RE: Maths vs. Music - Tuning and harmony
September 12, 2016 at 9:17 am
(This post was last modified: September 12, 2016 at 9:30 am by bennyboy.)
Okay, that's quite a thoughtful point. Let me start by saying that as soon as you leave equal tempering, and if you are going to tune dynamically, there is no true enharmonic equivalence at all-- they are, in fact, different notes.
My treatment would be much as you see in music theory. When you have what would normally be a flat, but you want it to serve an upward-rising "leading" function, you write it as a sharp. If you have what would normally be a sharp, but you want it to have a downward-rising leading function, you write it as a flat. In other words, you are using the nomenclature as defined by the new key. In music school, I wrote a paper on this, and the professors at that time (around 2000) wwere pretty please with the term I used: "microtonal passing tone." That really seemed to resonate with them (so to speak ;P).
So I think we can be perfectly comfortable with the idea of a micro-bend from one version of the pitch to another-- in the direction of intent. So if you want an upward function, you'd start with a lower pitch, and "brighten" it by sliding toward the higher pitch, which would be closer to the desired destination pitch (i.e. the tonic if rising or the third if descending) and therefore should feel more "leading". Here's a comical exaggerated example of that kind of effect (at around 1:40):
My treatment would be much as you see in music theory. When you have what would normally be a flat, but you want it to serve an upward-rising "leading" function, you write it as a sharp. If you have what would normally be a sharp, but you want it to have a downward-rising leading function, you write it as a flat. In other words, you are using the nomenclature as defined by the new key. In music school, I wrote a paper on this, and the professors at that time (around 2000) wwere pretty please with the term I used: "microtonal passing tone." That really seemed to resonate with them (so to speak ;P).
So I think we can be perfectly comfortable with the idea of a micro-bend from one version of the pitch to another-- in the direction of intent. So if you want an upward function, you'd start with a lower pitch, and "brighten" it by sliding toward the higher pitch, which would be closer to the desired destination pitch (i.e. the tonic if rising or the third if descending) and therefore should feel more "leading". Here's a comical exaggerated example of that kind of effect (at around 1:40):
