- The 12 unique notes
- Rare notes
- Accidentals – sharps, flats and naturals
- Writing and reading notes in pop and jazz
- Basic information about scales
- How many notes are in a scale
- Categorising scales
- Distances between notes – semitones
- Distances between notes – other intervals
- The numeric pattern for scales
- Applying numeric patterns in practice
- Different ways of learning scales
- Basic information about chords
- How many notes are in a chord
- Major scale chord examples
- Distances between notes – thirds
- Different ways of learning chords
- The name/quality chords
Finding the 12 unique keys/notes
If you look at a piano you can see certain shapes and patterns re-accruing over and over again. That can be clearly seen with the 2+3 black keys groupings. There are 3 white keys surrounding the 2 black note grouping and 4 white keys surrounding the 3 black note grouping. Altogether they form 12 keys (2+3 black and 3+4 white).
These 12 keys are the 12 unique keys/notes we need to learn. Once we have learned them you will know all the keys of the keyboard since they just repeat themselves in another register. We are going to get back to the 12 unique notes soon.
Finding middle C on the keyboard
Almost all examples in this lesson series are written in the key of C or in the key center of C. It is important to know how to find it. We can find C on the left side of the 2 note black grouping (the white key). The next step is to find the “middle C” since there are many “C”s on the keyboard. If we have a full sized 88 keys piano we can press the highest key (the right-most) and then move down until we find the same key an octave lower. (An octave is the distance between two of the “same” notes such as C to C in the example. We cover that when we go through intervals). We do this for 4 octaves down the keyboard. Alternately we can start from the lowest C on the keyboard and move 3 octaves up the keyboard. We will often use this middle C (and C in general) as a reference key and/or key center.
The piano staffs
A (piano) staff is made of 5 vertical lines. Notes are written either on the lines or between the lines. The higher you go up the keyboard the higher the notes are written on staff. It also works in the other direction. The lower you go down the keyboard the lower the notes are written on the staff.
At some point the 5 lines are not enough so you have to draw an “extra tiny line” for each new note that either goes above the fifth line or below the first line. These extra lines are called ledger lines.
Piano is usually played with two hands and each hand “occupies” a certain register on the piano. The register is determined by clef placed in front of each row of 5 lines. The “normal” clef called a treble clef. The “dot” from which the clef starts lands on the second line from bottom to top (on the G key which explains why the table clef is sometimes called a G clef). In order to not put tens of ledger lines under the first line when going into the lower part of the piano, the bass register uses the bass clef which resembles an ear. The “dot” lands on the third line from bottom to top (on the F key signifying the name F key for the clef as well). When writing and reading piano scores the treble clef is placed above the bass clef as a default setting. Usually the right hand plays what is written in the treble clef and the left hand what is written in the bass clef. Look at the illustration below for reference.
When we get into the extreme ends on the keyboard (highest and lowest notes) we use a marking called an 8va (=ottava). It means that the notes written are played either an octave above or an octave below than written. If the 8va marking is above the section (= 8va alta) then we play the notes an octave higher than written. If the 8va marking is below the section (8va bassa) then we play the notes an octave lower than written. There are also the ultra rare 15ma (=quindicecima) markings that signify the notes being played 2 octaves above or below than written. This is the case for the keys at the very end of the keyboard and is very rare. Look at the illustration below for reference. Notice how much easier it is to read the second set of notes is compared to the first one.
The position of middle C on the treble staff is on the first ledger line below the lowest line. On the bass clef it is on the first ledger line above the highest line. In the illustration below (that shows the “C” note in different octave ranges) the middle C is in the fourth bar (box) from the left. Notice how the C alternates from being on the line to being between the lines with each octave.
The 12 unique notes
Below is an illustration of the 12 unique notes and how they are written on the staff. We might have to re-visit this illustration again as we learn more things about theory. We can notice that the C major scale (all white keys = C,D,E,F,G,A,B,C) is written on the staff by alternating notes on the line and between the line. For the other notes (black keys) we add some signs before the notes to alter them. These are called accidentals and we cover them during next segments. We can also notice that there are two different ways to name he black keys. This has to do with something called enharmonic equivalents and we cover that as well during the next segments.
You might have noticed the 12 notes are written twice with some of the notes staying the same and some of them have ben changed. This has to do with a thing called enharmonic equivalent. It just means that the same key (as in a physical piano key) can be written in several ways on a staff paper. The key is still the same but the function of that key relative to the other keys may be different.
