We created a file of incredible resolution – the text of Alice in Wonderland reduced to 1pt size would replicate a high resolution photograph – but present something that is easier to understand and view in a side-by-side when magnified.

Alice in wonderland is replicated better by seven shades rather than three shades because of simple mathematics. The typical grayscale is comprised of 256 gray levels. Epson divides this into three inks. Piezography K7 curves are actually made of 256 divisions from more than 64,000 possible grays. Piezography K7 uses seven of these curves to print 256 gray levels. K6 uses six of these curves. The result of using Piezography is that it is much easier to print the gradations.

Another way of thinking about it is having 256 apples which three people have to carry (Epson ABW). Each person would need to carry nearly 86 apples which is quite an arm full.  With Piezography the 256 apples are carried by seven persons, each holding only 37 apples – representing less than half the work. The Epson printer is good – but not that good when it comes to reproducing black & white with only three shades of black. Piezography K7 is excellent! K7 far exceeds the capability of the printer on which it is installed.

Speaking of apples – round and small like printer dots…a better way to understand why Piezography K7 prints with greater detail in the same printer that can not print at that same level of detail when used with Epson ABW – is to understand printer dots. Printer dots are comprised of ink droplets which are sprayed in a pattern according to the dithering requirements. Epson ABW has only three shades with which to replicate 256 gray levels.  There are not enough shades in which to reproduce the lightest tones, so Epson relies on a dithering pattern that spreads the dots of ink apart. When the ink dots are spread wide apart, the human eye is fooled into seeing lighter tones. But, when the ink dots are spread apart like that, there is no ink with which to print fine detail.

Piezography K7 curves never print dots of ink spread apart. Instead, more dilutions of ink (shades) are used with which to carry the shades of gray that the Epson ABW dither cannot. Because the dots of ink are so close together when Piezography K7 is used, the detail which was not able to print with Epson ABW is clearly printed with K7. That is what you are seeing when you look at the Alice in Wonderland test above. K7 prints many more dots of ink per inch than can Epson ABW. The QuadTone RIP allows us to design a curve structure that prints dots of ink always touching and adjacent to each other. No paper white comes through that does not have one of the ink shades printing solid upon it.

We know some users who design their own curves with QuadTone RIP have not been able to reproduce our effect. The K7 curves are produced by our own software. Curve design and linearization is an art in itself.

Piezography has a number of variations that make a near infinitude of possibilities when all of the ink/paper variations are considered. Piezography pigment is so finely milled that the tone of a paper has an enormous affect on the final “hue” of Piezography ink.

For example, Piezography Neutral ink does not appear “neutral” on all papers. It was designed to appear achromatic (with equal amounts of red, green, blue) to human eyes when viewed under 5000k on Hahnemuhle Photo Rag paper. The tone of Photo Rag is similar to other sheets such as Innova Photo Cotton Smooth and Alise Bright White. But when the paper beneath Piezography Neutral inks is changed to a warmer or cooler white, the neutral tone shifts warmer of cooler. This is true for all of the Piezography inks.

So in one sense, it is possible to customize one’s output through careful paper selection. Yet there are also paper brands such as Canson which has such a unique coating formulation, that the selection of a sheet has no bearing on what the tone of the ink might be. In one example, Canson Rag Photographique which is about the same tone as Hahnemuhle Photo Rag creates a chocolate brown color when printed with Piezography Selenium inks. Yet the same ink on Hahnemuhle Photo Rag creates the imitation of selenium toned fiber base print. Currently, Canson is the only paper we know displaying its own characteristic shift that is not necessarily related to paper color. It offers some interesting possibilities that we did not anticipate.

Another way to customize Piezography is through ink blending. There are four major inks choices in the K7/K6 series: Neutral, Selenium, Sepia and Warm Neutral. Piezography Special Edition ink is one of our most popular products. But, it is a blended ink. Jon Cone blended this ink to celebrate a more complex ink formulation he created that produced the triple-split-toning of the Ashes and Snow exhibition and collector’s prints for photographer Gregory Colbert.

Special Edition ink use neutral shades in the highlights, and blends portions of selenium and sepia through the mid-tones, and finally sepia in the darkest portions of the tonal scale. The recipe is a secret. The process is not.

To blend an ink only requires understanding of how the Piezography K7/K6 system uses curves.

