myBook.typ

#set heading(numbering: "1.1.1 -")
#show table.cell.where(y: 0): strong

#set document(
    title: [Patterns in Music],
    author: "Alessandro Bettarini"
    )

#import "@preview/chordx:0.6.1": chart-chord
#let chart-chord-sharp = chart-chord.with(size: 20pt, background: silver)
#let chart-chord-round = chart-chord.with(size: 1.5em, design: "round")

#align(center, block[
  #title()
  by\
  Alessandro Bettarini\
  3 January 2026
  #rect[
    Harmony theory and applications to\
    cello and guitar
  ]
])

#pagebreak()
#outline(depth: 3)

//#outline(
//  title: [List of Figures],
//  target: figure.where(kind: image))

#pagebreak()
#set page(numbering: "p1")

= Theory
Music has 3 elements:
- rhythm
- melody
- harmony

In this document we are dealing mainly with _harmony_.

== Intervals
#table(
    columns: 4,
    align: (left, horizon, center, center),
    stroke: 1pt,
    fill: (x, y) => if y == 0 { gray.lighten(40%) },
    table.header[structure][][roman][semitones],

[], [unison], [I], [0],
[H], [half], [], [1],
[W], [whole], [II], [2],
[W + H\ H + W], [minor third], [♭III], [3],
[W + W], [major third], [III], [4],
[], [fourth], [IV], [5],
[], [tritone], [], [6],
[III + ♭III\ ♭III + III], [fifth], [V], [7],
[V + IV\ IV + V], [octave], [I], [12]
    )

- Within one octave there are 12 unique note names. Beyond that the note names just repeat.
- The degrees *III* and *VII* can be either "major" or "minor".
- The degree *V* can be any of "natural" or "augmented" or "diminished".

== Scales

=== Major diatonic // scale
- For the major scale 7 notes are selected from the 12 semitones available in one octave. The 7 unique note names are A B C D E F G (La Si Do Re Mi Fa Sol).
  - Note that the piano keyboard is a device that makes that selection stand out visually just for the key of C major.
  - Example: in the key of C major the 'root' is C
- The sequence of intervals starting from the root is W W H W W W H, which corresponds to the scale degrees (1, 2, 3, 4, 5, 6, 7). This is alson known as the "Ionian" mode of the major scale.
- There are 12 different major scales (see chapter #link(<circle_anchor>)["Circle of fifths"])
- The major scale is the reference against which all other scales are defined.

#block( breakable: false, [
The 7 modes of the major scale are (the characteristic notes of each mode are highlighted):
#table(
    columns: 4,
    align: (center,center,left,center),
    stroke: 1pt,
    fill: (_, y) => if y == 0 or y == 8 { gray.lighten(40%) },
    table.header(repeat: true,
                [mode],[name],[spelling],[comment]),

[I], [Ionian], [(1, 2, 3, 4, 5, 6, 7)], [*major*],
[II], [Dorian], [(1, 2, ♭3, 4, 5, #highlight[6], ♭7)], [],
[III], [Phrygian], [(1, #highlight[♭2], ♭3, 4, 5, ♭6, ♭7)], [],
[IV], [Lydian], [(1, 2, 3, #highlight[♯4], 5, 6, 7)], [],
[V], [Mixolydian], [(1, 2, 3, [4], 5, 6, #highlight[♭7])], [11#super[th] avoid note],
[VI], [Aeolian], [(1, 2, ♭3, 4, 5, ♭6, ♭7)], [*natural minor*],
[VII], [Locrian], [(1, #highlight[♭2], ♭3, 4, #highlight[♭5], ♭6, ♭7)], [],
//table.hline(),
[],[],[],[],
[V],[Mixolydian],[(1, 2, 3, 4, 5, 6, #highlight[♭7])],[11#super[th] no avoid]
    )
])

- Example:
    #table(
    columns: 2,
    fill: (_, y) => if y == 0 or y == 8 { gray.lighten(40%) },

    [], [is one of the modes of the scale],

    [C Ionian], [C major],
    [C Dorian], [B♭ major],
    [C Phrygian], [A♭ major],
    [C Lydian], [G major],
    [C Mixolydian], [F major],
    [C Aeolian], [E♭ major],
    [C Locrian], [D♭ major]
    ) 

The following table shows, for example, that
- C Phrygian is in the key of A♭ major
- G Mixolydian is in the key of C major

#figure(
    table(columns:13,
    fill: (x, y) => if y == 0 or x == 0 { gray.lighten(40%) },
    [Ionian],  [C],  [.],[D], [.],[E],[F], [.],[G],[.],[A],[.],[B],
    [Dorian],  [B♭], [.],[C], [.],[D],[E♭],[.],[F], [.],[G],[.],[A],
    [Phrygian],[A♭], [.],[B♭],[.],[C],[D♭],[.],[E♭],[.],[F],[.],[G],
    [Lydian],  [G],  [.],[A], [.],[B],[C], [.],[D],[.],[E],[.],[F♯],
    [Mixolydian],[F],[.],[G], [.],[A],[B♭],[.],[C],[.],[D],[.],[E],
    [Aeolian], [E♭], [.],[F], [.],[G],[A♭],[.],[B♭],[.],[C],[.],[D],
    [Locrian], [D♭], [.],[E♭],[.],[F],[G♭],[.],[A♭],[.],[B♭],[.],[C]
    )
) <modes_vs_keys>

#line(length: 100%)
=== Natural Minor // scale
- This is the Aeolian mode of the major scale, and it is used in classical music as the descending melodic minor.

