Lowering an accented character

Question

In the given MWE, the new sd command produces ^ carets higher than the hat carets. Is there a way to adjusted the newcommand at the bottom of the preamble to lower these carets to match? (Alegreya can be downloaded for free from FontSquirrel.)

It might seem silly, but I'm really going after the look of the \newcommand carets more than the hat carets.

%XeLaTeX
\documentclass{article}
\usepackage{mathspec}
\setmainfont[
    Extension = .otf,
    UprightFont = Alegreya-Regular,
    ItalicFont = Alegreya-Italic,
    BoldFont = Alegreya-Bold,
    BoldItalicFont = Alegreya-BoldItalic,
    UprightFeatures = {SmallCapsFont = AlegreyaSC-Regular},
    ItalicFeatures = {SmallCapsFont = AlegreyaSC-Italic},
    BoldFeatures = {SmallCapsFont = AlegreyaSC-Bold},
    BoldItalicFeatures = {SmallCapsFont = AlegreyaSC-BoldItalic},
    Ligatures = TeX]
    {Alegreya}
\setmathsfont(Digits,Latin,Greek)
    [Numbers=OldStyle]{Alegreya}
\newcommand{\sd}[1]{\accent"02C6 #1}

\begin{document}

\sd{1} $\hat{1}$ \sd{2} $\hat{2}$ \sd{3} $\hat{3}$ \sd{4} $\hat{4}$ \sd{5} $\hat{5}$ \sd{6} $\hat{6}$ \sd{7} $\hat{7}$

\end{document}

Oddly, the sd carets were exactly what I wanted when the following was the fontspec:

\setmainfont[
  SmallCapsFont={Alegreya SC},
  ItalicFeatures={SmallCapsFont=AlegreyaSC-Italic},
  BoldFeatures={SmallCapsFont=AlegreyaSC-Bold},
  BoldItalicFeatures={SmallCapsFont=AlegreyaSC-BoldItalic},
  Ligatures=TeX,
]{Alegreya}

For ligature and international character reasons, I had to clarify the fontspec as you saw in the original MWE; can anyone explain why that might be?

The answer may be in How do I lower the \widetilde accent, but to be honest I don't even know where to begin.

Answer 1

You can fix the height of the character by using \halign instead of \accent:

\documentclass{article}
\usepackage{mathspec}
\setmainfont[
    Extension = .ttf, % I only have TrueType
    UprightFont = *-Regular,
    ItalicFont = *-Italic,
    BoldFont = *-Bold,
    BoldItalicFont = *-BoldItalic,
    UprightFeatures = {SmallCapsFont = *SC-Regular},
    ItalicFeatures = {SmallCapsFont = *SC-Italic},
    BoldFeatures = {SmallCapsFont = *SC-Bold},
    BoldItalicFeatures = {SmallCapsFont = *SC-BoldItalic},
    Ligatures = TeX
]{Alegreya}
\setmathsfont(Digits,Latin,Greek)[
  Numbers=OldStyle
]{Alegreya-Regular}
\DeclareRobustCommand{\sd}[1]{%
  \leavevmode
  \vbox{\offinterlineskip
    \ialign{%
      ##\cr
      \hidewidth\char"02C6 \hidewidth\cr
      \noalign{\kern-0.95ex}
      #1\cr
    }%
  }%
}

\begin{document}

\sd{1} $\hat{1}$ \sd{2} $\hat{2}$ \sd{3} $\hat{3}$ 
\sd{4} $\hat{4}$ \sd{5} $\hat{5}$ \sd{6} $\hat{6}$ 
\sd{7} $\hat{7}$ \sd{8} $\hat{8}$ \sd{9} $\hat{9}$
\sd{0} $\hat{0}$

\end{document}