Pain free guide to Sagittal: Difference between revisions

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[[Sagittal]] is one of the ~~coolest~~ systems for microtonal [[notation]]. It allows virtually any [[tuning]] to be notated with ease and it's pretty easy to get the hang of if you're good with standard notation already. If you are not then this will not be much use to you as it only adds to the complexity that [[12edo]] normally has. ~~Anyway, let's check it out!!~~

[[Sagittal]] is one of the best systems for microtonal [[notation]]. It allows virtually any [[tuning]] to be notated with ease and it's pretty easy to get the hang of if you're good with standard notation already. If you are not then this will not be much use to you as it only adds to the complexity that [[12edo]] normally has.

== Basics ==

Sagittal is basically a way to notate ANY tuning practically with regular old notation you learned since Miss Betty Jo sat you down to read your first music in piano lessons when you were ~~little… OR maybe~~ you ~~were older~~, and ~~maybe you could even already drive!~~ or ~~weren't four years OLD~~, ~~SOME PEOPLE DO LEARN A LITTLE OLDER THAN 3!! …~~

Sagittal is basically a way to notate ANY tuning practically with regular old notation you learned since Miss Betty Jo sat you down to read your first music in piano lessons when you were little. Sagittal is a sort of extension of regular notation, but it's designed so that it can accommodate almost any tuning (at least, most practical tunings can be notated in it). “How does it do this?”, you may ask. Well, first of all, in sagittal, the normal lines and spaces that have no accidental signs (naturals) change depending on the tuning we are in. You see, normal notation works by a chain of seven fifths producing the scale natural notes or white keys on the piano: C D E F G A B C. This works well because of technical and historical reasons that are beyond the scope of this article–you can read about it more on [[Chain of fifths]] and [[5L 2s]]. The point is, the chain of fifths is important. Chains of fifths make logical sense when building a notation system, and sagittal always corresponds the natural notes on the staff with the closest possible equivalent to a chain of fifths in the tuning.

Whoops, started ranting there haha… Well sagittal is a sort of extension of regular notation except it's designed so that it can accommodate any tuning, well almost any tuning, but most practical tunings can be notated in it. “How does it do this?”, you may ask. Well, first of all, in sagittal, the normal lines and spaces that have no accidental signs (naturals) change depending on the tuning we are in. You see, normal notation works by a chain of seven fifths producing the scale natural notes or white keys on the piano: C D E F G A B C. This works well because of technical reasons that are beyond the scope of this article, so you can read about that elsewhere. Point is, you need to know this: "CHAIN OF FIFTHS GOOD!! ME LIKE CHAIN OF FIFTHS!!" haha JK, moving on… Chains of fifths make logical sense when building a notation system, and sagittal always corresponds the natural notes on the staff with the closest possible equivalent to a chain of fifths in the tuning.

It doesn't matter if the fifth in your tuning is really inaccurate, it still forms a chain corresponding to the naturals on the staff. [[5edo]] (dividing the [[octave]] into 5 equal parts tuning) for example, has 3\5, a 720 cent interval, which is the closest possible interval to a fifth in 5edo. Therefore, the notes correspond to the chain of five fifths… "BUT WAIT A MINUTE! THAT MAKES NO SENSE, THERE HAVE TO BE SEVEN PITCHES!” Exactly, that's why with 5edo, we only need to use five of the pitches on the staff which end up LOOKING like this if we write out 5edo:

It doesn't matter if the fifth in your tuning ~~totally sucks~~, it still forms a chain corresponding to the naturals on the staff.

[[5edo]] (dividing the [[octave]] into 5 equal parts tuning) for example, has 3\5, a 720 cent interval, which is the closest possible interval to a fifth in 5edo. Therefore, the notes correspond to the chain of five fifths… "BUT WAIT A MINUTE! THAT MAKES NO SENSE, THERE HAVE TO BE SEVEN PITCHES!” Exactly, that's why with 5edo, we only need to use five of the pitches on the staff which end up LOOKING like this if we write out 5edo:

[[File:Screen_Shot_2015-07-30_at_10.23.01_PM.png|alt=Screen Shot 2015-07-30 at 10.23.01 PM.png|400x147px|Screen Shot 2015-07-30 at 10.23.01 PM.png]] To the left you can see that it corresponds to the normal pentatonic major scale (C D E G A C) that most people are familiar with in music.

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assume that these pitches are tuned roughly to 7edo without the need of small accidental signs for the natural scale. However when we get to [[9edo]], something interesting happens…

9edo has well, more than seven pitches, and there are only seven pitches on the staff before it repeats. Sagittal doesn't allow to changes the staff, additional lines, or other things like that. ~~The way~~ 9edo ~~is notated is by using A CHAIN OF FIFTHS MINUS TWO :D Basically~~, you construct a chain of seven fifths like intervals, the remaining two are notated by adding an accidental next to them. This is where things get a little tricky, but also cool.

9edo has well, more than seven pitches, and there are only seven pitches on the staff before it repeats. Sagittal doesn't allow to changes the staff, additional lines, or other things like that. So for 9edo, you construct a chain of seven fifths like intervals, the remaining two are notated by adding an accidental next to them. This is where things get a little tricky, but also cool.

== Accidental markings ==

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You'll notice that the scale left on the naturals becomes 2 1 1 2 1 1 1 or the mavila scale of 9edo which is awesome and sensible because you can play in [[mavila]] 7- in 9edo and write it all out in all nine keys logically. Why? Because if you go by this circle of fifths logic here, AND you can notate a scale using the natural notes, it's going to work really well for notating it in all keys.

We'll talk more about key signatures a little later!!

We'll talk more about key signatures a little later!

