User:Userminusone/Intervallic Polarity
Intervallic Polarity is an extension to the idea of consonance/dissonance, which was invented by me, Userminusone. (As of right now, this is nothing more than the way that I personally hear intervals, but I hope this idea catches on and gets extended/generalized by others in the microtonal/xenharmonic community)
Introduction: A few words used to describe some common JI intervals
Most will agree that the intervals, 1/1, 2/1, 3/2, and 4/3 have a rather plain sound to them. (This could also be said about 9/8 and 16/9, depending on context) In addition, many will say that simple 5-limit intervals such as 5/4, 8/5, 5/3, and 6/5 (and in some cases, 9/5, 10/9, 15/8, and 16/15) have a very sweet sound to them.
At the 7-limit, descriptions for even the relatively simple ratios are not as clear. In my opinion, 7/4 and 7/6 have a warm sensation that is similar but different to the sensation given by the 5-limit intervals. (This isn't the case for 8/7, 12/7, 14/9, and 9/7) In terms of 7/5 and 10/7, it seems that 7/5 is warm like the 5-limit intervals are, while 10/7 is not.
Further descriptions, based on my own microtonal experience
1/1, 4/3, 3/2, and 2/1 are "cleanly plain"
16/15, 10/9, 6/5, 5/4, 8/5, 5/3, 9/5, and 15/8 are "lightly warm"
7/4 and 7/6 are "darkly warm"
9/8 and 16/9 are "somewhat cleanly plain"
8/7, 9/7, 12/7, and 14/9 are "overbright" or "hotly dissonant"
7/5 is somewhere between "lightly warm" and "darkly warm"
10/7 is "bright" but not "overbright"
11/8, 11/6, and 12/11 are "warmly suspended"
16/11 is "disconnectedly suspended"
11/9 and 18/11 are "icy" or "coldly suspended"
32/27, 81/64, 128/81, and 27/16 are "dirtily plain" or "plainly dissonant"
Intervallic Polarity
Now we get to Intervallic Polarity. This measures the aesthetic of an interval by assigning it with a signed value. Values close to zero represent intervals that have a plainer sound, such as 9/8, 4/3, 3/2, 16/9, and other simple pythagorean intervals. Large positive values represent intervals that are "dark" or "hot", such as 7/4, 8/7, 7/6, 12/7, and so on. (The reason that I assigned these intervals with positive values is because they appear in tunings such as 5edo and 17edo, which have a "sharp" sound) Large negative values represent intervals that are "suspended" or "icy", such as 11/8, 16/11, 11/6, 12/11, and so on. (Analogous to intervals with positive values, the reason that I assigned these intervals with negative values is because they appear in tunings such as 7edo and 19edo, which have a "flat" sound)
DISCLAIMER: I haven't assigned any specific values of intervallic polarity to the intervals I described above. As of now, there is only positive, negative, and zero polarity for describing intervals, but hopefully, with the help of more experienced microtonalists, a more exact description of Intervallic Polarity can be formed.
Closing Thoughts
It seems that values of Intervallic Polarity have either a 12-tet or a diatonic bias, with the zero-polarity intervals being derived from Pythagorean (fifths-based) tuning. I'm not sure if this is a good thing or a bad thing.
In addition, it seems that Intervallic Polarity isn't symmetrical to the octave. (For example, 7/5 seems to have negative intervallic polarity while 10/7 seems to have positive intervallic polarity). Like the supposed diatonic bias, I'm not sure if this is a good thing or a bad thing either.