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Fractals & Music: more detail

Fractal Music, Hypercards and More Mathematical Recreations from "Scientific American" by Martin Gardner, 1991-11-30

Fractals in Music: Introductory Mathematics for Musical Analysis Second Edition (Inmusic) by Charles Madden, 2007-04-23

Music and Mathematics: From Pythagoras to Fractals

Fractal Music, Hypercards and More. Mathematical Recreations from Scientific Ame by Martin Gardner, 1992-01-01

Fractal Music, Hypercards and More : Mathematical Recreations from Scientific Am by Martin Gardner, 1991-01-01

Fractal Fantasy, the Art of Mathematics by Charles Fitch, Music by Michael Angelo Strasmich, 1987

Music And Mathematics: From Pythagoras To Fractals by Raymond Flood, Robin Wilson, Robin J. Wilson John Fauvel, 2003

Formalised composition on the spectral and fractal trails (Skrifter fran Musikvetenskapliga institutionen, Goteborgs Universitet) by Magnus Eldenius, 1998

lists with details

Chaos Theory, Fractals, Animation, Music Videos As A Scientific Experiment In Li
A free educational science, music, arts and entertainment site where you can downloadfree music videos of fractals in MPEG, MPEG2, DVD, DivX/MPEG4, Microsoft
http://gawain.membrane.com/multimedia/classic_fractal_animation/
Fractals And Music
fractals and music by Gustavo DiazJerez Electronic musician, Oct 1, 1999.
http://emusician.com/ar/emusic_fractals_music/

Extractions: Most musicians have seen fractal images-those hauntingly beautiful pictures generated through mathematical equations. But how many people are aware that the same equations can be used to create hauntingly beautiful music? This article will explore fractals and discuss how they can be employed in musical composition. The technique is so versatile that you can use it to create music in any style, and it has great potential for adding an exciting new element to your music. Studying music from a mathematical point of view is nothing new; it dates back to ancient Greece. Around the fifth century B.C., Pythagoras uncovered mathematical relationships in music, in which musical intervals are represented as ratios of whole numbers. For example, the interval of an octave would be represented in the Pythagorean system as a 2:1 ratio because the frequency of the higher pitch is twice that of the lower. By the same system, the interval of a fifth would be 3:2, a fourth 4:3, and so forth. Other systems relating music to math have been developed, mainly in the 20th century. Among the many examples are Joseph Schillinger's System of Musical Composition and a method of composition developed by Olivier Messiaen in the 1940s. The more recent discovery of fractals and particularly their link to music has opened a door to composers, behind which lies immense creative possibility.
Fractovia.org: Fractal Art
Galleries, discussion of fractals as art. Large list of freeware fractal generators, screen savers, music software, with links and reviews.
http://www.fractovia.org/
Fractal Music
fractals, Chaos, and music An academic paper covering some of the researchthat has been done on relations between fractals and music.
http://thinks.com/webguide/fractal-music.htm

Extractions: An academic paper covering some of the research that has been done on relations between fractals and music. A few computer programs which can be used to generate fractal music - The Well-Tempered Fractal and MusiNum - are discussed, and also possible practical uses for software which can be used to hear patterns in fractals. Fractal Music by David Spondike Dedicated to the sharing of tools and information for exploring and advancing the musical use of fractals. This site contains numerous examples of fractal music, downloadable software you can use to compose original fractal music, and some information and activities designed to help you better understand fractals.
Main
Sterlingware, Flarium, Fractal Explorer galleries and fractal music.
http://www.fractal-vibes.com/fvc/fractals.html

Extractions: Fractal Art Herein are several galleries of fractal images, each the graphical representation of fractal equations iterated over and over several million times. If fractals are not already familiar to you, check the "About Fractals" page to learn more. Sterling-Ware Gallery #1 Flaruim-24 Gallery #1 Fractal Explorer Gallery #1
Fractals And Fractal Art
See and hear what can be done with fractals in music and Art; find out more aboutfractals; learn about the software used to create fractal art and music
http://thinks.com/webguide/fractal.htm

Extractions: Amazing Seattle Fractals! Doug Harrington's site has an online, step by step fractal tutorial, complete with screenshots to help people create their own fractal art. It also features fractal art galleries,fractal animations,free fractal software and a free fractal screensaver (rated by ZD Net as an Editor's Pick 5 Star Download). Doug's fractal art has been featured at M.O.C.A.(Museum of Computer Art) and has won several other site awards. Art Matrix Fractals
Softology
Windows application that generates fractals, cellular automata, attractors, IFS, Lsystems, music, and other related simulations. Supports 2D and 3D fractal generation and movies.
http://www.softology.com.au/

