 2 THE FRENCH HORN ................................................................................................................ 10 2.1 ORIGINS AND DEVELOPMENT .......................................................................................................... 10 2.2 THE MODERN INSTRUMENT ............................................................................................................. 14 2.3 METHOD OF PLAYING ...................................................................................................................... 16 2.4 NOTES PRODUCED BY THE INSTRUMENT ......................................................................................... 19 2.5 REPERTOIRE .................................................................................................................................... 19 2.6 QUIRKS OF THE INSTRUMENT .......................................................................................................... 20 3 THE PHYSICS OF SOUND PRODUCTION ........................................................................... 22 3.1 OVERVIEW ...................................................................................................................................... 22 3.2 THEORY – THE CLOSED -OPEN CYLINDRICAL PIPE ............................................................................ 23 3.3 THEORY – THE CLOSED -OPEN CONICAL PIPE ................................................................................... 24 3.4 INPUT IMPEDANCE .......................................................................................................................... 26 3.5 PRODUCING THE VIBRATIONS - THE FUNCTION OF THE LIPS ............................................................. 27 3.6 NON -LINEARITY OF THE LIP VIBRATION ........................................................................................... 29 3.7 ‘R EGIMES ’ OF OSCILLATION ............................................................................................................ 29 3.8 PEDAL NOTES .................................................................................................................................. 31 3.9 EQUIVALENT CONE LENGTH ............................................................................................................ 32 3.10 SECTIONS OF THE INSTRUMENT ....................................................................................................... 34 3.11 MOUTHPIECE AND MOUTHPIPE ........................................................................................................ 34 3.12 CYLINDRICAL TUBING ..................................................................................................................... 36 3.13 VALVES / TUNING SLIDES ................................................................................................................ 37 3.14 FLARE / BELL .................................................................................................................................. 37 4 EXPERIMENTS .......................................................................................................................... 42 4.1 OVERVIEW ...................................................................................................................................... 42 4.2 METHODOLOGY .............................................................................................................................. 42 4.3 MEASUREMENT EQUIPMENT AND ANALYSIS .................................................................................... 44 4.4 RESULTS – HORN ............................................................................................................................. 46 4.5 RESULTS – HOSE MOUTHPIPE / HOSE BELL ....................................................................................... 48 4.6 RESULTS – HORN MOUTHPIPE / HOSEPIPE BELL ................................................................................ 51 4.7 RESULTS – HOSE MOUTHPIPE , HORN BELL ....................................................................................... 54 A STUDY OF FRENCH HORN HARMONICS PAGE 5 OF 78 5 ANALYSIS ................................................................................................................................... 57 5.1 GENERAL OVERVIEW ...................................................................................................................... 57 5.2 THE LOWEST HARMONIC ................................................................................................................. 58 5.3 MEASURING THE REAL FUNDAMENTAL ........................................................................................... 61 5.4 EFFECT OF THE HORN MOUTHPIPE ................................................................................................... 65 5.5 EFFECT OF THE BELL ....................................................................................................................... 67 5.6 SOURCES OF ERROR ........................................................................................................................ 68 5.7 FURTHER WORK .............................................................................................................................. 68 6 CONCLUSIONS .......................................................................................................................... 70 APPENDIX A – REFERENCES / BIBLIOGRAPHY....................................................................... 71 APPENDIX B – INSTRUMENT MANUFACTURE ........................................................................ 72 APPENDIX C - MEASURING EQUIPMENT .................................................................................. 75 APPENDIX D – CD CONTENTS ....................................................................................................... 76 APPENDIX E – GLOSSARY OF TERMS ........................................................................................ 78 A STUDY OF FRENCH HORN HARMONICS PAGE 6 OF 78 1 INTRODUCTION There cannot be many brass players who have not tried to play a piece of hosepipe for fun at some point in their careers. The procedure is simple – place the instrument’s mouthpiece in the end of the hose, a kitchen funnel at the other end, and literally minutes of amusement are sure to follow. An interested party might notice that the hosepipe instrument plays a slightly different set of pitches to a real instrument, and that many notes are out of tune. On the surface there would seem to be no logical reason why the horn should be any different to any bit of central heating pipe or hosepipe. The purpose of this project is to study the acoustic reasons why these differences occur. 1.1 Scope The basic objectives of this
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