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This work is licensed under a

Creative Commons - Attribution - ShareAlike 4.0 International License

(CC-by-SA 4.0 International).

Visit the following URL for more information:

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Book version:

This book were compiled using Luaand Lilypond programs on '2024-06-04 at 11:19'. Source code used are available at https://gitlab.com/cnngimenez/music-exercises.

Git were used as distributed version control system. Source code revision used were "fa64bb3b76d3616af50f2912d6f835973b5cc320" on branch "main".

Table of Contents

List of Tables

1. About This Book

This chapter describes writing and format conventions used on this book. This book kind of contents and languages are also discussed, as well as their written representation.

This book homepage can be visited by the URL: https://gitlab.com/cnngimenez/music-exercises

1.1. Font, text size, and line spacing

The font, size, and line spacing were specifically selected for easy and better readability. Sans serif font (in particular, Latin Modern Sans), 14 pt size, and 1.25 line spacing were used to help people with reading difficulties, such as dyslexia. See https://webaim.org/techniques/fonts/ for more information.

There is no perfect font, or size, nor a perfect decision regarding the type of format and text. However, this book source code is free and open source (see 7), the authors allow to modify and to create new editions to fit other needs, as long as the license and authors are respected. Therefore, it is possible to create new versions of this book with other styles and formatting, to suit the needs for other audiences.

1.2. Format and Writing Conventions

This sections describes the format and structure conventions used in this book. This conventions may not be strict, but are the prefered way used to write this work.

Titles are written with initial uppercases.

Relevant concepts are in bold to help the reader to find them (emphasis are not encouraged). One or several index entries are used when this important concepts are mentioned. Then, the reader can search a concept or term on the Index , go to the indicated page and find it easily.

Musics scores are written inline and centered when they are short and do not disturb the flow of - the reading. More than two lines of staves, are used in a "floating box" environments which position itself on the top or bottom page whenever it is near and there is space, or in another page. For example, a large code such as 1 is a floating box, but a simpler stave with a scale like this one:

atb-1.png

This inline stave can be found inline, expecting not to disturb the reader too much. The eye movement should be continuous, and the understanding of the paragraphs were not to be disturbed.

atb-2.png

Figure 1: An example score.

Moreover, to refer to a particular score in this book, such as the previous one, the "Figure NUMBER" format are used (for PDF or generated resources), in a similar way as the figures, chapters or any object of this book.

1.3. Content Conventions

All content are synthesis from other formal resources. Academic and technical resources are preferred, such as journal or congress papers, books, and any material that were under some peer-review process. The paragraphs and texts that refers to these contents are cited and references. See the Reference section of this book

This book may have reference content, as well as curiosities or anything about music theory and singing. Other instruments may be included as well in their respective chapters.

2. Intervals

Interval is the difference in pitch between two sounds. Interval names refers to the difference in notes in a scale: C and D is a second; C and E is a third because C, D and E counts three notes; and so on. Major and minor intervals indicate a difference in one more semitone or one less semitone respectively. For example, C and E is a minor third (3 notes, but 1½ tones) C and E♯ is major third (3 notes, but 2 tones)

The 1 describe the interval names, their usual abreviatures, and their semitones and tones distance from the first note.

Table 1: Interval names and their tones and semitones.
Interval name Abrev. Semitones Tones
Perfect unison P1 0 0
Minor second m2 1 ½
Major second M2 2 1
Minor third m3 3 1½
Major third M3 4 2
Perfect fourth P4 5 2½
- - 6 3
Perfect fifth P5 7 3½
Minor sixth m6 8 4
Major sixth M6 9 4½
Minor seventh m7 10 5
Major seventh M7 11 5½
Perfect octave P8 12 6

3. Scales

This chapter list all major and minor scales. Some information for each scale is provided.

3.1. Key Signatures

The key signature is a notation to avoid repeating the flat (♭) or sharp (♯) or any other alteration to specific notes. For instance, to state that all Fs should be sharped.

There are conventions to construct key signatures: The order in which the amount of flats or sharps appears in the different major scales. The major scale with 1 sharp is G major, which is F♯ the first; then the scale with 2 sharps is D major, which is F♯ and then C♯; and so on. Similarly, with flat signatures: the major scale with 1 flat is F major, which is B♭; then the scale with 2 flats is B♭ major, which is B♭ and then E♭; and so on \autocite{blatter07:_revis_music_theor}.

