Sagittal notation: Difference between revisions

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=== Revo ===

The '''Revo''' flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: {{sagittal| /||\ }} {{sagittal| \!!/ }} {{sagittal| /X\ }} {{sagittal| \Y/ }}. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. {{sagittal| /| }}{{sagittal| # }} becomes {{sagittal| /||| }} and {{sagittal| !) }}{{sagittal| b }} becomes {{sagittal| !!!) }}. ~~When~~ the ~~Sagittal part~~ alters in the opposite direction to the ~~sharp or flat part~~, ~~the rules~~ are not ~~so simple, e.g~~. {{sagittal| \! }}{{sagittal| # }} becomes {{sagittal| ||\ }} ~~and~~ {{sagittal| |) }}{{sagittal| b }} becomes {{sagittal| !!) }}; one must ~~simply~~ learn these ''~~[[2187/2048#Notation|~~apotome]] complements''.

The '''Revo''' flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: {{sagittal| /||\ }} {{sagittal| \!!/ }} {{sagittal| /X\ }} {{sagittal| \Y/ }}. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. {{sagittal| /| }}{{sagittal| # }} becomes {{sagittal| /||| }} and {{sagittal| !) }}{{sagittal| b }} becomes {{sagittal| !!!) }}, as expected. [[2187/2048#Notation|''Apotome'']] ''complements'', that arise when the Sagital accidental alters in the opposite direction to the apotome, are not predictable. {{sagittal| \! }}{{sagittal| # }} becomes {{sagittal| ||\ }}, {{sagittal| |) }}{{sagittal| b }} becomes {{sagittal| !!) }}, {{sagittal| \!/ }}{{sagittal| # }} becomes {{sagittal|(|) }}, {{sagittal| \!)}}{{sagittal| # }} becomes {{sagittal|(|\}} ; one must learn these ''apotome complements'' by rote memorization.

{| class="wikitable"

|+Table of apotome complements<ref>https://sagittal.org/sagittal.pdf p. 24 Figure 13</ref>

|Symbol

|{{sagittal|h}}

|{{sagittal|)| }}

|{{sagittal| |(}}

|{{sagittal|~| }}

|{{sagittal|)|(}}

|{{sagittal|)~| }}

|{{sagittal|~|(}}

|{{sagittal| |~}}

|{{sagittal|~~|}}

|{{sagittal|)|~}}

|{{sagittal|/|}}

|{{sagittal|)/|}}

|{{sagittal| |)}}

|{{sagittal|)|)}}

|{{sagittal| |\}}

|{{sagittal|(|}}

|{{sagittal|~|)}}

|{{sagittal|/|~}}

|{{sagittal|~|)}}

|{{sagittal|~|\}}

|{{sagittal|//| }}

|{{sagittal|)//| }}

|{{sagittal|/|)}}

|{{sagittal|(|~}}

|{{sagittal|/|\}}

|{{sagittal|(/| }}

| rowspan="2" |{{sagittal|)/|\}}

|-

|Complement

|{{sagittal|/||\}}

|{{sagittal|(| |~}}

|{{sagittal|/||)}}

|{{sagittal|)//|| }}

|{{sagittal|//|| }}

|{{sagittal|~||\}}

|{{sagittal|(||(}}

|{{sagittal|/||~}}

|{{sagittal|~||)}}

|{{sagittal|(|| }}

|{{sagittal|||\}}

|{{sagittal|)||)}}

|{{sagittal|||)}}

|{{sagittal|)/|| }}

|{{sagittal|/|| }}

|{{sagittal|)|| ~}}

|{{sagittal|~~|| }}

|{{sagittal|||~}}

|{{sagittal|~||(}}

|{{sagittal|)~||}}

|{{sagittal|)||(}}

|{{sagittal|)|\\}}

|{{sagittal|(|\}}

|{{sagittal||\\}}

|{{sagittal|(|)}}

|{{sagittal||\)}}

|}

{{sagittal|)/|\}} is its own apotome complement.

== Notation software support ==

=== Sibelius ===

Sagibelius 2.0 – plugins for using Sagittal notation in Sibelius 4 and up. By [http://www.jacobbarton.net/2011/10/sagibelius-2-0-released/ Jacob Barton]. Hosted on this wiki. Donationware.

