Combining pattern structure

This does not describe current behaviour - this is upcoming in version 1.0.0.

A core feature of Tidal is the ease in which two patterns can be combined.

For example, these are two patterns being combined by adding together their elements:

"2 3" + "4 5 6"

The result of the above is equivalent to the pattern "6 [7 8] 9". But why?

Lets look cloesr. The two patterns line up over time like this:

  |  2  |  3  |
+ | 4 | 5 | 6 |

Unlike in previous versions of Tidal, when you combine two patterns in this way, by default the structure now comes from _both patterns_. This means you end up with _four_ events, because the 5 in the middle lines up both with the 2 and the 3, and gets split in half between them. We can add the resulting pattern to our table:

  |  2  |  3  |
+ | 4 | 5 | 6 |
= | 6 |7|8| 9 |

You can see that the 4 fits inside 2, so where they intersect, you get a new event equal to their sum 6.

Also see that the event with value 5 is cut in half, to create two, shorter events. Half matches with the 2 event and the other half matches with the 3 event.

The fourth and final event comes from the intersection of 3 and 6, giving a value of 9.

Structure from the left

In previous versions of Tidal, the structure always came from the left. You can still do this, but in this case using |+`.

For example:

"2 3" |+ "4 5 6"

In the above example, you end up with structure from the first (leftmost) pattern, like this:

   |  2  |  3  |
|+ | 4 | 5 | 6 |
 = |  6  |  8  |

You can see the structure comes from the 2 and 3. 2 lines up with 4, and the start of 3 is in 5, so you end up with 2+4=6 and 3+5=8.

Structure from the right

Likewise, you can take the structure from the right, with +|. So "2 3" +| "4 5 6" looks like:

   |  2  |  3  |
+| | 4 | 5 | 6 |
 = | 6 | 7 | 9 |

All the operators

Note that + is actually an alias for |+|. So |+ is to take the structure from the left, +| from the right, and |+| or + for both. Here are all the basic operators you can use to combine structure:

Function	Both	Left	Right
Add	|+| (or +)	|+	+|
Subtract	|-| (or -)	|-	-|
Multiply	|*| (or *)	|*	*|
Divide	|/| (or /)	|/	/|
Modulo	|%|	|%	%|
Left values	|<|	|<	<|
Right values	|>|	|>	>|

The last two are interesting, they let you only take values from one side. So for example you could take structure from the left, but values from the right with |>, for example:

   |  2  |  3  |
|> | 4 | 5 | 6 |
 = |  4  |  5  |

This is very similar to how |+| used to work in the versions of tidal prior to 1.0.0 - it took structure from the left, but values from the right. Accordingly and # maintains this behaviour in the new tidal.