Userminusone: New microtonal theory

2021-08-01T21:39:51Z

New microtonal theory

New page

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.

User:Userminusone/Intervallic Polarity - Revision history

Userminusone: New microtonal theory