User:Aura/On 159edo Music Theory (Part 2): Difference between revisions
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''It is recommended that one read [[User:Aura/On 159edo Music Theory (Part 1)|Part 1]] prior to reading this article'' | ''It is recommended that one read [[User:Aura/On 159edo Music Theory (Part 1)|Part 1]] 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. | 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. | |||
{| class="wikitable" | |||
|+Table of 159edo Perfect Triads | |||
|- | |||
! Name | |||
! Notation (from D) | |||
! Steps | |||
! Approximate JI | |||
! Notes | |||
|- | |||
| 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 | |||
|} | |||
Latest revision as of 15:49, 31 March 2026
It is recommended that one read Part 1 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.
| Name | Notation (from D) | Steps | Approximate JI | Notes |
|---|---|---|---|---|
| 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 |