#line(length: 100%)
=== Melodic Minor // scale
- Here we consider only the _ascending_ scale, because the descending is the same as the Aeolian mode of the major scale. @levine // page 56
- No avoid notes
- The two dominant chords are a _triton_ apart

#table(
    columns: 6,
    align: horizon,
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    table.header[reference\ to major][spelling][triad][4-notes][aka][comment],

[II], [(1, 2, ♭3, 4, 5, 6, 7)], [(min) I-], [I-(maj7)], [minor-major], [Dorian ♯7],
[III], [(1, ♭2, ♭3, 4, 5, 6, ♭7)], [(min) II-], [II-7(♭9)], [ Dorian ♭9], [Phrygian ♯6],
[IV], [(1, 2, 3, ♯4, ♯5, 6, 7)], [(augm) ♭III+], [], [Lydian augmented], [Lydian ♯5],
[V], [(1, 2, 3, ♯4, 5, 6, ♭7)], [(maj) IV], [IV7], [Lydian dominant], [Mixolydian ♯4\ Lydian ♭7],
[VI], [(1, 2, 3, 4, 5, ♭6, ♭7)], [(maj) V], [V7], [Ionian ♭6 ♭7], [Aeolian ♯3],
[VII], [(1, 2, ♭3, 4, ♭5, ♭6, ♭7)], [(dim) VI#sym.degree], [VIø], [], [Locrian ♯2],
[♯I], [(♯1, 2, 3, 4, 5, 6, 7)\ (1, ♭2, ♭3, ♭4, ♭5, ♭6, ♭7)], [(dim) VII#sym.degree], [VIIø], [Hendrix], [Ionian ♯1]
    )

#line(length: 100%)
=== Harmonic Minor // scale
- melodic deficiencies
- tonality powerful and unambiguous

#table(
    columns: 6,
    align: horizon,
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    table.header[reference\ to major][spelling][triad][4-notes][alterations][comment],

[VI], [(1, 2, ♭3, 4, 5, ♭6, 7)], [(min) I-], [I-(maj7)], [], [Aeolian ♯7],
[VII], [(1, ♭2, ♭3, 4, ♭5, 6, ♭7)], [(dim) II#sym.degree], [IIø], [], [Locrian ♯6],
[I], [(1, 2, 3, 4, ♯5, 6, 7)], [(augm) ♭III+], [♭III△(♯5)], [], [Ionian ♯5],
[II], [(1, 2, ♭3, ♯4, 5, 6, ♭7)], [(min) IV-], [IV-7], [], [Dorian ♯4],
[III], [(1, ♭2, 3, 4, 5, ♭6, ♭7)], [(maj) V], [V7], [], [Phrygian ♯3],
[IV], [(1, ♯2, 3, ♯4, 5, 6, 7)], [(maj) ♭VI], [♭VI△], [], [Lydian ♯2],
[♯V], [(♯1, 2, 3, 4, 5, 6, ♭7)\ (1, ♭2, ♭3, ♭4, ♭5, ♭6, 𝄫7)], [(dim) VII#sym.degree], [VII#sym.degree], [], [Mixolydian ♯1]
    )

#line(length: 100%)
=== Harmonic Major // scale

#table(
    columns: 6,
    align: horizon,
    stroke: 1pt,
    fill: (x, y) => if y == 0 { gray.lighten(40%) },
    table.header[reference\ to major][spelling][triad][4-notes][alterations][comment],

[I], [(1, 2, 3, 4, 5, ♭6, 7)], [maj], [I△], [♭13], [Ionian ♭6],
[II], [(1, 2, ♭3, 4, ♭5, 6, ♭7)], [dim], [IIø], [], [Dorian ♭5],
[III], [(1, ♭2, ♭3, ♭4, 5, ♭6, ♭7)], [min], [III7], [(♭9)(♭11)(♭13)], [Phrygian ♭4],
[IV], [(1, 2, ♭3, ♯4, 5, 6, 7)], [min], [IV-(maj7)], [♯11], [Lydian ♭3],
[V], [(1, ♭2, 3, 4, 5, 6, ♭7)], [maj], [V7], [♭9], [Mixolydian ♭2],
[♭VI], [(1, ♯2, 3, ♯4, 5, 6, 7)], [aug], [], [(♯9)(♯11)], [Aeolian ♭1\ Lydian aug ♯2],
[VII], [(1, ♭2, ♭3, 4, ♭5, ♭6, 𝄫7)], [dim], [VII#sym.degree], [(♭9)(♭13)], [Locrian ♭7],
    )

#line(length: 100%)
=== Diminished // 17 scale
- 8 notes
- 2 modes. The sequence of intervals starting from the root is
  - WH WH WH WH
  - HW HW HW HW

There are only 3 different diminished scales, if we dispense with enharmonic spellings. @coker1964

#line(length: 100%)
=== Whole Tone // 18 scale
- 6 notes
- 1 mode. The sequence of intervals starting from the root is
  - W W W W W W

There are only 2 different whole-tone scales, if we dispense with enharmonic spellings.

#line(length: 100%)
=== Chromatic
- 12 notes
- 1 mode. The sequence of intervals starting from the root is
  - H H H H H H H H H H H H

*Usage*: passing tones

#line(length: 100%)
=== Bebop
- 8 notes

The bebop scales are four of the traditional scales with an added chromatic passing note. @levine @coker1991 // levine-p171 coker1991-p40
- Ionian + passing note between 5th and 6th
- Dorian + passing note between 3rd and 4th
- *dominant* = mixolydian + passing note between 7th and root
- melodic minor + passing note between 5th and 6th

#line(length: 100%)

//#pagebreak()
=== Pentatonic // scale
- 5 notes
- 5 modes

#table(
    columns: 3,
    align: center,
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    table.header[][spelling][],

[Mode I], [(1, 2, 3, 5, 6)], [major],
[Mode II], [(1, 2, 4, 5, ♭7)], [],
[Mode III], [(1, ♭3, 4, ♭6, ♭7)], [],
[Mode IV], [(1, 2, 4, 5, 6)], [],
[Mode V], [(1, ♭3, 4, 5, ♭7)], [minor]
    )

//#line(length: 100%)

==== Usage: basic
Play a *minor* pentatonic over _minor_ chords and a *major* pentatonic over _major_ chords.

