The stave is a method of notating notes over time, the first stave is called the treble clef and defines these notes:
---A
G
--------------------------------------------------------------------------------F----------------
E
----------------------------------------------------------------D--------------------------------
C
------------------------------------------------B------------------------------------------------
A
--------------------------------G----------------------------------------------------------------
F
----------------E--------------------------------------------------------------------------------
D
C---
In the anchor system:
---9*
7*
--------------------------------------------------------------------------------5*---------------
4*
----------------------------------------------------------------2*-------------------------------
0*
------------------------------------------------11*----------------------------------------------
9*
--------------------------------7*---------------------------------------------------------------
5*
----------------4*-------------------------------------------------------------------------------
2*
0*--
The way we specify a note is by drawing a filled circle on the stave like this
-------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------
--------xxxxx------------------------------------------------------------------------------------
xxxxxxx
--------xxxxx------------------------------------------------------------------------------------
This note is a 5*.
Usually the standard clef contains 5 lines but more may be added if notes end up going higher than the five lines, these lines are called ledger lines and look like this:
xxxxx
-xxxxxxx-
xxxxx
----------
-------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------
You might have realized that we have not defined what note this is based on our original lines, but to determine it you just have to continue the pattern and realize that it is a 0*.
In general as we move upwards between consecutive lines and spaces then we ascend through the 0* major scale and when we move down we descend it.
A key signature is notation which specifies a modification of the standard notes that we've just defined on a stave. The symbol "b" represents a step down by one and a "#" represents a step up by one.
---9*
7*
------------------------------------------------------------------------------------5*---------------
4*
--------------------------------------------------------------------2*-------------------------------
0*
b---------------------------------------------------10*----------------------------------------------
9*
------------------------------------7*---------------------------------------------------------------
5*
--------------------4*-------------------------------------------------------------------------------
2*
----0*--
Notice that here the space that usually represents a 11* now represents an 10* as the "b" symbol is "flattening" it. In addition to flattening just the specific 11* located at the same vertical position as the "b" it also affects any other 11*'s for example the ones that would appear on ledger lines
The standard usage for key signatures is to specify a major or minor key, so for example if we look at the notes defined in the above stave you might realize that it represents the notes in an 5* major scale since, those notes are: 5* 7* 9* 10* 0* 2* 4* 5*, also since we know about relative keys this could also be thought of as the 2* minor which defines the same notes 2* 4* 5* 7* 9* 10* 0* 2*.
---9*
7*
------------------------------------------------------------------------------------5*---------------
b 3*
--------------------------------------------------------------------2*-------------------------------
0*
b---------------------------------------------------10*----------------------------------------------
9*
------------------------------------7*---------------------------------------------------------------
5*
--------------------3*-------------------------------------------------------------------------------
2*
----0*--
Note: Both 4*'s changed to 3*'s not just the one that matched in vertical position.
This key signature with two flats represents another key, this time it represents the 10* major key, as we can see from 10* 0* 2* 3* 5* 7* 9* 10* or 7* minor.
---9*
# 8*
#-----------------------------------------------------------------------------------6*---------------
4*
----------#---------------------------------------------------------3*-------------------------------
# 1*
----------------------------------------------------11*----------------------------------------------
9*
------------------------------------8*---------------------------------------------------------------
6*
--------------------4*-------------------------------------------------------------------------------
3*
----1*--
The same idea applies for sharps, in this case it's representing 4* major: 4* 6* 8* 9* 11* 1* 3* 4* or 1* minor
Since in the anchor system we don't really use notes that often, it'll be useful for us to be able to read anchored intervals directly off the stave. Let's start with the example we ended with in the last section, the one where our stave represented the notes in a 4* major scale.
Since we're working with a 4* major scale then the standard thing to do here would be to set our anchor note as 4*, and then replacing their notes by anchor intervals, we get:
---5
# 4
#-----------------------------------------------------------------------------------2----------------
0
----------#---------------------------------------------------------11-------------------------------
# 9
----------------------------------------------------7------------------------------------------------
5
------------------------------------4----------------------------------------------------------------
2
--------------------0--------------------------------------------------------------------------------
11
----9---
The main observation here is that it looks like the original stave except things have been "rotated" a little bit so that the space that represented the 4* is now a 0. This should make sense since the original stave represented a major scale and the new stave represents a major scale just starting from a different note.
This process of "anchoring" our stave will work with any key signature. The general process is to take the key signature and then choose either the major or minor key that it represents, set your anchor as that keys root and then determine the anchor intervals of the stave by subtracting the anchor from each note.