A whole book can be written on enharmonic equivalents and we need to keep the lessons practical. For now it is good to know that some notes have two options of being written and they both represent the same physical key on the piano. It is very simple to find out which keys have an enharmonic equivalent by thinking from the opposite perspective. All the black keys (5) have one and can be written in two possible ways.
In addition to that, C,B, E and F have ones as well (B#,Cb,Fb and E#) but those are extremely rare to see outside of music theory. So we can omit them and mark C,B,E and F as unchangeable. The rest of the keys (D,G and A) are also unchangeable. So out of the 12 unique notes 5 (the black ones) have an enharmonic equivalent each and 7 (the white ones) are unchangeable. That is pretty simple to remember. Look at the 12 unique note illustration again for reference.
Accidentals – sharps, flats and naturals
You might have noticed the “hashtag” (#) sign and the “small b” (b) sighs that are put before or after a note. Those are called accidentals. They are put before the note in notation and after the note if it presented as a letter or a chord. Look at the 12 unique note illustration below to see the difference.
Any note can be raised or lowered at any given time. In notation that is done by putting accidentals before a note. Accidentals are simply a specific sign placed in font of a note to indicate that it is modified. The most common accidentals are the sharp sign (#) the flat sign (b) and the natural sign (♮). A “#” means the note raised by a semitone. (A semitone is one physical piano key. For example if you play a G with a # (that is G#) you play the next physical key after G which is G#) A “b” means the note is lowered by a semitone.
If a note is already altered (raised or lowered) and needs be returned to its unaltered (=natural) state a natural sign (♮) is used in front of the note. A natural sign (♮) “cancels out” any accidentals.
There are also rare cases where a double-sharp sign (x) and a double-flat sign (bb) are used. A “x” means the note raised by two semitones. A “bb” means the note is lowered by two semitones. The illustration below shows you also how to pronounce notes with flats, sharps and naturals.
Let us look look at the 12 unique notes illustration again and try to see where some notes have a sharp sign (are sharpened) and some have a flat sign (are flatted).
A key center (or just a key) is metaphorically a strong gravitational pull in music. In a way a key center is like the a black hole and notes and chords that are close by tend to gravitate towards it. Both melodies and harmonies tend to resolve themselves into that key. These things become clearer when we look more closely into chord pairs, progressions and improvisation.
Each key center has a specific amount of flats and sharps. In order for us not to write them every time they occur we simply put them in the beginning of the staff. Each key has its own amount of sharps or flats. The key centers can have any amount ranging from 0-7 sharps or flats. That means that there are 15 key centers altogether (7 sharps + 7 flats + C major that has no sharps nor flats)*. Below is an illustration of all the possible key centers. Notice the order of sharps and flats when writing them on the staff.
*(That means that the rare enharmonic equivalents (Cb,Fb,B#,E#) do not have a key signature and exist only as individual notes and even then mainly in theory books. If they had theoretical key signatures the signatures would have to contain double-sharps or double-flats which is impractical.)
Intervals 1 (Semitones)
The “distance” between any two notes is called an interval. A semitone is the smallest interval possible on the piano and most western instruments. (Another “name” for a semitone is a minor second interval). When you press any key on the piano then the key that is right next to it either to the right or the left side (can be either black or white) will always be a semitone away. There are 12 semitones within an octave. In practice this means that we can play at the maximum 12 unique notes before we repeat any note (in a different register). A semitone is also called a half tone. Two semitones are are called also called a whole tone.
Intervals 2 (1-8)
There are other intervals besides a semitone. In fact there are 12 unique intervals within any octave range – the same number as there are semitones and unique notes. Intervals are referenced to a specific note so an interval is the “distance” between that note and another note. For example if we start on C (and give it a number – “1”) each interval is now referenced to that C note. We can name the intervals in several ways. The chart below shows the most common ways of naming intervals – using intervals and semitones.
Intervals are named using specific methods. Some are more common within classical education and some are more common within jazz/contemporary education. Classically and “traditionally” they are named by adding a prefix (minor, major, perfect) to an ordinal number (2nd, 4th, 7th etc.) with some exceptions. The exceptions are the (perfect) unison (1),the (perfect) octave (8) and the tritone (#4/b5). Here are some examples: minor 3rd, major 6th, perfect 4th, major 7th, tritone, (perfect) unison, (perfect) octave.
