William Lynch's Thoughts on Septimal Harmony and 22 EDO

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This page reflects the POV of William Lynch.

Since I have alot of crap in my head and had no where to put it yet, I thought I'd write down a bunch of junk on here.

Chord Types

I personally feel that tetrads rather than triads should be considered full sonorities in 22 EDO and with septimal harmony in general. I consider there to be four main sonorities:

Major, Minor, Super, and Sub. While there are triads for these, they generally sound more interesting and distinct as tetrads. Major tetrad is of course 4:5:6:7 while minor is 10:12:15:17, Super is 14:18:21:27 and Sub is 6:7:9:11. Now while obviously these chords don't all exist in the same temperament universe, I consider them all to be consonant resolved sonorities. Some argue that 14:18:21:27 is not a consonant tetrad but it is as it's built from perfect fifths just like the other three. I consider it a main sonority despite it's biting brassy flavor which I love.

It's not just that, using 14:18:21:27 is much more distinct from major chords than just the super triad 14:18:21. While 14:18:21 can sound like a major triad, 14:18:21:27 doesn't really sound much at all like a major seventh chord. Now, I'm not saying triads are bad, but they tend to be boring in the septimal world. If you're using 5-limit porcupine or what have you, then go for triads however, I have a different approach I find useful :)

There are a huge amount of dissonant chord possibilities in 22 EDO and each one demands testing and experimentation. The most useful thus far in my explorations is the major Super Seventh chord which is basically a major triad with a super seventh. So if 4:5:6:7 is a tonic tetrad then this chord would be the septimal version of a dominant chord. If we play a F major tetrad as the tonic then I think a Bb Major Super Seventh chord works very well for the dominant. Because of voice leading, the dominant like chord is on the fourth not the fifth in this case.

Basically when a BbMS7 resolves to an Fh7 (F Harmonic Seventh), we end up with a inward motion of a dissonant 9/7 resolving to a more consonant 7/5. The Super seventh in the Bb chord creates powerful small step voice leading with resolves to the Fh7 tonic. Chances are, this may not work with minor tetrads but I'm not entirely sure yet.

Another interesting chord is the magic seventh chord which may be seen as the septimal or higher limit version of a diminished chord. Let's say perhaps we take our Fh7 chord again and contract it to a F*7 chord (F Magic Seventh), we then get a movement of the 5/4 turning to 6/5, 3/2 moving down to a 16/11, and the 7/4 remains as a common tone. This magic seventh chord could be used with Super seventh chords as well if we started from a F super seventh chord and moved to a F*7 it would be 9/7 moves down to 6/5, 3/2 again to 16/11, and 27/14 moving to a 7/4.


Ah Superpyth, that temperament which is sort-a like meantone, same structure but it's not the same at all. I personally think Superpyth demands an approach different than meantone, it tempers differently and sounds way too different. To be continued...


Porcupine is such a freakin awesome temperament and MOS. I have heard of people harmonizing the 7-note MOS with major and minor triads and while this works, it's kind of boring when there are only four. I personally like using subsets 8:9:10:11:12 clusters but spread out so the ninth and 11th are an octave higher than the root and 3rd.

Basically, just as people a long time ago stopped using only perfect fifths and began to find thirds as consonance, I feel that the 10 step or 11/8 interval should be considered a new point of restful consonance. Because porcupine tends to be undecimal like, it's a gateway to using the 11th harmonic and subharmonic within 5 limit structures. It's about as