Flutopedia - an Encyclopedia for the Native American Flute

Sign up for our Flute Newsletter

 


 
Previous PageNext Page
Flutopedia.com

Acoustics and Psycho-Acoustics References

This is a list of references related to acoustics and psycho-acoustics that are cited throughout Flutopedia.

The references on this page are a sub-set of the complete list of Flutopedia references.

For information on the format and other details of these citations, see the main references page.

Acoustics and Psycho-Acoustics References

[Allen-SA 1916] Herbert Stanley Allen and Harry Moore. A Text-book of Practical Physics, published by Macmillan Publishing Ltd., 1916, 622 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: Octave Notation

[Backus 1964] John Backus. “Effect of Wall Material on the Steady-State Tone Quality of Woodwind Instruments”, Journal of the Acoustical Society of America, Volume 36, Number 10, 1964, pages 1881–1887, doi:10.1121/1.1919286 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: FAQ for the Native American Flute

Abstract: A clarinet blown with an artificial embouchure was connected to one end of a large pipe with absorbing material at the other end so that the sound usually radiated was absorbed instead. Under these conditions, the sound radiated from the vibrating body was measured and found to be 48 dB below the sound normally produced by the instrument at the same location. Acceleration levels measured on the body with a vibration meter were correlated with the sound radiated by the body, both for the artificially blown clarinet and for clarinets set into vibration with an attachment energized by a complex signal. The figures obtained were used to check other woodwind instruments. Results showed that the body sound should be at least 37 dB below the normal sound for all instruments measured. The effect of nonrigid walls was checked by comparing tubes of brass and soft TYGON plastic blown on the embouchure, measuring the harmonic structure of the internal standing wave produced and the frequencies and Q's of the resonance modes. The differences were small. It is concluded that the vibrations of the walls of a woodwind instrument do not affect its steady tone either by radiating sound themselves or by affecting the harmonic structure of the internal standing wave.

[Barbour 1951] James Murray Barbour. Tuning and Temperament: A Historical Survey, published by the Michigan State College Press, East Lansing, Michigan, 1951. Publication tuningtemperamen00barb on Archive.org (open access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

From the preface: This book is based upon my unpublished Cornell dissertation, Equal Temperament: Its History from Ramis (1482) to Rameau (1737), Ithaca, 1932. As the title indicates, the emphasis in the dissertation was upon individual writers. In the present work the emphasis is on the theories rather than on their promulgators. Since a great many tuning systems are discussed, a separate chapter is devoted to each of the principal varieties of tuning, with subsidiary divisions wherever necessary. Even so, the whole subject is so complex that it seemed best that these chapters be preceded by a running account (with a minimum of mathematics) of the entire history of tuning and temperament. Chapter I also contains the principal account of the Pythagorean tuning, for it is unnecessary to spend a chapter upon a tuning system that exists in one form only.

[Benade 1967] A. H. Benade and F. Jansson. An Informal Preliminary Report on the Acoustics of Brass Instrument Bores (Chiefly on the Wave Equations in Theory and Experiment), April 1967, 24 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Benade 1977] Arthur H. Benade. Acoustical Evolution of Wind Instruments — A course (Physics 323) taught by A. H. Benade in the fall of 1977, Case Western University, Cleveland, Ohio, 1977, 80 pages and 3 illustrations. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Benade 1990] Arthur H. Benade. Fundamentals of Musical Acoustics, Second, Revised Edition, published by Dover Publications, Inc., New York, 1990, 596 pages, ISBN 0-486-26484-X (978-0-486-26484-4), softcover. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: Finger Hole Size, FAQ for the Native American Flute

[Blanc 2010] François Blanc, Benoît Fabre, Nicolas Montgermont, Patricio De La Cuadra, and André Almeida. “Scaling of Flute-Like Instruments: An Analysis from the Point Of View of the Hydrodynamic Instability of the Jet”, Acta Acustica united with Acustica, Volume 96, Number 4, July/August 2010, pages 642–653, doi:10.3813/AAA.918319 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: Flute Crafting Dimensions

Abstract: The scaling of a family of five baroque recorders is studied considering two aspects: the compass of each instrument and the control parameters. The observations are interpreted in terms of the homogeneity of the timbre. The control parameters are measured on an experienced player performing a simple scale task on each of the instruments, and are described in the frame of the hydrodynamic jet behaviour.

On the family studied, the geometrical parameters appear to be adjusted so that the control parameters are similar on all the instruments. Low-pitched instruments present an enrichment of their spectra in high frequencies.

[Bruno 2006] Thomas J. Bruno and Paris D. N. Svoronos. CRC Handbook of Fundamental Spectroscopic Correlation Charts, published by CRC Press, 2006, 225 pages, ISBN 0-8493-3250-8 (978-0-8493-3250-0). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: The Color of Sound - Pitch-to-Color Calculator

