Delta-rational chord: Difference between revisions

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Inversions and revoicings of DR chords may not be DR, unlike the case with JI chords where inversions and revoicing of JI chords stay JI.

== Notation ==

=== ~~Increment~~ notation ===

=== Step notation ===

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, what we call ''~~increments~~''.

Some, but not all, delta-rational chords can be described as a list of steps 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, what we call ''steps''.

If you have some sets of ~~increments~~ related to each other but not to other sets of ~~increments~~, you could write the related sets with variables a, b, c or use one fewer letter by writing one set with positive integers without variables: an +a +b +a +b chord can also be written +1 +a +1 +a.

If you have some sets of steps related to each other but not to other sets of steps, you could write the related sets with variables a, b, c or use one fewer letter by writing one set with positive integers without variables: an +a +b +a +b chord can also be written +1 +a +1 +a.

== Mathematical definition ==

@@ Line 5: / Line 5: @@
 Inversions and revoicings of DR chords may not be DR, unlike the case with JI chords where inversions and revoicing of JI chords stay JI.
 == Notation ==
-=== Increment notation ===
+=== Step notation ===
-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, what we call ''increments''.
+Some, but not all, delta-rational chords can be described as a list of steps 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, what we call ''steps''.
-If you have some sets of increments related to each other but not to other sets of increments, you could write the related sets with variables a, b, c or use one fewer letter by writing one set with positive integers without variables: an +a +b +a +b chord can also be written +1 +a +1 +a.
+If you have some sets of steps related to each other but not to other sets of steps, you could write the related sets with variables a, b, c or use one fewer letter by writing one set with positive integers without variables: an +a +b +a +b chord can also be written +1 +a +1 +a.
 == Mathematical definition ==