Which manual says that?

The XF reference manual on page 26.

Looks like a cut-and-paste error.

Source: https://usa.yamaha.com/files/download/other_assets/4/323564/motifxf_en_rm_a0.pdf

VCM Equalizer 501
This effect emulates the characteristics of analog
equalizers used in the 1970s, recreating a warm, high-quality flanger effect.

VCM Flanger
These effects emulate the characteristics of analog flanger
used in the 1970s, recreating a warm, high-quality flanger
effect.

No doubt.

Extra Credit: Additional Reading On the “VCM EQ 501” and Equalizers in the Motif XF

Equalizers I

Equalizers II

Equalizers III

Wow, great links!

Is the 501 based on a particular piece of hardware?

Probably one or a combo. Listed as modeling vintage "boutique analog" hardware. The VCM effects were ready for public consumption around 2003 and articles mention 2 years of development time. So probably around 2001 the dev teams had to decide which hardware to model. One can look around 2001 to see if there's anything of note that was popular that fits the general description. Although the VCM 6xx equalizer does list more about its origins (for that different EQ). It says it's based on analog EQ from the 70s. At least narrows, for that EQ, choices of source hardware by a decade. There are other VCM EQs that list the specific hardware they are sourced from. Mainly because the hardware company is collaborating with Yamaha so there's benefit in advertising their product names licensed as software versions of the hardware counterparts.

Sometimes the GUI's "picture" of what the VCM effect looks like can give clues too. Motif XF had a more "this is what the pedal or effect looks like physically" way of representing effects - with knobs and virtual knob/switch labels on the screen. The VCM EQ 501 "look" matches how some of the dbx EQs look like - although dbx may be copying something else as well. I didn't drill down very far with this guessing game.

Maybe an insider (Yamaha employee) can sprinkle more clues or give an answer outright.

Is the 501 based on a particular piece of hardware?

Yamaha does not definitively point out exactly what is being modeled... it is not as if it is being made available separately for sale. The VCM items you find in the synths are based on “classic” gear. If you are old enough to have worked with the gear from back-in-the-day, it is usually fairly easy to get a very good idea about what is being modeled. And it really is about capturing the reason these classic items became classics (frankly, back in the day, who knew they would be “classic”?)

Since I was a recording engineer back in those very days, I can fill in a little of the story from my own experience. The better the gear, the better the recording... this is always true. But just because you have great gear doesn’t mean the engineer using it will make it sound great... this also is always true. That said...

Studios got reputations, mixing consoles got reputations, studio monitors got reputations.... but just because you had access to them didn’t automatically make a great recording. There is skill involved (making this point because, it ain’t just the gear!)

That being said, consoles like API and Neve got reputations for what is now called “classic” sound. The demand for a modular pre-amps, EQs, Compressor unit that could be moved from studio to studio was in full effect. If an engineer got a reputation for “a sound”, they wanted to ensure they could get their sound wherever they were asked to work... they wanted their favorite EQ, their favorite Compressors, favorite pre-amps, etc., to take with them. As recording companies started closing their dedicated studios, more and more recording engineers started to freelance... which meant you went where the work was...

NS10 became popular during this very time, because although many were carrying around their own small speakers, like the little cube Auratones, and others, the largest monitors you would carry yourself (as an engineer) were a pair of Yamaha NS10. Soon it became a studio staple... everywhere you went the small bookshelf reference monitors were NS10. Same was happening with processors like EQs, compressors and preamps. Rarely in studios did you have the ability to process every channel — often you had to rent these modular units depending on the number of simultaneous inputs you were recording.

The 500 series was born... a rack mount standard that allowed modular devices to be ported from studio to studio. Oh, there were all kinds of discussion as to whether if you pulled a channel strip out of a console, how much of a loss in sound is there. I remember a major discussion about how the sheer mass of the console it is contained in made a difference to how a channel strip behaved. Some insisted that if you removed the strip from the console there was a loss in sound quality. It was the “thing” to argue over back then...