[Canright 1985] David Canright. “Pentatonics I Have Known”, 1/1, the Journal of the Just Intonation Network, Volume 1, Number 2, 1985, retrieved January 28, 2015. Pentatonics I Have Known Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Carlos 1996] Wendy Carlos. “Three Asymmetric Divisions of the Octave”, 1996. Three Asymmetric Divisions of the Octave Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Coltman 1968] John W. Coltman. “Sounding Mechanism of the Flute and Organ Pipe”, Journal of the Acoustic Society of America, Volume 44, 1968, pages 983–992, doi:10.1121/1.1911240 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Measurements on an artificially blown and mechanically excited flute head joint provide values of the complex acoustic back-pressure generated by the blowing jet. The magnitude of the acoustic back-pressure is calculable from the jet momentum and is approximately twice the static blowing pressure times the ratio of the lip-aperture area to the tube cross-section area. The phase of the induced back-pressure relative to the oscillation volume velocity is determined by the lip-to-edge distance and the velocity of propagation of a wave on the jet. Adjustment of this phase is demonstrated to be the major means by which the flutist selects the desired mode of oscillation of the instrument. The efficiency of conversion from jet power to acoustic oscillation power is low (2.4% at 440 Hz) and is about equal to the ratio of particle velocities in the air column and the jet. Nonlinear (turbulent) losses are measured and are substantial. Stroboscopic views of the jet motion under explicitly stated oscillation conditions show the large amplitude of the jet wave and its phase relative to the stimulating acoustic disturbance.

[Coltman 1971] John W. Coltman. “Effect of Material on Flute Tone Quality”, Journal of the Acoustical Society of America, Volume 49, Number 2, Part 2, 1971, pages 520–523. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: FAQ for the Native American Flute

Abstract: Three keyless flutes of identical internal dimensions were made of thin silver, heavy copper, and wood, respectively. They were played out of sight of musically experienced observers, who were asked to determine only whether tonese were alike or different. No statistically significant correlation between the listeners' scores and the material of the instrument body was found. Flutists who played the flutes, using an arrangement to eliminate visual or tactile clies, were unable to identify again a previously selected instrument.

[Coltman 1973] John W. Coltman. “Material Used in Flute Construction”, Woodwind World, Volume 12, Number 1, February 1973, pages 20–21. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Cook 2014] Perry R. Cook and Dan Trueman. “Spherical Radiation From Stringed Instruments: Measured, Modeled, and Reproduced”, 2014, 9 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Directional impulse responses were collected for six stringed instruments, including two classical acoustic guitars, an archtop jazz acoustic/electric guitar, a mandolin, a violin, and a Hardanger (Norwegian folk) fiddle. Impulse responses were recorded simultaneously from 12 microphones spaced uniformly at the vertices of an icosahedron. Data was collected for all instruments with a human player holding the instrument, and for some instruments also with the instrument suspended without being held by the player. For one guitar, the violin, and the mandolin, the position was adjusted by small angles, and a total of 72 impulse responses (six sets of 12 microphones) were collected. Various signal processing techniques were used to investigate, factor, store, and implement the collected impulse responses. A software workbench was created which allows virtual microphones to be placed around a virtual instrument, and then allows signals to be processed through the resulting derived transfer functions. Signal sources for the application include plucked and bowed string physical synthesis models, or any external sound source. Instrument body transfer characteristics can be parametrically edited, adjusting body size, main resonances, etc. Applications of the database and application software have included adding directional radiation models to physical models for virtual reality and composition, and adding more realistic body resonances to electronic stringed instruments for real-time performance.

[Cramer 1993] Owen Cramer. “The Variation of the Specific Heat Ratio and the Speed of Sound in Air with Temperature, Pressure, Humidity, and CO2 Concentration”, Journal of the Acoustic Society of America, Volume 93, Issue 5, May 1993, pages 2510–2516, doi:10.1121/1.405827 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: Electronic Tuners and the Native American Flute, Right in Tune - article by Clint Goss

Abstract: This paper describes a precise numerical calculation of the specific heat ratio and speed of sound in air as a function of temperature, pressure, humidity, and CO2 concentration. The above parameters are calculated utilizing classical thermodynamic relationships and a real gas equation of state over the temperature range 0°C–30°C. The shortcomings of previous determinations are also discussed. For both parameters, the coefficients of an interpolating equation are given, which are suitable for use in applications requiring high precision. The overall uncertainty in the specific heat ratio is estimated to be less than 320 ppm and the uncertainty in the speed of sound is similarly estimated to be less than 300 ppm.

[Dean 1979] E. A. Dean. Atmospheric Effects on the Speed of Sound, published by the US Army Electronics Research and Development Command, Atmospheric Sciences Laboratory, August 1979, 60 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: Intervals, CrossTune - Tool for Tuning a Native American flute for a Different Environment

Abstract: The small-signal speed of sound in humid air is calculated from a model which includes the real-gas effects from the equation of state for humid air and the vibrational dispersion due to N2, O2, and CO2 relaxation. Other atmospheric effects such as dispersion due to viscothermal and rotational relaxation, heat radiation, propagation along the air-ground boundary, the density gradient, turbulance, aerosols and fogs are considered and found to be unimportant for frequencies between 1Hz and 5 HHz (at one atmosphere). The uncertainty in predicting the sound speed varies between 0.22 m/sec at -90C to 0.05 m/sec at 90C. Experimental results in humid air at 20C and 30C are in excellent agreement with the model. For the propagation frequency of 20 Hz, it is found that the presently used sound-ranging formula, c - 20.06 Ts, where Ts = .75tv + .25t + 273.2 (tv = virtual temperature), differs by up to 0.5 m/sec over the range -60C to 60C. A correction to the "sonic" temperature determination is suggested with results in deviations of less than 0.05 m/sec over the temperature range from -60C to 50C and for relative humidities from 5% to 100%.