In jazz/contemporary music a simpler version of a number with an accidental is used instead. The numbers are all relative to the major scale of the reference key. If an interval is a minor a simple b is put in front. The examples above would look like this : b3, 6, 4, 7, #4, 1, 8. As you can see it is much easier and clearer. That is the method we are going to use throughout the lessons for the most part but still will use some “traditional” interval language for some topics. I call this the numeric pattern. More on this later.
This might seem very confusing in text form. In order to not overcomplicate things I have provided a table with the information regarding intervals within an octave range (1-8). The reference note is C. (All other notes are related to that one. I have put abbreviations in brackets.) Below the table is an illustration on the subject.
|Note||“Traditional”||Numeric Pattern||Semitones From C|
|C||Perfect Unison (P1)||1||0|
|D#/Db||Minor 2nd (m2)||#1/b2||1|
|D||Major 2nd (M2)||2||2|
|D#/Eb||Minor 3rd (m3)||#3/b3||3|
|E||Major 3rd (M3)||3||4|
|F||Perfect 4th (P4)||4||5|
|G||Perfect 5th (P5)||5||7|
|G#/Ab||Minor 6th (m6)||#5/b6||8|
|A||Major 6th (M6)||6||9|
|A#/Bb||Minor 7th (m7)||b7*||10|
|B||Major 7th (M7)||7||11|
|C||Perfect Octave (P8)||8||12|
*#6 is not used in jazz/contemporary notation
Intervals 3 (8-)
The previous pare covered intervals within an octave range. In jazz/contemporary music intervals over an octave (8) are used especially with chords and voicings (how a chord is spread out). In theory we cover two octaves (1-15) but in practice we only use the following numbers from the second octave 9, (10 sometimes in voicings), 11 and 13. we can notice that they each have a lower octave equivalent : 2, (3), 4 and 6. The 9,11 and 13 are called extension notes and we cover them in Chapter 2. Below is a table of the intervals used over one octave. Here the accidentals refer to a specific choice so there is only one option. (For example there is only a Db=b9 and no C#=#8 option). The octave (8) and quindicecime (15) are added for reference.
|Note||Numeric Pattern||Semitones From C|
Rhythms And Rhythm Notation
Some information regarding reading rhythm notation
Understanding and explaining rhythms and how they are written in notation might take several lessons. That is why it is important to just look at the basic components of rhythms and how to be able to read them. We are mainly interested in what types of rhythm patterns we might commonly encounter in modern notation and in the lessons. We can always read more about the subject in addition to the lessons. You can look at the illustration at any time for reference while reading the text.
Notes are named according their duration. Most commonly they are measured in how many beats they “contain”. There are two main ways of naming the duration of notes – the “English” and the “American” method. The “English” method uses names such as quaver, semiquaver etc. while the “American” method uses quarter note, eight note etc. Most jazz/contemporary education uses the “American” way and so do we.
The time signature is the two-part number that is written after the clef. It stays the same until a new time signature is presented. The upper number says how many beats are in a bar (“the box”). The lower number then determines the duration of each beat. The most common time signature is 4/4 followed by 3/4. For example 4/4 means that there are 4 bets per bar and each beat is 1/4 whole note (quarter note) long. For example 5/8 (that would be very rare) would mean there are 5 beats per measure and each beat is 1/8 whole note (eight note) long. A “C” as a time signature stands for “common time” and basically means 4/4. A “crossed C” as a time signature stands for “alla breve” and basically means 2/2. More on the duration and the naming of notes later.
Let us look at the notes in order starting from the “longest” note and going all the way to 1/16th the value of that note. Note that there are other notes as well besides those but those are the ones you will most likely encounter in your musical endeavours.
Look at the illustration below while reading this text to better understand the subject. Next to each note (bar/column 2) there is the same value of rest and how it is drawn. The rests are quite hard to remember and draw. (At least they were and are still for me). Also there is the triplet equivalent of the note in the 3rd bar/column. More on that later. All examples are in 4/4.
The “longest” note is a whole note. It “contains” 4 beats so it fills a whole bar. (A bar is sometimes called a measure). A bar (= 4 beats) thus contains 1 whole note. It is drawn as a hollow circle.
