Lesson one: notes, intervals, scales and chords
In the introduction you have been given practical as well as historical reasons to study continuo on your baroque lute, so now it is time for a first lesson. Before you can study real continuo, however, you must be able to read from bass and treble clefs and you will have to know a little bit about music theory. To help you on your way I have turned to an early 18th century manuscript from the former Raudnitz library of the Lobkowitz family, now in the possession of the Prague University Library (Ms. II Kk 51). This manuscript is filled with simple exercises written in staff notation parallel to tablature. It teaches the basics of music theory, including continuo playing, in examples for 11-course baroque lute. Using these as guides, I have attempted to make something similar.
Music is made of sounds. A sound of a fixed pitch is called a tone. To distinguish between the pitches, tones have been given the names of the first seven letters of the alphabet: a, b, c, d, e, f and g, where b is higher than a, c higher than b, etc. Although there are a sheer infinite number of pitches in music, only seven names are used for the tones. Rising in pitch after reaching g, we will continuo with a, b, c, etc. Descending in pitch after reaching a, we will continue with g, f, e, etc. To distinguish between different tones with the same name, I use a wide-spread and unambiguous system. It divides all tones in groups of seven, beginning every group with c. The tones contained in each group belong to the same octave. These octaves also have common names. This is how they are written, starting with the lowest group:
|C” D” E” F” G” A” B”||sub-contra|
|C’ D’ E’ F’ G’ A’ B’||contra|
|C D E F G A B||great|
|c d e f g a b||small|
|c’ d’ e’ f’ g’ a’ b’||one-line|
|c” d” e” f” g” a” b”||two-line|
Sometimes subscript numerals are used for the lower groups, placed before or after the capitals (e.g. 2C or C²) and superscript numerals for the higher groups, placed after the small letters (e.g. c¹). The tone c’ is called middle c.
A tone written in musical notation is called a note. Notes are written on a staff of five staff lines. Notes can be placed through a staff line or in between two staff lines. If the note is too high or too low for the five regular staff lines, ledger lines are used. These are staff lines the length of one note only, extending the range of the staff. To fix the pitch of a note on a staff, clefs are used. In my exercises I will often use a staff system with two staves. The lower staff makes use of the bass clef and the higher staff of the treble clef. The bass clef fixes the position of the F and the treble clef fixes the position of the g’. You can imagine one ledger line between these two staves. The note written through this ledger line is middle c or c’.
In such a staff system we can notate the notes of music for baroque lute without using too many ledger lines. Reading from a staff system will also prepare you for continuo playing. Here are all the notes on the first six courses of a baroque lute, written on two staves and in tablature. Familiarise yourself with this notation.
We can raise every tone a so-called half step by placing a sharp (♯) in front of the note. A half step is the distance of one fret on the lute. Likewise we can lower every note a half step by placing a flat (♭) in front of the note. A sharp or flat before a note is valid for that note only, and for all notes of the same pitch till the end of the measure. A sharp or flat at the beginning of the staff is valid for the whole piece. One sharp at the beginning of the staff will raise every f to f-sharp and the second sharp will raise every c to c-sharp. One flat at the beginning of the staff will lower every b to b-flat and the second flat will lower every e to e-flat. To temporarily cancel a sharp or flat a natural (♮) is used. A natural before a note is valid for that note only, and all notes of the same pitch till the end of the measure.
The sharps or flats at the beginning of the key signature are called the key signature. Be aware that especially the rules concerning the validity of sharps, flats and naturals in front of notes have not been the same throughout history, so be careful when playing from older scores. Here are all the f-sharps, c-sharps, b-flats and e-flats on the fingerboard of the baroque lute:
Tablature tells us of each note on which string and in which position we have to play it. Staff notation does not. It is left to you to decide where on the lute you want to play each individual note. If we want to take advantage of this freedom, we must know all the alternative places on the fingerboard for each note. I have made an overview of all notes on all strings. You might want to keep that near you until you can find your way unaided.
You have to make yourself familiar with staff notation, so this is a good moment for your first excercise: you can take any music with single lines to each part, instrumental or vocal, and play the notes on the separate staves. It is not important to learn to play the pieces, because the only aim of the exercise is to familiarise yourself with staff notation.