[Deutsch 1975] Diana Deutsch. “Two-channel Listening to Musical Scales”, Journal of the Acoustical Society of America, Volume 57, Number 5, published by the Acoustical Society of America, May 1975, pages 1156–1160, doi:10.1121/1.380573 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Deutsch 2006] Diana Deutsch. “The Enigma of Absolute Pitch”, Acoustics Today, Volume 2, Number 4, 2006, pages 11–18, doi:10.1121/1.2961141 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Deutsch 2008] Diana Deutsch, Kevin Dooley, and Trevor Henthorn. “Pitch Circularity from Tones Comprising Full Harmonic Series”, Journal of the Acoustical Society of America, Volume 124, Number 1, published by the Acoustical Society of America, July 2008, pages 589–597, doi:10.1121/1.2931957 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Deutsch 2010] Diana Deutsch. “The Paradox of Pitch Circularity”, Acoustics Today, Volume 6, Number 3, July 2010, pages 8–15, doi:10.1121/1.3488670 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Dodge-ES 1945] Ernest S. Dodge. “The Acoustics of Three Maori Flutes”, Journal of the Polynesian Society, Volume 54, Number 1, published by the Polynesian Society, March 1945, pages 39–61. Publication 20702995 on JSTOR (subscription access). The Acoustics of Three Maori Flutes Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Everest 2001] F. Alton Everest. The Master Handbook of Acoustics, published by McGraw-Hill, New York, 2001, 592 pages, ISBN 0-07-136097-2 (978-0-07-136097-5). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: FAQ for the Native American Flute, Intervals

Publisher's description: The goal of this book is to apply the principles of acoustics to the audio arts. This involves serving as an interpreter of major trends and the literature for students and practitioners in the audio field. Along with covering the more theoretical aspects of acoustics, the book applies the theory to the design of specialized audio spaces such as the home listening room, the control room, and the multi-track-recording studio.

[Fastl 2007] Hugo Fastl and Eberhard Zwicker. Psychoacoustics: Facts and Models, Third Edition, Springer Series in Information Sciences, Volume 22, published by Springer, 2007, 462 pages, ISBN 3-540-23159-5 (978-3-540-23159-2). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Publisher's description: This book offers a unique, comprehensive summary of information describing the processing of sound by the human hearing system. It includes quantitative relations between sound stimuli and auditory perception in terms of hearing sensations, for which quantitative models are given, as well as an unequalled collection of data on the human hearing system as a receiver of acoustic information. In addition, many examples of the practical application of the results of basic research in fields such as noise control, audiology, or sound quality engineering are detailed. The third edition includes an additional chapter on audio-visual interactions and applications, plus more on applications throughout. Acoustic demonstrations on a CD included with this edition further illustrate and amplify basic and applied psychoacoustic phenomena.

[Fletcher-NH 1994] Neville H. Fletcher. “Acoustic and Aerodynamic Determinants of the Sound Quality of Flutes”, Meeting of the Acoustical Society of America, Cambridge, Massachussets, June 6–10, 1994, 1994, 23 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: A theoretical description of the interaction of a plane jet with an acoustic flow field is presented, along with a discussion of the interaction of this jet with the lip of a tube resonator to produce a self-sustained oscillation. This description is related to the sound production mechanism in flutes of various families, and the factors controlling pitch, overblowing, and harmonic development of the sound are discussed. Performance techniques are also briefly described. Despite the reasonable success of this description, it is pointed out that the concept of a mixing region conceals our ignorance of the aerodynamic processes taking place, and in particular the role of vorticity. It is surmised that invocation of these processes will prove necessary to a proper understanding of details of the art of embouchure-hole and head-joint design.

[Fletcher-NH 1999a] Neville H. Fletcher. “The Nonlinear Physics of Musical Instruments”, Rep. Prog. Phys, Volume 62, 1999, pages 723–764. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Musical instruments are often thought of as linear harmonic systems, and a first-order description of their operation can indeed be given on this basis, once we recognise a few inharmonic exceptions such as drums and bells. A closer examination, however, shows that the reality is very different from this. Sustained-tone instruments, such as violins, flutes and trumpets, have resonators that are only approximately harmonic, and their operation and harmonic sound spectrum both rely upon the extreme nonlinearity of their driving mechanisms. Such instruments might be described as ‘essentially nonlinear’. In impulsively excited instruments, such as pianos, guitars, gongs and cymbals, however, the nonlinearity is ‘incidental’, although it may produce striking aural results, including transitions to chaotic behaviour. This paper reviews the basic physics of a wide variety of musical instruments and investigates the role of nonlinearity in their operation.

[Forinash 2015] K. Forinash. An Interactive eBook on the Physics of Sound, published by Indiana University Southeast, 2015, retrieved January 28, 2015. See the Physics of Sound Indiana University Southeast web site Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Forster 2010] Cris Forster. Musical Mathematics — On the Art and Science of Acoustic Instruments, published by Chronicle Books, San Francisco, California, 2010, 952 pages, ISBN 0-8118-7407-9 (978-0-8118-7407-6). See the Chrysalis Foundation web site Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Publisher's description: Musical Mathematics is the definitive tome for the adventurous musician. Integrating mathematics, music history, and hands-on experience, this volume serves as a comprehensive guide to the tunings and scales of acoustic instruments from around the world. Author, composer, and builder Cris Forster illuminates the mathematical principles of acoustic music, offering practical information and new discoveries about both traditional and innovative instruments. With this knowledge readers can improve, or begin to build, their own instruments inspired by Forster's creations shown in 16 color plates. For those ready to step outside musical conventions and those whose curiosity about the science of sound is never satisfied, Musical Mathematics is the map to a new musical world.

