Maths vs. Music - Tuning and harmony

[Alex K]

No, not placeboing

[Alex K]

I should try to split thread, but I don't know if my Mod skillz are sufficient

Edit: Ok, here we go...

[Alex K]

When art meets science!  Love it.

Yeah, right off the first C-chord you can hear that the just-tempered one has that choir-style "power major" sound, and leaves the equal-tuned on sounding distinctly flat.

To be honest, I find it very hard to hear any sourness in the jazz.  I think it's because I'm so used to hearing jazz played on out-of-tune pianos anyway, and sourness is a proper part of the jazz palette anyway.   I did notice an event at 1:16 in the first sample and 1:38 in the second (why the different timings?).

I just played both separately with two different tuning settings, and probably didn't exactly play the same thing twice. There's probably a way to play back a single Midi-recorded piece with different tunings, but I haven't found that button (or rather, sub-menu of the sub-menu) yet, so it's two separate recordings.

 I wouldn't say either sounded "bad," but the second was definitely a more jarring moment.  In a way I kind of enjoyed that little slap to the face.

To me the second one does indeed sound like it is played on a detuned bar piano. There appear to be some seriously flat notes in those 7,9 chords.

[bennyboy]

Nice job on the new thread, Alex!

[bennyboy]

To me the second one does indeed sound like it is played on a detuned bar piano. There appear to be some seriously flat notes in those 7,9 chords.

Yep. My opinion is that just tuning is great for the main triads, and crap for anything else. Hence my project idea-- specify exactly what note and system EACH note derives from, to guarantee a properly-tuned dynamic listening experience!

so let's say I'm in the key of C, playing a V-flat9 chord. Where are the notes, G-B-D-F-Aflat coming from?

I'd guess you'd want GBD built off the G for the purest major sonority, and the F and a-flat from the minor iv, f, for the best resolution in/to C. OR would you treat the extended chord as part of B-flat7, and use the A-flat which is subdominant to that? That might work if you wanted to modulate to c-.

It seems to me the best way to achieve this would be to record the song in equal tempering, and then go through the painstaking process, starting with the tonic, of saying where EVERY SINGLE note is derived. In fact, I'd even say there's another level of artistry there, since you and I might not choose the same tuning arrangement for this or that chord or section.

[Alex K]

To me the second one does indeed sound like it is played on a detuned bar piano. There appear to be some seriously flat notes in those 7,9 chords.

Yep.  My opinion is that just tuning is great for the main triads, and crap for anything else.  Hence my project idea-- specify exactly what note and system EACH note derives from, to guarantee a properly-tuned dynamic listening experience!

so let's say I'm in the key of C, playing a V-flat9 chord.  Where are the notes, G-B-D-F-Aflat coming from?

I'd guess you'd want GBD built off the G for the purest major sonority, and the F and a-flat from the minor iv, f,  for the best resolution in/to C.  OR would you treat the extended chord as part of B-flat7, and use the A-flat which is subdominant to that?  That might work if you wanted to modulate to c-.

It seems to me the best way to achieve this would be to record the song in equal tempering, and then go through the painstaking process, starting with the tonic, of saying where EVERY SINGLE note is derived.  In fact, I'd even say there's another level of artistry there, since you and I might not choose the same tuning arrangement for this or that chord or section.

Yes, I meant to replay to your idea sooner, I find this super interesting.

I'm a harmony theory noob, so I don't grasp all the implications of this yet.

Always the mathematician, I'm trying to think of examples where this is explicitly impossible, just to get a feel of how far one can go with this technique of dynamically just tuning or how you called it. I suppose enharmonic modulation

https://en.wikipedia.org/wiki/Modulation...modulation

would become awkward simply because during the transition from one key to the other, what is the same pitch in equal tuning appears in two different contexts which would have slightly different pitch in either key in a just tuning -
or one would have to fudge at some point...

[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):

[bennyboy]

A little more on that. . .

I find it useful to think of key-defining notes as detuned version of the desired note (tonic or third): in other words, it's more of an effect than a harmonic device. Here's a fun game to play: get a friend or family member, and have them hold a single note while you start very low and slowly slide up into unison. That "lock on" feeling, in my opinion, is the essence of the major/minor system.

So trying to mathematically coordinate harmonies that are coherent in both the before and after keys doesn't really matter too much. You get to make an arbitrary artistic decision in between about which harmonies / leading note pitches you will use, and which decision you choose will affect how the song is perceived by the listener.

[bennyboy]

Okay, so here's some info on the MIDI tuning system.  It turns out it allows for VERY small divisions of cents, so maybe a MIDI VST plugin will do what I need. 

https://en.wikipedia.org/wiki/MIDI_Tuning_Standard


which has stuff like:


This is straightforward enough (middle C = 60 by definition, and A is 9 semitones above that), so d = the equal-tempered semitone you want + a pitch fraction.  That fraction must be converted to a 14-bit fraction of 100 cents.  The math is a little confusing-- I'm not sure how to represent the fraction in 14 bits.  And I'm also not sure how to test if the playback is as fine as I want it to be-- unless I am generating all the soundwaves myself.


I guess the first step would be to write a little tuner that would let you set the justification of each of the 12 tones in a textbox.  Then you'd take in MIDI notes and forward them to a sound generator for playback with the adjusted pitches, thereby (I hope) allowing you to instantly tune ANY instrument you'd like.

I think this will work, and I think (hopefully) it can be achieved in a couple days.

[Alex K]

Nah, I was just too busy to engage. As a proof of principle, you could just try to write down a not too long chord progression specifying the pitches, and I can try to render them some time