Sagittal notation: Difference between revisions

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=== Herculean ===

It adds the [[schisma]] diacritic to the Promethean symbol set, which can be stacked with the remaining alterations, allowing for a maximum resolution of 58EDA, of which a great edo is [[612edo|612]]. When used for JI, it defines the ''Standard Ultra Precision JI'' capable of writing in the 23-limit with higher precision.

It adds the [[schisma]] accent (a diacritic) to the Promethean symbol set, which can be stacked with the remaining alterations, allowing for a maximum resolution of 58EDA, of which a great edo is [[612edo|612]]. When used for JI, it defines the ''Standard Ultra Precision JI'' capable of writing in the 23-limit with higher precision.

=== 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, The zeta peak [[2460edo]] has been used as a base to define the mina as an interval measure, and the Olympian set of intervals generally, due to its extremely precise 27-odd-limit palette. 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|(!/}} .

It adds the [[4096/4095|''mina'']] accent 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, The zeta peak [[2460edo]] has been used as a base to define the mina as an interval measure, and the Olympian set of intervals generally, due to its extremely precise 27-odd-limit palette. 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 ===

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. The strict zeta peak [[8539edo]] has been used to define the tina as an interval measure, due its insanely precise 27-odd-limit (and beyond) interval palette. 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>

It adds the ''tina'' accent 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. The strict zeta peak [[8539edo]] has been used to define the tina as an interval measure, due its insanely precise 27-odd-limit (and beyond) interval palette. 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>

== Prime approximations ==

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Tempered systems might yield better or worse approximations to each just interval. Used for JI, only some non-Pythagorean intervals in the 23-limit will ever be exact. The error gets increasingly small however, down to hundredths of a cent in Magrathean.

== Gallery ==

== Gallery of core accidentals ==

=== Spartan single-shaft ===

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=== Herculean extension ~~diacritics~~ ===

== Gallery of accents ==

Fine-grained Sagittal notations starting with Herculean can use accents, also called diacritics, to the left of a sagittal or a bare shaft, to indicate very subtle distinctions in pitch.

=== Herculean extension accents ===

Ai and ao are not ~~diacritics~~ but bare shafts which do not alter the pitch. They are used when there would otherwise be bare ~~diacritics~~.

Ai and ao are not accents but bare shafts which do not alter the pitch. They are used when there would otherwise be bare accents.

{| class="wikitable"

|- style="text-align: center;"

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|5s down

|}

The interval is called a "schisma". The ~~diacritic~~'s shape is called "tick" (up or down).

The interval is called a "schisma". The accent's shape is called "tick" (up or down).

=== Olympian extension ~~diacritics~~ ===

=== Olympian extension accents ===

{| class="wikitable"

|- style="text-align: center;"

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The average unit interval is called a "mina" (rhymes with ballerina) and is approximately 0.42 of a cent. The shapes are called "wing" and "bird".

=== Magrathean extension ~~diacritics~~ ===

=== Magrathean extension accents ===

{| class="wikitable"

|- style="text-align: center;"

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|77/(5⋅37)n down

|}

The average unit interval is called a "tina" (rhymes with ballerina) and is approximately 0.14 of a cent. The new shapes are called "horn" and "wedge". 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. The "i/o" ~~diacritic~~, whose shape is called "dot", represents some unit fraction of a tina, often a half as shown, but it is intentionally left to be defined by the user.<ref name=":0" />

The average unit interval is called a "tina" (rhymes with ballerina) and is approximately 0.14 of a cent. The new shapes are called "horn" and "wedge". 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. The "i/o" accent, whose shape is called "dot", represents some unit fraction of a tina, often a half as shown, but it is intentionally left to be defined by the user.<ref name=":0" />