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=== 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 peaks]] [[130edo|130]], [[142edo|142]], among many others.

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.

<nowiki>*</nowiki>In this set, ratios of 13 are represented by reusing the accidentals for ratios of 35 (7*5). This is because the resulting interval, [[512/315]] (the ~13/8 interval) is only 0.4 ¢ ([[4096/4095]]) from just. The prime 13 will not have a distinct accidental up until the Olympian set.

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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As an alternative, 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 (the Revo flavor). The standard natural is used alone in both Evo and Revo variants, but only to cancel a previous accidental when a barline will not suffice.

~~In this set, ratios of 13 are represented by reusing the accidentals for ratios of 35 (7*5). Thusly, [[8505/8192]] (the ~13/8 interval) is only 0.4 ¢ ([[4096/4095]]) from just.~~ Sagittal extensions following Spartan allow notation of JI ratios with primes beyond 13 (and 13 proper), 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 Evo versus Revo is available with each extension.

Sagittal extensions following Spartan allow notation of JI ratios with primes beyond 13 (and 13 proper), 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 Evo versus Revo is available with each extension.

=== Athenian ===

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=== Olympian ===

It adds the [[4096/4095|''mina'']] diacritic to the Herculean symbol set, able to be stacked up to twice with the schisma and the remaining alterations, allowing for a maximum resolution of 233EDA. When used for JI, it defines the ''Standard Extreme Precision JI'' capable of writing in the 47-limit with great precision.

It adds the [[4096/4095|''mina'']] diacritic to the Herculean symbol set, able to be stacked up to twice with the schisma and the remaining alterations, allowing for a maximum resolution of 233EDA. When used for JI, it defines the ''Standard Extreme Precision JI'' capable of writing in the 47-limit with great precision. It also is the smallest precision level that has an "exact" mapping for prime 13, thanks to the mina's appearance. 13/8 is now written as a major sixth minus the 35 large diesis and a mina. From C, this would be C - A{{sagittal|(!/}}{{sagittal|,}} .