[Fullekrug 2010] Martin Füllekrug. Magnetic Activity and Schumann Resonance, published by the Northern California Earthquake Data Center, September 23, 2010, retrieved December 15, 2010. Magnetic Activity and Schumann Resonance Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: Pitch-to-Frequency Calculator (2)

[Giatti 2001] Anna Giatti and Mara Miniati. Acoustics and Its Instruments «l'Acustica e I Suoi Strumenti», published by Giunti Industrie Grafiche S.p.A., in Italian and English, 2001, 144 pages, ISBN 88-09-02183-5 (978-88-09-02183-9), softcover. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Hagerman 1980] B. Hagerman and J. Sundberg. “Fundamental Frequency Adjustment in Barbershop Singing”, Journal of Research in Singing, Volume 4, Number 1, 1980, pages 3–17. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Heathwaite 2010] Andrew Heathwaite. Gallery of Just Intervals, Sepember 14, 2010, retrieved January 28, 2015. Gallery of Just Intervals Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Heathwaite 2011] Andrew Heathwaite. Overtone Scales, October 17, 2011, retrieved January 28, 2015. Overtone Scales Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Helmholtz 1912] Hermann L. F. Helmholtz, M.D.; Alexander J. Ellis (translator). On the Sensations of Tone as a Physiological Basis for the Theory of Music, Fourth Edition, published by Longmans, Green, and Co., London, New York, Bombay, and Calcutta, 1912, 575 pages. translated from the Fourth German edition of 1877. First German Edition published in 1863. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: Octave Notation, Glossary of Native American Flute Terms

[Hirschberg 1999] Avraham Hirschberg. Luchtwervels in een blokfluit «Air Vortices in a Recorder», in Dutch, 1999, retrieved September 28, 2010. Luchtwervels in een blokfluit Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Five citations: Intervals (2), Anatomy of the Native American Flute (2), A Brief History of the Native American Flute

Abstract: The physical modeling of musical instruments is of great interest. Tool builders use the models to the sound of their instruments to improve the sound of music others are trying best to imitate electronically. Wind instruments are difficult to model because the characteristic tone is determined by the nonlinear dynamics of swirling air currents in the instrument. Laboratory experiments show how the air vortices behave in a flute or organ pipe.

[Jing 2003] M. Jing. “A Theoretical Study of the Vibration and Acoustics of Ancient Chinese Bells”, Journal of the Acoustic Society of America, Volume 114, Number 3, September 2003, pages 1622–1628, doi:10.1121/1.1600727. Publication 14514215 on PubMed/NCBI (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: In this paper, the acoustics of an ancient Chinese bell, which was made some 3000 years B.C., is studied theoretically. In ancient times, a set of the bells was used as a musical instrument. Unlike a western church bell and an ancient Indian bell, an ancient Chinese bell has two interesting acoustics. First, two tones can be heard separately as the bell is struck at two special points. The interval between the two pitches is always a minor or major third. Second, tones of the bell attenuate quickly, which is necessary for a musical instrument. So, an ancient Chinese bell is sometimes called a two-tone bell or a music bell. Although a three-dimensional model should be used to simulate the acoustics of the bell, a simplified model proposed in this paper does give some insight. Based on the lens-shaped cross section of an ancient Chinese bell, two tones of an ancient Chinese bell can be simulated by the vibration of a double-circular arch and the quick attenuation of tones can be simulated by acoustics of a cylinder with the lens-shaped cross section like a double-circular arch. Numerical results on the vibration and acoustics of the models are presented.

[Lefebvre 2010] Antoine Lefebvre. Computational Acoustic Methods for the Design of Woodwind Instruments, Ph.D. dissertation – McGill University, Montreal, Quebec, Canada, December 2010, xiv + 151 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: Glossary of Native American Flute Terms

Abstract: This thesis presents a number of methods for the computational analysis of woodwind instruments. The Transmission-Matrix Method (TMM) for the calculation of the input impedance of an instrument is described. An approach based on the Finite Element Method (FEM) is applied to the determination of the transmission-matrix parameters of woodwind instrument toneholes, from which new formulas are developed that extend the range of validity of current theories. The effect of a hanging keypad is investigated and discrepancies with current theories are found for short toneholes. This approach was applied as well to toneholes on a conical bore, and we conclude that the tonehole transmission matrix parameters developed on a cylindrical bore are equally valid for use on a conical bore.

A boundary condition for the approximation of the boundary layer losses for use with the FEM was developed, and it enables the simulation of complete woodwind instruments. The comparison of the simulations of instruments with many open or closed toneholes with calculations using the TMM reveal discrepancies that are most likely attributable to internal or external tonehole interactions. This is not taken into account in the TMM and poses a limit to its accuracy. The maximal error is found to be smaller than 10 cents. The effect of the curvature of the main bore is investigated using the FEM. The radiation impedance of a wind instrument bell is calculated using the FEM and compared to TMM calculations; we conclude that the TMM is not appropriate for the simulation of flaring bells.

Finally, a method is presented for the calculation of the tonehole positions and dimensions under various constraints using an optimization algorithm, which is based on the estimation of the playing frequencies using the Transmission-Matrix Method. A number of simple woodwind instruments are designed using this algorithm and prototypes evaluated.