3.2. Sharp (#) Key Signatures

The 2 and 4 shows the key signatures written in conventional way. The first score shows the key signatures ordered by the sharp (♯) appearance in the major scales. The second one shows the signatures ordered by the scale name.

To recognise the key signature name faster on 2, look for the last ♯ on the key signature and add ½T to obtain it.

For example, the third key signature on the figure has the ♯ on C♯, adding ½T is D which is the name of the key signature. The next one has the last ♯ on G♯, adding ½T is A.

1.png

Figure 2: Sharp key signatures ordered by the major scale appearance.

2.png

Figure 3: Double sharp key signatures.

sharp-key-by-scale.png

Figure 4: Sharp key signatures ordered by scale note.

3.2.1. Flat (b) Key Signatures

The 5 and 6 shows the key signatures written in conventional way. The first score shows the key signatures ordered by the flat (♭) appearance in the major scales. The second one shows the signatures ordered by the scale name.

To recognise the key signature name faster, on 5 after two flats on the key (from B♭ key signature), the penultimate ♭ in the key indicates the scale note.

For instance, B♭ key signatures have the last ♭ in E♭, and the penultimate is B♭; also E♭ key signature have the last last ♭ in A♭, and the penultimate in E♭; and so on.

flat-keys-by-appea.png

Figure 5: Flat key signatures ordered by the major scale appearance.

flat-keys-by-scale.png

Figure 6: Flat key signatures ordered by scale note.

3.3. Scale Degrees and Functional Names

Scale degrees is a nomenclature used to provide a conventional number to each pitch within a scale. Degrees are provided in numbers, which the first degree (1°) is the first pitch of the scale.

Each degree has a functional name. The 2 display each degree and their corresponding functional name. The prefix "sub-" and "super-" is used to indincate below and above respectively .

When reproducing a scale on an instrument, and stopping at the 7° degree, it usually provides an unfinished sensation. A needed tendency to end playing the scale by using the next note, the tonic. This is the reason of the name "leading tone" for this degree.

Table 2: Scale degrees and their names.
Degree Functional name
1° Tonic
2° Supertonic
3° Mediant
4° Subdominant
5° Dominant
6° Submediant
7°nil Leading tone

3.4. Major Scales

The major scale tones and semitones are shown on 3 . The most representative major scale is the C major, which is the first row on the table. The second row describes the tones and semitones distance between each note. The third row describes the interval name between the notes, which M2 is major seconds (1T distance) and m2 is minor second (½T distance). The fourth row is the interval between the first note of the scale and the current note.

Later, in 3.6, the relative major and minor scale concept is introduced. This introduces a relation between these two types of scales: despite the different structure of the minor scale, the same notes are used to create a it from a major scale. For instance, the notes from C major scale are also the same notes from the A minor scale.

To obtain the relative minor scale of a specific major scale, the rule is:

  • Major scale → minor scale : augment 1½ to the scale note.
  • Minor scale → major scale : diminish 1½ to the scale note.
Table 3: Tones and semitones used on the major scale.
Notes: C   D   E   F   G   A   B   C
Tones:   1T   1T   ½T   1T   1T   1T   ½T  
Intervals:   M2   M2   2m   M2   M2   2M   m2  
Intervals:   M2   M3   P4   P5   M6   M7   P8  

3.4.1. C Major Scale

C-major.png

The relative minor scale is: A minor (see 3.5.7).

Relative minor scale:
A minor.
Equivalent scale:
C major, B♯ major
Equivalent scale most used:
C
Tonic:
C
Mediant:
E
Dominant:
G
Chord:
C - E - G

3.4.2. D Major Scale

D-major.png

The relative minor scale is: B and C♭ minor (see 3.5.8).

Relative minor scale:
B and C♭ minor.
Tonic:
D
Mediant:
F♯
Dominant:
A
Chord:
D - F♯ - A

3.4.3. E Major Scale

E-major.png

The relative minor scale is: C♯ and D♭ minor (see 3.4.8).

Relative minor scale:
C♯ and D♭ minor.
Equivalent scale:
E major, F♭ major
Equivalent scale most used:
E
Tonic:
E
Mediant:
G♯
Dominant:
B
Chord:
E - G♯ - B

3.4.4. F Major Scale

F-major.png

The relative minor scale is: D minor (see 3.5.3).

