View source for User:Aura/On 159edo Music Theory (Part 3)

 ''It is recommended that one read [[User:Aura/On 159edo Music Theory (Part 1)|Part 1]] and [[User:Aura/On 159edo Music Theory (Part 2)|Part 2]] prior to reading this article''

Now that we have covered the intervals of [[159edo]] as well as the possible trines, it's time we begin looking at possible triads.  To lay a few ground rules, the most consonant triads tend not only to involve the closest approximations of consonant just intervals, but the trine that forms their backbone is also consonant in as of itself.  One should note that even in the best-case scenarios, fourth-bounded triads will be ambisonant, as there is not much room for full-fledged consonance in triads like these due to the location of trill thresholds relative to both the top and bottom notes of the triad.

== Perfect Fifth-Bounded Triads ==
Because 159edo has so many notes, there are a lot of triads to go over just counting those bounded by the perfect fifth- in fact, there are as many as twenty-eight of them which can be treated as something other than the enharmonics of suspensions.  With that in mind, we will cover these first.

{{UserTag|Au|Aura|0040ff|As with the trines table in the previous part, most of the names given here are unique to me at present, but some, such as the Ptolemaic major and Ptolemaic minor are more objectively descriptive.}} 

{| class="wikitable" 
|+Table of 159edo Perfect Triads
|-
! Name
! Notation (from D)
! Steps
! Approximate JI
! Notes
|-
| Mirabilometric Major
| D, 
| 0, 50, 93
|
|
|-
| Mirabilometric Minor
| D,
| 0, 43, 93
|
|
|-
| Ptolemaic Major
| D, F#↓, A 
| 0, 51, 93
| 4:5:6
| This is the first of two triads that can be considered fully-resolved in Baroque, Classical, and Romantic harmony
|-
| Ptolemaic Minor
| D, F↑, A 
| 0, 42, 93
| 1/(4:5:6)
| This is the second of two triads that can be considered fully-resolved in Baroque, Classical, and Romantic harmony
|-
| Palingenetic Major
| D, F#\, A 
| 0, 53, 93
| 1/(21:25:42)
| This is the first of two triads that approximate [[12edo]] qualities
|-
| Palingenetic Minor
| D, F/, A 
| 0, 40, 93
| 21:25:42
| This is the second of two triads that approximate [[12edo]] qualities
|-
| Septendecimean Major
| D, F#↓/, A 
| 0, 52, 93
| 102:128:153
| This is the first of two triads named for approximating both the 17-limit and meantone 
|-
| Septendecimean Minor
| D, F↑\, A 
| 0, 41, 93
| 1/(102:128:153)
| This is the second of two triads named for approximating both the 17-limit and meantone
|-
| Pythagorean Major
| D, F#, A 
| 0, 54, 93
| 64:81:96
| This is the first of two triads that can be considered mildly unstable in both Medieval and Neo-Medieval harmony
|-
| Pythagorean Minor
| D, F, A 
| 0, 39, 93
| 1/(64:81:96)
| This is the first of two triads that can be considered mildly unstable in both Medieval and Neo-Medieval harmony
|-
| Neo-Gothic Major
| D, F#/, A 
| 0, 55, 93
| 22:28:33
| This is the first of two triads that can be used in both Neo-Medieval and Western-Classical-based paradiatonic harmony
|-
| Neo-Gothic Minor
| D, F\, A 
| 0, 38, 93
| 1/(22:28:33)
| This is the first of two triads that can be used in both Neo-Medieval and Western-Classical-based paradiatonic harmony
|}