A half note (1/2) contains 2 beats each so a bar contains 2 half notes. It is drawn as a hollow circle with a line.
A quarter note (1/4) contains 1 beat each so a bar contains 4 quarter notes. It is drawn as a full (not hollow) note with a line and a tail.
An eight note (1/8) contains 1/2 beat each so a bar contains 8 eight notes. It is drawn as a full note with a line and tail. The tail is usually connected to the next one making a beam. It is easier to read the value (how long) of the note by looking at the beam. A beam with one line means that the value of the notes are an eight note each. Usually they are connected 2 at a time. The illustration below has 4 of them connected which is also not uncommon.
A sixteenth note (1/16) contains 1/4 beat each so a bar contains 16 sixteenth notes. It is drawn as a full circle with a line and a double-tail. The beam has two lines. Usually 4 are connected at a time as is the case in the illustration.
There are other notes besides these but these are the most common.
Notice that each note contains twice the amount of the previous one. So for example a two half notes make a whole note, two eight notes make a quarter note etc.
A triplet occurs when we “stuff” 3 notes over the duration of two. (It is in fact a common part of a family of duplets where several notes are “stuffed” over the duration of others. Each “number” has its own name such as triplet for 3, quintuplet for 5, nonuplet for 9 etc. The triplet is the most common and it the only one we use during these lessons.) It contains 3 notes of 1/2 of the value of the main note. This sounds confusing but it is easy to explain with an example.
A whole note contains 2 half notes so a triplet over the duration of a whole note contains one half note triplet. So whole note = half note triplet (3 half notes over the duration of a whole note). With the same logic half note = quarter note triplet ; quarter note = eight note triplet; eight note = sixteenth note triplet. Sixteenth note triplet (32nd note triplet) is not presented since we only cover notes up to the sixteenth note value.
The most common triplet is the eight note triplet so we can focus mainly on that during the lessons and exercises. (It is the third row in the illustration.)
A dotted note adds 50% to the value (length) of the note. It is simply drawn by adding a dot next to the note. A dotted half note will thus have 150% the value of a half note. That means that it has the value of a half note plus a quarter note. In general dotted notes have the value of the note plus one value of the note that is one “tier” shorten than it. Once again several examples can help us understand that.
A dotted quarter note = quarter note + eight note ; a dotted eight note = eight note + sixteenth note etc. The illustration below shows a dotted half note. There are several ways to think about it. It is either a “half note and a half”, “half note and a quarter note” or “three quarter notes “glued” together”. Or any way that helps us remember that a dotted note has 150% the value of the base note.
CHECKED UNTIL HERE!W
A scale is basically a number of notes played in sequence. At some point this sequence starts repeating itself so the scale is played over again (in another register). Any scale scale can be constructed by knowing two things:
- How many notes are in the scale
- What is the distance between each note
How many notes are in a scale
In order to know the number of notes in a scale we have to know what is the possible theoretical range of notes available in a scale. The theoretical minimum is 1 although few people would consider that a scale. The theoretical maximum is 12 since there are 12 unique tones within an octave (look at the pictures below). In fact the 12 note is the same chromatic scale from above although it is quite debatable if it is a “proper” scale. It is used as a starting scale for improvisation and practicing rhythmic passages and phrasing. We will cover those in more details in Chapter 4 (Soloing And Improvisation).
Commonly used scales have between 5-8 notes with 7 being the most common number of notes in a scale. For example the major and minor scales have 7 notes.
Generically scales can be categorised into categories based on the number of notes they have in them. The categories are named using the greek number words as prefixes (penta-, hexa-, hepta, octa-) and the greek word for tone which is “tonic” as a suffix. So for example a pentatonic scale would mean it is a scale consisting of 5 notes. The exception is the name of the chromatic scale.
Now this a general categorisation and each type of category can hold many different specific scales that fall into that category. For example a major scale falls under the heptatonic scale category while a minor blues scale falls under the hexatonic scale category. In practice you will rarely hear someone use the terms “hexatonic scale” or “heptatonic scale”. Instead we use the “plain” “C major scale” or “C minor blues scale” etc. The exception is the pentatonic scale that is commonly used both as a category and as a specific scale. Later on we will check out scale/chord qualities and learn more about naming specific scales/chords within these categories.