[Lefebvre 2011] Antoine Lefebvre and Gary P. Scavone. “On the Bore Shape of Conical Instruments”, Canadian Acoustics / Acoustique canadienne, Volume 39, Number 3, 2011, pages 128–129. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Lefebvre 2012] Antoine Lefebvre and Gary P. Scavone. “Characterization of Woodwind Instrument Toneholes with the Finite Element Method”, Journal of the Acoustical Society of America, Volume 131, Number 4, April 2012, pages 3153–3163, doi:10.1121/1.3685481. Publication 22501087 on PubMed/NCBI (subscription access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: Flute Crafting Dimensions

Abstract: A method is proposed to determine the transfer matrix parameters of a discontinuity in a waveguide with the finite element method (FEM). This is used to characterize open and closed woodwind instrument toneholes and develop expressions for the shunt and series equivalent lengths. Two types of toneholes are characterized: Unflanged toneholes made of thin material, such as found on saxophones and concert flutes, and toneholes drilled through a thick material, such as found on most instruments made of wood. The results are compared with previous tonehole models from the literature. In general, the proposed expressions provide a better fit across a wide range of frequencies and tonehole sizes than previous results. For tall toneholes, the results are in general agreement with previous models. For shorter tonehole heights, some discrepancies from previous results are found that are most important for larger diameter toneholes. Finally, the impact of a main bore taper (conicity) on the characterization of toneholes was investigated and found to be negligible for taper angles common in musical instruments.

[Lefebvre 2013] Antoine Lefebvre, Gary P. Scavone, and Jean Kergomard. “External Tonehole Interactions in Woodwind Instruments”, Acta Acustica united with Acustica, Volume 99, June 21, 2013, pages 975–985. Publication 1207.5490 on Archive.org (open access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: The classical Transfer-Matrix Method (TMM) is often used to calculate the input impedance of woodwind instruments. However, the TMM ignores the possible influence of the radiated sound from toneholes on other open holes. In this paper a method is proposed to account for external tonehole interactions. We describe the Transfer-Matrix Method with external Interaction (TMMI) and then compare results using this approach with the Finite Element Method (FEM) and TMM, as well as with experimental data. It is found that the external tonehole interactions increase the amount of radiated energy, reduce slightly the lower resonance frequencies, and modify significantly the response near and above the tonehole lattice cutoff frequency. In an appendix, a simple perturbation of the TMM to account for external interactions is investigated, though it is found to be inadequate at low frequencies and for holes spaced far apart.

[Lewis-P 1998] Pierre Lewis. Understanding Temperaments, Version 1.2, 1998. Understanding Temperaments Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Mather-R 1972] Roger Mather. “The Influence of Tube Material and Thickness on Flute Tone Quality”, Woodwind World, September 1972. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[McGlade 2004] John McGlade, Heng Yang, and Victor P. Pasko. “Effects of Solar Flares on the First Schumann Resonance Frequency”, NSF EE REU PENN STATE Annual Research Journal, Volume 2, 2004, pages 42–51. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: Pitch-to-Frequency Calculator

Abstract: Variations in the exact Schumann Resonance frequencies occur due to changes in the conductivity profile of the Earth-ionosphere cavity. Aside from seasonal and diurnal cycles, these changes are also caused by factors such as X-ray bursts and high-energy particle precipitation from the sun. The discrete data we get from an FDTD model does not allow us to obtain the Schumann Resonance frequencies directly, and the resolution in the frequency domain is contingent upon sampling time. In this paper, the method of choice in determining the Schumann Resonance frequencies is through exponential approximation. Exponential approximation is effective because it can detect the slight shift in Schumann Resonance frequencies based on a short sampling time, which is desirable in order to reduce computer calculation time. In this paper we use the Prony Method of Exponential Approximation to find this slight frequency shift in a short sampling time.

[McIntyre 1983] M. E. McIntyre, R. T. Schumacher, and J. Woodhouse. “On the Oscillations of Musical Instruments”, Journal of the Acoustical Society of America, Volume 74, Number 5, November 1983, pages 1325–1345. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: Glossary of Native American Flute Terms, Anatomy of the Native American Flute

[Messiaen 1944] Olivier Messiaen; John Satterfield (translation). The Technique of My Musical Language — La technique de mon langage musical, published by Alfonse Leduc, Paris, France, 1944. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Miller-DC 1909] Dayton C. Miller. “The Influence of the Material of Wind-Instruments on the Tone Quality”, Science, New Series, Volume 29, Number 735, January 29, 1909, pages 161–171. Publication 1636184 on JSTOR (subscription access). Publication jstor-1636184 on Archive.org (open access). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Monzo 2004] Joseph L. Monzo. “The Measurement of Aristoxenus's Divisions of the Tetrachord”, 2004. The Measurement of Aristoxenus's Divisions of the Tetrachord Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Nickolaenko 2002] A. P. Nickolaenko and M. Hayakawa. Resonances in the Earth-Ionosphere Cavity, Modern approaches in geophysics, Volume 19, published by Springer, 2002, 380 pages, ISBN 1-4020-0754-X (978-1-4020-0754-5). Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: Pitch-to-Frequency Calculator

Publisher's description: This book on electromagnetic resonance phenomena describes a general approach to physical problems, ways to solve them, and properties of the solutions obtained. Attention is given to the discussion and interpretation of formal and experimental data and their links to global atmospheric conditions such as the dynamics of global thunderstorm activity, variations of the effective height of the lower ionosphere, etc. Schumann resonance is related to worldwide thunderstorm activity, and simultaneously, to global properties of the lower ionosphere. Transverse resonance is predominantly a local phenomenon containing information on the local height and conductivity of the lower ionosphere and on nearby thunderstorm activity. Transient events in ELF-VLF radio propagation are also treated. These are natural pulsed radio signals and/or abrupt changes of manmade VLF radio signals. The transients associated with cloud-to-ionosphere discharges (red sprites, blue jets, trolls) are discussed, and clarification of the underlying physical ideas and their practical applications to pioneer results achieved in the field recently are emphasised.

