Sagittal notation: Difference between revisions
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A sub-flavor of Evo is '''Evo-SZ''' (Evo with Stein–Zimmermann). This is where any sagittals that are notating exactly half the alteration of a sharp or flat (most often {{sagittal| /|\ }} {{sagittal| \!/ }}) are replaced by the Stein–Zimmermann semisharp {{sagittal| > }} and narrow reversed flat {{sagittal| < }}, and the corresponding combinations (most often {{sagittal| /|\ }}{{sagittal| # }} and {{sagittal| \!/ }}{{sagittal| b }}) are replaced by {{sagittal| ># }} and {{sagittal| <b }}. The narrow variants of the fractional flats {{sagittal| < }} (U+E284) and {{sagittal| <b }} (U+E285) are preferred because they preserve the Sagittal principle that the visual size of a symbol should indicate the relative size of its alteration and they reduce left-right confusion. | A sub-flavor of Evo is '''Evo-SZ''' (Evo with Stein–Zimmermann). This is where any sagittals that are notating exactly half the alteration of a sharp or flat (most often {{sagittal| /|\ }} {{sagittal| \!/ }}) are replaced by the Stein–Zimmermann semisharp {{sagittal| > }} and narrow reversed flat {{sagittal| < }}, and the corresponding combinations (most often {{sagittal| /|\ }}{{sagittal| # }} and {{sagittal| \!/ }}{{sagittal| b }}) are replaced by {{sagittal| ># }} and {{sagittal| <b }}. The narrow variants of the fractional flats {{sagittal| < }} (U+E284) and {{sagittal| <b }} (U+E285) are preferred because they preserve the Sagittal principle that the visual size of a symbol should indicate the relative size of its alteration and they reduce left-right confusion. | ||
In tempered systems, Evo-SZ {{sagittal|>}} {{sagittal|<}} {{sagittal|>#}} {{sagittal|<b}} accidentals ''may instead'' be distinct from Sagittals like {{sagittal| /|\ }}{{sagittal| \!/ }}, when the apotome can be split in two equal parts as in [[Hemipyth|Hemipythagorean]], as literal half-sharps and half-flats, and there is a distinction between mapped neutral thirds like [[11/9|~11/9]] and [ | In tempered systems, Evo-SZ {{sagittal|>}} {{sagittal|<}} {{sagittal|>#}} {{sagittal|<b}} accidentals ''may instead'' be distinct from Sagittals like {{sagittal| /|\ }}{{sagittal| \!/ }}, when the apotome can be split in two equal parts as in [[Hemipyth|Hemipythagorean]], as literal half-sharps and half-flats, and there is a distinction between mapped neutral thirds like [[11/9|~11/9]] and [[Sqrt(3/2)|hemififths]], in particularly fine-grained EDOs like [[270edo|270]] or [[311edo|311]]. There is no need for this in coarser EDOs like [[24edo|24]], [[31edo|31]] or [[41edo|41]], where the mappings of the irrational hemififth and rational neutral thirds coincide. | ||
=== Revo === | === Revo === | ||
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== The symbol sets == | == The symbol sets == | ||
Sagittal symbols are defined in 6 "official" symbol sets, each one being defined as spliting the [[2187/2048|apotome]] in psuedoequal or equal parts (latter being '''EDA'''). It is not necessary to learn the | Sagittal symbols are defined in 6 "official" symbol sets, each one being defined as spliting the [[2187/2048|apotome]] in psuedoequal or equal parts (latter being '''EDA'''). It is not necessary to learn all of the Sagittal notation sets to be able to compose with it. The '''Spartan''' and '''Athenian''' sets will be more than enough for most purposes. | ||
Sagittal accidentals are not intended to be combined with one another, except in the Prime Factor JI notation, 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, accent marks (from the Herculean and subsequent extensions) may be added to distinguish these commas. | Sagittal accidentals are not intended to be combined with one another, except in the Prime Factor JI notation, 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, accent marks (from the Herculean and subsequent extensions) may be added to distinguish these commas. | ||
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=== Sharps/Flats === | === Sharps/Flats === | ||
Using {{sagittal| # }} and {{sagittal| b }} (or {{sagittal|/||\}} {{sagittal|\!!/}} for Revo flavor) is still ''technically'' Sagittal notation, however, it's just a reskin. | Using {{sagittal| # }} and {{sagittal| b }} (or {{sagittal|/||\}} {{sagittal|\!!/}} for Revo flavor) is still ''technically'' Sagittal notation, however, it's just a reskin of the usual chain-of-fifths notation. Ditto for Stein-Zimmermann half-sharps and half-flats in [[hemipythagorean]]. | ||
=== Spartan === | === Spartan === | ||
It is the simplest and coarsest of the Sagittal sets. The Spartan set has a maximum resolution of 13EDA<ref>https://forum.sagittal.org/viewtopic.php?t=516</ref>, which is ''sufficient'' to notate 13-limit just intonation (if used for JI), and all EDOs which are at most sharp-13, including all EDOs from 1 up to 111, the [[Zeta peak edo|zeta | It is the simplest and coarsest of the Sagittal sets. The Spartan set has a maximum resolution of 13EDA<ref>https://forum.sagittal.org/viewtopic.php?t=516</ref>, which is ''sufficient'' to notate 13-limit just intonation (if used for JI), and all EDOs which are at most sharp-13, including all EDOs from 1 up to 111, the [[Zeta peak edo|zeta peaks]] [[130edo|130]], [[142edo|142]], among many others. | ||
