May 13, 2008

Links Summary B

Scientific Approach - Interactive Sites

http://www.jensign.com/JavaScience/www/plucker.html
String Plucker
Excellent java applet_fourier_w/FormulasAndRelativeStrengths
More and Less buttons refer to changing the number of partials present, relative strengths shown at bottom.

http://www.phys.unsw.edu.au/~jw/strings.html Joe Wolfe, composer, guitarist and professor of acoustics at The University of New South Wales. Good article explaining harmonics, extensive research in many areas of the physics of music. Good insights on strings. Some interactive Flash animations embedded.

http://www.falstad.com/mathphysics.html
Paul Falstad - a programmer, has done some great work here creating the best applets I have yet seen on this subject. The most relevant seem to be:

http://falstad.com/loadedstring/ This is the closest animation to my understanding of harmonic generators on a string.
http://www.falstad.com/circosc/
http://falstad.com/fourier/
http://www.falstad.com/coupled

 

http://www.acoustics.salford.ac.uk/feschools/waves/bungyvideo.htm
Video of a plucked string
This is the idea represented in the "Wavesums 1" animation, page14.

http://www.upscale.utoronto.ca/PVB/Harrison/Flash All Flash - take a look at (among others):  -Classical Mechanics/Simple Harmonic Motion - Soundwaves/Pressure and Displacement Waves -Soundwaves/Temperament - Waves/Standing Waves With a Node at Both Ends Also,  http://www.upscale.utoronto.ca> Virtual Bookshelf >Classical >Standing Waves - David Harrison is senior lecturer at the University of Toronto, Physics Department.( 01.29.05 - He has updated at least one relevant animation and has a new tutorial on actionscripting for physics)

From Educypedia which is a gold mine of animations and applets.

http://www.educypedia.be/

http://www.educypedia.be/education/physicswaves.htm
http://www.educypedia.be/education/sound.htm
http://www.educypedia.be/electronics/javaaudio.htm
http://www.educypedia.be/education/physicsmechanicsmotion.htm

A few of the most relevant:

From NoriMari KATO
http://www2.biglobe.ne.jp/~norimari/science/JavaEd/e-wave1.html

Physics applets by C.K. Ng
http://www.ngsir.netfirms.com/englishhtm/TwaveA.htm
transverse traveling wave
http://www.ngsir.netfirms.com/englishhtm/TwaveStatA.htm
transverse stationary wave
http://www.ngsir.netfirms.com/englishhtm/Lwave.htm
longitudinal travelling wave

 

B.Surendranath Reddy.
http://www.schulphysik.de/suren/Applets.html
Applet Menu >Waves >Longitudinal waves
................................>Transverse Waves
............................... >Adding Transverse Waves

and
......................>Oscillations >Phase Difference
........................................ >Forced Oscillations
are of particular interest to me right now

 

I believe the following combination of applets and animations may furnish some idea of the flow and vector analysis of the energy between the molecules of the plucked string (elasticity and momentum). I would like to clarify the relation between Fourier Analysis and string elasticity

This might be combined with Benjamin Crowell's analysis noted in http://www.lightandmatter.com/ Vibrations and Waves pdf P45 and in the "Fundamental" and "Vectors"animations. See also Falstad, "coupled" applet above.

http://lectureonline.cl.msu.edu/~mmp/applist/coupled/osc2.htm
From W. Bauer - Good Coupled Oscilator- "This is how waves propagate" - to be placed next to:

http://www2.biglobe.ne.jp/~norimari/science/JavaApp/nami1/e-nami.html From NoriMari KATO

Fourier Applets

http://www.jhu.edu/~signals/phasorlecture2/indexphasorlect2.htm Excellent fourier analysis animations- the math is generally beyond me. The third animation here was influential in my own work with the Circular Functions animations.
http://vak-nat.feo.hvu.nl/simulaties/simulaties/geluid/geluid/CGI-BIN/showharm.html good image + sound
http://www.univie.ac.at/future.media/moe/galerie/fourier/fourier.html nice fourier "qualitative" understanding from Maths Online http://www.fys.kuleuven.ac.be/pradem/applets/vinap/golven/fourier2/fourier2.html fourier applet originally from Manfred Thole
http://homepages.gac.edu/~huber/fourier/
modified Thole applet source code included by Prof. Thomas Huber
http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=33
fourier applet from Prof. Fu-Kwun Hwang NTNU
http://www.colorado.edu/physics/2000/applets/fourier.html
interesting interface here http://www.math.duke.edu/education/ccp/materials/postcalc/music/music2_6.html This page from a Duke University site has an excellent fourier analysis applet. Everything before this page is also good, everything after it is too difficult for me to comment on.