Curves are designed for the QuadTone RIP application to control each of the six or more print heads of the selected Epson printer. Rather than send an RGB image file that is then converted into color ink droplets by the Epson printer driver, a grayscale image is sent to the QuadTone RIP which is a unique printer driver. QTR drives each print head in a controlled way by taking data that is embedded in a QTR “Curve”. A curve is actually made up of six or more curves. Each of these six or more individual curves is responsible for controlling each of the six or more print heads. Without a lengthy explanation that would take up an entire topic by itself, and has already been covered in depth on this blog, a curve represents what percentage of image tone density is represented as a percentage of ink shade at that particular print head. As long as all of the Piezography ink shade densities in an ink set are similar to the ink shade densities in another Piezography ink set – the same curve can be used. And that is exactly how we designed Piezography inks and QTR curves. We designed the inks so that they are interchangeable.

A single QTR curve works for each of the different Piezography ink sets. This means that you can mix the different Piezography ink sets as long as you keep the same shade order. This is how we split tone the inks. One of the best examples of a split tone ink set is when Selenium inks are used to print shades 5 and higher, and Sepia is used to print shades 4 and lower. But, blending – is when literally the inks are blended together. In other words, two different inks of the same shade are poured together into a bottle and shaken. Then this ink is put into a cartridge. My Special Edition inks are a blend of Selenium and Sepia.

Blending Neutral into Sepia or Selenium is like adding neutral density and is not that effective unless a subtle shift is required. But Neutral inks can be made to be warmer or colder by blending some Sepia or Selenium into them. WarmNeutral ink can be made warmer with some Sepia. Selenium can be made more complex with some Sepia or some Warm Neutral… You can buy all of these inks in small bottles and we sell empty Nalgene bottles for your mixing, as well as 60ml syringes with 4 inch blunt needles. The best way to experiment is with a desktop printer and sets of refillable carts. You can then transpose the results to large format with less expense. You only need to make certain that you do not mix one shade of an ink with a different shade of another ink. It has to be the same shade of one ink with the same shade of another ink.

Empty bottles are located here: http://shopping.netsuite.com/s.nl/c.362672/sc.15/category.9280/it.C/.f

Refillable carts are located here: http://shopping.netsuite.com/s.nl/c.362672/sc.15/category.1313/.f

There are two RIPs which support Piezography inks. The ErgoSoft StudioPrint RIP (SPR) is expensive and very full-featured. It has enormous flexibility at a high cost. The other, QuadTone RIP (QTR) is inexpensive ($50) and because we produce the media linearizations for it with our own Piezography software – the output quality is actually higher. We use both products in our studio. We run QTR to produce all single ink set prints including our glossy prints. We use SPR to blend between two or more ink sets.

QuadTone RIP by Roy Harrington is based upon open-source code and we embraced this concept after our way to early for primetime ICC based Piezography BW ICC system of 2003. In 2003, we had invented an ICC profiling system for monochromatic ink shades that used the Epson RGB driver. But, the average consumer did not understand how to use ICC profiles, or began to mis-apply the workflow necessary to produce proper color management. ICC workflow is much more mainstream these days, but open source software is much more mainstream than ICCs which depend upon the OEM’s printer driver.

About 2004/2005 we began to look seriously at QTR. The QTR is an individual ink jet head printer driver. QTR is able to control each individual ink jet head. QTR uses a system of curves to manipulate a grayscale image file. It uses a curve for each ink jet head. Because a different shade of ink is associated with each ink jet head, a different curve is necessary for each shade of ink. These curves are grouped together into a file that is (still called a curve.)

We tried to use the QTR tools to make “curves” (a profile in QTR) and found that that the tools were suitable for making 3 and 4 shade curves. But, to make 6 and 7 shade curves that would be suitable to our next generation 6 and 7 shade inks…well it was just not possible to reach the standard that we had delivered with PiezographyBW ICC.

I always want each new generation of Piezography to be better than the one before. PiezographyBW ICC was a quantum leap in quality and functionality over the PiezographyBW plugin. We believed that seven shades of ink (K7) would dramatically improve the output of the ICC based system that used only 4 shades of PiezoTone inks. My answer was in developing a QTR profiling application. We developed in-house (as usual) a profiling app that can linearize up to 8 ink channels and output a QTR compatible curve set.

