Valentine/Chords: Difference between revisions

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The chords are ordered by generator steps. This chord ordering is useful because you can tell how often it will occur in a scale of valentine.

Example 1: Chord #13 is generators 0-5-9 and is a traditional five-limit major chord, 1/1-5/4-3/2. It occurs for the first time on the ninth generation, and will therefore occur six times (15-9) in valentine[15].

Example 1: Chord #13 is generators 0-5-9 and is a traditional five-limit major chord, 1/1-5/4-3/2. It occurs for the first time on the ninth generation, and will therefore occur six times (15-9=6) in valentine[15].

Example 2: Chord #38 is generators 0-8-13, which is 1/1-5/4-7/5, occurs for the first time on the thirteenth generation, and therefore appears only twice (15-13) in valentine[15].

Example 2: Chord #38 is generators 0-8-13, which is 1/1-5/4-7/5, occurs for the first time on the thirteenth generation, and therefore appears only twice (15-13=2) in valentine[15].

Each of the triads generated has three "inversions", i.e., can be written starting on any one of the three tones in the triad. The first chord is based on the number of generator steps for each tone. This ordering makes it easy to see how often it will occur in a given MOS, as noted in the examples above, but it may seem surprising if you're new to it: For example, chord #8 is 1/1-8/7-10/7, but it might seem more "natural" to use 1/1-5/4-7/4, which is listed as the second inversion. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.

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 The chords are ordered by generator steps. This chord ordering is useful because you can tell how often it will occur in a scale of valentine.
-Example 1: Chord #13 is generators 0-5-9 and is a traditional five-limit major chord, 1/1-5/4-3/2. It occurs for the first time on the ninth generation, and will therefore occur six times (15-9) in valentine[15].
+Example 1: Chord #13 is generators 0-5-9 and is a traditional five-limit major chord, 1/1-5/4-3/2. It occurs for the first time on the ninth generation, and will therefore occur six times (15-9=6) in valentine[15].
-Example 2: Chord #38 is generators 0-8-13, which is 1/1-5/4-7/5, occurs for the first time on the thirteenth generation, and therefore appears only twice (15-13) in valentine[15].
+Example 2: Chord #38 is generators 0-8-13, which is 1/1-5/4-7/5, occurs for the first time on the thirteenth generation, and therefore appears only twice (15-13=2) in valentine[15].
 Each of the triads generated has three "inversions", i.e., can be written starting on any one of the three tones in the triad. The first chord is based on the number of generator steps for each tone. This ordering makes it easy to see how often it will occur in a given MOS, as noted in the examples above, but it may seem surprising if you're new to it: For example, chord #8 is 1/1-8/7-10/7, but it might seem more "natural" to use 1/1-5/4-7/4, which is listed as the second inversion. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.