The table below shows the most commonly used scale types, their amount of notes and an example of a scale that uses that generic type. H/W stands for “half/whole”. It is not necessary to know this at this stage and it is not relevant to this lesson. For now it is enough to know that scales have 5-8 notes and that most scales we will encounter will consist of 7 notes.
The numeric pattern for scales
So now we understood that we need to know the number of notes and the intervals within the scale to construct it. For that we will use a method called a numeric pattern. It is basically just using the number of intervals from the illustration above as many times as there are notes in the scale. We usually learn the numeric pattern for each scale by heart. An example will help out here. For example the C major scale has 7 notes and the numeric pattern is 1-2-3-4-5-6-7. Below is an illustration of this.
A harmonic minor scale has a 1-2-b3-4-5-b6-7-1 numeric pattern and would look like this:
This are the basics behind building and understanding scales. We have to notice that each scale has its own numeric pattern that we memorise. After that we can build the same scale staring on any key following the same pattern. The way to do that will become apparent during the next lessons that cover scales.
Applying numeric patterns in practice
Below are two examples of the major scale pattern used over two different root (=base/first) notes. The first example is a C major scale and the second is an E major scale. Both “sound” the same because they both use the same pattern (1-2-3-4-5-6-7) just starting on another key. The C major scales has no black keys while the E major scales has both white and black keys.
It is important to understand the numeric pattern approach as with time it becomes more clear how scales and chords are connected together and represent two sides of the same coin. The numeric pattern “code” can thus be used for both scales and chords later.
Different ways of learning scales
There are two main methods to learn to compose scales:
- Counting each individual interval using semitones
- Using the numeric pattern of the scale
The first method can be quite tedious but it might be the only way beginning students can start to learn scales. Simply learn the semitone sequence for each scale note by note and construct an interval-based mapping of the scale based on a string of semitones. In practice it is not so difficult since most scales will use just intervals of half steps (=1 semitone) and whole steps (=2 semitones aka. seconds) with the occasional (minor/major) third interval (=3/4 semitones). For example the major scale has a 2-2-1-2-2-2-1 semitone interval sequence. Look at the illustration below for reference.
The second way is the one we will aim for in the long term. The numeric pattern of any major scale is the reference point to any scale since the major scale has no modified (=altered) numbers (=notes) in it (compare the major scale to the harmonic minor scale in the illustrations above). So once we know a major scale pattern we can modify it by raising and/or lowering notes from it and thus creating new scales. For example the major scale has a 1-2-3-4-5-6-7-1 numeric pattern.
Look at the illustration below for reference. It is an illustration from the next lesson but we can already see how scales are constructed by looking at it. Within a few lesson we will drop out the semitones sequence and just use the numeric patterns from then on. But for he first few lessons we will have both.
All of this may seem a bit confusing but it will come clear when we start going further through the lessons. So do not worry if you cannot understand everything at the moment.
Most basic chords are constructed by stacking intervals larger than a whole step (larger than 2 semitones) on top of each other. There are some exceptions but for the most part this rule is universal. This makes chords have that “leaping” element as compared to scales which have a “stepping” element. These “jumps” distinguish chords from scales. Both use the same notes of a scale but are positioned differently. You can think of scales as linear scales and chords as “horizontal scales with skips”.
The most common stacked interval is a third. A major third consists of 4 semitones and a minor third consist of 3 semitones. There are also other types of intervals being stacked such as fourths or fifths but the most common interval is a third. Let us look at an example. Bellow is an illustration of a C major seventh chord (usually abbreviated as Cmaj7). We can see that it has the following sequence of stacked thirds : major 3rd, minor 3rd and major 3rd. That will also mean that the semitone sequence is 4-3-4. We can see that both scales and chords use the same type of “construction method” with the numeric pattern and the semitones sequence.
Any chord can be constructed by knowing the same two things as with scales:
- How many notes are in a chord
- What is the distance between each note
How many notes are in a chord
Let us look at the possible range for chord notes as we did with scales. The theoretical minimum amount of notes is 2 since 1 note cannot be a chord. Technically 2 notes might not be enough since it is considered “just” an interval. But some might suggest that it is enough to create a harmony so it stands on some gray area.