==== Usage: Herbie Hancock
Play always a *minor* pentatonic: @marbinPenta

  - For _minor_ and _dominant_ chords
      - A whole step up (2, 4, 5, 6, 1)

  - For _major_ chords
      - Half step down (7, 2, 3, ♭5, 6)

  - For _altered_ chords
     - A minor third up (♭3, ♭5, ♭6, ♭7, ♭2)

==== Usage: inside to outside
Mode I (major) pentatonic on each of the 12 half steps of the octave

#table(
    columns: 3,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    table.header[½ step][][],
  
[1], [(#highlight[*1*], 2, 3, 5, 6)], [Mode I (major)],
[2], [ (#highlight[*♭2*], ♭3, 4, ♭6, ♭7)], [],
[3], [ (#highlight[*2*], 3, ♯4, 6, 7)], [],
[4], [ (1, #highlight[*♭3*], 4, 5, ♭7)], [Mode V (minor)],
[5], [ (♭2, #highlight[*3*], ♯4, ♯5, 7)], [],
[6], [ (1, 2, #highlight[*4*], 5, 6)], [Mode IV],
[7], [ (♭2, ♭3, #highlight[*♯4*], ♯5, ♯6)], [],
[8], [ (2, 3, #highlight[*5*], 6, 7)], [],
[9], [ (1, ♭3, 4, #highlight[*♭6*], ♭7)], [Mode III],
[10], [ (♭2, 3, ♯4, #highlight[*6*], 7)], [],
[11], [ (1, 2, 4, 5, #highlight[*♭7*])], [Mode II],
[12], [ (♭2, ♭3, ♯4, ♯5, #highlight[*7*])], []
)

#block( breakable: false, [
  *Inside to outside classification* @ricker

  - Over *dominant* seventh chords\
      `1---4---11---8---6---9---3---7---2---5---10---12`
  - Over *minor* seventh chords\
      `4---11---6---9---2---1---7---8---12---3---10---5`
  - Over *major* seventh chords\
      `1---8---3---5---10---6---11---12---4---9---7---2`
])

==== Usage: over II-V-I
// https://www.youtube.com/watch?v=ywTStRl4GQc
- D- #sym.arrow.r.double A- minor pentatonic (1,2,4,5,♭7)
- G7alt #sym.arrow.r.double B♭ minor pentatonic (♭2,♯2,♯4,♭6,♭7)
- C #sym.arrow.r.double A- minor pentatonic (1,2,3,5,6)

#line(length: 100%)

//#pagebreak()
=== Altered Pentatonic // scales
- For *dominant* seventh chords
    - lowered fifth, built on 2 and ♭6 degree
        - (#highlight[2], 3, ♯4, 6, ♭7)
        - (1, ♯2, 3, #highlight[♭6], ♭7)

    - lowered second, built on root, ♭3, ♭5, 6 degree
        - (#highlight[1], ♭2, 3, 5, 6)
        - (1, #highlight[♭3], ♭4, 5, ♭7)
        - (♭2, ♭3, #highlight[♭5], 𝄫6, ♭7)
        - (♭2, 3, ♯4, #highlight[6], ♭7)

- For *diminished* seventh chords
    - lowered second, built one step above any diminished chord member
        - (#highlight[2], ♭3, ♯4, 6, 7)
        - (1, 2, #highlight[4], ♭5, 6)
        - (1, ♭3, 4, #highlight[♭6], 𝄫7)
        - (1, ♭3, ♯4, ♯5, #highlight[7])

#pagebreak()
== Chords // theory

- *Modal* harmony
  - Chords are built by stacking fourths
  - In jazz to improvise a melodic line a suitable technique is the "Triad pairs" 

- *Tonal* harmony
  - The notes of a chord are derived by selecting notes in thirds, that is, by skipping every second note of the scale.
  - The skill of the jazz melody improviser is to follow the rapid chord changes, for example in Jazz Be-Bop.

  - *1-octave* harmony
    - triads: "root", "third", "fifth"
    - 4-notes: "root", "third", "fifth", "seventh"
  - *2-octaves* harmony (chord extensions: 9th, 11th, 13th)

*Drop 2* chords are seventh chords that are built by dropping the second highest note of a closed position chord down one octave, making that note the bass note of the chord. Example Cmaj7 is played as Cmaj7/G

#line(length: 100%)
=== Superimposition

Ninth, eleventh, and thirteenth chords are produced by superimposing third intervals above the seventh chord. @coker1964 // p68

Examples:

#table(
    columns: 4,
    //align: center,
    stroke: 1pt,
    column-gutter: (0pt, 5pt, 0pt),

    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    table.header[][spelling][two triads][],

[C△(9)(♯11)(13)], [(1, 3, 5, 7, 9, ♯11, 13)], [(1,3,5,7) + (1,3,5)#sub[built on 2]], [*C* and *D*],
[C△(9)], [(1, 3, 5, 7, 9)], [(1,3,5) + (1,3,5)#sub[built on 5]], [*C* and *G*],
[C△(♯9)(♯11)], [(1, 3, 5, 7, ♯9, ♯11)], [(1,3,5) + (1,3,5)#sub[built on 7]], [*C* and *B*],
[C△(9)(♯11)], [(1, 3, 5, 7, 9, ♯11)], [(1,3,5) + (1,♭3,5)#sub[built on 7]], [*C* and *B-*],
[C-7(9)(11)], [(1, ♭3, 5, ♭7, 9, 11)], [(1,♭3,5) + (1,3,5)#sub[built on ♭7]], [*C-* and *B♭*],
[C7(♯9)], [(1, 3, 5, ♭7, ♯9)], [(1,3,5) + (1,3,5)#sub[built on ♭3]], [*C* and *E♭*],
    )

#line(length: 30%)

*Triads*

Example:  @fewell // p11
- In the key of F major the triad *G-* {dorian mode} can be extended by playing
    - a triad *F* starting from the minor 7th of G.

