Manny’s FM-Xpert #2: “I’m Fixing a Hole Where the Timbre is Thin…”

Manny’s FM-Xpert is a deep dive into the the FM-X engines of the MONTAGE and MODX Music Synthesizers. This five article series is delivered in an accessible and entertaining way and includes MONTAGE content programmed by Manny himself. The other articles in the series are accessible via the links below: Manny FM-Xpert 1: “Acoustic Eccentricities […]

Manny’s FM-Xpert is a deep dive into the the FM-X engines of the MONTAGE and MODX Music Synthesizers. This five article series is delivered in an accessible and entertaining way and includes MONTAGE content programmed by Manny himself. The other articles in the series are accessible via the links below:

Manny FM-Xpert 1: “Acoustic Eccentricities and Stuff”
Manny FM-Xpert 3: “It’s Just a Phase, Man”
Manny FM-Xpert 4: “The Envelopes, Please”
Manny FM-Xpert 5: “Everybody’s Doin’ the Knob-O-Motion”

I’m Fixing a Hole Where the Timbre is Thin…

Download the updated file associated with this article series here! (Manny FMXpert.X7L)

Filling out our piano sound: In the first part of the FM-Xpert examples series, I broke down in detail using 4 of the 8 Parts in our FM-X Performance to create the body timbre, the overtone quirks of the lower and upper registers, and the hammer attack noise and ‘thunk’ of an acoustic piano. But those basic building blocks left us with a timbre that was ‘thin’ and missing some significant harmonic content. In this article I’m going to address the ‘timbral holes’ in our FM-X Piano and use the remaining 4 Parts to add additional components for the missing harmonics in order to fill out and ‘warm up’ the sound to replicate the rich & full dynamic characteristics of the piano. So, let start fixing the holes where our timbre is thin, to keep our ears from wandering….

Please reference the companion video on YouTube here. So, let’s continue with the example Performance “MF.HCM Piano Ex1” and select scene 6 to isolate Parts 2, 3 & 4 which are used together to fill out both the sustaining high harmonics and body timbre, as well as create additional hammer attack brightness in the lower register. Play the notes below E3 at very soft and very hard velocities and pay close attention to the timbral response. These Parts are following the same general approach as Part 8, with Part 2 using Algorithm 25 and Parts 3 & 4 using Algorithm 67:


Part 2 is used to warm up and fill out the basic Part 1 Piano timbre, and I’ll get to it in a moment when discussing the Insert Effects. I’ve used Parts 3 & 4 to give a multitude of 2 Op Stacks combined and blended together to generate additional body and high harmonic content.

You may wonder why so many 2-Op Stacks – that’s 8 Stacks in two Parts. The short answer — the lower register of a piano has a LOT of bright upper harmonics that behave very ‘linear’ in regards to volume & brightness with velocity dynamics, which is not how FM behaves. The longer, geeky answer is that harmonic creation is very non-linear, dynamically speaking, in FM because of Bessel Function behaviors.

Quick technical detour — To get more & brighter harmonic content in FM, we increase the Modulation Index, which is the output level of the Modulator Operator input to the Carrier Operator. However, the math of the FM algorithm dictates that the relative amplitudes and the phase of those various harmonics will change in a non linear manner with the Index. Thus a waveform that we’ve made with nice ‘integrated’ harmonic amplitude relationships can literally ‘disintegrate’ with the Modulation Index changes, resulting in what we hear as ‘holes’ or ‘voids’ in the harmonic series – this is the classic FM characteristic that people have historically described as ‘thin’ or ‘digital’ sounding, which sometimes is really cool and what we want for some sounds – but which is definitely not what we want to maintain the rich & full dynamic harmonic integrity of our piano timbre. With more Modulator stacking and branching you have in your algorithm, along with the higher Frequency Ratios used to get those high harmonics, the more complicated it gets. Thus to get a ‘linear’ dynamic response I decided to mix together those eight 2-Op Stacks available in Algorithm 67 from 2 Parts. Each Stack has different Operator Ratios and Waveforms, each adding different harmonic spectra components in the mid, upper mid, high, and upper high harmonic range, etc. Then the relative amplitudes of each harmonic range are controlled by straightforward mixing of the Carrier Operator Levels. Thus, we don’t have to worry about the Modulator Index/FM math issues. Additionally, instead of using much Velocity Sensitivity for the Modulator Op levels (i.e. Modulation Index) for dynamic brightness I’m using velocity control of Filter cutoff to get the appropriate linear dynamic brightness response and prevent the timbre from ‘disintegrating.’ Essentially, it’s using a hybrid combination of additive and FM synthesis concepts.

There are additional tricks used in Parts 2, 3 and 4 to finesse, filling out, and warming up the timbre. The first is basic detuning of the Operators across all 3 Parts, as well as the Parts themselves. The second is the use of the Chorus Insert Effect for Part 3. The third is a slow LFO Pitch Modulation of selected Operators across all three Parts to recreate the harmonic ‘beating’ movement in sustained piano overtones. This helps to replicate the richness in a piano where there are multiple strings closely tuned for the majority of the notes. Another trick is liberal use of Part EQ. As mentioned above, using the Modulator Index gets very wonky when trying to make specific tonal changes in the harmonic balance without having FM math phase issues begin to make the timbre disintegrate. EQ is a quick & linear way to vary the tone, and Montage has powerful EQ available per Part. I used a lot of parametric equalization in throughout all the Parts, and here’s the particular settings for Parts 3 & 4:

I’ve also used the Phaser Insert Effect as a trick to alter timbre for Parts 2 & 4. Now, I mentioned previously that certain changes in harmonic phase can make an FM timbre fall apart, so why use a Phaser? The (grossly) simplified reasons are Phaser parameters do not change with velocity dynamics, and with the Phaser Insert Effect the phase of the entire waveform as a whole is uniformly altered by the effect, not individual harmonics within the Operator groups as occurs in the FM synthesis Bessel Function domain. Thus, the Phaser effect with values of 0-5 for the Depth actually becomes a simple tone controller, without the waveform harmonic ‘disintegration’ issues (BTW – the next article, “It’s Just a Phase, man…” will be a deep dive into FM phase phenomena).

