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Sagittal notation: Difference between revisions

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Eufalesio (talk | contribs)
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Added Promethean single-shaft, Herculean, Olympian, and Magrathean extensions to the gallery, missing Promethean multi-shaft, and formatting the tables correctly
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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 complete Sagittal microtonal notation system. The '''Spartan''' and '''Athenian''' sets will be more than enough for most purposes.  
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 complete Sagittal microtonal notation system. 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.
[https://www.desmos.com/calculator/iehdworjko You can look up what the minimum precision is required to write an EDO in this Desmos graph.]


=== Sharps/Flats ===
=== Sharps/Flats ===
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=== Magrathean ===
=== Magrathean ===
It adds the ''tina'' diacritic (1 step of [[8539edo]]) 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>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'' diacritic (1 step of [[8539edo]]) 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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{{sge|//X  |\\Y  | ran |  896/891  | 11/7k | mid=48px }}
{{sge|//X  |\\Y  | ran |  896/891  | 11/7k | mid=48px }}
</div>
</div>
=== Promethean extension single-shaft ===
{{sge| )¦  | )!  | r |  513/512  | 19s | mid=48px }}
{{sge| ~¦  | ~!  | s |  2187/2176  | 17k | mid=48px }}
{{sge| )~¦  | )~!  | sr |  144/143  | 143C | mid=48px }}
{{sge| ~~¦  | ~~!  | sh |  99/88  | 49/11C | mid=48px }}
{{sge| )¦~  | )!~  | raz |  19683/19456  | 19C | mid=48px }}
{{sge| )¦)  | )!)  | rat |  57/56  | 19/7C | mid=48px }}
{{sge| ~¦)  | ~!)  | sat |  49/48  | 49S | mid=48px }}
{{sge| ~¦\  | ~!/  | sak |  16767/16384  | 23S | mid=48px }}
{{sge| )//¦  | )\\!  | phr |  416/405  | 13/5M | mid=48px }}
{{sge| (¦~  | (!~  | jaz |  176/171  | 19/11M | mid=48px }}
{{sge| (/¦  | (\!  | jp |  4096/3969  | 49M | mid=48px }}
{{sge| )/¦\  | )\!/  | prak |  405/392  | 49/5M | mid=48px }}
{{sge| ¦\) | !/)  | kt |  8680203/8388608  | 49L | mid=48px }}
{{sge| ¦\\|!//|kh|373977/360448|19/11L|| mid=48px }}
{{sge| )¦\\ | )!//  | rakh |  885735/851968  | 13/5L | mid=48px }}
=== Promethean extension multi-shaft ===
Multi-shaft sagittals are only used in the [[#Revo|Revo]] flavor of Sagittal.
TBA
=== Herculean extension diacritics ===
{| class="wikitable"
!<nowiki>|</nowiki>
!<nowiki>|</nowiki>
|-
|ai
|ao
|-
| colspan="2" |unison
|}
Ai and ao are used to write bare diacritics in the following extensions, like the schisma, schismina, and tina.
{| class="wikitable"
!{{sagittal|'}}
!{{sagittal|.}}
|-
|bi
|bo
|-
|[https://en.xen.wiki/w/Schisma 5s up]
|5s down
|}
=== Olympian extension diacritics ===
{| class="wikitable"
!{{sagittal|`}}
!{{sagittal|,}}
!{{sagittal|``}}
!{{sagittal|,,}}
|-
|mi
|mo
|mimi
|momo
|-
|[https://en.xen.wiki/w/4096/4095 35/13sx] up
|35/13sx down
|[https://en.xen.wiki/w/2080/2079 77/65sx] up
|77/65sx down
|}
The diacritic is called "mina".
=== Magrathean extension diacritics ===
{| class="wikitable"
!{{sagittal|@1}}
!{{sagittal|l1}}
!{{sagittal|@2}}
!{{sagittal|l2}}
!{{sagittal|`}}
!{{sagittal|,}}
!{{sagittal|@4}}
!{{sagittal|l4}}
!{{sagittal|@5}}
!{{sagittal|l5}}
!{{sagittal|``}}
!{{sagittal|,,}}
!{{sagittal|@7}}
!{{sagittal|l7}}
!{{sagittal|@8}}
!{{sagittal|l8}}
!{{sagittal|@8}}
!{{sagittal|l8}}
!{{sagittal|@9}}
!{{sagittal|l9}}
!{{sagittal|@.}}
!{{sagittal|l.}}
|-
|qui
|quo
|quiqui
|quoquo
|mi
|mo
|quimi
|quomo
|quiquimi
|quoquomo
|mimi
|momo
|quimimi
|quomomo
|quiquimimi
|quoquomomo
|quiquimimi
|quoquomomo
|mimimi
|momomo
|i
|o
|-
|10241/10240 up
|10241/10240 up
|5832/5831 up
|5832/5831 down
|[https://en.xen.wiki/w/4096/4095 35/13sx] up
|35/13sx down
|3025/3024 up
|3025/3024 up
|2401/2400 up
|2401/2400 down
|[https://en.xen.wiki/w/2080/2079 77/65sx] up
|77/65sx down
|1701/1700 up
|1701/1700 down
|382976/382725 up
|382976/382725 down
|382976/382725 up
|382976/382725 down
|131072/130977  up
|131072/130977  down
|1515591/1515520  up
|1515591/1515520  down
|}
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 fractions of a cent. The "i/o" diacritic is a fraction of a tina, left arbitrary intentionally.<ref name=":0" />


== See also ==
== See also ==
Retrieved from "https://en.xen.wiki/w/Sagittal_notation"