Relative minor scale:
D minor.
Equivalent scale:
F major, E♯ major
Equivalent scale most used:
F
Tonic:
F
Mediant:
A
Dominant:
C
Chord:
F - A - C

3.4.5. G Major Scale

G-major.png

The relative minor scale is: E and F♭ minor (see 3.5.4).

Relative minor scale:
E and F♭ minor.
Tonic:
G
Mediant:
B
Dominant:
D
Chord:
G - B - D

3.4.6. A Major Scale

A-major.png

The relative minor scale is: F♯ and G♭ minor (see 3.5.11).

Relative minor scale:
F♯ and G♭ minor.
Tonic:
A
Mediant:
C♯
Dominant:
E
Chord:
A - C♯ - E

3.4.7. B Major Scale

B-major.png

The relative minor scale is: G♯ and A♭ minor (see 3.5.12).

Relative minor scale:
G♯ and A♭ minor.
Equivalent scale:
B major, C♭ major
Equivalent scale most used:
B
Tonic:
B
Mediant:
D♯
Dominant:
F♯
Chord:
B - D♯ - F♯

3.4.8. C#/Db Major Scale

Cis-major.png

Des-major.png

The relative minor scale is: A♯ and B♭ minor (see 3.5.13).

3.4.9. D#/Eb Major Scale

Dis-major.png

Ees-major.png

The relative minor scale is: C and B♯ minor (see 3.5.2).

3.4.10. F#/Gb Major Scale

Fis-major.png

Ges-major.png

The relative minor scale is: D♯ and E♭ minor (see 3.5.10).

3.4.11. G#/Ab Major Scale}

Gis-major.png

Aes-major.png

The relative minor scale is: F and E♯ minor (see 3.5.11).

3.4.12. A#/Bb Major Scale

Ais-major.png

Bes-major.png

The relative minor scale is: G minor (see 3.5.6).

3.5. Minor Scales

The structure of the minor scale is shown on 4 .

Table 4: Tones and semitones used on the minor scale.
A   B   C   D   E   F   G   A
  1T   ½T   1T   1T   ½T   1T   1T  

The relative major scale of a minor scale is calculated by 1½T above. For example: 1½T above A is C, then corresponding major scale of the A Minor Scale is the C Major Scale.

Therefore, the rule is:

  • Major scale → minor scale : augment 1½ to the scale note.
  • Minor scale → major scale : diminish 1½ to the scale note.

3.5.1. Minor Scale Key Signatures

3.5.2. C Minor Scale

C-minor.png

The relative major scale is: D♯ and E♭ major (see 3.5.10).

3.5.3. D Minor Scale

D-minor.png

The relative major scale is: F and E♯ major (see 3.4.4).

3.5.4. E Minor Scale

E-minor.png

The relative major scale is: G major (see 3.4.5).

3.5.5. F Minor Scale

F-minor.png

The relative major scale is: G♯ and A♭ major (see 3.4.11).

3.5.6. G Minor Scale

G-minor.png

The relative major scale is: A♯ and B♭ major (see 3.4.12).

3.5.7. A Minor Scale

A-minor.png

The relative major scale is: C and B♯ major (see 3.4.1).

3.5.8. B Minor Scale

B-minor.png

The relative major scale is: D major (see 3.4.2).

3.5.9. C#/Db Minor Scale

Cis-minor.png

Des-minor.png

The relative major scale is: E major (see 3.4.3).

3.5.10. D#/Eb Minor Scale

Dis-minor.png

Ees-minor.png

The relative major scale is: F♯ and G♭ major (see 3.4.10).

3.5.11. F#/Gb Minor Scale

Fis-minor.png

Ges-minor.png

The relative major scale is: A major (see 3.4.6).

3.5.12. G#/Ab Minor Scale

Gis-minor.png

Aes-minor.png

The relative major scale is: B major (see 3.4.7).

3.5.13. A#/Bb Minor Scale

Ais-minor.png

Bes-minor.png

The relative major scale is: C♯ and D♭ major (see 3.4.8).

3.6. Relative Major and Minor Scales

Same key signatures in scales are called relative scales or relative keys .