 

http://www.schulphysik.de/java/physlet/applets/piano1.html

http://lectureonline.cl.msu.edu/~mmp/kap13/cd361a.htm
A good mass on a spring applet came up on a googleSearch.

http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=236
Applet shows uniform circular motion is intimately related to a simple harmonic motion

http://www.hazelwood.k12.mo.us/~grichert/sciweb/waves.htm
Virtual Labs & Simulations by Gary Richert

Other Authoritative Sites

http://www.kettering.edu/~drussell/ Animated graphics from Dr. Dan Russell a professor of applied physics at Kettering University.The following are particularly relevant: http://www.kettering.edu/~drussell/guitars/index.html
http://www.kettering.edu/~drussell/demos.html

http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Web-basics.htm A very high quality site from the Institute of Sound and Vibration Research. WARNING, the animations are very large, up to 12MB, you will need patience even on a fast connection. I am not sure I would have the patience to view these on a dial-up connection, you can however read the text quickly enough.

http://www.music.sc.edu/fs/bain/atmi02/hs/index.html

http://www.music.sc.edu/fs/bain/atmi02/index.html

Reginald Bain | University of South Carolina | School of Music
This author has created a collection of Web-based multimedia resources entitled "The Harmonic Series: A path to understanding musical intervals, scales, tuning and timbre" designed to introduce the harmonic series and related concepts to musicians. (Note the site does not appear to have been updated since 2002 and appears to be suffering as a result of recent browser changes. There are still some good things here.)

http://www.speech.kth.se/music/acviguit4/index.html
Accoustics for Violin and Guitar Makers - Erik Jansson. This is a book in pdf format, the title explains its purpose. I have found it very useful and informative and at a level I can understand. Thanks Erik, my appreciation.

http://www.jmdl.com/howard/
Howard Wright's doctoral thesis on the acoustics and psychoacoustics of the guitar plus other items of interest. Many thanks.

http://www.astro.cf.ac.uk/groups/acoucomp/
Musical Acoustic Group - Cardiff University, Dr. Bernard Richardson. They seem to have a particular affinity for the guitar here, which makes them particularly interesting to me.

http://cnx.rice.edu/content/m12413/latest/
Standing Waves

http://www.educatorscorner.com/index.cgi?CONTENT_ID=371
Engineering and the Guitar
...The guitar touches on a rich set of engineering principles, among them: resonant frequency, period, amplitude, distortion, harmonics, wavelength, stress & strain, elastic limit, am, fm, damping coefficient, Doppler effect, step response, coupled oscillations, fft's and signal processing. Let's play around with some of these and see what we can learn from the simple acoustic guitar.
http://www.educatorscorner.com/index.cgi?CONTENT_ID=2486
good complex waveform applet
http://www.educatorscorner.com/index.cgi?CONTENT_ID=2481
their complete list of applets

http://www.du.edu/~jcalvert/waves/strings.htm Dr. J. B. Calvert, Associate Professor Emeritus of Engineering, University of Denver - excellent professional discussion of the topic of string vibrations, detailed discussion of sound in general. Engineering student level.

http://www.silcom.com/~aludwig/ -Art is an audiophile and a former NASA engineer. The section "What is Sound" contains a wonderful description of the movement of air molecules. Much of the rest is for rocket scientists though I have browsed with interest.

http://www.lexlrf.org/pub/index.html This is where you can obtain the book "Who is Fourier? (For about $25-30 U.S.) - the cover states "This book introduces to the lay person the field of complex Fourier analysis using a very easy to understand build-up approach" In it, "Every student in the group explained in detail how they came to understand each step." I am working on the book now (01.29.05 p129 out of 435) and somewhat stuck on "discrete fourier expansions" - I am reviewing. It starts with cartoons, continues through calculus and is concerned with communication. There are some excellent ideas for animation.

Math Sites

Some are general purpose sites, not specific to music.

http://www-groups.dcs.st-and.ac.uk/~history/Extras/Archibald_music_1.html
1923 Raymond Clare Archibald of Brown University -
Presidential Address to the Mathematical Association of America on Mathematicians and Music.

http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html
http://www.maths.abdn.ac.uk/~bensondj/html/music.pdf
Prof. David Benson's pdf book on math and music (NOTE: 8.8 Mb - Sometimes in a fairly advanced language - that is, calculus. The introductory chapters are as far as I get so far - quite good.)

http://www.sju.edu/~rhall/research.html
There are several articles here by Dr. Rachel W. Hall Department of Math and CS, St. Joseph's University. I am taking a closer look at:
The Mathematics of Musical Instruments (PDF format).

http://library.thinkquest.org/4116/Music/music.htm
Website put up by 6th grade students - some indication of what they feel is important to them.

http://hyperphysics.phy-astr.gsu.edu/hbase/hmat.html
Hypermath - a useful practical extenson of Rod Nav's Hyperphysics website.

http://id.mind.net/~zona/index.html
In Zona Land you will find educational and entertaining items pertaining to physics, to the mathematical sciences, and to mathematics in general. By Edward A. Zobel. Particularly: http://id.mind.net/~zona/mmts/trigonometryRealms/trigonometryRealms.html

http://id.mind.net/~zona/mstm/physics/waves/waves.html

http://archives.math.utk.edu/articles/atuyl/confrac/index.html

http://www.cut-the-knot.org/front.shtml (home page)
http://www.cut-the-knot.org/geometry.shtml
http://www.cut-the-knot.org/Curriculum/index.shtml (list of applets)
http://www.cut-the-knot.org/collection.shtml

http://archives.math.utk.edu/visual.calculus/index.html
(Visual Calculus)

http://www.univie.ac.at/future.media/moe/ (maths online)
http://www.univie.ac.at/future.media/moe/galerie.html

http://www-groups.dcs.st-and.ac.uk/~history/
This site provides historical and biographical material on math.Good for perspective.

http://plato.stanford.edu/entries/archytas/
RE: Archytas - We also have his proof showing that ratios of the form (n+1) : n, which are important in music theory, cannot be divided by a mean proportional.

http://nlvm.usu.edu/en/nav/frames_asid_133_g_3_t_3.html?open=instructions

The National Library of Virtual Manipulatives (NLVM) is an NSF supported project that began in 1999 to develop a library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-12 emphasis). The project includes dissemination and extensive internal and external evaluation.