We use the application (we call Barney, or sometimes The Piezography Profiler) to create curve sets for each of our supported printers. These curve sets are for a core base of popular papers. When we complete a new edition we send these curves to Roy Harrington who incorporates these curves into his QTR software. We do not charge the customer for these curves. We do not charge Roy for these curves. When you download and install QTR – these curves are installed automatically into your computer and will be available for your when you operate the RIP. We do make custom curves for those who wish to use media we do not already support, or wish to have their aging printer linearized (rather than freshening up the printer by replacing worn print heads). But generally speaking, when you download QTR for your Piezography supported printer – you have a turn-key system.

This is what I am doing behind the scenes to make your Piezography experience a magnificent one!

Curves Architecture

The anatomy of a curves structure is related to how much total ink the paper can absorb, what is the combination of shades that will produce the deepest dMax (its not black alone), and the amount of ink shades that need to be structured, overlapped and feathered in and out without leaving any sign of their presence. I create a curve structure based upon using as much density that is practical on the lightest shade first. As I feather in the second ink it affects the shape and height of the bell curve of the first ink. I have a method that lets me rough in this process quickly – but it takes several days to make a set of curves that on their own are near perfection.

An algorithm is used that smooths the curves (although the process actually roughs them up a bit.) And the end result is that by measuring 255 printed patches of ink and the paper white, the algorithm is able to produce a perfect linearization from dMin to dMax. The curves are then plotted at 256 locations each curve, choosing the appropriate point out of more than 64,000 levels – in order to combine together into one media profile.  A media profile is made for each of the papers we generally support, and these are made available to the author of QTR who then includes them in the installation package. It is possible to order custom curves for QTR. We supply the 256 patch target, a special Master Curve, and a set of instructions to follow. The charge as of this writing is only $99 each.

Here is the link to downloading QTR for Piezography. Please pay your $50 shareware to the author.

Here is the link to our manual on using QTR. We do it a bit differently than the way it is done in the manual supplied with the download.

Below is an actual curve for QTR made by the Piezography profiler for the Epson 2400 printer, K7 inks and Hahnemuhle Photo Rag paper.

Piezography Glossy is a rare beast right now. It’s the newest incarnation of the black & white inkjet systems Jon Cone has been developing since 1994. Mostly, printing customers have been coming to Vermont to work with Jon Cone in his studio – to check it out – relate to it in terms of their own work, and to test their own belief system in traditional look photography. Piezography Glossy ( we call it Piezography MPS or K8 in official release form) is to the air-dried silver print, what Piezography K7 is to the palladium/platinum print. For those of you who have tried your hand at Piezography K7 matte printing – you are well aware of the high standard that the system produces. Piezography Glossy has again raised the bar this time significantly higher.

Note: Piezography Selenium MPS and Selenium K7 are the same inks. We use K7 where we mean matte only. We mean MPS for the Gloss only components. Piezography Selenium K7 inks shades 2-7 are matte and glossy compatible. The ink has a triple encapsulation method that makes them compatible with both surfaces. For matte only printing we supply the traditional Shade 1 black (bottled as “Neutral” Shade 1), and instead of supplying a Gloss Optimizer in the unused 8th position we supply a bottle of PiezoFlush. A Glossy MPS system adds the MPS Shade 1 Black and the Glossy Optimizer and requires optional workflow in comparison to the matte only version to utilize it.

Piezography MPS is similar to the traditional air-dried silver print in dMax (2.70 and higher), has a surface which is imitative of an air-dried glossy fiber paper, has zero metamerism, and zero bronzing, and has a perfect gloss differential…but there the similarities end. Piezography Glossy is capable of higher detail than silver paper, and has a greater dynamic range with better shadow and highlight detail. Piezography MPS may be the best printing method you have ever tried.

Note: “MPS” is short for Master Printmaking System.

Piezography MPS is a very high resolution process. If an image file is of extremely high optical resolution* is printed, it will resolve significantly more detail than Canon, Epson and HP inkjet processes can using their own drivers or other RIPs. Yet, Piezography MPS is an inkjet process that is resident on one of these platforms and is technically possible to adapt to any of these printers. Right now there is no plan to adapt it to any platform other than Epson.

*Piezography will continue to resolve detail at resolutions as high as 1,800 ppi.