</div>

== See also ==

@@ Line 141: / Line 141: @@
 === Herculean ===
-It adds the [[schisma]] diacritic to the Promethean symbol set, which can be stacked with the remaining alterations, allowing for a maximum resolution of 58EDA, of which a great edo is [[612edo|612]]. When used for JI, it defines the ''Standard Ultra Precision JI'' capable of writing in the 23-limit with higher precision.
+It adds the [[schisma]] accent (a diacritic) to the Promethean symbol set, which can be stacked with the remaining alterations, allowing for a maximum resolution of 58EDA, of which a great edo is [[612edo|612]]. When used for JI, it defines the ''Standard Ultra Precision JI'' capable of writing in the 23-limit with higher precision.
 === 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, The zeta peak [[2460edo]] has been used as a base to define the mina as an interval measure, and the Olympian set of intervals generally, due to its extremely precise 27-odd-limit palette. 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|(!/}} .
+It adds the [[4096/4095|''mina'']] accent 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, The zeta peak [[2460edo]] has been used as a base to define the mina as an interval measure, and the Olympian set of intervals generally, due to its extremely precise 27-odd-limit palette. 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 ===
-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. The strict zeta peak [[8539edo]] has been used to define the tina as an interval measure, due its insanely precise 27-odd-limit (and beyond) interval palette. 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>
+It adds the ''tina'' accent 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. The strict zeta peak [[8539edo]] has been used to define the tina as an interval measure, due its insanely precise 27-odd-limit (and beyond) interval palette. 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>
 == Prime approximations ==
@@ Line 194: / Line 194: @@
 Tempered systems might yield better or worse approximations to each just interval. Used for JI, only some non-Pythagorean intervals in the 23-limit will ever be exact. The error gets increasingly small however, down to hundredths of a cent in Magrathean.
-== Gallery ==
+== Gallery of core accidentals ==
 === Spartan single-shaft ===
 {{sge|  ¦( |  !( | n   | 5120/5103 | 7/5 kleisma }}
@@ Line 329: / Line 329: @@
 {{sge| (X~ | (Y~    | r  |  81/76  | 19s }}
-=== Herculean extension diacritics ===
+== Gallery of accents ==
+Fine-grained Sagittal notations starting with Herculean can use accents, also called diacritics, to the left of a sagittal or a bare shaft, to indicate very subtle distinctions in pitch.
+<div class="mw-collapsible mw-collapsed">
+=== Herculean extension accents ===
 {{sge| ¦ | ! | &NoBreak; | 1/1 | shaft }}
-Ai and ao are not diacritics but bare shafts which do not alter the pitch. They are used when there would otherwise be bare diacritics.
+Ai and ao are not accents but bare shafts which do not alter the pitch. They are used when there would otherwise be bare accents.
 {| class="wikitable"
 |- style="text-align: center;"
@@ Line 343: / Line 346: @@
 |5s down
 |}
-The interval is called a "schisma". The diacritic's shape is called "tick" (up or down).
+The interval is called a "schisma". The accent's shape is called "tick" (up or down).
-=== Olympian extension diacritics ===
+=== Olympian extension accents ===
 {| class="wikitable"
 |- style="text-align: center;"
@@ Line 365: / Line 368: @@
 The average unit interval is called a "mina" (rhymes with ballerina) and is approximately 0.42 of a cent. The shapes are called "wing" and "bird".
-=== Magrathean extension diacritics ===
+=== Magrathean extension accents ===
 {| class="wikitable"
 |- style="text-align: center;"
@@ Line 446: / Line 449: @@
 |77/(5⋅37)n down
 |}
-The average unit interval is called a "tina" (rhymes with ballerina) and is approximately 0.14 of a cent. The new shapes are called "horn" and "wedge". 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. The "i/o" diacritic, whose shape is called "dot", represents some unit fraction of a tina, often a half as shown, but it is intentionally left to be defined by the user.<ref name=":0" />
+The average unit interval is called a "tina" (rhymes with ballerina) and is approximately 0.14 of a cent. The new shapes are called "horn" and "wedge". 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. The "i/o" accent, whose shape is called "dot", represents some unit fraction of a tina, often a half as shown, but it is intentionally left to be defined by the user.<ref name=":0" />
+</div>
 == See also ==