[Ondraskova 2009] Adriena Ondraskova, Sebastian Sevcik, and Pavel Kostecky. “A Significant Decrease of the Fundamental Schumann Resonance Frequency During the Solar Cycle Minimum of 2008–9 as Observed at Modra Observatory”, Contributions to Geophysics and Deodesy, Volume 39, Number 4, 2009, pages 345–354. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Three citations: Pitch-to-Frequency Calculator (3)

Abstract: The Schumann resonances (SR) are electromagnetic eigenmodes of the resonator bounded by the Earth’s surface and the lower ionosphere. The SR frequency variability has been studied for more than 4 decades. Using data from the period 1988 to 2002, S´atori et al. (2005) showed that the SR fundamental mode frequency decreased on the 11-year time scale by 0.07 – 0.2 Hz, depending on which component of the field was used for estimation and likely also on the location of the observer. A decrease by 0.30 Hz from the latest solar cycle maximum to the minimum of 2009 is found in data from Modra Observatory. This extraordinary fall of the fundamental mode frequency can be attributed to the unprecedented drop in the ionizing radiation in X-ray frequency band. Although the patterns of the daily and seasonal variations remain the same in the solar cycle minimum as in the solar cycle maximum, they are significantly shifted to lower frequencies during the minimum. Analysis of the daily frequency range suggests that the main thunderstorm regions during the north hemisphere summer are smaller in the solar cycle minimum than in the maximum.

[Parncutt 2001] Richard Parncutt. “Critical Comparison of Acoustical and Perceptual Theories of the Origin of Musical Scales”, Proceedings of the International Symposium of Musical Acoustics, Perugia, Italy. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Polk 1983] Charles Polk. “Natural and Man-Made Noise in the Earth — Ionosphere Cavity at Extremely Low Frequencies”, Space Science Reviews, Volume 35, Number 1, May 1983, pages 83–89, doi:10.1007/BF00173695 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: Pitch-to-Frequency Calculator

Abstract: The equations for the Earth-ionosphere cavity resonance fields are given and some of the approximations used in their derivation are indicated. Typical electric and magnetic 5 to 20 Hz Schumann resonance field intensities are listed and compared with the level of other natural and man-made electromagnetic noise. Applications of Schumann resonances to thunderstorm location and measurement of global lightning activity are reviewed briefly. Ionospheric conductivity profiles appropriate for this frequency range are discussed and the importance of atmospheric conductivity below 60 km is pointed out.

[Prairie 2006] Michael Prairie. Understanding the Acoustics of The Native American-Style Flute, October 4, 2006, 62 pages. See the Mike Prairie's acoustic of the flute web page. Understanding the Acoustics of The Native American-Style Flute Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: Breath Pressure in Ethnic Wind Instruments

From the Preface: This paper represents a compilation of my understanding of the physics of the flute so far, and is currently an evolving document. It is written from the perspective of the Native American style flute with a fixed sound hole configuration and a limited second-octave range. The treatment is appropriate for the penny whistle as well. Most of the treatment is also consistent with mouth-blown flutes like the simple-system Irish flute or the shakuhachi, but no effort is made to account for embouchure variations.

[Prairie 2011] Michael Prairie. Back Pressure, November 25, 2011, 3 pages. See the Mike Prairie's acoustic of the flute web page. Back Pressure Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Three citations: Flute Crafting Dimensions (2), Breath Pressure in Ethnic Wind Instruments

Summary: An article on how the back-pressure is related to some of the basic dynamics of the interaction between the jet and the air column in a flute.

[Prairie 2014] Michael Prairie. Nodal Interference, August 30, 2014, 4 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: Nodal Interference

[Price 2010] Lew Paxton Price. “How I Make Flutes Today”, Voice of the Wind, Year 2010, Volume 1, published by the International Native American Flute Association, Suffolk, Virginia, February 2010. See the Lew Paxton Price web site. How I Make Flutes Today Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Two citations: FAQ about Crafting Native American Flutes, Flute Crafting Dimensions

[Price 2011] Lew Paxton Price. Flute Physics, 2011. Flute Physics Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Rawcliffe 1992] Susan Rawcliffe. “Complex Acoustics in Pre-Columbian Flute Systems”, Experimental Musical Instruments, Volume 8, Number 2, December 1992, +18 line drawings and diagrams + 11 pages. See the Windworld web site Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Publisher's description: The author describes the advanced techniques of construction that were used in manipulating sound in Pre-Columbian clay flutes. She addresses the designs of flute apertures and hoods, body shapes, vessel flutes, tubular flutes and hybrid forms, such as ball and tube flutes, whistles and ocarinas. Timbre and tuning is also touched upon and the article also includes an extensive appendix, notes and bibliography.

[Rawcliffe 1992a] Susan Rawcliffe. “Complex Acoustics in Pre-Columbian Flute Systems”, contained in [Robertson 1992], 1992, pages 35–63. cassette number 8. Also published in the Journal of the National Council on Education in the Ceramic Arts, Volume 14, 1993-4. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Over a span of 30 centuries, Mesoamerican Pre-Hispanic societies developed a unique flute organology. They made flutes, pipes, ocarinas and whistles in a great diversity of form, timbre, and tunings. As an artist-musician for about 25 years, I have been making ceramic flutes and sound sculptures, many of which were inspired by my explorations into these ancient and wonderful wind instruments. Because I wanted to build a better flute, I studied the patterns to be found in both the ancient and my own flutes. The laws of acoustics dictate the range of possibilities for instrument construction within which design decisions are made according to cultural and individual preferences. Some instruments are dissected to illustrate choices made by their creators in order to produce particular sounds. Many of the most complex and time consuming innovations of the Pre-Hispanic artisans resulted in instruments of restricted pitch but rich timbre.