*Melodic extensions* // Fewell

To find the melodic extension of a #highlight[*minor*] triad, play: // p18
- a minor triad built on the root
- a major triad from the ♭3rd degree
- a minor triad built on the 5th degree
- a major triad from the ♭7th degree

#line(length: 30%)

The same triads can be used to play over the relative #highlight[*major*] chord (example: G- #sym.arrow.l.r.double B♭△) // p23

Examples:
- G-, *B♭*, D-, F
- A-, *C*, E-, G

#line(length: 30%)

Over #highlight[*dominant 7th*] chords, more related chords are found by moving _down_ from the triad in intervals of diatonic thirds. // p38

Example:
- the triad *G-* can be extended by playing
    - a triad *E-7(♭5)*, or an inversion of *G-6*
    - *C7(9)*

All the melodic extensions of *G-* can be used to play phrases over the *C7* chord.

Charlie Christian: over a dominant 7 chord, play a minor triad starting from the 5th degree of the chord, or a min7(♭5) arpeggio from the 3rd degree.

Example:
- over G7 play a *D-* triad or a *B-7(♭5)* arpeggio. // p39

#line(length: 100%)
=== Guide tones
The most important guide tones are the 3rd and 7th degree of a chord. They serve two roles:
+ making melodic connections in solos
+ creating good _voice leading_ in chord progressions

There are 4 types of guide-tone resolutions: // [1]p82
+ direct: play arpeggios connected by the guide tones resolving at the point where the chord changes.
+ indirect: an extra note is played between the 7th and the 3rd.
+ chromatic: resolution from a half step below.
+ double-chromatic: resolution from below by two notes in chromatic sequence.

==== Voice Leading // [1]p67
- 2-note
- 3-note (add chord tones and tensions)

==== Enclosure
An enclosure is a linear or melodic device in which an object note is approached by both the upper (half step above) and lower (half step below) leading tones. @coker1991 // p50

#line(length: 100%)
=== Triad pairs
- First choose two triads that fit a particular harmony and don't have any notes in common 
- To have more movement, choose two adjacecnt triads because they don't have any repeated notes (they create a hexatonic scale). @marbinTriads
- Then create melodic lines by alternating patterns of 3 notes of the first chord, followed by 3 notes from the second chord, using inversions of the chords in any combination.

Possible pairs: @jlv
- Major/minor triad pair
  
  Example: *C△* and *D-*, over *B♭△(#11)*, *G7sus*, and *D-7*

- Augmented/major triad pair

  Example: *C+* and *D△*, over *D7(♯11)*, *F♯ø*

- Major/diminished triad pair

  Example: *C△* and *D#sym.degree*, over *G7(♭9)sus*, *E7alt*, and *F-(maj7)*

- Major/major triad pair

  Example: *C△* and *F♯△*, over *C13(♭9)*, and *G#sym.degree 7*

- Diminished/minor triad pair

  Example: *C#sym.degree* and *D♭-*, over *D♭-(maj7)*, and *B♭ø*


#line(length: 100%)
=== Chord substitutions // [1]p80
The minor 5th of any dominant chord can be sustitued in place of the dominant itself. @baker // p17

#line(length: 100%)

#pagebreak()
== Arpeggio

An _arpeggio_ is a melody using the notes of a chord. It can be played as a sequence of thirds. A third can be either minor (min) or major (MAJ) therefore the possibilities are:

=== Triads (3-notes)
They span 1 octave

  - min,min,min,min #sym.arrow.r.double diminished
  - min,MAJ,Fourth #sym.arrow.r.double minor
  - MAJ,min,Fourth #sym.arrow.r.double major
  - MAJ,MAJ,MAJ #sym.arrow.r.double augmented (whole-tone)

=== Seventh (4-notes)
- (1,3,5,7) They span 1 octave
- (3,5,7,9)

=== Extended (7-notes) <arp2oct_theory>
They span 2 octaves.

A _pattern_ is a sequence of steps. Each _step_ is a 3#super[rd].

For each pattern in the following tables:
- there are always 3 MAJ and 4 min steps, they just appear in different order.
- There are at most 2 _consecutive_ M.
- There are 7 steps, but the last one is added to reach the root note again, therefore each pattern has only 6 independent steps, resulting in a theoretical set of 64 patterns (=Q number in the tables). There are only 28 cases that meet these criteria, and they are all listed in the 4 tables below.
- each step can be derived from the other 6 according to the following rule:
    - m if the other 6 steps have 3 M
    - M if the other 6 steps have 2 M

#align(right, block[
    #align(left, block[
    #rect[
        *Legend:*\
        k: cumulative alteration\
        m: min (minor 3#super[rd])\
        M: MAJ (major 3#super[rd])\
        i: index\
        P: binary interpretation (m=0,M=1)\
        P#sub[i+1] = RotateLeft(P#sub[i])\
        Q#sub[i+1] = P#sub[i+1] / 2
    ]
    ])
])

// To make a table referenceable, you should place it within a figure.
#figure(
table(
    columns: 6,
    align: center,
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    table.header[pattern][mode][k][i][P][Q],

[M m M m M m m], [Lydian], [♯4],[1],[84],[42],
[M m M m m M m], [Ionian], [♮4],[3],[82],[41],
[M m m M m M m], [Mixolydian], [♭7],[5],[74],[37],
[m M m M m M m], [Dorian], [♭3],[7],[42],[21],
[m M m M m m M], [Aeolian], [♭6],[2],[41],[20],
[m M m m M m M], [Phrygian], [♭2],[4],[37],[18],
[m m M m m M M], [Locrian], [♭5],[6],[21],[10]
    ),
    caption: "Major modes"
) 

