In most of the books and literature about drumming I have, the
half-open hi-hat is typeset as in the attached PNG file with an
articulation that looks somewhat like the empty set in the Symbol font
or the character Ø.

Unfortunately, LilyPond does not seem to have an articulation
character that could be used directly to typeset half-open hi-hats in
this manner.  Therefore, I have (prototypically) designed an
articulation character based on the "open" character in the Feta font
(see the attached PDF file):

fet_beginchar ("halfopen (unstopped)", "halfopen");
        save thin, height, width, thick;

        factor = 4/3;
        height# = 5/4 width#;
        height# = factor * staff_space#;
        thin = .6 linethickness + 0.06 staff_space;

        set_char_box (width# / 2, width# / 2, height# / 2, height# / 2);

        define_pixels (width, height);

        2 thick + 0.6 (height / factor - 2 thin) = width / factor;

        penpos1 (thick, 0);
        penpos2 (thin, 90);
        penpos3 (thick, 180);
        penpos4 (thin, 270);
        z1r = (w / factor, 0);
        z2r = (0, h / factor);
        z3r = (-w / factor, 0);
        z4r = (0, -h / factor);

        penlabels (1, 2, 3, 4);

        penstroke z1e{up}
                  .. z2e{left}
                  .. z3e{down}
                  .. z4e{right}
                  .. cycle;

        draw_brush ((-w, -h), thin, (w, h), thin);
fet_endchar;

Is there a chance that you would consider this character for inclusion
in LilyPond 2.13?  If so, I would start working on optimizing the
design of the character and also start working on modifying LilyPond
to enable this character to be used (any hints on what needs to be
modified are certainly most welcome).

Best regards, Carsten Steger

<<attachment: halfopenhihat.png>>

Attachment: halfopen.pdf
Description: Adobe PDF document

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