Extractions: Main Gallery Software Links ... Contact Welcome. Softology develops high quality applications for Windows at affordable prices. These web pages have been kept relatively simple to speed download times. If you want some eye candy, download Visions Of Chaos and you will be able to make more pretty pictures and movies than your hard drive can hold. Main Gallery Software Links ... Contact
Fractals
fractals as music. Fractal equations and other complex systems areused in computer programming to generate random numbers. However
http://www.davesabine.com/media/fractals.asp

Extractions: Fractals as Music A fractal is a geometric shape that is complex and detailed in structure at any level of magnification. Many fractals are self-similar, meaning that each small portion of the fractal can be viewed as a reduced scale replica of the whole. ( I found the previous statement on an abandoned web page...I don't know who wrote it, but it simply defines the concept perfectly. For example, a natural example of fractal geometry can be seen in snowflakes in the sense that all snowflakes are almost identical in form yet the structure of a snowflake will never be duplicated exactly. Each flake differs slightly from all other flakes. Moreover, when a snowflake is magnified, each isolated portion of the flake is nearly identical to the whole flake! Other natural examples of fractals include ashes, tree bark, tree branches, broccoli stems, bubbles, carpet. Fractal mathematics is related very closely to chaos theory . Chaos theory is the study of forever-changing complex systems. Chaos theory is commonly misunderstood to be a belief that the universe is absolutely chaotic. However in fact, chaos theory suggests that objects, actions, environments, etc. that we perceive as chaotic may actually contain perfect order according to a complex system which we don't have the capacity to fully understand yet; therefore these systems, due to their complexity, seem like chaos.
Fractals In Music : Introductory Mathematics For Musical Analysis
fractals in music Introductory Mathematics for musical Analysis. From the Publisherfractals in music is an interesting crossover between disciplines.
http://hallmathematics.com/pure_mathematics/154.shtml

Extractions: Establishing a new genre of musical analysis, Fractals in Music goes beyond the usual analysis of chord structures and period forms to examine such topics as: Fibonacci number and golden mean proportions; Statistics for distinguishing among styles; Fourier analysis of melodic structure; Inner/outer form. It is intended for anyone interested in music or fractals and who has some knowledge of algebra and trigonometry. The many illustrations clarify such concepts as self-similarity and transforms. As the first of a series of advanced volumes, Fractals in Music is expected to be on the shelves of musicians for decades to come. From the Publisher Fractals in Music is an interesting crossover between disciplines. It shows how the mathematics of chaos theory and fractal geometry can be applied to understanding music in ways that may be more applicable to the technological age than current musical analysis is. Advertised as "music theory for the new millennium," it discusses Fibonacci numbers, statistics, and Fourier analysis, as well as randomicity, correlation, and inner/outer form.
HallMathematics.com Fractals In Music Introductory
HallMathematics.com fractals in music Introductory Mathematics for musicalAnalysis (Inmusic (Salt Lake City, Utah), No. 1.). HallMathematics.com.
http://hallmathematics.com/index.php/Mode/product/AsinSearch/0967172756/name/Fra
Music & Research Links: Nonlinear Science And Fractals
Composition Algorithmic Composition, a Definition Bruce Jacob, UMCP (algorithmiccomposition) Dynamical Systems and music fractals, Chaos, and music music, Mind
http://members.aol.com/dspondike/mnr/mnrfractal.html
Www.simtel.net: Realtm04.zip (Animate Fractals With Music From Sound Card)
Animate fractalswith music from sound card. Animate fractals with music from sound card. File Size 769387. File Date 199705-23 230000.
http://www1.simtel.net/pub/pd/39927.html

Extractions: Program Information var defaultAd = ''; var freqDays = 1; var freq = 1; var bsid = '18502'; var bsads = '7'; var bsloc = '1462494983'; var bswx = 720; var bshx = 300; var s = bswx + 'x' + bshx; var c = '916'; var cb = '2' Category: MS-DOS / Animation programs Publisher: Simtel Legacy File Name: realtm04.zip Downloads: Ware Type: Legacy File Size: 751.4 KBytes File Date: Description: Animate fractals with music from sound card What is Get it On CD? Top 5 Downloads, last week, in MS-DOS / Animation programs 3danim.zip Create high speed 3-D animation vfd_16d.zip FLC/FLI/AVI BMP/TGA/GIF cross-compiler flimaker.zip Autodesk Animator FLImaker, converts to FLI toon30.zip CARTOON v3.0: Draw/Animate long musical movies me20.zip Complete PC Movie creation system v2.0
Fractals In Music
fractals in music, About fractals in music Establishing a new genreof musical analysis, fractals IN music, a new book by Charles
http://hometown.aol.com/chasmadden/myhomepageindex.html

