DirectWrite'ing glyphs such that the em square has a specific size

I'm working on an application that renders music notation. The musical symbol are specified in regular font files, which use the convention that the height of the em square corresponds to the height of a regular five-line staff of music. For example, the glyph for a note head is approximately 0.25 em high, the distance between two lines of the staff.

When it comes to rendering, I use a coordinate system in which 4 units corresponds to the height of a five-line staff of music. Therefore, I need to render glyphs such that the em square ends up rendered 4 units high. However DirectWrite only allows specifying text size in device independent pixels (DIPs) and I'm confused about how to juggle between the coordinate systems. There are two parts to this:

• From a given font size in DIPs I can compute a height in physical pixels, but what is mapped to that height? The em square or some other design-space metric?
• What if I'm using some arbitrary transformation matrix? How do I specify DIPs in order to get meaningful values in the coordinate system I am using?

And for good measure:

• If get this to work, is this going to mess up font hinting because my DIP values don't have a clear relationship to physical pixels?

After some more experimentation and research, I have come to the following conclusions.

• The font size specifies the size of the EM square as drawn. Drawing at 12 DIPs means that the EM square is scaled to use 12 DIPs of vertical space.
• The top Y coordinate of the layoutRect parameter of the ID2D1RenderTarget::DrawText function is mapped to the top of the font's ascent (for the first line of text).
• The identity matrix gives a coordinate system in which (0, 0) is the top-left and (width, height), as retrieved from ID2D1RenderTarget::GetSize, is the bottom-right, in DIPs. Which means for any transformation matrix, the font size unit should match the unit in the render target's coordinate system and a vertical line of 42 units will be as high as the EM square with a font size of 42 units.

I was unable to find information about the effect of arbitrary transformations on font hinting, however.