Chord complexity: Difference between revisions

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1. Given some fundamental frequency ''f'', an ''N''-note chord built from very high harmonics of ''f'' will be a weaker match than an N-note chord built from lower harmonics of ''f''. In other words, 4:5:6 matches "1" better than 5:6:7. This is just a restatement of our definition of the simple complexity above.

2. Given some fundamental frequency ''f'' and a chord built from ''f''{{-'}}s harmonics, adding ''another'' note from ''f''{{-'}}s harmonics always ''increases'' the strength of the match to ''f''. In other words, 4:5:6:7 matches "1" better than 4:5:6.

2. Given some fundamental frequency ''f'' and a chord built from ''f''{{`s}} harmonics, adding ''another'' note from ''f''{{`s}} harmonics always ''increases'' the strength of the match to ''f''. In other words, 4:5:6:7 matches "1" better than 4:5:6.

The second proposition is the interesting one. It means that the chord 1:2 evokes "1" less than 1:2:3, which is less than 1:2:3:4, and so on, so that the chord 1:2:3:4:... evokes the frequency "1" most strongly.

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 . Given some fundamental frequency ''f'', an ''N''-note chord built from very high harmonics of ''f'' will be a weaker match than an N-note chord built from lower harmonics of ''f''. In other words, 4:5:6 matches "1" better than 5:6:7. This is just a restatement of our definition of the simple complexity above.
-. Given some fundamental frequency ''f'' and a chord built from ''f''{{-'}}s harmonics, adding ''another'' note from ''f''{{-'}}s harmonics always ''increases'' the strength of the match to ''f''. In other words, 4:5:6:7 matches "1" better than 4:5:6.
+. Given some fundamental frequency ''f'' and a chord built from ''f''{{`s}} harmonics, adding ''another'' note from ''f''{{`s}} harmonics always ''increases'' the strength of the match to ''f''. In other words, 4:5:6:7 matches "1" better than 4:5:6.
 The second proposition is the interesting one. It means that the chord 1:2 evokes "1" less than 1:2:3, which is less than 1:2:3:4, and so on, so that the chord 1:2:3:4:... evokes the frequency "1" most strongly.