Physics Sites

Some are general purpose sites, not specific to music.

http://www.engr.colostate.edu/~dga/high_speed_video/#Musical_Instruments

Guitar string vibration - high speed film showing the motion of a plucked guitar string

http://www.compadre.org/

The Physics Front, a collection of resources for pre-college physics teachers.

Of particular interest for Musemath purposes:
http://www.compadre.org/precollege/static/unit.cfm?sb=8

and therin particularly, the link to:
http://phet.colorado.edu/new/simulations/index.php?cat=Sound_and_Waves

http://phet.colorado.edu/web-pages/index.html

"The Physics Education Technology (PhET) project is an ongoing effort to provide an extensive suite of simulations for teaching and learning physics and to make these resources both freely available from the PhET website (phet.colorado.edu) and easy to incorporate into classrooms. The simulations (sims) are animated, interactive, and game-like environments in which students learn through exploration."

http://www.myphysicslab.com/
Erik Neumann, 2004
The applets take a while to download but seem worth the wait, and the math is included.

http://www.rwc.uc.edu/koehler/biophys/contents.html
Kenneth R. Koehler's site dating from 1996 - short text modules approximating my level of interest and understanding. The introduction is http://www.rwc.uc.edu/koehler/biophys/text.html

http://physics.webplasma.com/index.html
Physics For Beginners - Integrates text with short animations. I have been interested in the following module: http://physics.webplasma.com/physics11.html#ucm

http://highered.mcgraw-hill.com/sites/0072437316/student_view0/chapter46/animations.html#
A simple animation on the ear. I'm not thinking of doing any myself as I suspect some even better ones are out there already or soon will be. I may look about a bit more - especially regarding what I understand to be something of a logarithmic nature to the processes of the basilar membrane.

http://www.physpharm.fmd.uwo.ca/undergrad/medsweb/
Medical flash animation on the ear:
Session 4 Auditory Physiology

(I have to right click and save as an swf - it requires th flash authoring software -this may be a limitation on my computer - I may duplicate it in accord with the License below.)

Creative Commons License 2.5

-check out the language section: could that kind of filtering (or something similar) be applied to tuning preferences??

On thesamesubject:

http://library.thinkquest.org/05aug/00386/hearing/index.htm

http://www.iurc.montp.inserm.fr/cric/audition/english/ear/ear.htm#top

http://www.infj.ulst.ac.uk/~pnic/HumanEar/Andy's%20Stuff/MScProject/workingcode_Local/RunTest.html

http://www.maxanim.com/physiology/Cochlear%20Structures/Cochlear%20Structures.htm

http://www.jimmyr.com/blog/Sound_Waves_Through_Salt_18_2007.php BE VERY CAUTIOUS WITH VOLUME - this is piercing and loud - keep your hand on the volume control.
Chladni Patterns very well demonstrated.
Sound Waves Through Salt
"Awesome experiment in which salt is placed over a large speaker and you can see what kind of interference patterns are made from the sound waves. The results are pretty amazing."

http://www.srjc.moe.edu.sg/physics/physresos.htm
physicsAnimationResources
A-level Physics Online Resources
http://www.srjc.moe.edu.sg/physics/physresos.htm#t1

http://programlama.wordpress.com/2006/04/14/
Here is someone's collection of resources- good resources (German)

http://www.psigate.ac.uk/newsite/

PSIgate is a free service that offers access to high quality Web resources in the physical sciences; PSIgate (Physical Sciences Information Gateway) is the physical sciences hub of the Resource Discovery Network (RDN). http://www.rdn.ac.uk/
The RDN selects, catalogues and delivers high-quality Internet resources for further and higher education: the best of the Web.
...freely available to all.

http://www.tonmeister.ca/main/textbook/node231.html...Geoff Martin re: becoming a recording engineer....
...I'm trying to make the concepts presented here as accessible as possible without reducing the level of the content, so it can make a good introduction that covers a lot of ground....

http://230nsc1.phy-astr.gsu.edu/hbase/hph.html
"HyperPhysics is an exploration environment for concepts in physics which employs concept maps and other linking strategies to facilitate smooth navigation" - The actual physics often goes over my head fairly rapidly but the organization here keeps me interested.

http://honolulu.hawaii.edu/distance/sci122/Programs/sg.html
Richard Brill - Physical Science: The study of matter and energy and their interactions...We have not a clue to what matter and energy really are...We’ll be interested in the ideas and ideals of science more than we are interested in the facts.

http://plus.maths.org/issue31/features/woodhouse/index.html

Why is the violin so hard to play?
by J Woodhouse and PM Galluzzo

... a fundamental distinction between the physics of plucked and bowed strings.