The relative minor scale of a major scale is calculated by 1½T below. For example: 1½T below of C is A, then corresponding minor scale of the C Major Scale is the A Minor Scale. 5 shows all the major scales and their relative minor scales.

Therefore, the rule is:

  • Major scale → minor scale : augment 1½ to the scale note.
  • Minor scale → major scale : diminish 1½ to the scale note.
Table 5: Major and minor relative scales.
Major Scale: C C♯ D D♯ E F F♯ G G♯ A A♯ B
Minor Scale: A A♯ B C C♯ D D♯ E F F♯ G G♯

3.7. Chromatic Scale

3.7.1. Chromatic Scale in a Treble Clef

The 7 shows the chromatic scale in a treble (G) clef. For each note, the note name and scale is displayed with the frequency below. For example, the first note is C at the fourth scale, which in frequency is 261.63 Hz.

chrom-refer-trebl.png

Figure 7: Chromatic scale with note and frequency (in Hz) reference.

3.7.2. Chromatic Scale in a Suboctave Treble Clef

The 8 …

chrom-refer-suboc.png

Figure 8: Chromatic scale references using treble suboctave clef.

3.7.3. Chromatic Scale in a Bass and Treble Clef

The 9 …

chrom-refer-trebl-bass.png

Figure 9: Chromatic scale references using treble and bass clefs.

3.8. The Blues Scale

This scale can also be formed by diminishing three notes from the major scale: the third, fifth, and seventh tones. These notes are called blues notes .

From a minor scale, a blues scale can be formed by omiting the second and sixth tones. Then, new tones are added between the fourth and fifth. For example, to form the A blues scale from A minor scale, the B (second) and F (sixth) notes must be removed. The 10 shows the A minor scale above and A Blues scale below. The red notes are the one to be removed to create the Blues scale.

creat-blues-from-minor-scale.png

Figure 10: Creating the A Blues scale from the A minor scale.

The 6 shows the tones and semitones used for the blues scale. The notes in the first row are from the C blues scale.

Table 6: Tones and semitones used on the pentatonic blues minor scale.
Notes: C   E♭   F   G♭   G   B♭   C  
Distance:   1½T   1T   ½T   ½T   1½T   1T    
Intervals: 1   3♭   4   5♭   5   7♭   8  
Intervals: T m3   P4   A4   P5   m7     T  
Blue note:     B       B       B      

3.8.1. C Blues Scale

C-blues.png

This scale can be formed from C minor scale (see 3.5.2), and D♯ (E♭) major scale (see 3.4.9).

3.8.2. D Blues Scale

D-blues.png

This scale can be formed from D minor scale (see 3.5.3), and F major scale (see 3.4.4).

3.8.3. E Blues Scale

E-blues.png

This scale can be formed from E minor scale (see 3.5.4), and G major scale (see 3.4.5).

3.8.4. F Blues Scale

F-blues.png

This scale can be formed from F minor scale (see 3.5.5), and G♯ (A♭) major scale (see 3.4.11).

3.8.5. G Blues Scale

G-blues.png

This scale can be formed from G minor scale (see 3.5.6), and A♯ (B♭) major scale (see 3.4.12).

3.8.6. A Blues Scale

A-blues.png

This scale can be formed from A minor scale (see 3.5.7), and C major scale (see 3.4.1).

3.8.7. B Blues Scale

B-blues.png

This scale can be formed from B minor scale (see 3.5.8), and D major scale (see 3.4.2).

3.8.8. C# Blues Scale

Cis-blues.png

This scale can be formed from C♯ minor scale (see 3.5.9), and E major scale (see 3.4.3).

3.8.9. D# Blues Scale

Dis-blues.png

This scale can be formed from D♯ minor scale (see 3.5.10), and F♯ (G♭) major scale (see 3.4.10).

3.8.10. F# Blues Scale

Fis-blues.png

This scale can be formed from F♯ minor scale (see 3.5.11), and A major scale (see 3.4.6).

3.8.11. G# Blues Scale

Gis-blues.png

This scale can be formed from G♯ minor scale (see 3.5.12), and B major scale (see 3.4.7).

3.8.12. A# Blues Scale

Ais-blues.png

This scale can be formed from A♯ minor scale (see 3.5.13), and C♯ (D♭) major scale (see 3.4.8).