Note: Piezography MPS uses a unique printer driver called QuadTone RIP (QTR) that is capable of transforming a supported printer from its native RGB driver to a multiple channel driver according to how many print heads it has. QTR has also been driving the Piezography K7 matte ink sets. Jon Cone produced a profiling application that is able to produce media specific profiles that are compatible with QTR, and take advantage of the QTR driver by having it print at significantly higher frequencies in the highlights and mid-range (where detail is most noticeable). Cone’s profiler organizes seven partitions of seven densities of carbon ink in a complex series of printing curves that produces a near perfect Gamma 2.2 linearization from dMin to dMax. Think of it as the traditional “S curve” transformed into a perfect diagonal. You may never have seen your work like this before. Very few displays and monitors are capable of revealing the tonal latitude that Piezography Glossy is capable of. These curves are supplied for free as part of the $50 shareware download of the QuadTone RIP.

Piezography Glossy prints are available now either through our online printing services or as a complete inking system that you can adapt to a supported Epson printer, and perhaps upgrade your current Piezography system.

InkjetMall sells combined matte and glossy systems only for the Epson R2880 and the Epson Pro3800 printer. Glossy only or Matte only systems are available for the Epson R800, R1800, 2400, 4800, 4880, 7800, 7880, 9800 and 9880 printers. Matte only systems are available for the Epson 1400, 2100/2200, 7600 and 9600 printers. The Epson Ultrachrome or Claria color ink sets of these supported printers are replaced by six or seven shades of a triple-encapsulated, modified carbon pigment Piezography brand ink called Selenium K7 MPS. In glossy compatible systems, an eighth “ink” is supplied as the Piezography Gloss Optimizer. This is a clear formulation which produces a thin layer of polyester over the entire surface of the print, an essential ingredient of the Piezography Glossy process. The seven shades of ink produce a pure monochromatic tone that mimics traditional selenium toning. Changing the base color of the paper has a great effect on the actual tone produced by this ink set giving the user a wide range of possible tone to work with.

The Piezography formulation is compatible with the Epson inks and does not require flushing, though flushing remains a popular option for professional users of the system who appreciate having an extra set of flush cartridges with which to put their printer in “storage conditions” when not in use for long periods of time.

The procedure for making perfect Piezography Glossy prints is a two-part process. The inks are printed in anticipation of a second printing of Piezography Gloss Optimizer. An uncoated print has a very strange appearance that in no way indicates the perfectly linearized grayscale and ultra-deep dMax (up to 2.8). The overcoat process reveals the shadow detail and smooth tone hidden within the print, reminiscent of the magic of observing a print “come up” in the development tray.

The process is controlled from the QuadTone RIP using media profiles (called “curves” in QTR) produced by InkjetMall using its proprietary Piezography Profiler application. There is both an inks curve, and a Gloss Optimizer curve associated with a glossy paper. A full tone image is printed using the first curve with QuadTone RIP. The print is allowed to dry briefly and then is overprinted with the second curve that controls the Gloss Optimizer. Matte profiles are included in the download of QuadTone RIP. Customs are available as a service from InkjetMall. One glossy curve for Type5 is included with your purchase. Other glossy profiles are available as a custom profiling process from InkjetMall. You can extend Piezography Glossy to include your choice of paper provided you have a custom profile created ny InkjetMall. The charge for custom profiles is $99 each.

The most superlative results (as envisioned by its inventor Jon Cone) are obtained with the new JonCone Studio Type5 paper. Type5 was created to perfectly replicate the color and surface of Crane’s popular Museo Silver Rag paper. Where Museo Silver Rag does not produce the best results with Piezography inks, Type5 was designed specifically for it. The color of the ink and paper is an absolute perfect combination. The baryta surface is closest to a silver print in texture, and the smoothness and detail is superior to Silver Rag.

The systems we sell for MPS

Note: The 2880 and Pro 3800 are the only two printers for which we provide simultaneously both a matte and glossy system. In all other printers, the use of the photo black will result in a loss of dMax on matte papers of about 1.5 stops. These two systems allow us to configure both a matte and a photo black ink.

Epson 2880
When you purchase the Selenium MPS 2880 system, it ships to you with 9 inks in total. The 2880 CIS is capable of loading all nine inks – even though the 2880 printer has only 8 ink slots. The “photo black” rides piggy back on the print head and can be instantly swapped with the “matte black” ink. The other six shades of Selenium K7 inks are both matte and glossy compatible. The Gloss Optimizer is the “eighth” position.