 

For Musicians

Videos
(added May 2008 - These will probably need a separate page eventually. Sound and picture quality vary considerably and I find them inspiring for differing reasons, some perhaps personal. These are the best videos I could find in a day or two of searching, no more than that.

http://www.youtube.com/watch?v=qhrYSo6N6es&feature=related
Segovia, Villa-Lobos Estudio #1

http://www.youtube.com/watch?v=ox5J6agBfAs&feature=related
Segovia Chapdelaine Master Class

http://www.youtube.com/watch?v=CNjNXuGQaAE&feature=related
Andrés Segovia (Master Class 1965)

http://www.youtube.com/watch?v=2j4S9Qtt8UU
Andre Segovia videos.

http://www.youtube.com/watch?v=UuTrBL53G9c&feature=related
Los Romeros - original quartet

http://www.youtube.com/watch?v=PwXo4NqjblQ&feature=related
Los Romeros -recent version of the quartet

http://www.youtube.com/watch?v=0aali7ZgGko&feature=related
Los Romeros - recent version of the quartet
Giménez - La Boda de Luis Alonso

http://www.youtube.com/watch?v=Ok404bdnDYw&feature=related
Pepe Romero Master Class video

http://www.youtube.com/watch?v=h7gzwXMA06A&feature=related
Pepe Romero - Alegrias from Celedonio Romero's, Suite Andaluza

http://www.youtube.com/watch?v=3v1CTCZjCNo
Part One of Pepe Romero's flamenco set in tribute to Sabicas, Nino de Ricardo, and Paco Avila

http://www.youtube.com/watch?v=i7eJbhviUvM&feature=related
Angel Romero
Celedonio Romero - Suite Andaluza, Tango

http://www.youtube.com/watch?v=vUli7U8zojw&feature=related
Angel Romero Recital Part 7

http://www.ratingyoutube.com/watch?v=H2YMVDYJm2Q&feature=related
Manuel Barrueco - Michael Lawrence Films Bach Project

http://video.google.com/videoplay?docid=486827662602484644
Manuel Barrueco plays Asturias

http://video.google.com/videoplay?docid=2529976222552795924&q=&hl=en
"Sonata in B Minor" - Domenico Scarlatti

http://www.youtube.com/watch?v=HSECkRnpsDE
Cavatina - Ana Vidovic

http://www.youtube.com/watch?v=ra_xPVmADcI&feature=related
Ana Vidovic- Five Bagatelles, Allegro (William Walton)

http://www.youtube.com/watch?v=Jms6IHds_CM&feature=related
Ana Vidovic - Rodrigo - Sonata Giocosa, II. Andante moderato

http://www.youtube.com/watch?v=T1i_2HYmJkA&feature=related
John Williams & Julian Bream: C.Debussy-Clair de Lune

http://www.youtube.com/watch?v=AYpdUo__dM8&feature=related
John Williams n' Julian Bream - spanish dance no.1

http://www.youtube.com/watch?v=oPfZVflJdp0&feature=related
BWV - 1006 - Prelude from lute suite 4 - John Williams

http://www.youtube.com/watch?v=_JmAMqpzK8k&feature=related
John Williams : Hector Villa-Lobos - Prelude no.3

http://www.youtube.com/watch?v=SbW4rYYKxhg&feature=related
Julian Bream - Villa-Lobos - Preludes 3 & 4

http://www.youtube.com/watch?v=JbH4BD1YMnE&feature=related
Julian Bream improvises Indian music with Ali Akhbar Khan

http://www.youtube.com/watch?v=awHlAHsA_8M&feature=related
Rondo by Dionisio Aguado... played by Julian Bream

http://www.youtube.com/watch?v=UOvRJJ0tqsY&feature=related
Julian Bream, Peter Pears - Dowland - Fine Knacks for Ladies

http://www.youtube.com/watch?v=tDKd_n33mec&feature=related
Julian Bream - William Walton - Five Bagatelles, II. Lento

http://www.youtube.com/watch?v=5shxkuOrW9k&feature=related
Eliot Fisk play Escosesa

http://www.youtube.com/watch?v=LNcjPY1R3vY&feature=related
Eliot Fisk Julian Bream Pepe Romero Giuliani
La Rossiniana

http://www.youtube.com/watch?v=A_aeFVOi12I&feature=related
Liona Boyd - Gymnopédie No.1

http://www.youtube.com/watch?v=-qkKkYgJXDo&feature=related
Gran Jota de concierto Liona boyd

http://www.youtube.com/watch?v=AA66baUPMyg&feature=related
Liona Boyd - Fantasy For Guitar

http://www.visionmusic.com/tanenbaum/essential.html
David Tanenbaum - sor#5

http://video.google.com/videoplay?docid=-5057662961466486183&q=&hl=en
Sharon isbin plays Barrios

http://www.youtube.com/watch?v=p1Lg63-fmwk&feature=related
Presti-Lagoya Duo plays Beethoven Andante

http://www.youtube.com/watch?v=hqceqH5ZV1Y&feature=related
Presti-Lagoya duo plays Pierre Petit's "Toccata...

http://www.youtube.com/watch?v=NftZbCw5jt0&feature=related
Alexandre Lagoya plays Ponce Scherzino Mexicano

