July 20 , 2010
Essays, Research, Loose Ends...
Alternate Tunings
Attack, Decay, Sustain
Calculus
Copyright
Combining Math and Music
Composers On Music
CourantRobbins
Design
Future Plans
General Literature Extracts
Math Extracts
Math Websites
Monitor Resolution
Rule of 18
Some Interesting Items
12TET/EDO Tuning History
Tutorials
Why Use Only 7 Notes of the 12 Available
In the
Past
(old ideas and animations I'm not ready to throw
out)
"Prosthaphaeresis" I investigated this as a precurser for logarithims but it turned out somewhat irrelevent to tuning history.
Apparently it inspired Napier to create logarithms which is how Equal Temperament is explained mathematically today but geometric derivations of Equal Temperament existed earlier [Zhu Zaiyu (朱載堉), and Stevin ] and a practical approximation using the ratio 17/18 had been in use even earlier (Vincenzo Galilei - I am not quite certain if this is precisely the "Rule of 18" still in use by many luthiers today http://hyperphysics.phy-astr.gsu.edu/hbase/music/guita.html- for all I know, Galilei might have gotten the idea from a luthier.).
In only one sense can I relate Prosthaphaeresis directly to Equal Temperament and that is speculative, more philosophical than mathematical. - The idea that this method of approximating a solution provided the more practical predictions of physical phenomena (Tycho Brahe). The approximations of Equal Temperament might therefore be found more acceptable as the scientific revolution continued to find such methods reliable.
It still has practical use in engineering (beats and interference).
I think the method of highlighting each step of the demonstration is of some interest. I had always found it annoying to match up the symbols in a verbal description with the ones in a completed geometric drawing accompanying it. The method in the second animation here allows for a more dynamic approach closer to that of a teacher drawing one step at a time.
It can certainly be improved, if you wish to try your hand the source is included here. Source files for Prosthaphaeresis in a zip file (319kb)
Characteristic Modes I like this stuff and it makes a nice animation but can't find any explanation which doesn't require a better mathematical background than I currently have. I am not the person to be explaining this to anyone else.
Damped_Oscillation This was my first real use of actionscript. Thanks to David M. Harrison http://faraday.physics.utoronto.ca/PVB/Harrison
/Flash/Tutorial/FlashPhysics.htmlPick Animation - This was my original idea-before I knew any Flash, - at 120kb it was too large - If I learn scripting better I might correct and update it. The idea is to show the fingerboard as if it were a spreadsheet.
Fence This just shows some ideas I had before taking up music. It indicates a mathematical approach used in the visual arts.