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FM-X Operator Ratios Less Than 0.5

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Michael Trigoboff
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I am working on replicating the sound of Jerry Garcia's guitar using the methods described in Thor Zollinger's excellent instructions. I got to a point where I needed a modulator running at 1/3 the frequency of the carrier. But Montage FM-X operators only go down to a ratio of 1/2 (0.5). I figured out a way to get the ratio I need.

I set Note Shift of my Part to -24, which is two octaves down. Two octaves down is 1/4 of the frequency. Then I set the ratio of my carrier to 4.0. That brought my carrier back up to the same it would have been if I had a Note Shift of 0 and a carrier ratio of 1.0. So far, I was just back to where I started from. But now, if I set a modulator to ratio 0.5, that modulator's frequency will be 1/8 of the carrier's frequency. I can set any ratio from 1/8 (0.125) on up.

What I needed was to get a modulator with an actual ratio of 1/3, I set things up as described above and then set the modulator's ratio to 1.33 using its Coarse and Fine settings. 1.33 equals 4/3. 4/3 x 1/4 equals 1/3, the ratio I needed.

So far, I've mainly been making science fiction/theremin noises, to the great amusement of my wife. But hopefully I'm going to get to the point where it sounds more like Jerry's guitar.

I hope this will be useful to other folks. It was fun to figure out. The Montage is an absolutely amazing piece of equipment.

 
Posted : 06/08/2019 3:31 am
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Another way to do it without any of the transposing hassles is set the modulator to Fixed Freq mode, tune to approximately 87 Hz (you'll need to adjust the detune a bit) then set the Pitch Key tracking to 99.

This way you don't have to rememebr the sound is transposed when setting all your other key scaling, breakpoints etc.

 
Posted : 06/08/2019 5:38 am
Michael Trigoboff
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Another way to do it without any of the transposing hassles is set the modulator to Fixed Freq mode, tune to approximately 87 Hz (you'll need to adjust the detune a bit) then set the Pitch Key tracking to 99.

This way you don't have to rememebr the sound is transposed when setting all your other key scaling, breakpoints etc.

Very cool! Thanks...

Why ~87 Hz?

 
Posted : 06/08/2019 5:59 am
Jason
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Manny answered this in the "fixing a hole" thread.

Depending on the exact "ratio" you need is you multiply middle C pitch of approximately 261 Hz by the 'sub ratio' factor. In this case 261 x 1/3 = 87. If you wanted a ratio of 1/4, it would be 261 x 1/4 = 75.5. a ratio of 1/5 would be 261x 1/5 = 52.2 Hz. You use middle C as the reference as FM-X uses that note as the 'center' pitch when setting the Pitch Key Scaling in Fixed Freq mode. Again, you always will need to tweak the detune to get the tuning exact given the resolution of the Freq Fine parameter

 
Posted : 06/08/2019 6:50 am
Michael Trigoboff
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Does it say that middle C is the “pivot point” anywhere in the Montage documentation? I didn’t see it anywhere in the Reference Manual.

If not, I think it would be a good idea to add that information somewhere.

 
Posted : 07/08/2019 1:04 am
Jason
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Montage Reference manual page 135

Center Key (Pitch Key Follow Sensitivity Center Key)

"Default" is generally middle C but can be programmed to other notes.

In the GUI, this parameter is adjacent to the key/pitch follow setting.

 
Posted : 07/08/2019 2:39 am
Michael Trigoboff
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Another way to do it without any of the transposing hassles is set the modulator to Fixed Freq mode, tune to approximately 87 Hz (you'll need to adjust the detune a bit) then set the Pitch Key tracking to 99.

I just tried this and it works really well.

But I don’t understand how to adjust the detune. I didn’t hear any difference in the sound through the full range of detune adjustment. Do I just need to listen more carefully, or is there some other way to tell how to make that adjustment?

 
Posted : 07/08/2019 3:13 am
Michael Trigoboff
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Montage Reference manual page 135

Center Key (Pitch Key Follow Sensitivity Center Key)

"Default" is generally middle C but can be programmed to other notes.

In the GUI, this parameter is adjacent to the key/pitch follow setting.

I just looked, and the (default and current) setting on my Montage for that is C3. 261 Hz is C4.

Something isn’t right here...

 
Posted : 07/08/2019 3:16 am
Jason
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C3 is considered middle C in Yamaha.
Most non-Yamaha keyboards consider C4 as middle C (same freq as Yamaha's C3)

So not sure where your mapping of frequency is sourced from. Are you sure this isn't a translation problem of Yamaha middle C vs. other systems? Just checking. I still don't have my keyboard online.

I believe this thread discussion (open pastebin, then go to link inside pastebin) generally mirrors what I think is your confusion around the MIDI note names and frequency.

Link considered spam ... Go here to find link: https://pastebin.com/5GGmwBR8
(Cannot embed directly) Apologies for making the reader jump through hoops to see the referenced link. The forum considers the direct link spam (it's not).

You cannot use the "dictionary" or "encyclopedia" definition of middle C - since Yamaha's convention is generally the odd-man out. If you look at your source for frequency C4=261Hz - you should also notice the MIDI note range is not C-2 to G8. It'd be C-1 for the lowest note and G9 for the highest MIDI note.

