Delta-rational chord: Difference between revisions

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A delta-rational chord is determined by two things:

* the dyad formed by its lowermost two notes;

* its ''delta signature'' which has integer ratios, i.e. a list of (scaled) frequency increases between successive notes, their ratios showing the simple rational relationships, with a + before each increase. Note that it is whether the deltas are rationally related ''to each other'' that defines DR, not whether the deltas are related to the frequency of the root.

* its ''delta signature'' which has integer ratios, i.e. a list of (scaled) frequency increases between successive notes, their ratios showing the simple rational relationships, with a + before each increase. Note that it is whether the deltas are rationally related ''to each other'' that defines DR, not whether the deltas are related to the frequency of the root. If we divide every term by the first term to make the first term 1, the result is called a ''normalized delta signature''.

* Two delta signatures are equivalent if one can be obtained from the other by scaling by a positive real number. For example, +2+e+3 is equivalent to +2φ+eφ+3φ, and both signatures imply a delta-rational chord.

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 A delta-rational chord is determined by two things:
 * the dyad formed by its lowermost two notes;
-* its ''delta signature'' which has integer ratios, i.e. a list of (scaled) frequency increases between successive notes, their ratios showing the simple rational relationships, with a + before each increase. Note that it is whether the deltas are rationally related ''to each other'' that defines DR, not whether the deltas are related to the frequency of the root.
+* its ''delta signature'' which has integer ratios, i.e. a list of (scaled) frequency increases between successive notes, their ratios showing the simple rational relationships, with a + before each increase. Note that it is whether the deltas are rationally related ''to each other'' that defines DR, not whether the deltas are related to the frequency of the root. If we divide every term by the first term to make the first term 1, the result is called a ''normalized delta signature''.
 * Two delta signatures are equivalent if one can be obtained from the other by scaling by a positive real number. For example, +2+e+3 is equivalent to +2φ+eφ+3φ, and both signatures imply a delta-rational chord.