#figure(
table(
    columns: 5,
    align: (center,left,center,right),
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    table.header[pattern][arpeggio][i][P][Q],

[m M M m m M m],[1, ♭3, 5, 7, 9, 11, 13],[1],[50],[25],
[m M m m M M m],[1, ♭3, 5, ♭7, ♭9, 11, 13],[5],[38],[19],
[M M m m M m m],[1, 3, ♯5, 7, 9, ♯11, 13],[2],[100],[50],
[M m m M M m m],[1, 3, 5, ♭7, 9, ♯11, 13],[6],[76],[38],
[M m m M m m M],[1, 3, 5, ♭7, 9, 11, ♭13],[3],[73],[36],
[m m M M m m M],[1, ♭3, ♭5, ♭7, 9, 11, ♭13],[7],[25],[12],
[m m M m m M M],[1, ♭3, ♭5, ♭7, ♭9, ♭11, ♭13],[4],[19],[9]
    ),
    caption: "Melodic minor modes"
)

#figure(
table(
    columns: 5,
    align: (center,left,center,right),
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    table.header[pattern][arpeggio][i][P][Q],

[m M M m m m M],[1, ♭3, 5, 7, 9, 11, ♭13],[1],[49],[24],
[m m M m M M m],[1, ♭3, ♭5, ♭7, ♭9, 11, 13],[5],[22],[11],
[M M m m m M m],[1, 3, ♯5, 7, 9, 11, 13],[2],[98],[49],
[m M m M M m m],[1, ♭3, 5, ♭7, 9, ♯11, 13],[6],[44],[22],
[M m m m M m M],[1, 3, 5, ♭7, ♭9, 11, ♭13],[3],[69],[34],
[M m M M m m m],[1, 3, 5, 7, ♯9, ♯11, 13],[7],[88],[44],
[m m m M m M M],[1, ♭3, ♭5, 𝄫7, ♭9, ♭11, ♭13],[4],[11],[5]
    ),
    caption: "Harmonic minor modes"
)

#figure(
table(
    columns: 5,
    align: (center,left,center,right),
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    table.header[pattern][arpeggio][i][P][Q],

[M m M m m m M],[1, 3, 5, 7, 9, 11, ♭13],[1],[81],[40],
[m m M M m M m],[1, ♭3, ♭5, ♭7, 9, 11, 13],[5],[26],[13],
[m M m m m M M],[1, ♭3, 5, ♭7, ♭9, ♭11, ♭13],[2],[35],[17],
[m M M m M m m],[1, ♭3, 5, 7, 9, ♯11, 13],[6],[52],[26],
[M m m m M M m],[1, 3, 5, ♭7, ♭9, 11, 13],[3],[70],[35],
[M M m M m m m],[1, 3, ♯5, 7, ♯9, ♯11, 13],[7],[104],[52],
[m m m M M m M],[1, ♭3, ♭5, 𝄫7, ♭9, 11, ♭13],[4],[13],[6]
    ),
    caption: "Harmonic major modes"
)

#pagebreak()
== Notation

=== Accidentals
\
*In chiave*
- alterazioni permanenti che si trovano tra la _chiave_ e il _tempo_, e durano per tutto il brano. Queste alterazioni stabiliscono la tonalità per esempio: Re maggiore (2♯), o Fa minore (4♭)

  - diesis ♯ Sono 7 e procedono di quinta in quinta
  - bemolle ♭ Sono 7 e procedono di quarta in quarta

*Nella misura*
- alterazioni temporanee, in effetto solo durante la misura in cui appaiono
  
  - per alzare di un semitono una nota:
    - naturale
      - diesis ♯
    - che ha ♯
      - doppio diesis 𝄪
    - che ha ♭
      - bequadro ♮
    - che ha doppio bemolle 𝄫 @Dacci
      - bequadro e bemolle ♮♭

  - per abbassare di un semitono una nota:
    - naturale
      - bemolle ♭
    - che ha ♯
      - bequadro ♮
    - che ha ♭
      - doppio bemolle 𝄫
    - che ha doppio diesis 𝄪
      - bequadro e diesis ♮♯

  - per alzare di un tono una nota:
    - naturale
      - doppio diesis 𝄪
    - che ha doppio bemolle 𝄫
      - doppio bequadro ♮♮

  - per abbassare di un tono una nota:
    - naturale
      - doppio bemolle 𝄫
    - che ha doppio diesis 𝄪
      - doppio bequadro ♮♮

#pagebreak()
=== Clefs // chiavi
#columns(2, gutter: 8pt)[

  3 types:
  #rect[
  - *G*
    - treble (violino)
  - *C*
    - soprano
    - mezzo soprano
    - alto
    - tenor
  - *F*
    - baritone
    - bass
  ]

#colbreak()

  //https://en.wikipedia.org/wiki/File:Mnemonic_bass_alto_treble_clefs.svg))
  #figure( image("img/Mnemonic_bass_alto_treble_clefs.svg.png", width:80%))

]

=== Keys
Key signatures

Note that the accidentals establish the key independently from the clef. In the following two figures the keys are shown in the treble clef, but it is just an example

#figure( image("img/keys-major.png"), caption: [Major keys (treble clef)])
#figure( image("img/keys-minor.png"), caption: [Minor keys (treble clef)])

#block( breakable: false, [
#table(
    columns: 3,
    fill: (_, y) => if y == 0 or y == 6 { gray.lighten(40%) },

    [major key], [minor key], [accidentals],

    [B], [G♯-], [F♯ C♯ G♯ D♯ A♯],
    [E], [C♯-\ D♭-], [F♯ C♯ G♯ D♯],
    [A], [F♯-\ G♭-], [F♯ C♯ G♯],
    [D], [B-], [F♯ C♯],
    [G], [E-], [F♯],
    [C], [A-], [],
    [F], [D-], [B♭],
    [B♭], [G-], [B♭ E♭],
    [E♭], [C-], [B♭ E♭ A♭],
    [A♭], [F-], [B♭ E♭ A♭ D♭],
    [D♭], [A♯-\ B♭-], [B♭ E♭ A♭ D♭ G♭],
    [G♭], [D♯-\ E♭-], [B♭ E♭ A♭ D♭ G♭ C♭]
    )
])

==== Circle of fifths <circle_anchor>
- Interpret the previous table in a "circular" fashion, where the bottom line wraps around and joins the first line

#pagebreak()
= Application: Harmonica

Here we consider the 10-hole diatonic harmonica (for example Hohner "Blues Harp" and "Marine Band"), not the chromatic harmonica.