______________

Flamenco

http://www.youtube.com/watch?v=f2VROY01EAg
Sabicas- Arabian dance

http://www.youtube.com/watch?v=UizR_9aTnxU&feature=related
Sabicas - Zapateado En Re

http://www.youtube.com/watch?v=bidbOBPpKS0&feature=related
Sabicas

http://www.youtube.com/watch?v=c5zweApcVGA
Carlos Montoya - Farruca

http://www.youtube.com/watch?v=_7ITOrZEayw&feature=related
Paco Pena - fandangos

http://www.youtube.com/watch?v=0wY78lRUQyg&feature=related
Paco de Lucia "Cueva del Gato"

http://www.youtube.com/watch?v=HEZrB_FDw4c&feature=related
Paco De Lucia, John Mclaughlin y Al Di Meola - Mediterranean

_______________

Jazz

http://www.about-django.com/news/videos/videos.php
Django Reinhardt videos

http://www.youtube.com/watch?v=tl6C8WTnnPQ
Laurindo Almeida - Claire de lune

http://www.youtube.com/watch?v=yix7_fnhshk&feature=related
Laurindo Almeida Laurindo Almeida - One Note Samba with The Modern Jazz Quartet

END VIDEOS

______________

http://www.musictheory.net/ Ricci Adams, drummer, engineer, has a nice interactive teaching tool here, in Flash format, with sound, some of them downloadable. More for the musician than the mathematician.

http://www.egta.co.uk/content/home
European Guitar Teachers Assn.

http://www.teoria.com/
Comprehensive general music, again, more for the musician than the mathematician. Excellent in all respects. Thanks to Jose Rodriguez Alvira.

http://www.martindalecenter.com/Calculators1B_6_Mu.html A lot of good interactive links. Worthwhile site.

http://monxmood.free.fr/guitar/guitar2.html Interactive fretboard with sound- about 200kb. Also, a lot of fun interactive alternate tuning electronic instruments - all free as per the url. This site is from Paul Hirsh, multi-instrumentalist, multi-linguist and pretty good at creating interactive stuff for the internet. Another address for him: http://www.ii4i.net/

http://www.amarilli.co.uk/guitar/default.asp
http://www.amarilli.co.uk/guitar/howto.asp
Tuning guitar by beats

http://www.olle-eriksson.com/files/note2fretboard/
Just a nice simple applet for learning note reading on the guitar. Depending on your browser, it may require a rather large plug-in java download which is probably not worth the trouble on a slow dial-up connection.

http://cnx.rice.edu/content/m11639/latest/
Catherine Schmidt-Jones
Tunings - This is not interactive but I like her site and she is a music teacher with the perspective of a wind instrumantalist.

http://pages.globetrotter.net/roule/demos.htm
This page contains MIDI files (and a few audio/basic .au files) that illustrate, using short pieces, various historical tunings and temperaments.

http://members.aol.com/mathewsrfp/guitar.html
A pretty good pluckable guitar applet- change the chords and always pluck downwards-by Ted Mathews.

http://www.cite-des-sciences.fr/english/ala_cite/expo/explora/sons/anim/hauteur/jeu.htm
test your pitch sense

http://www.onlinetuningfork.com/
(self explanatory)

http://www.pauladams.org/Loss.html
(overcoming physical adversity on guitar)

For School Age

The Physics Education Technology (PhET) project is an ongoing effort to provide an extensive suite of simulations for teaching and learning physics and chemistry and to make these resources both freely available from the PhET website and easy to incorporate into classrooms.

Most relevent to Musemath: http://phet.colorado.edu/new/simulations/index.php?cat=Sound_and_Waves

The animations are not neccessarily self explanatory. They are designed for classroom use and some discussion by a teacher is assumed. For example, my favorite animation here is "stringWave"

You can play with it as much as you want though I suggest you bring this page up in a separate window and try the following sequence of steps first to watch standing waves form..

New Window ; Click on the word: stringWave

Then:

1. Upper right - check the "Timer" checkbox .

2. Click the "Oscilate" checkbox.

3. Click "Pause" button.

4. Set Amplitude to between 20 and 30.

5. Set "Damping" to 0.

6. (Leave "Frequency" at 50.)

7 On the timer, press "Start".

8. Click "Reset".

At about 1.8 seconds the wave will reflect from the fixed end and standing waves will start to form.

By about 8 seconds, it will be apparent that the amplitude increases continually and the nodes, (green dots) are not stationary. This teaches the most important lesson of all; mathematical models do not always duplicate nature precisely (and vice versa).

It is not impossible that it is doing exactly what the designer wants, it is not specific to a plucked string, (here there is continouous periodic addition of energy and no apparent limits to the elasicity of the string) There is more to physics than I can or should deal with, there are a number of variables, and a science teacher of some sort is apparently assumed here.

Musemath animations have plenty of problems of their own and the entire endeavor is still new.

 

http://cnx.org/content/m13513/latest/

This website has a few more ideas on what to do with this animation.

Here is where they explain how and why.
http://phet.colorado.edu/web-pages/research.html

This seems a good approach to interactive educational material. Quite beyond my capabilities. Articles on this page provide details. Two excerpts:

"A development process that involves multiple cycles of careful testing with students and refinement (or massive overhaul) is essential...