The maximum amount is a little bit more ambiguous. Theoretically it is 12 for the same reason as the one for scales – there are 12 unique notes within a scale. If we try to write a chord for the chromatic scale it might look something like this : Cmaj13b9#9#11b13#13(add9,11). As you can tell it is not very practical. So most chords are based on the seven note (heptatonic) scales. Shorter scales such as the blues and the pentatonic scales actually derive from these seven note scales and just have some notes taken away from them. That means that the chords for the seven note scales will apply to them as well.
So it seems seven notes are the maximum a chord can have. There is still something worthing knowing. There is an exception to this rule which is the octatonic scale. Technically 8 notes are possible in a chord but it is extremely rare to see an octatonic scale “fully extended” since it does not provide as pleasant a sound as the even note chords do. It has to do with the function of an octatonic chord – it is more of a transitional (temporary) chord. These things are not important to understand at the moment since they are not relevant to this lesson. But it is another thing to keep in mind. We will omit octatonic chords from this lesson for now.
So again we got to the conclusion that the range of a chord is between 2/3 and 7 notes. As a rule of thumb we can think that the maximum number of notes a chord can have is the maximum number of notes the scale it represents has.
Major Scale Chord Examples
C major has 7 notes so a “fully extended” chord that represents the chord is a Cmaj13 (add9,11) (C,E,G,B,D,F,A) since it has all the notes of that scale stacked in thirds. Look at the illustration below that has the “fully extended” chord for a C major scale. Notice that the numbers don’t go back to 2,4,6 once we goo over 7 – instead their second octave counterparts are used 9,11,13. More on this when we cover extensions and alterations.
Let us break the illustration down. So a Cmaj13 (add9,11) has all the notes from the scale and is thus representing the C major scale “to the maximum”. However by removing one note at a time away we get chords that also represent the same scale (with less notes). Below is a chart of all the chords that can represent a C major scale. We start with 2 notes and go all the way to the maximum number which is 7.
Some chords are more popular than others. Chords containing three notes (=triads, C triad in the chart) are the most used ones. The next most popular are four note chords (Cmaj7 in the chart). The 9 and the 13/6 are often used together in a chord. Chords with a 9 (Cmaj9 in the chart) or/and a 13 (Cmaj13, (implies a 9 as well) are common in jazz. The 11 is the least popular of the chords and the rarest. There is quite a lot of things to cover regarding chords and how they are played in practice. We will go over those in detail in this Chapter as well as Chapter 2 (Chords And Voicings). it is just good to know this information a bit in advance.
It is quite understandable that all the information so far can be overwhelming but it will become very clear with time and especially when we start learning scales and chords in practice and also doing the exercises and worksheets.
Distances between notes – thirds
The most common interval chords are made of is a third. The quality (major or minor) of the third depends on the scale the chord derives from. Each scale has a specific pattern of stacked thirds for the chord counterpart. We will look at this in detail when looking at triads and four note chords. In practice the distance between each note is either a minor third (3 semitones) or a major third (4 semitones). You can see that clearly in illustration 1a.9.
Different ways of learning chords:
- Using the semitone sequence of the chord
- Using the numeric pattern of the chord
These approaches are identical to the scale approaches. We have to just look at the thirds/semitones for each note of the chord. Look at illustration 1a.9 again for reference.
The name/quality of chords
Musicians usually name chords by using the word “quality” instead of “name”. In other words one may ask “what is the quality of a certain chord”. The four first notes of a chord will determine its quality and harmony while the other 3 (out of 7) will “complement” it without changing the underlining harmony. The quality of a chord is determined mainly by the underlining scale.
In practice the 1st note of a scale determines the root of a chord. The 3rd note determines the major/minor quality, the 5th note (if altered) determines the diminished/augmented quality and the 7th note determines if the chord is a major 7th, minor 7th or diminished 7th for example. We will get deeper into the subject as we cover four note chords, extensions, alterations and voicings. But as a general rule the following chart could give us a glimpse of how chord quality is determined.
What did we learn?
After this lesson you should be able to:
- Know the 12 unique notes/tones within an octave and how to find them on the keyboard and in notation.
- Understand how the chromatic scale is build and be ready to be able to construct it starting on any key.
- Understand how scales are build and be ready to start constructing them over the next lesson.
- Understand how chords are build and be ready to start constructing basic triads and four note chords during the next lessons.
If any of the above is not yet clear you can ask me directly!
Note: The exercises and worksheets are available to my students and are password-protected. Contact me for more info.
(c) Sibil Yanev 2019