# 31-EDO Alterations

The following table shows the alterations in the 31-tone equal-temperament system (31-EDO) with 5 degrees.

- std — Standard notation
Arrow symbols after Gould (U+E27A, U+E27B), and Standard sharp / flat symbols (U+E260 - U+E264). All symbols are placed either alone or a standard symbol is combined with an arrow.

- sag — Sagittal notation
4 × 2 Spartan Sagittal single-shaft and multi-shaft symbols (U+E30A … U+E335) after George D. Secor and David C. Keenan.

This is the "Pure Sagittal notation" in contrast to msag. It uses one distinct symbol for each degree up to the whole tone. For higher degree, two symbols are combined.

- msag — Mixed Sagittal notation
1 × 2 Spartan Sagittal single-shaft symbols (U+E30A, U+E30B), Standard sharp / flat symbols (U+E260 - U+E262, U+E264) and large double-sharp symbol (U+E47D). They are placed like std.

- stz — Stein / Zimmermann notation
Fractional sharp symbols and quarter-tone flat symbol after Richard Stein (U+E282 - U+E284), three-quarters-tone flat symbol after Bernd A. Zimmerman (U+E285), and Standard sharp / flat symbols (U+E260 - U+E264). They are placed like sag.

The notation uses the narrow variant of the reversed flat (U+E284, U+E285).

- sth — Stein / Half flat notation
Fractional sharp symbols after Richard Stein (U+E282, U+E283), half flat symbols (U+F612, U+F613), and Standard sharp / flat symbols (U+E260 - U+E264). They are placed like sag.

The half flat symbols are defined as “Optional glyphs” in the Ekmelos font since they are not included in SMuFL.