Sagittal notation: Difference between revisions

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|Complement

|{{sagittal|/||\}}

|{{sagittal|(| |~}}

|{{sagittal|(||~}}

|{{sagittal|/||)}}

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

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|{{sagittal|)/|| }}

|{{sagittal|/|| }}

|{{sagittal|)|| ~}}

|{{sagittal|(|| ~}}

|{{sagittal|~~|| }}

|{{sagittal|||~}}

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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 and including 111, the [[Zeta peak edo|zeta peaks]] [[130edo|130]], [[142edo|142]], among many others. If used with tempered systems, it can be used to write music in the 23-limit, such as with 94edo.

<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.

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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 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'']] 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 ===

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>

== Prime approximations ==

Here are some approximations to octave reduced primes from D, using the several precision sets available in JI. Values in parentheses are deviations in cents from just; if exact, none is displayed.

{| class="wikitable"

|

|5

|7

|11

|13

|17

|19

|23

|29

|31

|-

|Spartan

| rowspan="5" |F{{sagittal|||\}}

| rowspan="5" |C{{sagittal|!)}}

| rowspan="5" |G{{sagittal|/|\}}

| rowspan="3" |B{{sagittal|\!)}}(0.42)

|D{{sagittal|)||| }} (2.971)

| rowspan="2" |F{{sagittal||(}} (2.380)

|A{{sagittal|\\!}} (3.008)

|C{{sagittal||)}} (6.223)

| rowspan="2" |D{{sagittal|\!/}}(1.691)

|-

|Athenian

| rowspan="4" |E{{sagittal|(!!(}}

|A{{sagittal|~!!(}}(1.009)

| rowspan="2" |C{{sagittal|(| }} (0.339)

|-

|Promethean

| rowspan="3" |F{{sagittal|)| }}

| rowspan="3" |A{{sagittal|)~!!}}

|D{{sagittal|(\!}}(0.436)

|-

|Olympian

| rowspan="2" |B{{sagittal|,}}{{sagittal|\!)}}

|C {{sagittal|`}}{{sagittal|(| }} (0.130)

| rowspan="2" |D{{sagittal|,}}{{sagittal|(\!}} (0.013)

|-

|Magrathean

|C {{sagittal|@2}}{{sagittal|(| }} (0.039)

|}

== Gallery ==

=== Spartan single-shaft ===

@@ Line 49: / Line 49: @@
 |Complement
 |{{sagittal|/||\}}
-|{{sagittal|(| |~}}
+|{{sagittal|(||~}}
 |{{sagittal|/||)}}
 |{{sagittal|)//|| }}
@@ Line 63: / Line 63: @@
 |{{sagittal|)/|| }}
 |{{sagittal|/|| }}
-|{{sagittal|)|| ~}}
+|{{sagittal|(|| ~}}
 |{{sagittal|~~|| }}
 |{{sagittal|||~}}
@@ Line 117: / 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 and including 111, the [[Zeta peak edo|zeta peaks]] [[130edo|130]], [[142edo|142]], among many others. If used with tempered systems, it can be used to write music in the 23-limit, such as with 94edo.
 <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.
@@ Line 144: / 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 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'']] 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 ===
 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>
+== Prime approximations ==
+Here are some approximations to octave reduced primes from D, using the several precision sets available in JI. Values in parentheses are deviations in cents from just; if exact, none is displayed.
+{| class="wikitable"
+|
+|5
+|7
+|11
+|13
+|17
+|19
+|23
+|29
+|31
+|-
+|Spartan
+| rowspan="5" |F{{sagittal|||\}}
+| rowspan="5" |C{{sagittal|!)}}
+| rowspan="5" |G{{sagittal|/|\}}
+| rowspan="3" |B{{sagittal|\!)}}(0.42)
+|D{{sagittal|)||| }} (2.971)
+| rowspan="2" |F{{sagittal||(}} (2.380)
+|A{{sagittal|\\!}} (3.008)
+|C{{sagittal||)}} (6.223)
+| rowspan="2" |D{{sagittal|\!/}}(1.691)
+|-
+|Athenian
+| rowspan="4" |E{{sagittal|(!!(}}
+|A{{sagittal|~!!(}}(1.009)
+| rowspan="2" |C{{sagittal|(| }} (0.339)
+|-
+|Promethean
+| rowspan="3" |F{{sagittal|)| }}
+| rowspan="3" |A{{sagittal|)~!!}}
+|D{{sagittal|(\!}}(0.436)
+|-
+|Olympian
+| rowspan="2" |B{{sagittal|,}}{{sagittal|\!)}}
+|C {{sagittal|`}}{{sagittal|(| }} (0.130)
+| rowspan="2" |D{{sagittal|,}}{{sagittal|(\!}} (0.013)
+|-
+|Magrathean
+|C {{sagittal|@2}}{{sagittal|(| }} (0.039)
+|}
 == Gallery ==
 === Spartan single-shaft ===