At the time I’m still a young engineer, asking questions, trying to listen and learn everything I could. There were many, many 500 series modular components that hit the market... so what were the ones most sought after....? Well, most certainly the API and Neve EQ — depending on the engineer you asked.

When, years later, I was privileged to meet Rupert Neve at an Audio Engineering Society event, I asked him about so called “classic” gear versus the new stuff... and his response was enlightening. Basically, he said that back when there only was analog gear (it wasn’t classic back then), the goal was always getting the best possible sound. He was less concerned with was it analog or digital, the concern is with the sonic results. When you are aware of the limitations your understanding of what is an improvement become clearer. You could say that he was not looking back saying things were perfect when everything was Analog... back in the day you made analog do the best it could do. The goal is always great sound, not whether it’s analog or not.

The thing that captured the ears of engineers back in the day was how “musical” the EQ on an API or Neve console were... what does that mean? It’s a reaction, a feeling you get when EQ’ing something that the changes you are making enhance the musical signal. It’s something you ‘feel’. It’s that indescribable ‘thing’. Like why do people feel that way about certain analog synth filters.... they’ll say something counterintuitive like “Moog filters are phat”. That’s like an oxymoron, as a filter removes frequencies (it makes things thinner)... but there is a hard to describe ‘thing’ about what happens. An initial thickness that happens as soon as the filter is passing signal. That is the certain musicality in the device.

Back to EQs, and the late 1970s, seemed everyone wanted to capture the console channel strip in a rack mountable, portable format. But the leaders in mixing console EQs being emulated were API EQ and Neve EQ (and later SSL). Fast forward to the 21st Century, I’m quite sure what caught the ear of Mr. Neve about Yamaha’s VCM technology was its ability to capture that musicality (that certain something) that is the ultimate goal. My brief conversation with him predated the collaboration between a Neve and Yamaha on his VCM Portico EQs... and I had to smile when reading his comments on what the VCM approach to recreating the magic brings to the table.

At the end of the day, what actual schematics are being recreated in the VCM EQ 501 is of importance only from a curiosity standpoint. When I first joined Yamaha I used get very passionate about putting in print what exactly was being modeled or mimicked, but at the end of the day it is more important that when you use it, it does the job and enhances your so7nd. You gain nothing from knowing its an MXR stomp box versus another brand. If you owned an MXR Phase 90, when you call up the Phaser in your synth and you smile because it takes you to that same musical space, that is what matters. If you never owned one, never heard one, does it help to know what it is?

Many who ask about the origin only do so to dismiss it. That is (unfortunately) human nature. When Yamaha introduced the WX7 MIDI Wind Controller, the demonstrators would go out and perform... the first question they would get is “How’s the sax sound?” I watched the demonstrator tell the audience it didn’t do a sax sound... then go on to play harmonica, trumpet, drums, flute, oboe, synth lead, everything but a saxophone. The questioner would then go “Wow, it does all of those great sounds, how come it doesn’t do saxophone?”

Well, of course, it did. But the smart demonstrator never showed that first. The questioner only wanted to dismiss the product “That’s not a saxophone.” — which is a true statement and allows them to completely dismiss it without even listening to any other sounds. The demonstrator, (Tom Scott), would then say, “Look, I have my alto saxophone right here, when I want to sound like a saxophone I pick it up and play it.”

Read early reviews about the Electric Piano... you had these purest who refused to accept it because “that’s not a piano”. Observant but not really relevant... it comes down to, let it stand on its own merit.

Use the EQ because it enhances what you are doing... generally speaking, it’s attempting to recreate the vibe of the classic boutique 500 series modular EQs of the late 1970s early 1980s... kicked off by the popularity of the Neve and API console EQs which were all the rage (everyone was trying to emulate their musicality)...

Each of the Arpeggio Phrases has a source song - does knowing what it is help or hinder creativity?

Hope that is somewhat helpful. Maybe the new Portico EQs will trickle down some time in the future.
Read more about the collaboration
The Rupert Neve Connection
https://youtu.be/a_k--Gh8Xzk