Check out the link above for a cool basketball game that uses algebra, we will be playing this on Monday!
Friday, September 30, 2011
Algebra Basketball
Check out the link above for a cool basketball game that uses algebra, we will be playing this on Monday!
Sunday, September 25, 2011
Sunday, September 11, 2011
Michael Harrison's "Revelation"
Composer Michael Harrison has reversed the progression of music history with his 2007 experimental work "Revelation."
Throughout musical history, musicians had been working to find a way to eliminate the dissonant sounds of bad intervals, called "wolf tones" or "wolf intervals." These intervals are the sloppy leftovers that are unavoidable when building instruments using Just Intonation scales or any other scales that utilize perfect ratios, which would include practically every instrument made before the 1700s when Equal Temperment hit the scene.
Every musician back then would have loved to find an instrument that would get rid of these ugly Wolf notes, and the Equal Temperment provided them with this answer and the freedom to easily play in any key... but it came at a price. The beautiful, sparkling sounds of the pure ratios needed to be compromised in the process, so now every guitar, piano, or other "fretted" instrument today plays intervals of notes that are only approximations and are slightly dissonant.
Notes played based on the pure ratios are more rich, resonant, natural, and beautiful sounding in every way, but many of us rarely get to hear them played. Though there still do exist experimental purists out there, such as Michael Harrison. In his "Revelation", he uses a piano tuned to a Just Intonation, and not only uses these usually avoided Wolf Notes, he embraces them and makes them the centerpiece of his song.
These otherwise dissonant intervals create a kind of drone with an audible "beat" at which the pitches fall in and out of alignment. Normally musicians will tune until they cant hear the "beat" anymore, but Harrison uses it to set the tempo for "Revelation", and it provides an almost eerie droning canvas for which to paint over with the sparkling pure tones provided by the Just-ly tuned piano. It works, somehow, and is hauntingly beautiful,
Throughout musical history, musicians had been working to find a way to eliminate the dissonant sounds of bad intervals, called "wolf tones" or "wolf intervals." These intervals are the sloppy leftovers that are unavoidable when building instruments using Just Intonation scales or any other scales that utilize perfect ratios, which would include practically every instrument made before the 1700s when Equal Temperment hit the scene.
Every musician back then would have loved to find an instrument that would get rid of these ugly Wolf notes, and the Equal Temperment provided them with this answer and the freedom to easily play in any key... but it came at a price. The beautiful, sparkling sounds of the pure ratios needed to be compromised in the process, so now every guitar, piano, or other "fretted" instrument today plays intervals of notes that are only approximations and are slightly dissonant.
Notes played based on the pure ratios are more rich, resonant, natural, and beautiful sounding in every way, but many of us rarely get to hear them played. Though there still do exist experimental purists out there, such as Michael Harrison. In his "Revelation", he uses a piano tuned to a Just Intonation, and not only uses these usually avoided Wolf Notes, he embraces them and makes them the centerpiece of his song.
These otherwise dissonant intervals create a kind of drone with an audible "beat" at which the pitches fall in and out of alignment. Normally musicians will tune until they cant hear the "beat" anymore, but Harrison uses it to set the tempo for "Revelation", and it provides an almost eerie droning canvas for which to paint over with the sparkling pure tones provided by the Just-ly tuned piano. It works, somehow, and is hauntingly beautiful,
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