Epson 3800
When you purchase the Selenium MPS 3800 system, it ships with nine Refillable ink carts and can load both the matte and photo blacks, six shades of Selenium and the Gloss Optimizer. The Pro 3800 printer has nine individual slots in which nine Refillable Carts are inserted and does not require any manual intervention by the user when they wish to print on matte or photo papers. The changes are made within the QTR driver.

Epson R800/1800, R1900, 4000, 4800, 4880, 7800, 7880, 9800, 9880
On these we can configure a Gloss only solution for you in which case the printer contains the “photo black”, the six additional shades, and the Gloss Optimizer.

Epson 2200, 2400, 7600, 9600
If you have a legacy printer with only seven ink positions, its less convenient, but we can design a GLOSS ONLY solution for you. You would either have to provide a second printer with which to overcoat the print with Gloss Optimizer. Without the overprint, you would be required to spray the finished print with Lumijet spray. Without the overcoat or spray, the print will not be acceptable. These systems you will need to make contact with us – as we can not release an incomplete product.

If you’re on the fence over Glossy Piezography, we can tell you with confidence that once you’ve seen the dynamic range, the absence of bronzing, and the perfect gloss differential – you will not want to return to matte only printing. We encourage you to try before you buy, or try before you upgrade by printing one or more of your images with our online printing services. You can access these services by clicking here.

Upgrading an existing Selenium K7 printer
If you’re currently on the matte version of Selenium K7 inks on any of the above supported printers- you need only the MPS photo black and the gloss optimizer to upgrade your current system. Custom profiling for glossy media is available.

What about K6 and Glossy?
There are not enough ink positions to do what we need to do with only six inks positions.

What about if I want to customize my own solution that does not account for what InkjetMall is supporting?
There is a possibility by example, for customers to use an eight ink printer to hold both the matte black and photo blacks and use a second older printer to overcoat. There is probably a myriad of examples that our customers can come up with. In these situations, we need to produce custom profiles for the photo black position and produce a curve for gloss on the second printer. Please contact us.

My second generation ink (PiezoTone Warm Neutral) was a vastly superior formulation that could be used in all modern Epson printers. It had superior longevity as well as print head performance. It also had the “look” that I preferred. It was developed with my close friend who is also my chemist.

Warm Neutral prints are like the original Coca Cola!  Why it took me so long to reformulate a K7 version – I simply do not know…  Yet it is probably the most suitable all-purpose color tone of any K7 ink.  This is the second ink that I have formulated to work with MPS Black and the Piezography Gloss Optimizer – so that it is both matte and glossy compatible.

K7 Warm Neutral is the most under-utilized ink we sell. It should be the most popular!

• A Chronology of Photography; a Critical Survey of the History of Photography as a Medium of Art
• The Color Print Book: A Survey of Contemporary Color Photographic Print Making Methods for the Creative Photographer
• Handbook for Contemporary Photography

Arnold taught me most of what I know as a darkroom printer. He encouraged me to study the chemistry of photography. Although his tutelage was difficult (at best), his insistence that we make our own chemistry, fully understand the zone system, and become skilled practitioners of the darkroom was very influential in my later work as a development printmaker.

Arnold was very ill in his later life, suffering from terminal cancer. We had been in contact frequently and I was helping him to sort out some digital workflow. I asked Arnold to make me the definitive short-bath Selenium toned print on his favorite Ilford fiber based paper. That print was used for the *ab values to formulate Selenium K7 inks. We actually produced a software for use with our chemist that would allow us to achieve the match during formulation.

Selenium K7 is one of my favorite inks because I like Selenium toning – and I had so much respect for Arnold. It is also the first ink that I formulated that is also glossy compatible when used with the MPS shade 1 and the Piezography Gloss Optimizer.

Sepia inks are perfectly formulated (one shade at a time) so that the color tone *ab values are very close from shade to shade. Just like our Neutral ink set this produces a perfect reflection of color tone back to the human eye across the entire tonal range. It’s a very precise way to express a Sepia photograph without the illusion used by color inks. It is very monochromatic (yet toned.)

Sepia inks are often used by our printing customers to “SplitTone” from a cooler high tone. In this case, Sepia shades 2,3,4 are used in conjunction with either Selenium or Neutral shades 5,6,(7).

When viewed under a full spectrum 5000k light source (this is the color of white that a standard human sees as neutral), a photograph on these two papers will appear to be neutral.