[Rich-R 2010] Robert Rich. Tuning Presets in the MOTM 650, 2010, 3 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Robertson 1992] Carol E. Robertson (editor). Musical Repercussions of 1492: Encounters in Text and Performance, published by the Smithsonian Institution Press, Washington, D.C., 1992, 486 pages, ISBN 1-56098-183-0 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[Sajfert 2011] Vjekoslav Sajfert, Sonja Krstić, Dušan Popov, Nicolina Pop. “Absorption of Sound Waves”, Seria Fizică (Physics Series), Analele Universităţii de Vest din Timişoara (Annals of the West University of Timisoara), Volume 55, January 2011, pages 13–19. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: The effect of sound absorption in sound pipe was examined. It turned out those two types of absorption takes place in sound pipe: irreversible and reversible ones. Absorption of irreversible type has exponential distribution and for it relatively simply can be determined resulting absorption which essentially determined the quality of sound pipe. The reversible absorption decreases intensity of sound and it means that is a suitable to make instruments from the woods with minimal reversible absorption characteristics.

[Sengpiel 2009] Eberhard Sengpiel. Speed of Sound — Temperature Matters, Not Air Pressure, 2009, 1 page. Speed of Sound Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: FAQ for the Native American Flute

[Shepard-RN 1964] Roger N. Shepard. “Circularity in Judgements of Relative Pitch”, Journal of the Acoustical Society of America, Volume 36, Number 12, published by the Acoustical Society of America, December 1964, pages 2346–2353, doi:10.1121/1.1919362 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: A special set of computer-generated complex tones is shown to lead to a complete breakdown of transitivity in judgments of relative pitch. Indeed, the tones can be represented as equally spaced points around a circle in such a way that the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch. Diametrically opposed tones—though clearly different in pitch—are quite ambiguous as to the direction of the difference. The results demonstrate the operation of a “proximity principle” for the continuum of frequency and suggest that perceived pitch cannot be adequately represented by a purely rectilinear scale.

[Surjodiningrat 1972] Wasisto Surjodiningrat, P. J. Sudarjana, and Adhi Susanto. Tone Measurements of Outstanding Javanese Gamelan in Jogjakarta and Surakata, Second Revised Edition, published by Gadjah Mada University Press, Jogjakarta, Indonesia, 1972, vi + 59 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

[vanSchaik 2010] Wilhelm van Schaik, Mart Grooten, Twan Wernaart, and Cees van der Geld. “High Accuracy Acoustic Relative Humidity Measurement in Duct Flow with Air”, Sensors, Volume 10, August 9, 2010, pages 7421–7433, doi:10.3390/s100807421. sensors ISSN 1424-8220 www.mdpi.com/journal/sensors. High Accuracy Acoustic Relative Humidity Measurement in Duct Flow with Air Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: An acoustic relative humidity sensor for air-steam mixtures in duct flow is designed and tested. Theory, construction, calibration, considerations on dynamic response and results are presented. The measurement device is capable of measuring line averaged values of gas velocity, temperature and relative humidity (RH) instantaneously, by applying two ultrasonic transducers and an array of four temperature sensors. Measurement ranges are: gas velocity of 0–12 m=s with an error of 0.13 m=s, temperature 0–100 C with an error of 0.07 C and relative humidity 0–100% with accuracy better than 2 % RH above 50 C. Main advantage over conventional humidity sensors is the high sensitivity at high RH at temperatures exceeding 50 C, with accuracy increasing with increasing temperature. The sensors are non-intrusive and resist highly humid environments.

[Vey 2010] G. Le Vey. “Optimal Control Theory: A Method for the Design of Wind Instruments”, January 19, 2012, 14 pages, arXiv:1001.3217 Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: It has been asserted previously by the author that optimal control theory can be a valuable framework for theoretical studies about the shape that a wind instrument should have in order to satisfy some optimization criterion, inside a fairly general class. The purpose of the present work is to develop this new approach with a look at a specific criterion to be optimized. In this setting, the Webster horn equation is regarded as a controlled dynamical equation in the space variable. Pressure is the state, the control being made of two parts : one variable part, the inside diameter of the duct and one constant part, the weights of the elementary time-harmonic components of the velocity potential. Then one looks for a control that optimizes a criterion related to the definition of an oscillation regime as the cooperation of several natural modes of vibration with the excitation, the playing frequency being the one that maximizes the total generation of energy, as exposed by A.H. Benade, following H. Bouasse. At the same time the relevance of this criterion is questionned with the simulation results.

