Posted: Jan 18, 2016 4:23 pm
The last major item on my to do list for the first phase of my project was to come up with a sweet vs sour measurement for the set of pitches in a lick. It seems that people have been trying to come up with such a measurement and understanding of chords for a very long time, and while there are many putative theories on how this all works there doesn't seem to be one that puts the issue to bed. In short, the theories vary from: we respond to chords the way our cultural conditions us to respond to, we respond to chords because of how basic audio neural processing responds to the superposition of the harmonics in the notes. I, like many, imagine it's some combination of both; and that is what makes it difficult to come up with a definite theory. I'm still wading through some of the research on this but for now I have come up with my own measurement technique that attempts to take both cultural norms and the harmonic relationships in pitch sets into consideration. I could describe this in more detail but I'll just present the results and add detail if need be.

Lickmaker creates a Sweet measure and a Sour measure for each pitch set that it evaluates and then ranks each set on a scale from 1 to 10. A 10 on the sweet scale is the most sweet, likewise, a 10 on the sour scale is the most sour. The plot below shows where standard chords fall on the scale.

The sweet and sour components form a vector, I take the magnitude of the vector to come up with the sweetness magnitude. Here's a list of the sweetness magnitudes for standard chords.

Pow 10.0
Maj_i2 9.3
Maj 9.3
Maj_i1 9.2
Sus4 8.82
Sus4_i1 8.81
Maj6 8.29
Maj7 8.08
Maj13 7.14
7 7.07
Majb5 6.93
Maj11 6.62
7_#5 6.57
11n9 6.49
min_i2 6.46
min_i1 6.43
Maj9 6.36
min 6.23
Sus2 6.23
13 6.17
7_b5 5.69
9_i1 5.55
7_#9 5.43
9 5.43
dim 5.01
7_b9 4.99
min6 4.77
dim7 4.62
11 4.43
min7 4.33
min7_b5 3.95
min11 3.91
min13 3.86
min9 3.46

Power chords - root and perfect fifth rank a 10. (the scale can go higher, e.g. a root and an octave would be an 11- which is important because ...)

Looking at the chart we can see that the chords are generally divided along the lines that people generally think about chords, Major, Minor and dominant chords. Within these groups one my quibble over specific values and orders - but then again tastes vary.

I can now apply this metric to the founder set of licks I've been working with. The chart below shows where they fall.

This chart can't be directly compared to the one above for all chords because the Platko sweet/scour scale is adaptive. That is, if it "tastes" something that seems more sour it recalibrates what it "thinks" a sourness of 10 is. Sooooo. after tasting the blues licks in the founder set, it ranks the standard chords as being less our. as the figure below shows.

Now these last two figures can be compared to each other. And we can learn some things. Lick 3 seems to be about as sweet as a Power chord- and that's correct. Lick 10,11 which have minor third to Major 3rd hammer ons fall between the new major and minor chord groups. Lick 0 a standard blues run is measured as being more sour than standard chords. I imagine I'll tweak this over time but, all in all, I think it's not bad for now.

I should just note. This is looking at the notes as if they are being arpeggiated. If you strummed a 7 b9 chord it would sound more sour than Lick 0. The same sort of sweet sour measurement could be used to measure the sweet/sourness in a given beat or set unit of time but I'm not sure how useful that is - perhaps it would be a good way to weed out doublets created by adding a random note to check if the result is just too sour.

Any questions?