Because the inks are neutral, they will pick up the tone of any paper white and shift in that direction. The inks therefore can be made to appear warm on warmer papers and cool on cooler papers.

Neutral inks can appear “flatter” to the human perception system because we are not used to looking at neutral grays. There is no darkroom equivalent – yet this remains one of our most popular inks.

“The most beautiful print color since Agfa Brovira, perfect screen match, tack sharp, deep and detailed shadows… Spectacular product.”

Craig Wallace Dale
www.craigdale.com

This ink set was influenced heavily by my work for photographer Gregory Colbert and his Ashes and Snow exhibitions (the Nomadic Museum). The inks I developed for Colbert are extremely complex and they numbered 11. However, there were three subtle splits in the Ashes and Snow prints made for the Tokyo and Mexico City exhibitions. These are the prints seen my more than 10 million people! (You can read more about this by searching on this website for “MyStory”.)

I decided to blend a simple ink set of six shades for the Epson 1400 printer. I also developed a unique K6 curves architecture for this ink. Although the ink set is available for all the supported printer models, the 1400 kit is the purest expression of what I envisioned.

But, Piezography is more than just changing out the color inks in your EPSON printer and replacing it with Piezography shades of carbon black ink. You also need a special software to make the effect work. Piezography is inks and software working in harmony. Jon Cone develops a profiling application with which he produces K6 and K7 profiles for Roy Harrington’s QuadTone RIP. This combination is to date the highest quality implementation of the Piezography system – yet it is amazingly affordable. QuadTone RIP is only $50 and includes the Piezography profiles at no additional charge. For large format printers QTR can be used to amazingly good results for such an inexpensive RIP. StudioPrint by ErgoSoft includes a Piezography ink profiler in their product and we have long enjoyed their support for our inks. The advantage of a StudioPrint system is the ability to customize the inks – a subject entirely unto itself.

Because Piezography uses seven shades of black ink with which to produce the highest quality monochromatic photograph, Piezography can reproduce the image in a much higher quality by moving the printer dots of ink significantly closer together than can EPSON. Epson needs to dither its three shades so as to fool the eye into seeing more gradations than there are. K7 curves do not use any of the low frequency dithering patters (that include dots of ink far enough apart to allow paper to be visible between them). Piezography K7 curves only print at the upper frequencies where image detail is not lost to invisible paper white (the space between Epson dithered dots) but is rather presented in the final print has enhanced detail.

Resolution of over 360dpi is wasted on the Epson printer when used with conventional Epson driver or RIPs. However, when Piezography K7 curves are used with the QTR RIP – a resolution of up to 2000dpi results in extreme levels of detail. However, using increased resolution is defeated by resizing images in Photoshop. Photographers will want to capture as much resolution as possible in the original image via capture or scanning. We call this true optical resolution.

Piezography provides a set of ink curve sets for the QuadTone RIP driver that directs the EPSON printer to print each shade of Piezography black at a significantly higher dithering frequency. The best way to represent this is to put the two systems to a test which illustrates this concept and reveals the strengths and weaknesses between the two systems.

And below is an illustration of the curves architecture of the Piezography K7 Master Curve.

Piezography K7 master curve

From left to right represents the output gray ramp.  Above each part of this ramp are the inks that are responsible for printing that particular density of tone. The higher the curve, the more density of ink that is printing and therefore the closer the dots of ink are printing.  The deep blacks are made with Shades 1,2,3&4 and an area such as 85% gray is comprised of also of portions of those 4 shades. The mid-tone gray on the other hand is comprised of portions of Shades 4,5,6&7.  The highlights and 1/4 tones are where our eyes perceive detail. In the instance of Shade 7 it is printing very high up on the curve at nearly maximum density. By contrast, the Epson light black shade would only be printing at a low density because it requires a wider spaced dither to give the illusion of being very very light. Piezography actually prints a very, very, very light black shade of ink. It has the luxury therefore to print at higher frequencies eliminating the space between dither dots and producing tons more detail!

Finally – here is an actual density comparison to the three shades of Epson black inks in comparison to the seven shades of Piezography K7 inks:

Piezography K7 versus Epson Ultrachrome K3 equivalent densities

Perhaps this illustration is easier to visualize how having additional shades of gray allow an image to be divided into more mathematical gray variations. The Piezography K7 curves actually contain the ink density recipes for more than 64,000 gray levels.