Anyway, I’ve used the VCM Stereo Phaser in four of the eight Parts. This can create subtle or drastic tonal variations in each Part’s timbre without messing around with Operator Ratios, Waveforms or Modulation Index while maintaining the desired dynamic characteristics. Using the Phaser insert as a timbral waveshaper is one reason I choose to use an entire Part — Part 2 – as a modifier of the basic Piano timbre layered with Part 1 and using the Phaser to modify the timbre sound:


The overall timbre of the sound can be altered by simply tweaking the Manual, Feedback, Stage, Mode and Color parameters. Play around with these Parameters of Insert Effect A for Parts 2, 4, 7 & 8 to see how they shape the timbre, without damaging the dynamic response.

To look how I’ve approached the velocity dynamic hammer attack and high harmonics in the upper register, Select Scene 7 to hear Part 6 in isolation. The basic philosophy is the same as what was done with Parts 2, 3 & 4. Part 6 fills out the timbre along with adding additional ‘tuned percussion’ style attack transients, again using Algorithm 67 with the four 2-Op Stacks. Ops 1 & 2 create a basic sawtooth wave type timbre to warm up the sound. Then I’m using Stacks 3-4 and 5-6 to create wide-range velocity dynamic marimba/vibe type of tuned percussion harmonics for the upper register notes. Ops 3 & 6 are in the Fixed Freq mode, with the Pitch/Key parameter set to 86 and 31 respectively, to enhance the inharmonicity in the attack playing up the keyboard to help better approximate those quirks of upper piano notes mentioned in Part 1 of the article. Ops 7-8 add in some more key ‘thunk’ transients. Then this Part is using the Chorus insert effect for more detuning/thickening.

So, let’s review from the beginning to see how all these Parts with all their harmonic components fit together. Select Scene 2 again to hear the isolated basic FM body timbre for the lower and upper notes ranges. Play dynamically at low and high velocities and listen to how the timbre varies in the typical FM manner. These 2 Parts creating the body timbre use a fair amount of Modulator Operator Velocity sensitivity in addition to using Algorithm 25 which is a complex 6 Op Stacked & branched structure:

Thus the typical FM math harmonic phase and amplitude behavior with modulation index results in ‘holes and voids’ in the overall harmonic structure of the waveform. Next, select Scene 8 again to hear all the isolated body timbre ‘warming’ overtones, dynamic high harmonic brightness, and the ‘stuff’ and ‘acoustical eccentricity’ components across the lower and upper note ranges. Play dynamically at low and high velocities and listen to how the timbre varies in linear manner, getting brighter as you play louder without the ‘holes and voids’ behavior. As detailed above, this is because most of these Parts use Algorithm 67, giving a combination of eighteen simple 2 Op Stacks to work with:

Plus, all these 2 Op Stacks use minimal Modulator velocity sensitivity. Filter velocity control of the Part and velocity control of the individual Carrier levels of each of the various mid, upper mid, high, and upper high harmonic component Op Stacks is used instead for dynamic brightness that prevents the FM harmonic ‘holes and voids’. This gives the final sound a full and ‘integrated’ harmonic behavior across the dynamic range. The sustain pedal subtleties in the sound are enhanced by the use of the Damper Resonance Insert Effect on every Part. The final timbral tonal tweaks and ‘sonic space’ enhancements make use of the Stereophonic Optimizer Master Variation Effect, the Master EQ and the Master Reverb. Whew ! Finally go back to Scene 1 to play and enjoy the fully assembled acoustic Piano sound.

Wrapping up, these first two articles examined the concept of Harmonic Component Modeling and using discrete groups of FM-X Operators to recreate a specific portion of the overall sound “TX816” style. Using the Montage’s Filters for controlling dynamic harmonic behaviors minimizing the typical quirky “FM sound” from using too much Modulator velocity sensitivity. We then used additional 2 Op stacks to create additional components to fill out the timbral holes in the sound that result from those same FM math quirks. We used non-integer Operator Ratios and Fixed Freq Mode Operators to recreate real instrument “Acoustic Eccentricities” and synthesize “Stuff” in our sound. Finally we touched on how the Montage DSP and Effects can be used as timbral shapers to tweak and refine our sound without diving back into the FM parameters.

I hope you’ve enjoyed the overview in these first two articles, and I’ll get into some extra geeky deep diving of the finesse and polish of the acoustic piano tone and response in the next two FM-Xpert eXamples articles, “It’s Just a Phase, Man…” and “The Envelope(s), Please.”

The video for this article is available below! Check it out: I think it will provide more clarity to the concepts covered in this article:

Also, check out the additional Performances “MF.HCM Piano Ex2”, “MF.HCM Piano Ex3” and “MF.HCM Piano Ex4SA” to hear tonal variations of the upper and lower registers of our Piano sound, achieved by tweaks to various Ratio Frequencies of some Operators, along with EQ & Phaser Insert Effect tweaks.

Check out the previous article in the series here. Ready for next lesson? Next Up — “It’s just a Phase, Man…” here!

Want to share your questions/comments? Join the conversation on the Forum here.

Keep Reading

© 2024 Yamaha Corporation of America and Yamaha Corporation. All rights reserved.    Terms of Use | Privacy Policy | Contact Us