...the most critical features:

(1) highly interactive animation that provides direct and immediate response to user actions;
(2) an appealing environment and reasonably sophisticated graphics that literally invite the student to interact and explore;
(3) simple and intuitive controls, such as click-and-drag manipulation, sliders and radio buttons, with minimal reading required; and
(4) connections to real-life objects."

http://www.exploratorium.edu/music/index.html
Pretty much of a "must visit" if interested in interactive internet music education.

http://cnx.rice.edu/content/m11638/latest/
Math and Music (ideas for teachers)
Catherine Schmidt-Jones

http://www.acoustics.salford.ac.uk/schools/
"Sounds Amazing" -The Acoustics Department at Salford University has come up with this site designed for the education requirements for school-age in Great Britain. (April 9, 2006 - recently upgraded and improved)

http://www.artsalive.ca/en/mus/visitorcentres/kids.html
National Arts Centre - This site is good in itself and has some good links to the kid's pages of various symphony orchestras.

http://www.ndt-ed.org/EducationResources/HighSchool/Sound/introsound.htm

http://www.ndt-ed.org/EducationResources/HighSchool/Sound/vibration.htm

http://www.ndt-ed.org/EducationResources/educationresource.htm

Science seems to play an every increasing role in our society. The products that we buy and produce are becoming more technical and, therefore, jobs are becoming more technical. It is important to develop a good understanding of basic science. The materials at the links below have been developed to introduce some of the important scientific principles that are used in nondestructive testing. The materials were originally designed for middle and high school students, but students of all ages may find them useful for a review of information that may have become fuzzy or been forgotten with time."

http://acoustics.me.uic.edu/merit/index.html
http://acoustics.me.uic.edu/merit/lesson4/lesson4text.html
Science and Engineering in Music... This website is being developed as an educational tool for anyone interested in learning more about the math, science and engineering behind music and musical instruments. The material presented here compliments material taught in undergraduate and graduate level courses in vibrations and acoustics within the UIC Mechanical Engineering Program.

Historical Approach

There is a more complete list at "Timeline".

http://www.fiddletree.com/ then > Reflections > On the Pythagorean Tradition. The luthier Otis A. Tomas has a very well written article on the Pythagorean tradition in math and music. This is one of the sources for the "Harmony of the Spheres" animation.

http://www.medieval.org/emfaq/harmony/pyth.html an excellent historical study of pythagorean tuning.by Margo Schulter.

http://www.dolmetsch.com/theoryindex.htm
http://www.dolmetsch.com/poshistory.htm Dr. Brian Blood, Physicist, Recorder and Early Music Enthusiast, historical, authoritative, thorough - some excellent, well written material on general theory was obtained from scrolling down to "Pitch".

And some Guitar Histories

http://www.vihuelademano.com/rcmdias.htm#p4
Some very good historical information and pictures here re: evolution of the guitar.

http://www.classicalguitarmidi.com/history/guitares_evolution.html
Good pictures - takes a while to load on dialup

http://www.earlyromanticguitar.com/
…an educational overview of the early romantic 19th century guitar: the period composers and instruments, and the artists who specialize in that time period and style today…

http://wideopendoors.net/middleages_original/LifeTimes/Guitars.html
(apparently written by W. J. Bethancourt III and put up on the web by Aaron Rice)

http://www.standingstones.com/engguit.html
History of the guitar in England.

Other Tuning Systems

Musemath so far is a study in 12 tone equal temperament [12EDO -Equal Divisions of the Octave]. Other systems of music cannot be ignored and may become more important.

Alternate Tunings

(Note for Guitarists - if you search for "alternate tunings + guitar" you will find some open string variations that can be applied to the standard 12 fret/octave guitar, if you search for just "alternate tunings" you are more likely going to find microtonal guitars and synthesizers and a number of other instruments and systems of music.)

What I am looking for here is enough understanding to create an animation or two which would help explain some of the "alternate music" theory.

http://www.angelfire.com/music2/aah/microtonal/list.html
Andrew Heathwaite, webmaster - "I assembled this list mainly to help newcomers to microtonality find good, working links to real pieces."

(ror- These are downloadable, listenable mp3's etc., kept up through 2004 - hear if the music interests you:

includes:
http://www.oeaw.ac.at/kal/agm/
Ancient Greek Music
(from) the Commission for Ancient Literature of the Austrian Academy of Sciences.)

http://www.tonalsoft.com/index.html
http://www.tonalsoft.com/enc/just.htm
The company has an extensive free encyclopedia - focus is on microtonal music but includes Sumerian tuning math and frettings for the ancient Arab 'ud ("al-'ud") and other choice items.

http://fretfind.ekips.org/index.php
free fretfind tool for various tunings

http://www.justintonation.net/
The subject of alternate tunings (based on other than 12 tone equal temperament [12EDO -Equal Divisions of the Octave]) can be researched from this site. Carl Lumma's site has recordings of what he finds are some "Essential Microtonal Recordings". Kyle Gann has a nice article on alternate tunings.

http://eceserv0.ece.wisc.edu/~sethares/tet19/guitarchords19.html
From Bill Sethares; The 19 fret per octave guitar is discussed here.To get to his home page for more alternate tuning material : http://eceserv0.ece.wisc.edu/~sethares/index.html

http://www.terryblackburn.us/music/temperament/index.html
Terry Blackburn has a simple approach and common sense attitude towards "alternate tuning" that I find worth knowing about.

