Managanese Blue is a light-valued cyan that is typically granulating, so I would also call it an earth blue.
Genuine Manganese Blue (PB33) is a toxic pigment that has mostly been removed from major lines. The only major brand that still sells PB33 is Da Vinci; this is a mixture which also contains PB15 (Phthalo Blue). Other large-company versions (e.g. Daniel Smith, Holbein, Winsor & Newton) offer hues made from PB15 only.
Genuing PB33 is/was a non-staining, liftable, and highly granulating light blue that creates striking separation effects in mixes (especially visible in the mix with red above). Commercial Phthalo Blue does not typically have those properties, but Manganese Blue Hues mimic them as closely as possible. Some only aim to match the hue, while others also attempt granulation.
Observations of Da Vinci Manganese Blue Mixture

Hue: A bright, rather light, sky blue on the cyan/green-toned side. Higher-chroma and greener than Cerulean, less green than Cobalt Turquoise, and lighter-valued than Phthalo Blue Green Shade.
Gradient: Smooth
Granulation: Highly granulating
Tinting Strength: Moderate. While some versions of MB Hue are quite intentionally weak, I found DV’s version fairly easy to rewet and bold, though it doesn’t get very dark.
Transparency: Semi-transparent
Glazing: Glazes to a midtone sky blue that’s still not as dark a Phthalo Blue
Color Mixes: A range of color-separating cool pastels. I especially like the lavender and violet with Permanent Rose (PV19) and Carbazole Violet (PV23).
Comparison to Other Brands
All other versions from major commercial brands are hues made from PB15 – they don’t contain any PB33 genuine manganese.
Daniel Smith – Manganese Blue Hue

Granulation: Highly granulating. Daniel Smith’s version is said to be the most granulating/similar to PB33 for a PB15-only version. That said, I found that this mixed differently, creating textured mixes instead of color-separating as genuine PB33 does.
Brushfieel: I found this version very hard and gummy, quite texturally unpleasant.
Tinting Strength: Extremely weak. They went way out of their way to nerf Phthalo Blue. It’s so aggressively weak and difficult to rewet that I found it not practical to use in the field.
Misc: Some interesting qualities of this one are that it’s reflective (looks more opaque when wet) and naturally fluorescent (glows under blacklight), as Kim Crick shows in a video. Unlike fluorescent Opera Pink, it does not seem to be fugitive, so Crick’s speculation is that DS adds colorless optical brighteners (similar to those added to white paper).
Holbein – Manganese Blue Nova (PB15)

Granulation: Holbein’s version is more or less nongranulating. It’s kind of granulating (or at least textured) in masstone, but very smooth in dilute.
Gradient: Much smoother than DS’s.
Tinting Strength: Still noticeably weak compared to other paints, although I think this is the strongest of the MBH’s I’ve tried.
Brush feel: This is my preferred MB hue for feel; it feels more or less like other Holbein paints – smooth, easily rewet and creamy but not sticky or gummy.
Winsor & Newton – Manganese Blue Hue (PB15)

WN’s version is similar to Holbein’s, in that it has some masstone texture but is smooth in dilute.
Tinting Strength: Still very low, exacerbated by increasing difficulty in rewetting as the paint gets harder.
Brushfeel: I found it a bit gummy at first but within a few days it became quite hard, like many WN paints.
Color Mixes – Mixture
These mixes use DV Manganese Blue Mixture (PB33, PB15).
Hansa Yellow Medium (PY97)

Nice bold greens/turquoises.
Quinacridone Red (PV19)

Muted violets; more muted than I expected!
Cobalt Violet (PV14)

Very granulating lilacs and lavenders. This is Zoltan Szabo’s preferred snow shadow mix. Fun fact, these are both toxic pigments!
Terra Cotta (PR102)

Weird smudgy grays. Both these paints are granulating, but the mix weirdly didn’t show it.
Color Mixes – Hue
These mixes use Holbein Manganese Blue Nova.
Deep Scarlet (PR175)

Perylene Maroon (PR179)

Pyrrol Red (PR254)

My Review
I hate to say it, but I far prefer the DV mix with genuine PB33 to the nontoxic hues. The DV mix creates this magical color separation in mixes which others don’t. Although I think it’s likely that the Da Vinci mix doesn’t use much genuine PB33, I suppose it’s necessary to have some to make this color stand out from alternatives. The hues just feel like worse Phthalo Blue.
On my palette? Experimenting.
Favorite version: DV is definitely the most unique and special, and I liked the hue, granulation, and handling better than any of the hues. That said, Manganese Blue being more toxic than many other pigments requires more careful handling; on a pragmatic level, I’m not sure it’s worth the additional effort and thought. On a larger level, I feel like there are negative externalities in the production of manganese pigments that give me pause.
If I had to choose one of the hues, I’d go with Holbein, but I think I’d just prefer using a diluted Phthalo Blue.
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If people don’t drink their paint water, put their brushes in their mouths, keep pets and small kids away, and don’t dump the waste water down their sink, genuine manganese blue isn’t really a toxicity concern for painters.
Basically, treat it the same way one treats other pigments with soluble heavy metals, such as cobalt violet, Rinman’s green (PG 19), and manganese violet.
The focus on the toxicity of this pigment is really overblown, probably because everyone read Handprint’s summary. There are vastly more toxic pigments that are in heavy industrial use, like lead chromate and lead molybdate. But, yes, the soluble barium in PB 33 should be treated with due care.
All of these seem simple except for “don’t dump waste water down your sink,” since that is the most obvious way to dispose of dirty paint water. What do you do? Soak it all up into a paper towel and throw it away?
Right? I’m considering a Zero Water filter for cleaning (and reusing) my watercolour water when living offgrid. If you check out the European website there’s more info on its efficacy with cobalt and cadmium. Not sure about the toxicity in PB33. I went a little colour happy a while back and picked up a violet made with lithium. Woops?
“so aggressively weak” indeed! I purchased the Daniel Smith and the Winsor Newton and I swear I’ll use up both of the (5ml) tubes just in trying out colour mixes. Any suggestions on a similar hue with better tinting strength? I was hoping MBH would by my holy grail for sky blues, but I am sadly finding the weakness just kind if annoying. I’m considering mixing some with PB28; maybe that’ll have the oomph I’m looking for.
I’d probably recommend Cerulean Blue Genuine (PB35), it’s not as bright but it’s a light valued blue. Other than that, just diluting Phthalo Blue.