4. Voice Classification

It is important to not to hurry to classify the voice. This section is provided as a reference and not to provide any means to determine which kind of voice we possess. Therefore, avoid any premature diagnoses about the tessiture of any voice to prevent any harm to the student. Just begin with any comfortable (middle) part of the voice and work upwards and downwards \autocite{mckinney82}.

⚠️ It is important to not to hurry to classify the voice!

Work your voice from a comfortable range, and work it upwards and downards.

The 11 shows three intervals, which establish the range of the different type of voices. The fist interval is the twelfth range which that particular singer can handle, the two octaves that a professional singer should have, and the extreme ranges sometimes demanded. It is important to note, that the range may vary between individuals, and therefore may not be precise.

vocal-types-range.png

Figure 11: Vocal types and their ranges.

From the mentioned notes, the 7 can be deduced. This table mention the different voice types and their ranges in the same way.

Table 7: Voice types and their ranges.
Voice type "practical" "ideal" "extreme"
<> <> <> <>
Bass A2 to E4 F2 to F4 C2 to G4
Baritone B2 to F♯4 A♭2 to A♭4 G2 to B♭4
Tenor D3 to A4 C3 to C5 B♭2 to E♭5
Contralto A3 to E5 G3 to G5 E3 to B♭5
Mezzo C4 to G5 A3 to A5 G3 to C6
Soprano D4 to A5 C4 to C6 A3 to F6

Range is not the same as tessitura. Tessitura is not the total range, it is the part of the range comfortable or most used by the singer. Some singer may sing a song comfortably, others with the same range may feel the tune more demanding if some of the notes are very high.

5. Chords

A triad is a three simultaneous notes. It is a chord which each pitch are related by a specific intervals. Usually, the name is used to refer to the tertian triad, which each note on the chord are distanced in interval of a third. For example, using the C scale pitchs, their triads are as shown on 12.

The structure of each triad constructed in the scale differs between major and minor thirds on each interval. For instance, the triad constructed on 1° degree uses one M3 and then one m3, the triad on 2° uses m3 and then M3, and the triad on 7° degree uses m3 and m3 intervals. Following this analysis, three types of triads are found on the scale. They are named "major triads" for triads with M3 and m3 intervals, "minor triads" for m3 and M3 intervals, and "diminished triad" for m3 and m3. The 13 shows the same triads as 12 but ordered by their type \autocite{blatter07:_revis_music_theor}.

Also, 8 shows the triads notes formed from the C scale, their structure, name, and grades. The distribution of major, minor and diminished through the grades of the scale can be appreciated.

Table 8: Triads from C scale, their structures and names.
G A B C D E F G
E F G A B C D E
C D E F G A B C
M3-m3 m3-M3 m3-M3 M3-m3 M3-m3 m3-M3 m3-m3 M3-m3
Major Minor Minor Major Major Minor Dim. Major
1 2 3 4 5 6 7 8/1

c-triads.png

Figure 12: Triads constructed with C scale pitchs.

c-triads-order.png

Figure 13: C scale triads orderder by type.

5.1. Natural Major Chords

Table 9: Tones and semitones of the natural major chords
C   E   G   C
<>   <>   <>   <>
  2T   1T   2T  
  M3   m3   P4  

natural-major-chords.png

5.1.1. C Major Triads

c-major-triads.png

5.1.2. D Major Triads

d-major-triads.png

5.1.3. E Major Triads

e-major-triads.png

5.1.4. F Major Triads

f-major-triads.png

5.1.5. G Major Triads

g-major-triads.png

5.1.6. A Major Triads

a-major-triads.png

5.1.7. B Major Triads

b-major-triads.png

5.1.8. C#/Db Major Triads

cis-bes-major-triads.png

5.1.9. D#/Eb Major Triads

dis-ees-major-triads.png

5.1.10. F#/Gb Major Triads

fis-ges-major-triads.png

5.1.11. G#/Ab Major Triads

gis-aes-major-triads.png

5.1.12. A#/Bb Major Triads

ais-bes-major-triads.png

5.1.13. Guitar Natural Major Chords

guitar-natural-major-chords.png

5.2. Natural Minor Chords

Table 10: Tones and semitones of the natural minor chords.
A   C   E   A
<>   <>   <>   <>
  1T   2T   2T  
  m3   M3   P4  

natural-minor-chords.png

5.2.1. Guitar Minor Chords

guitar-minor-chords.png

5.2.2. Guitar 7th Minor Chords

guitar-7th-minor-chords.png

6. How This Book were Developed

This chapter describes how this book were developed, the compilation process, and conventions used in code. Writing style and conventions are not described here, refer to about-this-book.html#MissingReference instead.

