Talk:Sagittal notation: Difference between revisions

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== Dual-value harmonics (Sagittal edition)? ==

What notation should one use for systems with dual values for a harmonic? For instance, 55edo has a 7th harmonic that is far enough from just to merit interpretation as 7♯ with only mostly more raw error than 7♭, and the 7♯ would actually introduce less error in combination with the sharp (but not split) 5th harmonic, while 7♭ would introduce less error in combination withe flat 3rd and 11th harmonics or by itself. Similar situations occur with 48edo and 67edo with their split 5th harmonics, and with any dual-fifth system. (Posting this separately in Talk pages for Helmholtz-Ellis and Sagittal in case they have different answers.) [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:35, 24 August 2025 (UTC)

:Hi Lucius. Those questions would better have been asked on https://forum.sagittal.org since they are more about the notations than about this article. But if you look at the recommended sagittal notations in the wiki articles for the EDOs you mention, you will see that when some harmonic has two possible mappings in a given EDO we do not use the symbol for that harmonic in notating that EDO. In the case of EDOs that have two possible fifths we have different notations depending on which fifth you choose. See for example 23edo where we give a "23" notation and a "23b" (second best fifth) notation. If the error in the fifth is very great we recommend notating as a subset of a larger EDO. See for example 11edo. A convenient way to access all these notations is by clicking on this chart: https://sagittal.org/#periodic-table. You can get back to that chart from any notation by clicking the coloured tile in the top right corner of the notation image. [[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 02:51, 18 October 2025 (UTC)

== Primary and Secondary roles of glyphs? ==

On several pages describing an interval that can be tempered out as a comma or approximated as a chroma, I have seen text describing the Sagittal symbol for the interval, usually with reference to "primary" and "secondary" roles, yet the Sagittal notation page itself has no mention of such dual functionality. Anybody have an explanation of why and how the Sagittal symbols have primary and secondary roles? Also why some don't have this (for example [[64/63]] and [[5120/5103]]), but some do (for instance, [[28/27]], [[567/550]], [[1701/1664]], [[1053/1024]], [[2835/2816]], and [[40/39]])? Which one is primary and which one is secondary doesn't always seem to correlate with how complicated the ratio is (with 28/27 and 40/9, the simpler ratio is considered secondary, whereas for the other ratios, the opposite is true). [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:35, 24 August 2025 (UTC)

:That's a good point. You can find information about the primary role (of which there is exactly one) and secondary roles (of which there may be zero or more) for Sagittal symbols, beginning in the last paragraph on page 8 here: https://sagittal.org/sagittal.pdf and here: https://sagittal.org/whatpitch.txt (please ignore the linked spreadsheet which is out of date). The choice as to which of several nearby commas is assigned to the primary role of a symbol depends on the simplicity of the ''pitch ratio being notated'', not the comma used to notate it relative to the Pythagorean backbone. Of course a single comma can notate many different pitch ratios depending on the nominal and sharps or flats it is used with. So we are really considering the cumulative popularity of all the ratios notatable with that comma. You can read more about that here: [[N2D3P9]]. [[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 03:18, 18 October 2025 (UTC)

:I should also mention that a comma which is a secondary role for some unaccented sagittal symbol is almost always the primary role for an accented symbol having the previous symbol as its core. Or putting it another way, the secondary roles for an unaccented symbol (in the Spartan, Athenian or Promethean subsets) are usually (but not always) the primary roles of all the valid accented versions of that symbol (in their Herculean or Olympian supersets). Also the primary role can, in most cases, be thought of as the ''default'' meaning of a symbol in the absence of further information such as what EDO are we notating. [[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 03:35, 18 October 2025 (UTC)

== Musescore ==

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-- [[User:PrySigneToFexia|PrySigneToFexia]] at 12:25 2025.9.27 Sat (CST), talk at [[User talk:PrySigneToFexia|here]]

:I'm not familiar with MuseScore, but it's a valid choice to omit the higher precision extensions, as the ratios they notate are rarely used and therefore the added complexity may not be warranted. Magrathean in particular is something of a joke on the part of its authors (myself included), "Just how far can we push this idea". However, if MuseScore is using a recent version of the Bravura font, all the accents should be there, so you can compose your own Olympian symbols. To find their codepoints see: https://w3c.github.io/smufl/latest/tables/olympian-sagittal-extension-extreme-precision-accidental-diacritics.html. It's important to use the correct arrows so as to preserve an important property of Sagittal, namely that the visual size of a symbol is roughly proportional to the size of its pitch alteration. [[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 03:51, 18 October 2025 (UTC)