=== Magrathean ===

@@ Line 15: / Line 15: @@
 === Revo ===
-The '''Revo''' flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: {{sagittal| /||\ }} {{sagittal| \!!/ }} {{sagittal| /X\ }} {{sagittal| \Y/ }}. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. {{sagittal| /| }}{{sagittal| # }} becomes {{sagittal| /||| }} and {{sagittal| !) }}{{sagittal| b }} becomes {{sagittal| !!!) }}. When the Sagittal part alters in the opposite direction to the sharp or flat part, the rules are not so simple, e.g. {{sagittal| \! }}{{sagittal| # }} becomes {{sagittal| ||\ }} and {{sagittal| |) }}{{sagittal| b }} becomes {{sagittal| !!) }}; one must simply learn these ''[[2187/2048#Notation|apotome]] complements''.
+The '''Revo''' flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: {{sagittal| /||\ }} {{sagittal| \!!/ }} {{sagittal| /X\ }} {{sagittal| \Y/ }}. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. {{sagittal| /| }}{{sagittal| # }} becomes {{sagittal| /||| }} and {{sagittal| !) }}{{sagittal| b }} becomes {{sagittal| !!!) }}, as expected. [[2187/2048#Notation|''Apotome'']] ''complements'', that arise when the Sagital accidental alters in the opposite direction to the apotome, are not predictable. {{sagittal| \! }}{{sagittal| # }} becomes {{sagittal| ||\ }},  {{sagittal| |) }}{{sagittal| b }} becomes {{sagittal| !!) }}, {{sagittal| \!/ }}{{sagittal| # }} becomes {{sagittal|(|) }}, {{sagittal| \!)}}{{sagittal| # }} becomes {{sagittal|(|\}} ; one must learn these ''apotome complements'' by rote memorization.
+{| class="wikitable"
+|+Table of apotome complements<ref>https://sagittal.org/sagittal.pdf p. 24 Figure 13</ref>
+|Symbol
+|{{sagittal|h}}
+|{{sagittal|)| }}
+|{{sagittal| |(}}
+|{{sagittal|~| }}
+|{{sagittal|)|(}}
+|{{sagittal|)~| }}
+|{{sagittal|~|(}}
+|{{sagittal| |~}}
+|{{sagittal|~~|}}
+|{{sagittal|)|~}}
+|{{sagittal|/|}}
+|{{sagittal|)/|}}
+|{{sagittal| |)}}
+|{{sagittal|)|)}}
+|{{sagittal| |\}}
+|{{sagittal|(|}}
+|{{sagittal|~|)}}
+|{{sagittal|/|~}}
+|{{sagittal|~|)}}
+|{{sagittal|~|\}}
+|{{sagittal|//| }}
+|{{sagittal|)//| }}
+|{{sagittal|/|)}}
+|{{sagittal|(|~}}
+|{{sagittal|/|\}}
+|{{sagittal|(/| }}
+| rowspan="2" |{{sagittal|)/|\}}
+|-
+|Complement
+|{{sagittal|/||\}}
+|{{sagittal|(| |~}}
+|{{sagittal|/||)}}
+|{{sagittal|)//|| }}
+|{{sagittal|//|| }}
+|{{sagittal|~||\}}
+|{{sagittal|(||(}}
+|{{sagittal|/||~}}
+|{{sagittal|~||)}}
+|{{sagittal|(|| }}
+|{{sagittal|||\}}
+|{{sagittal|)||)}}
+|{{sagittal|||)}}
+|{{sagittal|)/|| }}
+|{{sagittal|/|| }}
+|{{sagittal|)|| ~}}
+|{{sagittal|~~|| }}
+|{{sagittal|||~}}
+|{{sagittal|~||(}}
+|{{sagittal|)~||}}
+|{{sagittal|)||(}}
+|{{sagittal|)|\\}}
+|{{sagittal|(|\}}
+|{{sagittal||\\}}
+|{{sagittal|(|)}}
+|{{sagittal||\)}}
+|}
+{{sagittal|)/|\}} is its own apotome complement.
 == Notation software support ==
 === Sibelius ===
 Sagibelius 2.0 – plugins for using Sagittal notation in Sibelius 4 and up. By [http://www.jacobbarton.net/2011/10/sagibelius-2-0-released/ Jacob Barton]. Hosted on this wiki. Donationware.
@@ Line 56: / Line 117: @@
 === 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 peaks]] [[130edo|130]], [[142edo|142]], among many others.
+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.
+<nowiki>*</nowiki>In this set, ratios of 13 are represented by reusing the accidentals for ratios of 35 (7*5). This is because the resulting interval, [[512/315]] (the ~13/8 interval) is only 0.4 ¢ ([[4096/4095]]) from just. The prime 13 will not have a distinct accidental up until the Olympian set.
 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).
@@ Line 62: / Line 125: @@
 As an alternative, 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 (the Revo flavor). The standard natural is used alone in both Evo and Revo variants, but only to cancel a previous accidental when a barline will not suffice.
-In this set, ratios of 13 are represented by reusing the accidentals for ratios of 35 (7*5). Thusly, [[8505/8192]] (the ~13/8 interval) is only 0.4 ¢ ([[4096/4095]]) from just. Sagittal extensions following Spartan allow notation of JI ratios with primes beyond 13 (and 13 proper), 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 Evo versus Revo is available with each extension.
+Sagittal extensions following Spartan allow notation of JI ratios with primes beyond 13 (and 13 proper), 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 Evo versus Revo is available with each extension.
 === Athenian ===
@@ Line 81: / Line 144: @@
 === Olympian ===
-It adds the [[4096/4095|''mina'']] diacritic to the Herculean symbol set, able to be stacked up to twice with the schisma and the remaining alterations, allowing for a maximum resolution of 233EDA. When used for JI, it defines the ''Standard Extreme Precision JI'' capable of writing in the 47-limit with great precision.
+It adds the [[4096/4095|''mina'']] diacritic to the Herculean symbol set, able to be stacked up to twice with the schisma and the remaining alterations, allowing for a maximum resolution of 233EDA. When used for JI, it defines the ''Standard Extreme Precision JI'' capable of writing in the 47-limit with great precision. It also is the smallest precision level that has an "exact" mapping for prime 13, thanks to the mina's appearance. 13/8 is now written as a major sixth minus the 35 large diesis and a mina. From C, this would be C - A{{sagittal|(!/}}{{sagittal|,}} .
 === Magrathean ===