The following diagrams show the scales that can be played on the *same* harmonica, without overblows and overdraws. By also using minimal overblows and overdraws the usefulness of each position can be further expanded.

Blues is typically played by a _cross_ harp with lots of overdraws and overblows, for example a harmonica labelled "C" can be used to play a blues in the key of *G* (chords G7, C7, D7).

For a very skilled player who can play all the overblows and overdraws the instrument becomes fully chromatic (any position could play any mode)

*Legend*:
- the blue line shows the path the mouth should follow to play a diatonic scale without missing any note of that scale. Note the reversal of the blow/draw pattern between hole 6 and 7.
#figure(  image("img/harp-legend.png", width: 100%))

The *same* harmonica can be used in any one of 12 "positions"

#pagebreak()
== Useful positions: 12, 1..6
- they correspond to the familiar 7 modes of the major scale

  #figure(  image("img/harp1.png", width: 100%))

#pagebreak()
== Not so useful positions: 7..11
- the root note of the scale must be played by overblowing or overdrawing as indicated

  #figure(  image("img/harp2.png", width: 100%))

#pagebreak()
= Application: Cello
This section also applies to tenor guitars and modified tenor ukuleles. These are 4-string instruments tuned in fifths: CGDA.

In general, the left hand can be used in either of the following two "grips"
- *minor* grip, narrow, spanning a minor third, 3 semitones, using fingers (1,2,4) or (1,3,4) depending on the key/position/string
- *major* grip, extended, spanning a major third, 4 semitones, using fingers (1,2,4) with a stretch of the distance between finger 1 and 2 to be the same as between finger 2 and 4. Finger 3 is not used.

== Left hand positions on the fingerboard

Usually beginners put 4 sticky tape markers on the fretboard corresponding to the blue lines in the following diagram.

#figure(
  image("img/cello/cello-positions.png", width: 100%),
  caption: [Cello left-hand positions]
  )

#pagebreak()
== Major scale pattern on fingerboard
It is useful to look at the following diagram through a carboard cutout that lets only 4 strings at a time to be viewed, positioned according to the key.

#figure(
  image("img/cello/cello-major.png", width: 100%),
  caption: [Major scale patterns, all keys]
  )

== Major scale and arpeggio (triads), all keys

#figure(
  image("img/cello/cello-arpeggio.png", width: 100%),
  caption: [Major scales and triad arpeggio, all keys]
  )

== Minor scales and arpeggio (triads), all keys
#figure(
  image("img/cello/final3a.png", width: 100%),
  caption: [Minor scales and triad arpeggio, keys with sharps]
  )

#figure(
  image("img/cello/final3b.png", width: 100%),
  caption: [Minor scales and triad arpeggio, keys with flats]
  )

#pagebreak()
== 7-note Arpeggio (2 octaves) // cello

For the theoretical background refer to @arp2oct_theory

*Legend:*
- A slanted line represents two notes played on two adjacent strings
- A vertical line represents two notes played on the same strings

#align(left, block[
    #figure(image("img/cello/cello-arp2-legend.png"))
])

Note that in the following figure the two diagrams represents exactly the same arpeggio *MAJ,min,MAJ,min,MAJ,min,min*

#figure(
  image("img/cello/cello-arp2-same.png", width:30%),
  caption: [Equivalent notation]
  )

=== major

- The last pattern on the right illustrates what you would get if you continued the diagram: the Lydian mode would be used again, but the root and all the notes would be one semitone lower compared to the Lydian mode on the left.
- all the patterns span 4 strings, and they have the same initial and final notes. The root being the same, means that each mode belongs to a different key. See @modes_vs_keys
- the first 3 patterns on the left are "major" because the green line starts by going up
- the next 3 patterns are "minor" because the green line starts by going down
- the last patterns (Locrian) is "diminished" because the green line starts by going down twice.

#figure(
  image("img/cello/cello-arp2.png"),
  caption: [Use only the narrow grip]
  )

#figure(
  image("img/cello/cello-arp2-noshift.png", width:85%),
  caption: [Alternative, without shifting position]
  )

=== melodic minor

#figure(
  image("img/cello/cello-arp2-mel-min.png", width:85%),
  caption: [Without shifting position]
  )

=== harmonic minor
TODO

=== harmonic major
TODO

#pagebreak()
= Application: Guitar
This section applies to 6-string guitars with standard tuning EADGBE.

