Spartan Sagittal single-shaft accidentals (U+E300–U+E30F)

Glyph Description Glyph Description
U+E300
accSagittal5v7KleismaUp
5:7 kleisma up, (5:7k, ~11:13k, 7C less 5C)
U+E301
accSagittal5v7KleismaDown
5:7 kleisma down
U+E302
accSagittal5CommaUp
5 comma up, (5C), 1° up [22 27 29 34 41 46 53 96 EDOs], 1/12-tone up
U+E303
accSagittal5CommaDown
5 comma down, 1° down [22 27 29 34 41 46 53 96 EDOs], 1/12-tone down
U+E304
accSagittal7CommaUp
7 comma up, (7C), 1° up [43 EDO], 2° up [72 EDO], 1/6-tone up
U+E305
accSagittal7CommaDown
7 comma down, 1° down [43 EDO], 2° down [72 EDO], 1/6-tone down
U+E306
accSagittal25SmallDiesisUp
25 small diesis up, (25S, ~5:13S, ~37S, 5C plus 5C), 2° up [53 EDO]
U+E307
accSagittal25SmallDiesisDown
25 small diesis down, 2° down [53 EDO]
U+E308
accSagittal35MediumDiesisUp
35 medium diesis up, (35M, ~13M, ~125M, 5C plus 7C), 2/9-tone up
U+E309
accSagittal35MediumDiesisDown
35 medium diesis down, 1°[50] 2°[27] down, 2/9-tone down
U+E30A
accSagittal11MediumDiesisUp
11 medium diesis up, (11M), 1°[17 31] 2°46 up, 1/4-tone up
U+E30B
accSagittal11MediumDiesisDown
11 medium diesis down, 1°[17 31] 2°46 down, 1/4-tone down
U+E30C
accSagittal11LargeDiesisUp
11 large diesis up, (11L), (sharp less 11M), 3° up [46 EDO]
U+E30D
accSagittal11LargeDiesisDown
11 large diesis down, 3° down [46 EDO]
U+E30E
accSagittal35LargeDiesisUp
35 large diesis up, (35L, ~13L, ~125L, sharp less 35M), 2°50 up
U+E30F
accSagittal35LargeDiesisDown
35 large diesis down, 2° down [50 EDO], 5/18-tone down

Implementation notes

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.