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How to edit Modulation in Sax tones BK-9
For starters, when you say sax, there's a world of difference between the SN Alto Sax (0020) and the saxes in the regular Tones.
You only have the sampled vibrato in the SN Sax, you can't add any by using the lever. In fact, pushing the lever up (not side to side) alters the timbre of the sound in a way I'm not fond of. To the point where I tend to defeat the Modulation Assign (set to OFF) because I have a bad habit of pushing up on the lever whether it does anything or not!
Also, unless you REALLY want that gliss up effect all the time (Yamaha do it better by either tasking a momentary switch to add it, or have it triggered only when you make a jump of over a certain interval), go into the Super NATURAL Edit page and set Bend Mode to OFF. You'll now be able to use the bend lever for scoops and bends, which is usually needed far more than glisses. It's a shame there's no easy way to have both (you'd have to write two different Performances and switch between them).
Now, as to saxes in the Normal Tones, yes there you CAN alter the vibrato depth, but only on some of them! You'll just have to experiment a bit. For starters, listen to the sax with no lever. Some of them have sampled vibrato, some of them are straight. Most of the ones with sampled vibrato, the lever is tasked to alter the filter cutoff subtly. I think this might be what you are talking about - some of the saxes' vibrato won't respond to the lever. But some do. You'll just have to experiment. It's part of the semi-preset nature of the Tones. You can go in and adjust SOME parameters, but not all. And which ones you can and can't is pretty much up to you to find out!
Don't forget, on the Normal Tones, there is also one other way to add vibrato... Go to the Tone Edit page, go down to Vibrato Rate/Depth/Delay. Here you can add a boatload more vibrato than the lever usually gives you, adjust its rate to where it matches the initial sampled vibrato, and then dial in sufficient delay that it only comes in on much longer held notes (if that's what you are after!). Because the BK-9 doesn't have aftertouch, I tend to use this quite a bit for solos when my LH is too tied up to use the lever much!
TBH, my favorite way of playing saxes needs a keyboard with a pitch strip. Then you can use finger motion (like rocking a vibrato on a cello) to induce however much depth and speed you want for every note. Far more realistic! If you are using the BK in a studio, if you have a Korg or a Kurzweil or anything with a pitch strip, try using that. It's also great for doing untongued notes (hold the note and place finger a whole or half step up or down on the strip, for an untongued jump).
Pitch strips rock! Saxes, guitars, solo strings, anything that basically articulates, pitch strips give you a lot of control. BTW, this is about the only way to add some extra vibrato to the SN Alto Sax...
Sorry I don't have a one stop fix for your issue. Much of it depends on the underlying patch architecture which isn't editable. But there are enough patches that you can usually find some that do have the parameters you need.
If there are any specific Tones you are having issues with, let me know and I'll take a look at the Tone on my BK-9...
In fairness, this was Roland's first (hopefully not last!) arranger with SN Tones, so the controls seem a bit of a 'work in progress'!
To be quite honest, I rarely use the SN sax. I am much more a fan of the BlowAltoVib (0706) once you take the default MFX off of it (the Enhancer makes it a bit too bright, upstairs). But several other regular saxes serve well in certain situations. In fairness, compared to most arrangers, you have far more basic sax sample sets to choose from, so you rarely have trouble making one fit. I also am a big fan of layering two together for a thicker sound, or sometimes using the velocity range parameter to make one sax morph into another as you play harder.
If you have a wind controller, all those growl and noise parameters can be mapped to the controllers that CC1 and CC2 control, along with volume and pitch, so you ought to be able to get a decent sax that way, but sampled saxes without a breath controller is always a tough one to nail.
BTW, don't forget that some parameters can be mapped to the extra Control Input, so you could do basic volume with one pedal and growl or noise with another. And obviously, a capable remote keyboard with flexible control assignments would be able to map almost anything to almost anything!
But yes, just from the front panel, the SN sax is a strange duck, with controls you'd like to see on the lever on sliders, and vice versa...
Listen to this sick demo by Italian musician Marco Parisi, using a ROLI Seaboard controller...
Pretty much the best keyboard sax I ever heard, and note he's doing it all one handed! No lever needed with a ROLI...