http://www.bikexprt.com/tunings/fibonaci.htm
The bike expert, John S. Allen also has an interest in alternate tunings. I may take a closer look at his study of fibonaci numbers and "matrix" tunings as it seems to be an alternative to the "continued fraction" approach used by Shroeder and in the"Equal Temperament 1 and 2" animations. (See the link to Fibonacci Numbers at the end of "Equal Temperament 2")

http://ccrma.stanford.edu/overview/
http://ccrma.stanford.edu/overview/pastmodeling.html
Computer Music (technical, academic - I understand very little, if any, of this but it certainly appears authoritative enough for those interested).

http://users.rcn.com/dante.interport//index.html
Dante Rosati , a teacher of guitar at Julliard, among other things provides us with some mp3 samples of his compositions on a 21 tone just intonation guitar. http://users.rcn.com/dante.interport//guitar.html .

http://www.freeplay.com/Writings/Tuning.pdf
This pdf manual is an excellent introduction to tuning with a subtitle of “The World Music Menu”.

http://www.rev.net/~aloe/music/tuning.html
A number of clear well written articles on Tuning on the site, this page includes additional links.

http://www.xs4all.nl/~huygensf/english/index.html
Huygens-Fokker Foundation - Centre for Microtonal Music (Especially 31tet, after Huygens)

http://www.chrysalis-foundation.org/Manuscript.htm
The site contains numerous detailed extracts from the book Musical Mathematics by Cris Forster - some of which go over my head and some is of interest. The extracts are on the left side of this page.

http://phy.mtu.edu/faculty/info/suits/scales.html
Just vs. Equal Temperament

Non-Western

Here are the sources I am currently using for Indian, Chinese, and Middle-Eastern music which can be sampled on the web and have some academic discussion as well.

Indian music
http://theory.tifr.res.in/~mukhi/Music/music.html

http://www.chrysalis-foundation.org/Bharata's_Vina.htm

Middle Eastern music:
http://www.maqamworld.com/

http://www.classicalarabicmusic.com/index.htm
It’s our commitment to present as much information about Classical Arabic Music as circumstances allow.A lot of good links here .

http://www.oud.gr/index.html
oud - Nikos Dimitriadis
v good - samples (widows media) - good links.

http://www.hinesmusic.com/What_Are_Makams.html

Chinese music
http://www.silkqin.com/08anal/tunings.htm
http://www.silkqin.com/index.html
http://www.silkqin.com/12more/links.htm
John Thompson

http://www.chinamusic.org/music.html
Los Angeles Classical Chinese Orchestra

http://www.ibiblio.org/chinese-music/
The Internet Chinese Music Archive

http://www.chrysalis-foundation.org/China's_Ch'in.htm
http://www.cechinatrans.demon.co.uk/ctm-psm.html
Some theory but no music samples.

Asimov, Isaac, Understanding Physics: Motion, Sound, and Heat,
Signet Books, The New American Library, Inc.301 Avenue of the Americas, NY NY 10019,1969

Bartholomew, Wilmer T; M.A.,M.Mus. - Acoustics of Music
© 1942 by Prentice-Hall, Inc., Englewood Cliffs, N.J. – 7th printing 1956)

Becker, Robert A. Ph.D. – Associate Professor of Physics, University of Illinois Introduction to Theoretical Mechanics
McGraw-Hill Book Company; NY, Toronto, London 1954
LCCN 54-6718

Bell, Eric Temple, - The Magic of Numbers,
Whittlesey House- McGraw-Hill Book Company, Inc. New York: London, 1946

Bronowski, J. - A Sense of the Future
Edited by Piero E. Ariotti in collaboration with Rita Bronowski
©1977 by The Massachusetts Institute of Technology
ISBN 0-262-02128-5

Bronowski, J - The Ascent of Man
Little, Brown and Company
Boston/Toronto
© 1973 by J.Bronowski
ISBN0-316-10930-4

Campbell & Greated - Musicians Guide to Acoustics
Schirmer (1987)

Cole, K.C - Sympathetic Vibrations
© 1985 by K.C. Cole
Permissions Department
William Morrow and Company, Inc.
105 Madison Ave., New York, N.Y. 10016
LCCN 84-60547
ISBN 0-688-03968-5

Courant, Richard and Robbins, Herbert - What is Mathematics?
Oxford University Press
London, New York, Toronto
© 1941 by Richard Courant

Crick, Francis - The Astonishing Hypothesis;
Touchstone, Rockefeller Center 1230 Avenue of the Americas, New York NY 10020, 1994
ISBN 0-684-80158-2

Herrigel, Eugen - Zen in the Art of Archery
© Renewed 1981 by Random House, Inc.
Vintage Books a Division of Random House, Inc. New York

Horgan, John - The End of Science
Broadway Books, Bantam Doubleday Dell Publishing Group, Inc., 154Broadway, NY NY 10036 – orig published: Reading Mass: Addison-Wesley Pub., c1996; ISBN 0-553-06174-7 (pbk)

Joyce, James - Ulysses
© 1914, 1918 by Margaret Caroline Anderson. © 1934 by the Modern Library, Inc. © 1942, 1946 by Nora Joseph Joyce - Random House, NY - 768 pages

Levenson ,Thomas - Measure for Measure
© 1994
Touchstone
Rockefeller Center
1230 Avenue of the Americas
NY, NY 0020
Simon & Schuster, Inc.
ISBN 0-671-78730-6
0-684-80434-4 (Pbk)

