Pain free guide to Sagittal
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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 12 EDO normally has. Anyway, let's check it out!! =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!! .... 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. It doesn't matter if the fifth in your tuning totally sucks, it still forms a chain corresponding to the naturals on the staff. 5-EDO 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 5 EDO. 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 5 EDO we only need to use five of the pitches on the staff which end up LOOKING like this if we write out 5 edo: [[image:Screen Shot 2015-07-30 at 10.23.01 PM.png width="400" height="147" align="left"]] 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. This is because a chain of five fifths will inevitably form C G D A E. The weird thing here is that 5 edo 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. 7 EDO is exactly like the major scale in that it corresponds to the naturals on the staff except that unlike 5 edo, all the lines and spaces pitches are used. This means that we can notate 7 EDO and [[image:Screen Shot 2015-07-30 at 10.31.21 PM.png width="576" height="148" align="left"]] assume that these pitches are tuned roughly to 7 EDO without the need of small accidental signs for the natural scale. However when we get to 9 EDO, something interesting happens... 9 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 9 EDO 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. =ACCIDENTAL MARKINGS= The point of sagittal is that it has alot of symbols designed to represent TINY pitch increments for any given tuning. It's cool in that it allows flexibility to suit a user's needs. If we wanna be abstract and just give the performer a general idea of what to do or write down ideas our self, we can do that. On the other hand if we want to be very VERY precise or notate something freakin insane like 72 EDO, then we can do that too, given that it's going to be way more tricky due to higher complexity. There are literally, multiple ways to notate the same tunings in sagittal and it all depends on the person. More on that in a minute ;) 9 EDO can be notated by adding an accidental marking which represents a difference of approximately 130 cents up. 9 EDO looks like this then notated out: [[image:Screen Shot 2015-07-30 at 10.58.24 PM.png width="648" height="141"]] ARTICLE UNDER CONSTRUCTION
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<html><head><title>Pain free guide to Sagittal</title></head><body>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 12 EDO normally has. Anyway, let's check it out!!<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="BASICS!!!!"></a><!-- ws:end:WikiTextHeadingRule:0 -->BASICS!!!!</h1> 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!! .... <br /> <br /> 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. <br /> It doesn't matter if the fifth in your tuning totally sucks, it still forms a chain corresponding to the naturals on the staff. <br /> <br /> 5-EDO 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 5 EDO. 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 5 EDO we only need to use five of the pitches on the staff which end up LOOKING like this if we write out 5 edo: <br /> <!-- ws:start:WikiTextLocalImageRule:4:<img src="/file/view/Screen%20Shot%202015-07-30%20at%2010.23.01%20PM.png/555985283/400x147/Screen%20Shot%202015-07-30%20at%2010.23.01%20PM.png" alt="" title="" style="height: 147px; width: 400px;" align="left" /> --><img src="/file/view/Screen%20Shot%202015-07-30%20at%2010.23.01%20PM.png/555985283/400x147/Screen%20Shot%202015-07-30%20at%2010.23.01%20PM.png" alt="Screen Shot 2015-07-30 at 10.23.01 PM.png" title="Screen Shot 2015-07-30 at 10.23.01 PM.png" style="height: 147px; width: 400px;" align="left" /><!-- ws:end:WikiTextLocalImageRule:4 --> 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.<br /> This is because a chain of five fifths will inevitably form C G D A E. The weird thing here is that 5 edo 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. <br /> <br /> <br /> <br /> 7 EDO is exactly like the major scale in that it corresponds to the naturals on the staff except that unlike 5 edo, all the lines and spaces pitches are used. This means that we can notate 7 EDO and <br /> <!-- ws:start:WikiTextLocalImageRule:5:<img src="/file/view/Screen%20Shot%202015-07-30%20at%2010.31.21%20PM.png/555985587/576x148/Screen%20Shot%202015-07-30%20at%2010.31.21%20PM.png" alt="" title="" style="height: 148px; width: 576px;" align="left" /> --><img src="/file/view/Screen%20Shot%202015-07-30%20at%2010.31.21%20PM.png/555985587/576x148/Screen%20Shot%202015-07-30%20at%2010.31.21%20PM.png" alt="Screen Shot 2015-07-30 at 10.31.21 PM.png" title="Screen Shot 2015-07-30 at 10.31.21 PM.png" style="height: 148px; width: 576px;" align="left" /><!-- ws:end:WikiTextLocalImageRule:5 --><br /> assume that these pitches are tuned roughly to 7 EDO without the need of small accidental signs for the natural scale. However when we get to 9 EDO, something interesting happens...<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> 9 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 9 EDO 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. <br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="ACCIDENTAL MARKINGS"></a><!-- ws:end:WikiTextHeadingRule:2 -->ACCIDENTAL MARKINGS</h1> <br /> The point of sagittal is that it has alot of symbols designed to represent TINY pitch increments for any given tuning. It's cool in that it allows flexibility to suit a user's needs. If we wanna be abstract and just give the performer a general idea of what to do or write down ideas our self, we can do that. On the other hand if we want to be very VERY precise or notate something freakin insane like 72 EDO, then we can do that too, given that it's going to be way more tricky due to higher complexity. There are literally, multiple ways to notate the same tunings in sagittal and it all depends on the person. More on that in a minute ;) <br /> <br /> 9 EDO can be notated by adding an accidental marking which represents a difference of approximately 130 cents up. 9 EDO looks like this then notated out: <br /> <!-- ws:start:WikiTextLocalImageRule:6:<img src="/file/view/Screen%20Shot%202015-07-30%20at%2010.58.24%20PM.png/555986775/648x141/Screen%20Shot%202015-07-30%20at%2010.58.24%20PM.png" alt="" title="" style="height: 141px; width: 648px;" /> --><img src="/file/view/Screen%20Shot%202015-07-30%20at%2010.58.24%20PM.png/555986775/648x141/Screen%20Shot%202015-07-30%20at%2010.58.24%20PM.png" alt="Screen Shot 2015-07-30 at 10.58.24 PM.png" title="Screen Shot 2015-07-30 at 10.58.24 PM.png" style="height: 141px; width: 648px;" /><!-- ws:end:WikiTextLocalImageRule:6 --><br /> <br /> ARTICLE UNDER CONSTRUCTION</body></html>