The eight pairs of single-shaft accidentals [[Sagittal notation#Spartan single-shaft|shown below]] are sufficient to provide these capabilities when used alone, and to the left of the standard sharp, flat and their doubles (the Evo flavor). | The eight pairs of single-shaft accidentals [[Sagittal notation#Spartan single-shaft|shown below]] are sufficient to provide these capabilities when used alone, and to the left of the standard sharp, flat and their doubles (the Evo flavor). | ||
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=== Athenian === | === Athenian === | ||
It is a handy symbol set, adding 10 symbol pairs to Spartan, with a total of 23 symbol pairs*, allowing for a maximum resolution of 21EDA. Early in the design of the Sagittal notation system, Secor and Keenan found that by extending the Spartan set with a further five pairs of single-shaft accidentals [[Sagittal notation#Athenian extension single-shaft|shown below]] an economical universal JI notation system could be defined, by dividing the apotome (Pythagorean sharp or flat) into 21 almost-equal divisions. This set of thirteen pairs is called the Athenian set. If the divisions were made exactly equal (5.4136 ¢), this would be an example of [[Brahmagupta]] temperament, of which the two most salient EDOs are 217 and 224. | It is a handy symbol set, adding 10 symbol pairs to Spartan, with a total of 23 symbol pairs*, allowing for a maximum resolution of 21EDA. Early in the design of the Sagittal notation system, Secor and Keenan found that by extending the Spartan set with a further five pairs of single-shaft accidentals [[Sagittal notation#Athenian extension single-shaft|shown below]] an economical universal JI notation system could be defined, by dividing the apotome (Pythagorean sharp or flat) into 21 almost-equal divisions. This set of thirteen pairs is called the Athenian set. If the divisions were made exactly equal (5.4136 ¢), this would be an example of [[Brahmagupta]] temperament, of which the two most salient EDOs are [[217edo|217]] and [[224edo|224]]. | ||
When used for JI, it defines the ''Standard Medium Precision JI,'' capable of writing in the 17-limit. | When used for JI, it defines the ''Standard Medium Precision JI,'' capable of writing in the 17-limit. | ||
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=== Trojan (12-EDO relative) === | === Trojan (12-EDO relative) === | ||
This is a special extension to Spartan which adds 3 more symbol sets, which is exclusively used to notate [[compton]] EDOs (12N EDOs up to [[312edo|312]]) in which the apotome is 100 cents. However, all of these EDOs lower than 168EDO can be notated using just Spartan, in which cases, depending on | This is a special extension to Spartan which adds 3 more symbol sets, which is exclusively used to notate [[compton]] EDOs (12N EDOs up to [[312edo|312]]) in which the apotome is 100 cents. However, all of these EDOs lower than 168EDO can be notated using just Spartan, in which cases, depending on the composer's needs, may prove Athenian to be more useful. | ||
=== Promethean === | === Promethean === | ||
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=== Magrathean === | === Magrathean === | ||
It adds the ''tina'' diacritic | It adds the ''tina'' diacritic to the Olympian symbol set, able to be stacked up to thrice with any of the symbols (three tinas make a ~mina), allowing for a whopping maximum resolution of 809EDA. When used for JI, it defines the ''Standard Insane Precision JI'' capable of writing in the 127-limit with astonishing precision. There is no level of precision higher than this, and it is unlikely that one will ever exist. Unless you want some hot sauce.<ref name=":0">https://forum.sagittal.org/viewtopic.php?p=2714&hilit=bomb#p2714 "A tina is approximately 1/809th of an apotome, 1/8539th of an octave (a [[Zeta peak edo|zeta-peak EDO]]), or 0.14 cents. The fractional-tina is generally half a tina but is intentionally arbitrary, because if you need any more precision than that, I have a bottle of Da' Bomb Beyond Insanity Hot Sauce with your name on it"</ref> | ||
== Gallery == | == Gallery == | ||
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|1515591/1515520 down | |1515591/1515520 down | ||
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The diacritic is called "tina". Notice how 3 tinas is approximately equal to one mina, so the system just equates the 3. Either way, this is an | The diacritic is called "tina". Notice how 3 tinas is ''approximately'' equal to one mina, so the system just equates the 3. Either way, this is an ''insane'' level of pitch precision, down to less than tenths of a cent. The "i/o" diacritic is a fraction of a tina, often a half, but it is left arbitrary intentionally.<ref name=":0" /> | ||
== See also == | == See also == | ||