== Scale Fingerings // Diteggiature
=== Modi scala maggiore diatonica // 2 fingering
Example G maggiore
#table(
    columns: 3,
    align: horizon,
    stroke: none,
    [], [], [], // prevent the 1st row from being bold

[I], [Ionian],[#figure( image("img/fig3-1-1.png",  width: 60%))],
[II], [Dorian], [#figure( image("img/fig3-1-2.png", width: 60%))],
[III], [Phrygian], [#figure( image("img/fig3-1-3.png", width: 60%))],
[IV], [Lydian], [#figure( image("img/fig3-1-4.png", width: 60%))],
[V], [Mixolydian], [#figure( image("img/fig3-1-5.png", width: 60%))],
[VI], [Aeolian], [#figure( image("img/fig3-1-6.png", width: 60%))],
[VII], [Locrian], [#figure( image("img/fig3-1-7.png", width: 60%))]
    )

=== Major scale - 5 frets // 21 fingering
Example C major

=== Modes of harmonic minor scale // 8 fingering
Example E minor

#table(
    columns: 3,
    align: horizon,
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },

    [], [], [], // prevent the 1st row from being bold

[♭III], [G△(♯5)],[#figure( image("img/page8-1.png",  width: 60%))],
[IV], [A-7], [#figure( image("img/page8-2.png", width: 60%))],
[V], [B7], [#figure( image("img/page8-3.png", width: 60%))],
[♭VI], [C△], [#figure( image("img/page8-4.png", width: 60%))],
[VII], [D♯#sym.degree], [#figure( image("img/page8-5.png", width: 60%))],
[I], [E-(maj7)], [#figure( image("img/page8-6.png", width: 60%))],
[II], [F♯ø], [#figure( image("img/page8-7.png", width: 60%))]
)

=== Modes of melodic minor scale (ascendent = jazz) // 12 fingering
Example E minor

TODO

=== Diminished // 17 fingering
#figure( image("img/p17-1.png",  width: 60%))
#figure( image("img/p17-2.png",  width: 90%))
#figure( image("img/p17-3.png",  width: 55%))

=== Whole-tone scale // 18 fingering
#figure( image("img/p18-1.png",  width: 80%))
#figure( image("img/p18-2.png",  width: 60%))

=== Pentatonic // 15 fingering

#figure( image("img/penta.jpg", width: 80%))

#pagebreak()
== Arpeggio

=== G major, 4 voices
==== Starting from 6#super[th] string // 3 arpeggio
TODO

==== Starting from 5#super[th] string // 4 arpeggio
TODO

#pagebreak()
=== G major, 5 voices
==== Starting from 6#super[th] string // 20 arpeggio

#table(
    columns: 3,
    align: horizon,
    stroke: none,
[G△9], [(1,3,5,7,9)],[#figure( image("img/p20-1.png",  width: 65%))],
[A-9], [(1,♭3,5,♭7,9)], [#figure( image("img/p20-2.png", width: 65%))],
[B-7], [(1,♭3,5,♭7,♭9)], [#figure( image("img/p20-3.png", width: 60%))],
[C△9], [(1,3,5,7,9)], [#figure( image("img/p20-4.png", width: 60%))],
[D9], [(1,3,5,♭7,9)], [#figure( image("img/p20-5.png", width: 65%))],
[E-9], [(1,♭3,5,♭7,9)], [#figure( image("img/p20-6.png", width: 65%))],
[F♯ø(♭9)], [(1,♭3,♭5,♭7,♭9)], [#figure( image("img/p20-7.png", width: 60%))]
    )

=== Diminished scale // 17 arpeggio
TODO

=== Whole-tone scale // 18 arpeggio
TODO

#pagebreak()
=== 7-note Arpeggio (2 octaves) // guitar

For the theoretical background refer to @arp2oct_theory

==== major
#table(
    columns: 4,
    align: horizon + center,
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    [Q],[mode],[arpeggio],[key],

[42], [Lyd],[#figure( image("img/gt/gt-arp7a.png", width: 65%))],[D],
[41], [Ion],[#figure( image("img/gt/gt-arp7b.png", width: 65%))],[G],
[37], [Mix],[#figure( image("img/gt/gt-arp7c.png", width: 65%))],[C],
[21], [Dor],[#figure( image("img/gt/gt-arp7d.png", width: 65%))],[F],
[20], [Aeo],[#figure( image("img/gt/gt-arp7e.png", width: 65%))],[B♭],
[18], [Phr],[#figure( image("img/gt/gt-arp7f.png", width: 65%))],[E♭],
[10], [Loc],[#figure( image("img/gt/gt-arp7g.png", width: 65%))],[A♭]
    )

#pagebreak()
==== melodic minor
#table(
    columns: 2,
    align: horizon + center,
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    [Q],[arpeggio],

[25], [#figure( image("img/gt/arp7-25.png", width: 65%))],
[19], [#figure( image("img/gt/arp7-19.png", width: 65%))],
[50], [#figure( image("img/gt/arp7-50.png", width: 65%))],
[38], [#figure( image("img/gt/arp7-38.png", width: 65%))],
[36], [#figure( image("img/gt/arp7-36.png", width: 65%))],
[12], [#figure( image("img/gt/arp7-12.png", width: 65%))],
[9], [#figure( image("img/gt/arp7-9.png", width: 65%))]
    )

#pagebreak()
==== harmonic minor
#table(
    columns: 2,
    align: horizon + center,
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    [Q],[arpeggio],

[24], [#figure( image("img/gt/arp7-24.png", width: 65%))],
[11], [#figure( image("img/gt/arp7-11.png", width: 65%))],
[49], [#figure( image("img/gt/arp7-49.png", width: 65%))],
[22], [#figure( image("img/gt/arp7-22.png", width: 65%))],
[34], [#figure( image("img/gt/arp7-34.png", width: 65%))],
[44], [#figure( image("img/gt/arp7-44.png", width: 65%))],
[5], [#figure( image("img/gt/arp7-5.png", width: 65%))]
    )

#pagebreak()
==== harmonic major
#table(
    columns: 2,
    align: horizon + center,
    stroke: 1pt,
    fill: (_, y) => if y == 0 { gray.lighten(40%) },
    [Q],[arpeggio],

[40], [#figure( image("img/gt/arp7-40.png", width: 65%))],
[13], [#figure( image("img/gt/arp7-13.png", width: 65%))],
[17], [#figure( image("img/gt/arp7-17.png", width: 65%))],
[26], [#figure( image("img/gt/arp7-26.png", width: 65%))],
[35], [#figure( image("img/gt/arp7-35.png", width: 65%))],
[52], [#figure( image("img/gt/arp7-52.png", width: 65%))],
[6], [#figure( image("img/gt/arp7-6.png", width: 65%))]
    )

#pagebreak()
== Chords

=== CAGED system
CAGED is a way of visualizing triadic harmony on the entire fretboard as you play songs. @marbinCaged

It's all about having _areas_ to see the fretboard harmonically

There are 5 major (and 5 minor) open chord forms.

