Delta-rational chord: Difference between revisions

Line 20:

Deltas that are ''free'', i.e. not required to be related to any other deltas are indicated with +?. For example, saying that a tetrad is "{{nowrap|+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 {{nowrap|+1 +? +1}}.

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 {{nowrap|+a +b +a +b}} chord can also be written {{nowrap|+1 +c +1 +c}} where c = b/a.

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 {{nowrap|+a +b +a +b}} chord can also be written {{nowrap|+1 +c +1 +c}} where {{nowrap|c {{=}} b/a}}.

Fully delta-rational chords always have a delta signature with no irrational ratios between terms.

Line 102:

sympy.nonlinsolve([err_squared_x, err_squared_y], [x, y])

</syntaxhighlight>

We similarly include a free variable to be optimized for every additional +?, after coalescing ~~each string of~~ consecutive +?'s ~~into one~~ and ~~eliminating intermediate notes~~. If two variables are related to each other but not to the integer deltas in the signatures, they have a common variable.

We similarly include a free variable to be optimized for every additional +?, after coalescing two consecutive +?'s and omitting the middle note. If two variables are related to each other but not to the integer deltas in the signatures, they have a common variable.

== DR chords in small edos ==

@@ Line 20: / Line 20: @@
 Deltas that are ''free'', i.e. not required to be related to any other deltas are indicated with +?. For example, saying that a tetrad is "{{nowrap|+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 {{nowrap|+1 +? +1}}.
-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 {{nowrap|+a +b +a +b}} chord can also be written {{nowrap|+1 +c +1 +c}} where c = b/a.
+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 {{nowrap|+a +b +a +b}} chord can also be written {{nowrap|+1 +c +1 +c}} where {{nowrap|c {{=}} b/a}}.
 Fully delta-rational chords always have a delta signature with no irrational ratios between terms.
@@ Line 102: / Line 102: @@
 sympy.nonlinsolve([err_squared_x, err_squared_y], [x, y])
 </syntaxhighlight>
-We similarly include a free variable to be optimized for every additional +?, after coalescing each string of consecutive +?'s into one and eliminating intermediate notes. If two variables are related to each other but not to the integer deltas in the signatures, they have a common variable.
+We similarly include a free variable to be optimized for every additional +?, after coalescing two consecutive +?'s and omitting the middle note. If two variables are related to each other but not to the integer deltas in the signatures, they have a common variable.
 == DR chords in small edos ==