The distance between two tones is called an interval. The interval between a tone and itself is called a unison. The interval between a tone and the one (higher or lower) is called a second. In order of increasing size the intervals are called third, fourth, fifth, sixth, seventh and octave. Here is an example with all intervals starting on c’:
We can increase or decrease an interval by raising or lowering either or both of the tones of the interval. In the vast majority of so-called classical music from the western world, the smallest notated distance is the aforementioned half step, exactly one fret distance on the lute. Two half steps are called a whole step or a whole tone. If we take this whole tone as a unit, we can make the following table of intervals, with examples of the intervals, starting on c:
c – c-flat
c – c
c – c-sharp
c – d-flat
c – d
c – e-flat
|2 c – e|
c – f-flat
c – f
c – f-sharp
c – g-flat
c – g
c – g-sharp
c – a-flat
c – a
c – b-flat
|5½ c – b|
c – c’-flat
c – c’
c – c’-sharp
Studying this table we can distinguish two groups of intervals. One group is made of pure intervals, which are called diminished and augmented when decreased or increased. These are the unison, fourth, fifth and octave. The other group has minor and major intervals, depending on their size. These are the second, third, sixth and seventh. Another thing we can see is that depending on how the tones are called, one interval can have two different names. For example, the distance from c to e is 2 whole steps and is called a major third. The distance between c and f-flat is also two whole steps but is called a diminished fourth. Although this is just a consequence of the naming system and has no practical consequences for playing the interval on a lute, it can be useful in determining the names of chords.
A scale is a sequence of eight consecutive tones with fixed intervals. The eighth tone is the start of the following, identical sequence. Although there are more scales, for now it is enough to learn major and minor scales. At this point it is useful to realise that all tones in a scale without sharps or flats are a whole tone apart, also called a major second, except for the intervals e-f and b-c, which are a half step, also called a minor second, apart.
The major scale is made of tones with the following intervals: major second – major second – minor second – major second – major second – major second – minor second. In other words, the consecutive tones in a major scale are 1 – 1 – ½ – 1 – 1 – 1 – ½ whole steps apart. Starting on the tone c, and writing the intervals in whole steps between the notes, it looks like this:
This is called the scale of C-major.
If we raise every tone by a whole step, starting on the tone d, we will get the scale of D-major. Raising the e a whole step gives an f-sharp. Raising the b a whole step gives a c-sharp. In stead of writing these sharps in front of every tone f and c in the scale, we will place the two sharps at the beginning of every staff:
Music written on staves with two sharps, together with the ending note d, is in the key of D-major.
The minor scale is made of tones with the following intervals: major second – minor second – major second – major second – minor second – major second – major second. In other words, the consecutive tones in a minor scale are 1 – ½ – 1 – 1 – ½ – 1 – 1 whole steps apart. Music that uses the minor scale, in other words music that is written in a minor key, often has the seventh and even sixth tone in the scale raised, especially in endings. However, this is not reflected in the key signature, so here I will give the scale without raised sixth and seventh tones. Starting on the tone a, and writing the intervals in whole steps between the tones, it looks like this:
With this knowledge we can calculate and play the major and minor scales of all keys. To help you along I have made a scales showing the notes in the keys of C, G, F, D and B-flat major and the keys of a, e, d, b and g minor. These are the keys with a maximum of two sharps or flats. I have begun and ended each scale with the tonic, the first tone of the scale, but included in between all tones from the 11th course till about the eighth fret of the first course.
Chords are three or more tones sounding together. The intervals between the tones in a chord are stacked thirds. Two stacked thirds will form a chord of three notes, called a triad. Making all possible combinations of major and minor thirds, we can form four different triads:
|first third||second third||triad|
Here are the four triads on the tone c’:
In all these chords the tone c’ is called the root. The third (in C-major chord: e) and the fifth (in C-major chord: g) do not have to be in the octave as they are written here, and it is allowed to include in the chord as many tones c, e and g as you like and from any octave. In continuo playing we do not usually play under the written bass, however, and if we do play under the bass it will only be a tone exactly an octave lower. Another rule, more a matter of good taste actually, is to limit the number of thirds, preferably to one only. Of course, the occasional exceptions will be allowed. Then, for the purpose of playing continuo, all the following chords of C-major, this time on the lower c of the small octave and all based on the same chords shape, can be equally good:
In the next lesson I will introduce more excercises with scales and intervals. You will also learn some useful chord shapes.
David van Ooijen 2009
This lesson is part of a series that first appeared in Nostalgia, the news letter of the Lute & Early Guitar Society of Japan.