Extractions: htmlAdWH('7003013', '120', '30'); htmlAdWH('7002044', '234', '60'); Main Create Edit Help Fractals in Music About Fractals in Music Establishing a new genre of musical analysis, FRACTALS IN MUSIC, a new book by Charles Madden, goes beyond the usual analysis of chord stuctures and period forms to examine such topics as: It is intended for advanced students of music theory, whether individuals, composers, students, or teachers. It is intelligible to anyone having some knowledge of algebra and trigonometry. The many illustrations clarify such concepts as self-similarity and transforms. Contents 1. Introduction Chaos Theory Fractal Geometry
Our Fractal Universe
Basic Information About Different Types of fractals; A Gallery of Beautiful fractals.Fractal music What Fractal music Is; How it is Made; How it Sounds. fractals
http://library.advanced.org/25810/cgi-bin/fido.cgi?whichtype=0&page=../sitemap.t
Our Fractal Universe
made? When most people make fractal music, they usually use one ofthe many programs available to convert fractals into music. This
http://library.advanced.org/25810/cgi-bin/fido.cgi?whichtype=0&page=../music/how
¡¶Gnomon: From Pharaoh To Fractals¡·
fractals in music Introductory Mathematics for musical Analysis» CharlesMadden Hardcover August 1999
http://www.fractal.com.cn/fxlz/fxlz090.htm

Extractions: Fractals in Music is an interesting crossover between discliplines. It shows how the mathematics of chaos theory and fractal geometry can be applied to understanding music in ways that may be more applicable to the technological age than current musical analysis is. Advertised as 'music theory for the new millennium,' it discusses Fibonacci numbers, statistics, and Fourier analysis, as well as randomicity, correlation, and inner/outer form. Although focusing on classical music, the concepts are equally applicable to popular music or jazz. Many non-musicians may find Fractals in Music interesting because of its tie to the well-known fractal images that have been popular for the past several years.
ICMA : Array
Book reviews. fractals in music Introductory Mathematics for musicalAnalysis. by Charles Madden. High Arts Press (ISBN 0967172756).
http://www.computermusic.org/array.php?artid=12
Using Fractals For Music
Selfsimilarity was a characteristic of all the fractals that they found to be musicallyinteresting. Heinrich Schenker's classical music analytical techniques
http://www.fractalmusiclab.com/music/whyfactals.htm

Extractions: Of all the algorithmic composition techniques, fractals seem to produce better sounding results. Some thoughts on why can be found in an early article by Charles Dodge and Curtis Bahn in Byte called Musical Fractals , (June 1986, pp185-196): Self-similarity was a characteristic of all the fractals that they found to be musically interesting. Certain compositional procedures that make new musical material by systematically transforming previous materials, i.e. canon, fugue, and motivic development, can result in clearly self-similar musical structures. Unity and coherence in music is often achieved by repetition and development of a smaller number of musical motifs or themes. The hierarchical structure of 'self-similar' fractals appears to inherently have some of these same qualities.
MuSoft Builders: Creating Music Out Of Fractals With A Musical Generator
Create music out of fractals, numbers, yourname or photo with a musical Generator.
http://www.musoft-builders.com/

Extractions: Welcome to MuSoft Builders MuSoft Builders is a developer of electronic composition, graphics and internet software. a Musical generator creates music out of fractals, numbers, text and graphics. The music can also be converted to MIDI so that it can be played by other MIDI programs. A Musical Generator is software of the month for december 2002 in the CNFractal Music Forum. CamCapture is a program to capture webcams. See the Products page for a description of both products, preview and download. a Musical Generator CamCapture Version 3.0 of a Musical Generator has been released! Try the beta of a Musical Generator (Version 3.1)! ... What is CamCapture 1.1? Both a Musical Generator and CamCapture have been awarded an editor pick from ZDNet (PC Magazine) . For their review of a Musical Generator click on the logo above. We have added a page on the making of music on p (in Dutch and English ). It has been reviewed in NRC Handelsblad (a Dutch newspaper). Home Products Register Support ... Meet CEO!
MuSoft Builders: Creating Music Out Of Fractals With A Musical Generator
Mailing List. This mailing list is up to now experimental. We have createda mailing list on a musical Generator, fractals and fractal music.
http://www.musoft-builders.com/links/maillist.shtml

Extractions: Mailing List This mailing list is up to now experimental. We have created a mailing list on a Musical Generator, fractals and fractal music. Just subscribe to the list and feel free to exchange your ideas on these subjects with other subscribers. When you subscribe you will receive a confirmation email with instructions to how to use the list. In order to subscribe just send an email to the Musical Generator mailing list with no subject and just one line with the following text: 'subscribe amg-list'. If you wish to unsubscribe, the message should be changed to 'unsubscribe amg-list'. Once you have confirmed your subscription to the mailing list you can send a message to amg-list@musoft-builders.com You can easily select the messages from the mailing list in your mail program because the subject of each message is preceded by [aMG]. Home Products Register Support ... MuSoft Builders

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