Talk:Sagittal notation

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Add link to "sharp" in gallery

I'd like to suggest adding a link to the page 2187/2048 on the word "sharp" in the Spartan multi-shaft accidentals gallery. Since I'm not familiar with the sagittal gallery entry template, maybe someone could help achieving this. --Fredg999 (talk) 21:25, 3 December 2024 (UTC)

Good idea. Done. I assume you only want "sharp" to be a link when it appears in the bottom row with no comma alteration, i.e. only for the  and  symbols. --Dave Keenan (talk) 02:11, 4 December 2024 (UTC)

Yes, that's perfect, thank you very much! --Fredg999 (talk) 02:26, 4 December 2024 (UTC)

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.) 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. 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). 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. 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. Dave Keenan (talk) 03:35, 18 October 2025 (UTC)

Musescore

For such sagittal notations, MuseScore 3 can only achieve the highest precision up to Herculean Extension. At least I don't find anything about Olympian Extension and Magrathean Extension.

By the way, I thought that pakai() and pakao() was ↑ and ↓.

-- PrySigneToFexia at 12:25 2025.9.27 Sat (CST), talk at 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. Dave Keenan (talk) 03:51, 18 October 2025 (UTC)

Hybrid of Revo Sagittal with HEJI, Sagittal Natural?

I just watched Sagittal: the universal microtonal notation system (2024-07-21 edition), and here is my comment (with embedded implicit questions):

Right off the bat I can think of a use case in which you would not only want but actually need to have both Revo Sagittal AND HEJI symbols: Rank-3 (2-dimensional) temperaments. In terms of mathematics, this means that you have that you have 2 generators (in addition to the equave/period), such as having both 3/2 for specifying your circle of fifths and 33/32 to select between separate circles of fifths, or to get some interval that is fairly close by but requires an inordinate number of fifths to reach even if your tuning system has a single circle of fifths.

In terms of acoustic instruments that have actually been built and played (including in videos on YouTube), think of a fluid piano or fluid dulcimer(*) which has the same 12 notes per octave(**) as on a piano, but then has sliders to bend the notes up or down (on-the-fly) by up to a whole tone (exact value not specified in the fluid piano videos, but they probably meant either a 12EDO whole tone or 9/8). I haven't seen notation used by the fluid piano/fluid dulcimer people (they seemed to prefer to play without written music in front of them), but it would be logical to use the note letters, sharps, and flats to indicate which of the 12 notes to play, and the Sagittal symbols to indicate how to modify each note. This is broadly similar to how a pedal harp works, except that while the pedal harp (or at least the standard version thereof) has only 7 notes per octave and then has you use the pedals to bend the pitch up or down by exactly a sharp or flat of the natural notes of 12EDO(***), the fluid piano and fluid dulcimer start with 12 notes per octave and let you bend pitch continuously.

(*)While these are rare instruments, some modern versions of the Chinese hammered dulcimer (Yangqin) have the same type of slider that can be shifted on the fly, and finger rings are also used to change the string stopping point on the fly.

(**)In principle, the same design could be added to an instrument with a different number of notes per octave, for example, the pedal harp if the existing fixed-point string stops were replaced with sliders, or a keyboard instrument defaulting to 17EDO or 19EDO and having the facility for on-the-fly pitch bend to depart from the points set by said tuning systems.

(***)Technically the pedal harp starts with the home positions of the pedals not stopping the strings at all, producing flats of all 7 lettered notes, and then has the pedal mechanism engage first one set of fixed-point string stops to get to the naturals, and then another to get to the sharps, but conceptually it is easier to think of it as giving on-the-fly pitch bend by a fixed amount 1\12 in either direction from each natural note of 12EDO. Unfortunately, all of the pedal harps I have seen or heard do not have any way to vary the pitch bend, and attempting to bend a pitch to in between positions instead causes a fearsome rattling when an affected string is plucked.

This use case would require just one modification to the Sagittal Spartan symbol set: the addition of a Sagittal natural, which would only cancel preceding Sagittal pitch alterations, while the existing HEJI natural would be restricted to cancel only HEJI accidentals(*). For example, a Sagittal symbol applied to a C♮ means to play the C♮ note (key on a keyboard, fret on a fretted string instrument, valve on a brass instrument, etc.) with a pitch modification specified by the Sagittal symbol (even if in the vicinity of a full sharp or flat in size(**), hence needing a Sagittal Revo symbol); likewise, a Sagittal symbol applied to a C♭ (whether in the key signature or as an accidental) means to play the C♭ note modified by the Sagittal symbol; but canceling the flat on the C♭ is not the same as canceling the Sagittal modification, whereas one means return to using the C♮ (which might possibly still have a Sagittal modification on it, whether the same or different), a Sagittal natural would be needed to return the affected note to its normal pitch, whether that is C♭ or C♮.

(*)Usually only flats and sharps and their doubles, but on an instrument having sufficient having more than 19 notes per octave, such as some early Baroque harpsichords having up to 36 notes per octave such as Nicola Vicentino's Arcicembalo or its 31 notes per octave (but less terrible ergonomics) derivative the Clavemusicum Omnitonum, more HEJI symbols would be useful, or even required if such an instrument was tuned to a system having multiple rings of fifths.

(**)If you needed to do the equivalent of a harp glissando, you would need to set one note to be exactly enharmonic with the next higher or lower note.

Added: Lucius Chiaraviglio (talk) 05:21, 21 July 2026 (UTC)
Last modified: Lucius Chiaraviglio (talk) 05:36, 21 July 2026 (UTC)

Setting aside that wiki talk pages are usually reserved for discussion about the wiki (description of existing work), not the topic itself (I suppose the best place would be the Sagittal forum), I believe that simply using a natural accidental followed by a restatement of whichever accidental needs to be carried over should suffice. That logic could be applied to any combination of two accidental symbol sets, although I know the rules for Kite's ups and downs are slightly different, e.g. an arrow alone implies a natural accidental, cancelling any prior sharp or flat. Furthermore, I think the Sagittal notation system is largely flexible enough to accommodate rank-3 tunings without any other symbols, especially the revo set. --Fredg999 (talk) 14:31, 21 July 2026 (UTC)