Sagittal notation: Difference between revisions

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== The Athenian symbol set ==

Early in the design of the Sagittal notation system, Secor and Keenan found that an economical JI notation system could be defined~~, which divided~~ the apotome (Pythagorean sharp or flat) into 21 almost-equal divisions. This required only 10 microtonal accidentals, although a few others were added for convenience in alternative spellings. This ~~is called the Athenian~~ symbol set (~~which includes~~ the Spartan set), ~~shown below~~. ~~Its symbols are defined to~~ exactly ~~notate~~ many common 11-limit ratios and the 17th harmonic, ~~and to approximate within ±0.4 ¢~~ many common 13-limit ratios. If the divisions were made exactly equal, this would be an example of [[Brahmagupta]] temperament.

Early in the design of the Sagittal notation system, Secor and Keenan found that an economical JI notation system could be defined by dividing the apotome (Pythagorean sharp or flat) into 21 almost-equal divisions. This required only five pairs of up and down microtonal accidentals, although a few others were added for convenience in alternative spellings. This 10-symbol set ([[Sagittal notation#Athenian extension single-shaft|shown below]]), in combination with the Spartan symbol set which it extends, is called the Athenian symbol set. It exactly notates many common 11-limit ratios and the 17th harmonic, while also approximating many common 13-limit ratios within ±0.4{{c}}. If the divisions were made exactly equal, this would be an example of [[Brahmagupta]] temperament.

== Gallery ==

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 == The Athenian symbol set ==
-Early in the design of the Sagittal notation system, Secor and Keenan found that an economical JI notation system could be defined, which divided the apotome (Pythagorean sharp or flat) into 21 almost-equal divisions. This required only 10 microtonal accidentals, although a few others were added for convenience in alternative spellings. This is called the Athenian symbol set (which includes the Spartan set), shown below. Its symbols are defined to exactly notate many common 11-limit ratios and the 17th harmonic, and to approximate within ±0.4 ¢ many common 13-limit ratios. If the divisions were made exactly equal, this would be an example of [[Brahmagupta]] temperament.
+Early in the design of the Sagittal notation system, Secor and Keenan found that an economical JI notation system could be defined by dividing the apotome (Pythagorean sharp or flat) into 21 almost-equal divisions. This required only five pairs of up and down microtonal accidentals, although a few others were added for convenience in alternative spellings. This 10-symbol set ([[Sagittal notation#Athenian extension single-shaft|shown below]]), in combination with the Spartan symbol set which it extends, is called the Athenian symbol set. It exactly notates many common 11-limit ratios and the 17th harmonic, while also approximating many common 13-limit ratios within ±0.4{{c}}. If the divisions were made exactly equal, this would be an example of [[Brahmagupta]] temperament.
 == Gallery ==