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 == Dual-value harmonics (Sagittal edition)? ==
 What notation should one use for systems with dual values for a harmonic?  For instance, 55edo has a 7th harmonic that is far enough from just to merit interpretation as 7♯ with only mostly more raw error than 7♭, and the 7♯ would actually introduce less error in combination with the sharp (but not split) 5th harmonic, while 7♭ would introduce less error in combination withe flat 3rd and 11th harmonics or by itself.  Similar situations occur with 48edo and 67edo with their split 5th harmonics, and with any dual-fifth system.  (Posting this separately in Talk pages for Helmholtz-Ellis and Sagittal in case they have different answers.)  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:35, 24 August 2025 (UTC)
+:Hi Lucius. Those questions would better have been asked on https://forum.sagittal.org since they are more about the notations than about this article. But if you look at the recommended sagittal notations in the wiki articles for the EDOs you mention, you will see that when some harmonic has two possible mappings in a given EDO we do not use the symbol for that harmonic in notating that EDO. In the case of EDOs that have two possible fifths we have different notations depending on which fifth you choose. See for example 23edo where we give a "23" notation and a "23b" (second best fifth) notation. If the error in the fifth is very great we recommend notating as a subset of a larger EDO. See for example 11edo. A convenient way to access all these notations is by clicking on this chart: https://sagittal.org/#periodic-table. You can get back to that chart from any notation by clicking the coloured tile in the top right corner of the notation image. [[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 02:51, 18 October 2025 (UTC)
 == Primary and Secondary roles of glyphs? ==
 On several pages describing an interval that can be tempered out as a comma or approximated as a chroma, I have seen text describing the Sagittal symbol for the interval, usually with reference to "primary" and "secondary" roles, yet the Sagittal notation page itself has no mention of such dual functionality. Anybody have an explanation of why and how the Sagittal symbols have primary and secondary roles?  Also why some don't have this (for example [[64/63]] and [[5120/5103]]), but some do (for instance, [[28/27]], [[567/550]], [[1701/1664]], [[1053/1024]], [[2835/2816]], and [[40/39]])? Which one is primary and which one is secondary doesn't always seem to correlate with how complicated the ratio is (with 28/27 and 40/9, the simpler ratio is considered secondary, whereas for the other ratios, the opposite is true).  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:35, 24 August 2025 (UTC)
+:That's a good point. You can find information about the primary role (of which there is exactly one) and secondary roles (of which there may be zero or more) for Sagittal symbols, beginning in the last paragraph on page 8 here: https://sagittal.org/sagittal.pdf and here: https://sagittal.org/whatpitch.txt (please ignore the linked spreadsheet which is out of date). The choice as to which of several nearby commas is assigned to the primary role of a symbol depends on the simplicity of the ''pitch ratio being notated'', not the comma used to notate it relative to the Pythagorean backbone. Of course a single comma can notate many different pitch ratios depending on the nominal and sharps or flats it is used with. So we are really considering the cumulative popularity of all the ratios notatable with that comma. You can read more about that here: [[N2D3P9]]. [[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 03:18, 18 October 2025 (UTC)
+:I should also mention that a comma which is a secondary role for some unaccented sagittal symbol is almost always the primary role for an accented symbol having the previous symbol as its core. Or putting it another way, the secondary roles for an unaccented symbol (in the Spartan, Athenian or Promethean subsets) are usually (but not always) the primary roles of all the valid accented versions of that symbol (in their Herculean or Olympian supersets). Also the primary role can, in most cases, be thought of as the ''default'' meaning of a symbol in the absence of further information such as what EDO are we notating. [[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 03:35, 18 October 2025 (UTC)
 == Musescore ==
@@ Line 21: / Line 27: @@
 -- [[User:PrySigneToFexia|PrySigneToFexia]] at 12:25 2025.9.27 Sat (CST), talk at [[User talk:PrySigneToFexia|here]]
+:I'm not familiar with MuseScore, but it's a valid choice to omit the higher precision extensions, as the ratios they notate are rarely used and therefore the added complexity may not be warranted. Magrathean in particular is something of a joke on the part of its authors (myself included), "Just how far can we push this idea". However, if MuseScore is using a recent version of the Bravura font, all the accents should be there, so you can compose your own Olympian symbols. To find their codepoints see: https://w3c.github.io/smufl/latest/tables/olympian-sagittal-extension-extreme-precision-accidental-diacritics.html. It's important to use the correct arrows so as to preserve an important property of Sagittal, namely that the visual size of a symbol is roughly proportional to the size of its pitch alteration. [[User:Dave Keenan|Dave Keenan]] ([[User talk:Dave Keenan|talk]]) 03:51, 18 October 2025 (UTC)