It is not necessary to implement the complete Sagittal microtonal
notation system. The Spartan set is sufficient to notate 13-limit just
intonation (JI), 1/12-tones, 50 common equal divisions of the octave
(EDOs), and their related linear temperaments.

The eight pairs of single-shaft accidentals above are sufficient to
provide these capabilities when used alone, and to the left of the
standard **accidentalDoubleFlat**, **accidentalFlat**, **accidentalSharp**,
and the almost-standard **accidentalLargeDoubleSharp**. This is called “mixed
Sagittal.”

As an alternative, the following group (the multi-shaft Spartans)
provides a complete set of stand-alone accidentals to replace each of
the above combinations of a single-shaft Sagittal with a standard
accidental. This is called “pure Sagittal.” The standard
**accidentalNatural** is used alone in both mixed and pure variants, but
only to cancel a previous accidental.

Sagittal accidentals are not intended to be combined with one another,
inasmuch as symbols representing useful combinations and powers of
primes are already provided. An accidental can often be used to
represent alternative commas that differ by 2 cents or less. In such
cases the intended comma ratio may be determined by the note to which it
is applied, or by the musical context. Alternatively, diacritics (from
the Herculean and subsequent extensions) may be added to distinguish
these commas. Commas which require diacritics for exact representation
are preceded by a tilde “\~” in the glyph descriptions.

Sagittal extensions following Spartan allow notation of JI ratios with
primes beyond 13, and more combinations of lower primes, as well as
finer tone-fractions, degrees of larger EDOs, and more complex
temperaments, all with single Sagittal accidentals. The same choice of
mixed versus pure is available with each extension. See
<http://sagittal.org> for more information.

Other Sagittal-compatible accidentals are
**accidentalQuarterToneSharpStein** and
**accidentalThreeQuarterTonesSharpStein** which may be substituted for
**accSagittal11MediumDiesisUp** and **accSagittalSharp11MUp**; the
**accidentalNarrowReversedFlat** and **accidentalNarrowReversedFlatAndFlat**
which may be substituted for **accSagittal11MediumDiesisDown** and
**accSagittalFlat11MDown**; and the **accidentalWilsonPlus** and
**accidentalWilsonMinus** which may be substituted for the
**accSagittal5CommaUp** and **accSagittal5CommaDown**.
