Posted:

**Feb 02, 2016 6:36 pm**I've been working on understanding the usefulness of the tension metrics and ways to mutate tension without changing entropy or sweet and sourness. The tension metric that seems to most lend itself to that is the sum of the change in tensions of the pitches as the lick is played. I.e. change in tension/time. I'll give an example of doing this with lick 0.

Here's where Lick 0 plots in sweet, sour, and sum of delta tension space.

And after mutating Lick 0 to with an eye towards creating tension variation and leaving other metrics unchanged. It's easy to see that the sweet and sourness didn't change but more variety of tensions are now available.

To do this I created a constructor that mutates the lick in ways that only effect delta tension and also limits the density of licks near a delta tension value. The number of permutations is n factorial the number of notes that can swap position so it's helpful to limit the number of varieties produced yet still get as wide a range of tension varieties as possible.

One type of mutation that can change delta tension without effecting other metrics is to permute note positions in the lick. Here's various tension metrics for the 6 versions of Lick 0 that I ended up with. They are sorted from lowest tension to highest tension. I don't allow bends to have note order changed so the g going to g# can't be swapped. It's pretty easy to see from the charts that the minimum tension has less peaks and valleys than the max tension version of Lick 0.

And here's the entropy plot for the set of 6 licks. They all fall on the same spot, so this mutation didn't change entropy.

It's a bit hard to know how much to trust the meaningfulness of these tension metrics. To help with that I sorted the founder set of licks by the sum of delta tension metric. The begging and end look right, the general trend looks reasonable. Here's the order sorted by tension. The tension value is printed next to the lick position number.

And here's how they sound in sorted order.

The first and last seem in the right place, and the trend seems right, but I find it harder to know if the rest are where they belong. That just may mean that my computer is more sensitive to small tension differences in a lick than I am.

You can also hear the variations of Lick 0 in sorted order here.

Here's where Lick 0 plots in sweet, sour, and sum of delta tension space.

And after mutating Lick 0 to with an eye towards creating tension variation and leaving other metrics unchanged. It's easy to see that the sweet and sourness didn't change but more variety of tensions are now available.

To do this I created a constructor that mutates the lick in ways that only effect delta tension and also limits the density of licks near a delta tension value. The number of permutations is n factorial the number of notes that can swap position so it's helpful to limit the number of varieties produced yet still get as wide a range of tension varieties as possible.

One type of mutation that can change delta tension without effecting other metrics is to permute note positions in the lick. Here's various tension metrics for the 6 versions of Lick 0 that I ended up with. They are sorted from lowest tension to highest tension. I don't allow bends to have note order changed so the g going to g# can't be swapped. It's pretty easy to see from the charts that the minimum tension has less peaks and valleys than the max tension version of Lick 0.

And here's the entropy plot for the set of 6 licks. They all fall on the same spot, so this mutation didn't change entropy.

It's a bit hard to know how much to trust the meaningfulness of these tension metrics. To help with that I sorted the founder set of licks by the sum of delta tension metric. The begging and end look right, the general trend looks reasonable. Here's the order sorted by tension. The tension value is printed next to the lick position number.

And here's how they sound in sorted order.

The first and last seem in the right place, and the trend seems right, but I find it harder to know if the rest are where they belong. That just may mean that my computer is more sensitive to small tension differences in a lick than I am.

You can also hear the variations of Lick 0 in sorted order here.