User:Grady/Harmonic similarity: Difference between revisions

Line 92:

Because 12edo has a perfectly tuned octave and near-perfectly tuned tritave, if any given interval is well approximated by the tuning system, then all the intervals that are harmonically similar to that interval will also be well approximated. Conversely, if an interval falls well outside of the tuning system, for example the [[7/4|subminor seventh]], then all the intervals that are harmonically similar to that interval, such as the [[7/6|subminor third]], will fall well outside of the tuning system as well. Because of this, not only do Western listeners not become acclimated to the subminor seventh itself, but they also don't become acclimated to other intervals that are similar in character, like the subminor third. If Western listeners regularly heard the subminor third but not the subminor seventh (which would be the case if [[9edo]] was the dominant tuning system instead, for example), then they might not find the subminor seventh as jarring, since they'd already be very familiar with a similar interval.

12edo even has a reasonable tuning of the [[5/1|fifth harmonic]], so it's arguably possible that this further contributes to the cohesion in harmonic similarity between the notes and intervals within the tuning system. However, it's debatable whether two frequencies separated by a factor of five have any non-negligible amount of harmonic similarity to each other.

12edo even has a reasonable tuning of the [[5/1|fifth harmonic]], so it's arguably possible that this further contributes to the cohesion in harmonic similarity between the notes and intervals within the tuning system. However, it's debatable whether two frequencies separated by a factor of five have any non-negligible amount of harmonic similarity to each other, or whether 12edo's tuning of the fifth harmonic is accurate enough for this to take effect.

=== The tritave versus the perfect fifth ===

Perhaps a more contentious implication of this theory is that it implies the tritave is a slightly stronger similarity relation than the perfect fifth. In Western music theory, they'd be thought of as equal in similarity, due to the abstraction of octave equivalence. However, this implication seems to generally align with the experiences of xenharmonic musicians, many of whom claim the tritave works better as an [[Interval of equivalence|equave]] than the perfect fifth.

@@ Line 92: / Line 92: @@
 Because 12edo has a perfectly tuned octave and near-perfectly tuned tritave, if any given interval is well approximated by the tuning system, then all the intervals that are harmonically similar to that interval will also be well approximated. Conversely, if an interval falls well outside of the tuning system, for example the [[7/4|subminor seventh]], then all the intervals that are harmonically similar to that interval, such as the [[7/6|subminor third]], will fall well outside of the tuning system as well. Because of this, not only do Western listeners not become acclimated to the subminor seventh itself, but they also don't become acclimated to other intervals that are similar in character, like the subminor third. If Western listeners regularly heard the subminor third but not the subminor seventh (which would be the case if [[9edo]] was the dominant tuning system instead, for example), then they might not find the subminor seventh as jarring, since they'd already be very familiar with a similar interval.
-edo even has a reasonable tuning of the [[5/1|fifth harmonic]], so it's arguably possible that this further contributes to the cohesion in harmonic similarity between the notes and intervals within the tuning system. However, it's debatable whether two frequencies separated by a factor of five have any non-negligible amount of harmonic similarity to each other.
+edo even has a reasonable tuning of the [[5/1|fifth harmonic]], so it's arguably possible that this further contributes to the cohesion in harmonic similarity between the notes and intervals within the tuning system. However, it's debatable whether two frequencies separated by a factor of five have any non-negligible amount of harmonic similarity to each other, or whether 12edo's tuning of the fifth harmonic is accurate enough for this to take effect.
 === The tritave versus the perfect fifth ===
 Perhaps a more contentious implication of this theory is that it implies the tritave is a slightly stronger similarity relation than the perfect fifth. In Western music theory, they'd be thought of as equal in similarity, due to the abstraction of octave equivalence. However, this implication seems to generally align with the experiences of xenharmonic musicians, many of whom claim the tritave works better as an [[Interval of equivalence|equave]] than the perfect fifth.