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• Desafinado, Part Five: Getting Down Without Hitting The Bottom

  Back in the 1960's a guy named Shepard published a paper which described a way to create a descending scale of twelve notes such that every consecutive pair was perceived as being two notes, the second one lower than the first. That's not hard -- every Read More... Posted Monday, April 18, 2005 12:49 PM by Eric Lippert | 4 Comments Filed under: Rarefied Heights, Science, Music

• Desafinado, Part Four: Rolling Your Own WAV Files

  We’ve established why every just about piano in the world -- in fact, every concert-pitched musical instrument in the world -- is slightly out of tune. No one actually plays perfect fifths; every fifth interval is slightly flat. Why don't we hear the Read More... Posted Friday, April 15, 2005 12:29 PM by Eric Lippert | 8 Comments Filed under: Rarefied Heights, Science, Music

• Desafinado, Part Three: Too Many Fifths

  Last time we established the diatonic scale which has the nice property that there are five tone intervals and six fifths: Note Frequency A 220.000 B 247.500 C 260.741 D 293.333 E 330.000 F 347.654 G 391.111 and then double for the next octave up and Read More... Posted Wednesday, April 13, 2005 12:27 PM by Eric Lippert | 4 Comments Filed under: Rarefied Heights, Science, Music

• Desafinado, Part Two: A Perfect Pythagorean Tuning

  Last time we talked about the Pythagorean's discovery that sounds with vibrations in the ratios 1:2 and 2:3 sound consonant to the human ear. Let's explore the consequences of that a bit. Suppose we're building a stringed instrument from scratch and we Read More... Posted Monday, April 11, 2005 12:22 PM by Eric Lippert | 3 Comments Filed under: Rarefied Heights, Science, Music

• Desafinado, Part One: Eric Continues His Obsession With The Greeks

  Whew. That's enough wacky VBScript for a while. As I said a long, long time ago now, I came up with the idea of doing a little "wacky VBScript" quiz in order to illustrate some of the weird corner cases in language design. I want to do a long -- potentially Read More... Posted Friday, April 08, 2005 1:02 PM by Eric Lippert | 8 Comments Filed under: Rarefied Heights, Science, Music