Pain free guide to Sagittal: Difference between revisions

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== 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 ~~may'be~~ you were older, and ~~may'be~~ 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… 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!! …

Whoops, started ranting there haha… Well sagittal is a sort of extension of regular notation except it's designed so that it can ~~accomodate~~ 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.

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 totally sucks, it still forms a chain corresponding to the naturals on the staff.

[[5edo]] ~~for example or~~ (dividing the [[octave]] into 5 equal parts tuning) has a 720 cent interval which is the closest possible ~~thing~~ 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:

[[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 major C D E G A C ~~scale~~ that most people are familiar with in music.

[[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.

This is because a chain of five fifths will inevitably form C G D A E. The weird thing here is that 5edo ~~is an even scale~~ meaning that no matter how we order the scale, it's the same mode, there is only one 5 tone mode. However if we analyze a 5 tone score, we can see that different positions in the scale do indeed have a different effect in music because we are moving lower or higher from the main tonic position. This is an example of how sagittal will allow us to really understand context of alternate tuned music.

This is because a chain of five fifths will inevitably form C G D A E. The weird thing here is that 5edo only has five notes, meaning that no matter how we order the scale, it's the same mode; there is only one 5 tone mode. However if we analyze a 5 tone score, we can see that different positions in the scale do indeed have a different effect in music, because we are moving lower or higher from the main tonic position. This is an example of how sagittal will allow us to really understand context of alternate tuned music.

[[7edo]] is exactly like the major scale ~~in that~~ it corresponds to the naturals on the staff except that unlike 5edo, all the lines and spaces pitches are used. This means we can

[[7edo]] is exactly like the major scale about how it corresponds to the naturals on the staff, except that unlike 5edo, all the lines and spaces pitches are used. This means we can

[[File:Screen_Shot_2015-07-30_at_10.31.21_PM.png|alt=Screen Shot 2015-07-30 at 10.31.21 PM.png|576x148px|Screen Shot 2015-07-30 at 10.31.21 PM.png]]

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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 ~~then~~ it repeats. Sagittal doesn't allow to ~~change~~ the staff, ~~add more~~ 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 ~~fifth~~ 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. 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.

== ACCIDENTAL MARKINGS ==

@@ Line 2: / Line 2: @@
 == 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 may'be you were older, and may'be 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… 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!! …
-Whoops, started ranting there haha… Well sagittal is a sort of extension of regular notation except it's designed so that it can accomodate 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.
+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 totally sucks, it still forms a chain corresponding to the naturals on the staff.
-[[5edo]] for example or (dividing the [[octave]] into 5 equal parts tuning) has a 720 cent interval which is the closest possible thing 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:
+[[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 major C D E G A C scale that most people are familiar with in music.
+[[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.
-This is because a chain of five fifths will inevitably form C G D A E. The weird thing here is that 5edo is an even scale meaning that no matter how we order the scale, it's the same mode, there is only one 5 tone mode. However if we analyze a 5 tone score, we can see that different positions in the scale do indeed have a different effect in music because we are moving lower or higher from the main tonic position. This is an example of how sagittal will allow us to really understand context of alternate tuned music.
+This is because a chain of five fifths will inevitably form C G D A E. The weird thing here is that 5edo only has five notes, meaning that no matter how we order the scale, it's the same mode; there is only one 5 tone mode. However if we analyze a 5 tone score, we can see that different positions in the scale do indeed have a different effect in music, because we are moving lower or higher from the main tonic position. This is an example of how sagittal will allow us to really understand context of alternate tuned music.
-[[7edo]] is exactly like the major scale in that it corresponds to the naturals on the staff except that unlike 5edo, all the lines and spaces pitches are used. This means we can
+[[7edo]] is exactly like the major scale about how it corresponds to the naturals on the staff, except that unlike 5edo, all the lines and spaces pitches are used. This means we can
 [[File:Screen_Shot_2015-07-30_at_10.31.21_PM.png|alt=Screen Shot 2015-07-30 at 10.31.21 PM.png|576x148px|Screen Shot 2015-07-30 at 10.31.21 PM.png]]
@@ Line 20: / Line 20: @@
 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 then it repeats. Sagittal doesn't allow to change the staff, add more 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 fifth 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. 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.
 == ACCIDENTAL MARKINGS ==