Lin Yutang - The Wisdom of China and India
Random House NY 1942

Macrae, Norman - John von Neumann
A Cornelia & Michael Bessie Book, Pantheon Books (Random House, Inc.), New York, 1992 ISBN 0-679-41308-1

Main, Ian G. - Vibrations and Waves in Physics
© Cambridge University Press 1978, 1984, 1993
Published by the Press Syndicate of the University of Cambridge
The Pitt Building,
Trumpington Street
Cambridge CB2 1RP
40 West 20th Street
New York, NY 10011-4211
ISBN 0 521 4186 2 hardback
ISBN 0 521 4470 1 paperback
(First Edition – ISBN 0 521 21662 1 hardback – ISBN 0 521 29220 4 paperback)

Montaigne, Michel de - Selected Essays
Translated by Donald M. Frame;
Classics Club © by Walter J. Black, Inc. Roslyn, NY 1943

Moravcsik, Michael J. - Musical Sound
© 1987 by Michael J Moravcsik
The Soloman Press
89-31 161 Street (Suite 611)
Jamaica, NY 11432
ISBN 0-934623-05-8

Motz, Lloyd and Weaver, Jefferson Hane - The Story of Mathematics
Avon Books
A division of
The Hearst Corporation
1350 Avenue of the Americas
© 1993 by Lloyd Motz and Jefferson Hane Weaver
Published by arrangement with Plenum Publishing Corporation
LCCN: 93-26527
ISBN: 0-380-72458-8
for copyright information
Plenum Publishing Corporation
233 Spring Street
New York, NY 10013

Newman, James R. - The World of Mathematics
© 1956 by James R. Newman
Simon and Schuster, Inc.
Rockefeller Center
630 Fifth Avenue
New York 20, NY
LCCN 5510060

Overbye, Dennis - Lonely Hearts of the Cosmos
Back Bay Books
Little, Brown and Company
Boston, New York, London
© 1991 by Dennis Overbye
Originally published by HarperCollins Publishers, 1991
ISBN 0-06-015964-2 (HC)
ISBN 0-316-64896-5 (Back Bay ed.)

Partch, Harry - Genesis of a Music, Second Edition
Da Capo Press
New York 1974

Pierce, J.R. - Symbols, Signals and Noise
The Nature and Process of Communication
© 1961 by John R. Pierce
Harper Modern Science Series
Edited by James R Newman
Harper & Brothers, New York

Pierce, John Robinson - The Science of Musical Sound
© 1983 by Scientific American
Scientific American Books, Inc.
Distributed by W. H. Freeman and Company
41 Madison Avenue, New York, New York 1010

Plato - Five Great Dialogues
Translated by B. Jowett Edited, with introduction by Louis Ropes Loomis
Published for the Classics Club by
Walter J. Black, Inc. Roslyn, NY 1942

Plutarch - Selected Lives and Essays
Translated from the Greek by Louis Ropes Loomis
Introduction by Edith Hamilton
Published for Classics Club by Walter J. Black, Inc, Roslyn, NY 1951

Rigden, John S. - Physics and the Sound of Music 2nd ed.
1977, 1985
John Wiley & Sons

Shakespeare - The Complete Works
Edited by G.B. Harrison
Harcourt, Brace& World, Inc. - New York, Chicago, San Francisco, Atlanta
© 1968 – ISBN 0-15-5 80530-4

Shlain, Leonard M. - Art & Physics
© 1991 by Leonard M. Shlain
Permissions Department
William Morrow and Company, Inc.
1350 Avenue of the Americas,
NY, NY 10019
ISBN 0-688-09752-9

Shroeder, Manfred - Fractals, Chaos and Power Laws
1991
W.H. Freeman and Company, New York

Sokolnikoff, I.S. and Redheffer, R.M. - Mathematics of Physics and Engineering
McGraw-Hill Book Company, Inc.
New York, Toronto, London 1958
LCCN 57-914

Sudo, Philip Toshio - Zen Guitar
Fireside (Simon & Shuster)
1997

Taylor, Charles - The Science and Technology of Tones and Tunes
IOP Publishing Ltd. 1992
Institute of Physics Publishing
Techno House
Redcliffe Way
Bristol BSI 6NX, UK
US Editorial Office: Institute of Physics Publishing
The Public Ledger Building, Suite 1035
Independence Square
Philadelphia, PA 19106

Taylor, Charles - Sounds of Music, Sci Prog. Oxf, and or Simon And Shuster, 1978 0-68415-476

Wood, Alexander (1879-1950) - The Physics of Music
Revised by J.M. Bowsher
Seventh Edition, 1944,1975
Chapman and Hall, Ltd.
11 New Fetter Lane
LondonEC4P 4EE
© 1975 by Chapman and Hall Ltd.
A Halstead Press Book
John Wiley & Sons, Inc., New York
ISBN 0 412 13250 8 (cased edition)
ISBN 0 412 21140 8 (Science Paperback Edition

Two books I have not read but are reviewed and come highly recomended from Brian Chandler at http://www.imaginatorium.org
Music by numbers
Some books tying music and mathematics together:

Robert Osserman - "Poetry of the Universe" (good)
Jamie James - "The Music of the Spheres" (better)

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