[Wolfe 2003] Joe Wolfe and John Smith. “Cutoff Frequencies and Cross Fingerings in Baroque, Classical, and Modern Flutes”, Journal of the Acoustic Society of America, Volume 114, Number 4, Part 1, October 2003, pages 2263–2272, doi:10.1121/1.1612487. Publication 14587623 on PubMed/NCBI (subscription access). Cutoff Frequencies and Cross Fingerings in Baroque, Classical, and Modern Flutes Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: Baroque, classical, and modern flutes have successively more and larger tone holes. This paper reports measurements of the standing waves in the bores of instruments representing these three classes. It presents the frequency dependence of propagation of standing waves in lattices of open tone holes and compares these measurements with the cutoff frequency: the frequency at which, in an idealized system, the standing waves propagate without loss in such a lattice. It also reports the dependence of the sound field in the bore of the instrument as a function of both frequency and position along the bore for both simple and "cross fingerings" (configurations in which one or more tone holes are closed below an open hole). These measurements show how "cross fingerings" produce a longer standing wave, a technique used to produce the nondiatonic notes on instruments with a small number of tone holes closed only by the unaided fingers. They also show why the changes from baroque to classical to modern gave the instruments a louder, brighter sound and a greater range.

[Yang-WJ 2005] Wen-Jei Yang and Shinzaburo Umeda. “Self-Sustained Flow Oscillations Due to Flow-Surface Interaction”, Sixteenth International Symposium on Transport Phenomena (ISTP-16), Prague, 2005, 2005, 10 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: The sound produced by wind as it whistles through long grass or roars through the trees in the forest is one of the most familiar sounds. It is observed that vortices are formed and carried off by the stream as the streaming of water past an obstacle. These flow oscillation phenomena are induced by follow-surface interaction and may become self-sustained under certain conditions. This paper presents flow-surface interaction which results in self-sustained flow oscillation (spatial instability) including edge tone in diamond-shaped cylinder bundles, cavity tone in wavy-finned tube bundles, perforation tone in perforated plate bundles, and vortexwake tone in circular cylinder bundles. Emphasis is placed on mechanisms, conditions for induction and frequency of oscillations.

[Yokoyama 2014] Hiroshi Yokoyama, Masaki Kobayashi, Hirofumi Onitsuka, Akira Miki, and Akiyoshi Iida. “Direct Numerical Simulation of Flow and Acoustic Fields Around an Air-Reed Instrument with Tone Holes”, 43rd International Congress on Noise Control Engineering (inter.noise 2014), Melbourne, Australia, November 16–19, 2014, 2014, 10 pages. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Abstract: In order to clarify flow and acoustic fields around a recorder with opened and closed tone holes, direct aeroacoustics simulation was performed with compressible Navier-Stokes equations. For validation of the computational accuracy, the velocity distribution and sound pressure level were experimentally measured. The predicted velocity profile of jet ejecting from the windway is in good agreement with that of experiment. The numerical results show that the fundamental frequency and sound pressure level of predicted sound are almost the same as that of experiments. The path of the standing wave of the recorder was estimated with the pressure distribution. The open-end corrections found to be longer than those for a conventional simple pipe due to the effects of the impinging jet on the edge and the uniform flow in the resonator. When the vortices of the jet from the windway are getting near to the edge, strong deformation of the vortices occurs and expansion wave radiates in the resonator. The amplitude and phase of the acoustic particle velocity are almost the same as those of the jet itself. It indicates that the acoustic field amplifies the fluctuations of the jet and maintains the acoustic and fluid relations.

[Yokoyama 2015] Hiroshi Yokoyama. World First Prediction of the Sound Radiating from a Recorder — Super-computer simulations explore how an air-reed instrument generates air flow and sound, July 2015. See the TUT Research web site Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

Summary: Hiroshi Yokoyama and his colleagues have achieved a world first, in accurately predicting the sound radiating from a recorder. The calculations for this study took two weeks using about 100 nodes of supercomputers. The findings will contribute to the proposal for new designs of musical instruments which are easy-to-play or totally new musical instruments.

[Young-RW 1939] R. W. Young. “Terminology for Logarithmic Frequency Units”, Journal of the Acoustical Society of America, Volume 11, Number 1, July 1939, pages 134–139, doi:10.1121/1.1916017. ISSN: 0001-4966. Search Google Scholar Flutopedia format citation APA format citation Chicago format citation MLA format citation Wikipedia format citation

One citation: Octave Notation

Abstract: Fletcher has proposed the use of a logarithmic frequency scale such that the frequency level equals the number of octaves, tones, or semitones that a given frequency lies above a reference frequency of 16.35 cycles/sec., a frequency which is in the neighborhood of that producing the lowest pitch audible to the average ear. The merits of such a scale are here briefly discussed, and arguments are presented in favor of this choice of reference frequency. Using frequency level as a count of octaves or semitones from the reference C0, a rational system of subscript notation follows logically for the designation of musical tones without the aid of staff notation. In addition to certain conveniences such as uniformity of characters and simplicity of subscripts (the eight C's of the piano, for example, are represented by C1 to C8) this method shows by a glance at the subscript the frequency level of a given tone counted in octaves from the reference C0 = 16.352 cycles/sec. From middle C4, frequency 261.63 cycles/sec., the interval is four octaves to the reference frequency, so that below C4 there are roughly four octaves of audible sound. Various subdivisions of the octave are considered in the light of their ease of calculation and significance, and the semitone, including its hundredth part, the cent, is shown to be particularly suitable. Consequently, for general use in which a unit smaller than the octave is necessary it is recommended that frequency level counted in semitones from the reference frequency be employed.

 
Previous PageNext Page

   
 

To cite this page on Wikipedia: <ref name="Goss_2016_refs_acou"> {{cite web |last=Goss |first=Clint |title= Acoustics and Psycho-Acoustics References for the Native American Flute |url=http://www.Flutopedia.com/refs_acou.htm |date=20 December 2016 |website=Flutopedia |access-date=<YOUR RETRIEVAL DATE> }}</ref>