Delta-rational chord: Difference between revisions

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JI chords and chords that are subsets of [[isodifferential chord]]s (these correspond to all chords of the form α : α + ''k''1 : ... : α + ''k''n for any positive number α and integers k1, ..., kn) are special cases of delta-rational chords, but in these chords ''all'' dyads are rationally related in frequency space, which we call '''fully delta-rational''' (FDR).

Some, but not all, delta-rational chords can be described as a list of increments between successive notes, their ratios showing the simple rational relationships and ? for no relationship (or no obvious one). For example saying that a tetrad is "+1 +? +1" means the first two notes and the last two notes have almost equal frequency difference (thus the ratio between the differences is 1/1), but the middle two notes are not in any simple relationship with the two outer dyads. The example 13edo chord is approximately +1 +? +1. Note that this notation only considers dyads between successive notes.

== Mathematical definition ==

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 JI chords and chords that are subsets of [[isodifferential chord]]s (these correspond to all chords of the form α : α + ''k''<sub>1</sub> : ... : α + ''k''<sub>n</sub> for any positive number α and integers k<sub>1</sub>, ..., k<sub>n</sub>) are special cases of delta-rational chords, but in these chords ''all'' dyads are rationally related in frequency space, which we call '''fully delta-rational''' (FDR).
+Some, but not all, delta-rational chords can be described as a list of increments between successive notes, their ratios showing the simple rational relationships and ? for no relationship (or no obvious one). For example saying that a tetrad is "+1 +? +1" means the first two notes and the last two notes have almost equal frequency difference (thus the ratio between the differences is 1/1), but the middle two notes are not in any simple relationship with the two outer dyads. The example 13edo chord is approximately +1 +? +1. Note that this notation only considers dyads between successive notes.
 == Mathematical definition ==