Spartan Sagittal single-shaft accidentals (U+E300–U+E30F)
5:7 kleisma up, (5:7k, ~11:13k, 7C less 5C)
5:7 kleisma down
5 comma up, (5C), 1° up [22 27 29 34 41 46 53 96 EDOs], 1/12-tone up
5 comma down, 1° down [22 27 29 34 41 46 53 96 EDOs], 1/12-tone down
7 comma up, (7C), 1° up [43 EDO], 2° up [72 EDO], 1/6-tone up
7 comma down, 1° down [43 EDO], 2° down [72 EDO], 1/6-tone down
25 small diesis up, (25S, ~5:13S, ~37S, 5C plus 5C), 2° up [53 EDO]
25 small diesis down, 2° down [53 EDO]
35 medium diesis up, (35M, ~13M, ~125M, 5C plus 7C), 2/9-tone up
35 medium diesis down, 1° 2° down, 2/9-tone down
11 medium diesis up, (11M), 1°[17 31] 2°46 up, 1/4-tone up
11 medium diesis down, 1°[17 31] 2°46 down, 1/4-tone down
11 large diesis up, (11L), (sharp less 11M), 3° up [46 EDO]
11 large diesis down, 3° down [46 EDO]
35 large diesis up, (35L, ~13L, ~125L, sharp less 35M), 2°50 up
35 large diesis down, 2° down [50 EDO], 5/18-tone down
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.