The project homepage is:

https://gitlab.com/cnngimenez/music-exercises

The source code can be downloaded, red, and studied from that Web page.

6.1. Org-mode

Org-mode is an Emacs major mode created to provide notes and document editing. The purpose is to use plain text syntax to create links, bold, italic, and several formats, allowing to use Emacs or any other editor.

Also, Emacs provide Babel library to execute source code written inside specific syntax in Org-mode. This allows code in other programming and markup languages to be executed and use its results inside an Org-mode file.

Moreover, several export mechanism can be used to generate, from a single Org-mode file, into other well-known file formats. These output formats are:

  • Lua, and its PDF generation.
  • HTML and Web technology.
  • Epub for E-Book support.
  • Possibly others.

This particular syntax were chosen for this book. It support Lilypond execution through the ob-lilypond (Org Babel Lilypond), and the export methods to generate PDF, Web pages, and Epub.

6.2. Implementing Conventions

Developer of this book should adhere to the Do not Repeat Yourself (DRY) principle. This means, any repeated code should be made modularised: create a macro, function, separated file, or similar ways to avoid copy-paste or repeated code or text. For example, the homepage is stored at the homepage macro, because it were repeated in this chapter, at the begining of the book, and at about-this-book.html#MissingReference. The results are always the same, and inconsistencies are avoided when changing its value by editing only once.

Index entries are defined near the bold concept. Most of the time, the concept is written in bold when mentioned, and at the end of the paragraph, one or several index entries are defined. For example, the index term is registered with #+index: tessitura in the same paragraph where the code *tessitura* appears.

Music scores are written within a Lilypond Source Block. The code at 1 illustrates how it is used, and the result is shown at 2 at about-this-book.html#MissingReference. 

#+name: score:env-example
#+caption: This is an example score.
#+begin_src :file lilypond/chapter-development/env-example.png
\score {
  \new Staff \relative c' {
    \clef "treble"    
    c8 d   e   f   g   a   b   c  \bar "|."
    d,   e   fis g   a   b   cis d |
    e,   fis gis a   b   cis dis e |
    f,   g   a   bes c   d   e   f |
    g,   a   b   c   d   e   fis g \bar "|."
  }
}
#+end_src

\score {
  \new Staff \relative c' {
    \clef "treble"    
    c8 d   e   f   g   a   b   c  \bar "|."
    d,   e   fis g   a   b   cis d |
    e,   fis gis a   b   cis dis e |
    f,   g   a   bes c   d   e   f |
    g,   a   b   c   d   e   fis g \bar "|."
  }
}

6.3. Tools: Lilypond and

This book was compiled using Lilypond and Lua.

The Emacs editor were used with Org-mode.

6.4. File structure

The file structure is as follows:

main.org

The main file. It includes the rest of the org files, separated as chapters or topics.

Included files are:

  • about-this-book.org
  • scales.org
  • chords.org
  • etc.
lilypond/*
Images generated by the Lilypond source blocks.

7. License

This chapter describes the license of this work and all the resources used.

7.1. This Work License

This work "Music Reference and Exercises" by Christian Gimenez is licensed under a Creative Commons - Attribution - ShareAlike 4.0 International License (CC-by-SA 4.0 International).

7.2. Images Licenses

Cover-100px.jpg

The cover image is called: "Saxophonist, District 54 Jazz Band Recording Session 11, Solid Sound Recording Studio, Hoffman Estates, IL, 2011." by H. Michael Miley. This image is licensed under the Creative Commons Attribution-Share Alike 2.0 Generic license. Obtained from: 

https://commons.wikimedia.org/wiki/File:Saxophonist_-_District_54_Jazz_Band_Recording_Session_11_-_Solid_Sound_Recording_Studio,_Hoffman_Estates,_IL,_2011.jpg
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Date: 20 may 2024

Author: Christian Gimenez

Created: 2024-06-04 mar 11:19

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