Delta-rational chord: Difference between revisions

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== Notation ==

=== Delta signature ===

~~Delta~~-rational ~~chords can be described with a~~ ''delta signature'' which has integer ratios, i.e. a list of (scaled) frequency increases 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 ''(frequency) deltas''.

A delta-rational chord is determined by two things:

* the dyad formed by its lowermodt 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

Dyads with no rational relationship (or no obvious one) are often indicated with +?.

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 ''(frequency) deltas''.

If you have some sets of deltas 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.

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 == Notation ==
 === Delta signature ===
-Delta-rational chords can be described with a ''delta signature'' which has integer ratios, i.e. a list of (scaled) frequency increases 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 ''(frequency) deltas''.
+A delta-rational chord is determined by two things:
+* the dyad formed by its lowermodt 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
+Dyads with no rational relationship (or no obvious one) are often indicated with +?.
+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 ''(frequency) deltas''.
 If you have some sets of deltas 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.