This doesn't match your keyboard of C-2 to G8 range (shifts everything down by a whole number). So once you can decipher the source of your frequency information to MIDI notes (not Yamaha standard) to Yamaha's standard - I think you'll be on the right track.

 
Posted : 07/08/2019 3:50 am
Michael Trigoboff
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Manny said the pivot frequency was ~261 Hz. I will have to check into this more tomorrow.

 
Posted : 07/08/2019 4:00 am
Michael Trigoboff
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C3 is considered middle C in Yamaha.
Most non-Yamaha keyboards consider C4 as middle C (same freq as Yamaha's C3)

Right you are. I just checked, and the key that recorded on a MIDI track as C3 produces 261 Hz.

My only remaining question is whether the setting you referenced on p. 185 of the Reference Manual actually affects the pivot frequency that Manny told me about. I messed around with it briefly, and it didn’t seem to. I’ll experiment with it further tomorrow.

 
Posted : 07/08/2019 5:38 am
Bad Mister
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Whether C3, C4 or C5 is middle “C” is a convention. Simply arm yourself with which convention is being used.
There are many (mostly silly) theories out there about this. It gets silly when you start thinking one is more correct than another. It all perspective.

Fact is, there is no right or wrong. It’s a convention. Fahrenheit is no more wrong than Celsius, or vice versa. Simply arm yourself with the convention being used. Once you know the conversion formula, your good to go. It doesn’t change how hot it is!

If you are piano-centric (because you believe the world of Keyboards most certainly revolves around the acoustic piano) you may get overly passionate about the C4 convention. “Well, obviously, C4 is correct... just count them!” From that perspective, who could argue?

The piano (circa 1700 AD) is the newbie! The Organ predates the piano by approximately 2,000 years, dating back to Pythagoras’ first pipe organ in 300 BC... which, by convention, had 61-key manuals, C-to-C. The third “C” was indeed the middle “C” on the keyboard. From this perspective, you can clearly see where that ‘convention’ comes from... the oldest of keyboards, the organ.

The sun does not revolve around the Earth just because we live here, in reality we revolve around it. Our sun is not the center of the universe... Keyboard history: there was, first, a 61-Key keyboard convention...
I’m pretty sure the conventions, C3/C4/C5, which, by the way, doesn’t really change anything musically, was altered probably based on conversations with non-musicians. (‘Scientific’ convention, means non-musicians)

For us, it’s more important to know which tuning convention is being used. When middle C = approx 261Hz and the A above it is exactly 440, we can pretty much guess Equal Temperament is being used. (Another convention, no more or less definitively correct, either).

The argument about Just Intonation versus Equal Temperament is yet another with no right or wrong (... they’re conventions)... just arm yourself with which is being used. If you drive a car in America you best stay on the right side of the road, if you drive the car in the UK or in Japan, you’d better know the convention!

 
Posted : 07/08/2019 10:33 am
Michael Trigoboff
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Thanks, Bad Mister.

My problem was that I didn’t know there were competing conventions. All of the MIDI note frequency charts I ran into showed C4 as 261 Hz.

Now that I know, it’s no problem. Software engineers like me are used to dealing with arbitrary standards. Hitting our heads against those walls is part of why they pay us the big bucks. 😀

 
Posted : 07/08/2019 5:30 pm
Michael Trigoboff
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My only remaining question is whether the setting you referenced on p. 185 of the Reference Manual actually affects the pivot frequency that Manny told me about. I messed around with it briefly, and it didn’t seem to. I’ll experiment with it further tomorrow.

It turns out that the setting from page 185 of the Reference Manual does not affect that pivot frequency

 
Posted : 09/08/2019 5:24 am
Jason
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Sorry - wrong key tracking (key tracking for PEG - not the operator itself). I've watched Manny's video again to get his lingo for "key tracking":

https://youtu.be/Ax0zRysLT1Q?t=688

Now straight with the parameter referenced - there is no center key setting for this.

Showing (in reference manual):

Pitch/Key (Pitch Key Follow Sensitivity)
Determines the sensitivity of the Key Follow effect (the degree depending on their position or octave
range). This is available only when “Freq Mode” is set to “Fixed.”
Settings: 0 – 99
0: All notes are the same pitch specified by Coarse and Fine.
99: Adjacent notes are pitched one semitone apart.

The documentation for the center key for FM-X is documented in the parameter manual page 11:

Pitch Key Follow Sensitivity Center Key
Determines the central note or pitch for Pitch Key Follow Sensitivity.
...
This parameter for the Normal Part (FM-X) is fixed to C3. You can not
change the value. This parameter is available only when “Oscillator Freq
Mode” is set to “Fixed.”

I usually treat the reference manual as my go-to source for what each parameter does. Then perhaps the data list if I want the "back end" description or other detail. The parameter manual I see as a glossary-with-useful-charts manual. But it does help complete the documentation. Then, and I'll often forget to check this, the "new features" documentation to be reminded of features that are "new" but never made their way into the documentation. You sort of have to bounce around if you can't find it in your first "go to" doc. I guess I reference the owner's manual for even higher-level stuff - but rarely.

You may want to merge all of these docs into one "Montage All" doc - so you can have just one place to search a given term. Assuming the term is unique enough - you'll be able to quickly run through all the docs in one swipe.
...

 
Posted : 09/08/2019 5:55 am
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