== 10edo and 11edo ==

@@ Line 1: / Line 1: @@
-[[Sagittal]] is one of the coolest systems for microtonal [[notation]]. It allows virtually any [[tuning]] to be notated with ease and it's pretty easy to get the hang of if you're good with standard notation already. If you are not then this will not be much use to you as it only adds to the complexity that [[12edo]] normally has. Anyway, let's check it out!!
+[[Sagittal]] is one of the best systems for microtonal [[notation]]. It allows virtually any [[tuning]] to be notated with ease and it's pretty easy to get the hang of if you're good with standard notation already. If you are not then this will not be much use to you as it only adds to the complexity that [[12edo]] normally has.
 == Basics ==
-Sagittal is basically a way to notate ANY tuning practically with regular old notation you learned since Miss Betty Jo sat you down to read your first music in piano lessons when you were little… OR maybe you were older, and maybe you could even already drive! or weren't four years OLD, SOME PEOPLE DO LEARN A LITTLE OLDER THAN 3!! …
+Sagittal is basically a way to notate ANY tuning practically with regular old notation you learned since Miss Betty Jo sat you down to read your first music in piano lessons when you were little. Sagittal is a sort of extension of regular notation, but it's designed so that it can accommodate almost any tuning (at least, most practical tunings can be notated in it). “How does it do this?”, you may ask. Well, first of all, in sagittal, the normal lines and spaces that have no accidental signs (naturals) change depending on the tuning we are in. You see, normal notation works by a chain of seven fifths producing the scale natural notes or white keys on the piano: C D E F G A B C. This works well because of technical and historical reasons that are beyond the scope of this article–you can read about it more on [[Chain of fifths]] and [[5L 2s]]. The point is, the chain of fifths is important. Chains of fifths make logical sense when building a notation system, and sagittal always corresponds the natural notes on the staff with the closest possible equivalent to a chain of fifths in the tuning.
-Whoops, started ranting there haha… Well sagittal is a sort of extension of regular notation except it's designed so that it can accommodate any tuning, well almost any tuning, but most practical tunings can be notated in it. “How does it do this?”, you may ask. Well, first of all, in sagittal, the normal lines and spaces that have no accidental signs (naturals) change depending on the tuning we are in. You see, normal notation works by a chain of seven fifths producing the scale natural notes or white keys on the piano: C D E F G A B C. This works well because of technical reasons that are beyond the scope of this article, so you can read about that elsewhere. Point is, you need to know this: "CHAIN OF FIFTHS GOOD!! ME LIKE CHAIN OF FIFTHS!!" haha JK, moving on… Chains of fifths make logical sense when building a notation system, and sagittal always corresponds the natural notes on the staff with the closest possible equivalent to a chain of fifths in the tuning.
+It doesn't matter if the fifth in your tuning is really inaccurate, it still forms a chain corresponding to the naturals on the staff. [[5edo]] (dividing the [[octave]] into 5 equal parts tuning) for example, has 3\5, a 720 cent interval, which is the closest possible interval to a fifth in 5edo. Therefore, the notes correspond to the chain of five fifths… "BUT WAIT A MINUTE! THAT MAKES NO SENSE, THERE HAVE TO BE SEVEN PITCHES!” Exactly, that's why with 5edo, we only need to use five of the pitches on the staff which end up LOOKING like this if we write out 5edo:
-It doesn't matter if the fifth in your tuning totally sucks, it still forms a chain corresponding to the naturals on the staff.
-[[5edo]] (dividing the [[octave]] into 5 equal parts tuning) for example, has 3\5, a 720 cent interval, which is the closest possible interval to a fifth in 5edo. Therefore, the notes correspond to the chain of five fifths… "BUT WAIT A MINUTE! THAT MAKES NO SENSE, THERE HAVE TO BE SEVEN PITCHES!” Exactly, that's why with 5edo, we only need to use five of the pitches on the staff which end up LOOKING like this if we write out 5edo:
 [[File:Screen_Shot_2015-07-30_at_10.23.01_PM.png|alt=Screen Shot 2015-07-30 at 10.23.01 PM.png|400x147px|Screen Shot 2015-07-30 at 10.23.01 PM.png]] To the left you can see that it corresponds to the normal pentatonic major scale (C D E G A C) that most people are familiar with in music.
@@ Line 20: / Line 16: @@
 assume that these pitches are tuned roughly to 7edo without the need of small accidental signs for the natural scale. However when we get to [[9edo]], something interesting happens…
-edo has well, more than seven pitches, and there are only seven pitches on the staff before it repeats. Sagittal doesn't allow to changes the staff, additional lines, or other things like that. The way 9edo is notated is by using A CHAIN OF FIFTHS MINUS TWO :D Basically, you construct a chain of seven fifths like intervals, the remaining two are notated by adding an accidental next to them. This is where things get a little tricky, but also cool.
+edo has well, more than seven pitches, and there are only seven pitches on the staff before it repeats. Sagittal doesn't allow to changes the staff, additional lines, or other things like that. So for 9edo, you construct a chain of seven fifths like intervals, the remaining two are notated by adding an accidental next to them. This is where things get a little tricky, but also cool.
 == Accidental markings ==
@@ Line 42: / Line 38: @@
 You'll notice that the scale left on the naturals becomes 2 1 1 2 1 1 1 or the mavila scale of 9edo which is awesome and sensible because you can play in [[mavila]] 7- in 9edo and write it all out in all nine keys logically. Why? Because if you go by this circle of fifths logic here, AND you can notate a scale using the natural notes, it's going to work really well for notating it in all keys.
-We'll talk more about key signatures a little later!!
+We'll talk more about key signatures a little later!
 == 10edo and 11edo ==