- *Major CAGED*

    #chart-chord-sharp(tabs: "x32o1o", fingers: "n32n1n")[C]
    #chart-chord-sharp(tabs: "oo222o", fingers: "nn234n")[A]
    #chart-chord-sharp(tabs: "32ooo3", fingers: "21nnn3")[G]
    #chart-chord-sharp(tabs: "o221oo", fingers: "n231nn")[E]
    #chart-chord-sharp(tabs: "xxo232", fingers: "nn0132")[D]

    Example "box 2"

    #chart-chord-sharp(tabs: "x4312x", fingers: "n4312n", fret: 4)[E]
    #chart-chord-sharp(tabs: "xn333n", fingers: "n0234n", fret: 5, capos: "115")[D]
    #chart-chord-sharp(tabs: "431144", fingers: "321144", fret: 5, capos: "412")[C]
    #chart-chord-sharp(tabs: "133211", fingers: "134211", fret: 5, capos: "116")[A]
    #chart-chord-sharp(tabs: "31134x", fingers: "21134n", fret: 5, capos: "145")[G]

    Example F  

    #chart-chord-sharp(tabs: "x4312x", fingers: "n4312n", fret: 5)[F] // C form
    #chart-chord-sharp(tabs: "xn333n", fingers: "nn234n", fret: 8, capos: "115")[F]  // A form
    #chart-chord-sharp(tabs: "431144", fingers: "321144", fret: 10, capos: "412")[F] // G form
    #chart-chord-sharp(tabs: "133211", fingers: "134211", fret: 1, capos: "116")[F] // E form
    #chart-chord-sharp(tabs: "31134x", fingers: "21134n", fret: 3, capos: "145")[F] // D form

- *Minor CAGED*

    // open
    #chart-chord-sharp(tabs: "331o1x", fingers: "341n2n")[C-]
    #chart-chord-sharp(tabs: "oo221o", fingers: "nnnnnn")[A-]
    #chart-chord-sharp(tabs: "31oo33", fingers: "21nn33")[G-]
    #chart-chord-sharp(tabs: "o22ooo", fingers: "nnnnnn")[E-]
    #chart-chord-sharp(tabs: "xxo231", fingers: "nnnnnn")[D-]

    Example "box 2"

    #chart-chord-sharp(tabs: "331x1x", fingers: "341n2n", fret: 5)[E-] // TBC
    #chart-chord-sharp(tabs: "x13321", fingers: "nnnnnn", fret: 5, capos: "115")[D-] // A-
    #chart-chord-sharp(tabs: "421144", fingers: "21n333", fret: 5)[C-]
    #chart-chord-sharp(tabs: "n33nnn", fingers: "123111", fret: 5, capos: "116")[A-]
    #chart-chord-sharp(tabs: "21134x", fingers: "21134n", fret: 5, capos: "145")[G-]

    Example C-

    #chart-chord-sharp(tabs: "331o1x", fingers: "341n2n")[C-]
    #chart-chord-sharp(tabs: "x13321", fingers: "nnnnnn", fret: 3, capos: "115")[C-] // A-
    #chart-chord-sharp(tabs: "421144", fingers: "21n333", fret: 5)[C-]
    #chart-chord-sharp(tabs: "133111", fingers: "123111", fret: 8, capos: "116")[C-]
    #chart-chord-sharp(tabs: "21134x", fingers: "21134n", fret: 10, capos: "145")[C-]

Connect each pair of major and relative minor chord with a pentatonic scale.

Example:
- C major #sym.arrow.l.r.double A- #sym.arrow.l.r.double box 4 (minor) // 5m 03s
- C major #sym.arrow.l.r.double A- (G- form) #sym.arrow.l.r.double box 5
- C major #sym.arrow.l.r.double A- #sym.arrow.l.r.double box 1
- C major #sym.arrow.l.r.double A- (E- form) #sym.arrow.l.r.double box 2
- C (D form) #sym.arrow.l.r.double A- (C- form) #sym.arrow.l.r.double box 3

This is good for arpeggiating chords.

Do this with _voice leading_: find the closest note when the harmony is changing.

=== Major 7th chords (key of G)

#line(length: 100%)
==== Root on 6#super[th] string // 5 chords
#chart-chord-sharp(tabs: "1x221x", fingers: "1n342n", fret: 3)[G△]
#chart-chord-sharp(tabs: "1xnnnx", fingers: "2n333n", fret: 5, capos: "124")[A-7]
#chart-chord-sharp(tabs: "1xnnnx", fingers: "2n333n", fret: 7, capos: "124")[B-7]
#chart-chord-sharp(tabs: "1x221x", fingers: "1n342n", fret: 8)[C△]
#chart-chord-sharp(tabs: "1x121x", fingers: "1n243n", fret: 10)[D7]
#chart-chord-sharp(tabs: "1xnnnx", fingers: "2n333n", fret: 12, capos: "124")[E-7]
#chart-chord-sharp(tabs: "3x332x", fingers: "2n341n", fret: 12)[F♯ø]

#figure( image("img/fig5-1-1.png", width: 100%) )

#line(length: 100%)
==== Root on 5#super[th] string // 6 chords
#chart-chord-sharp(tabs: "xn3n2n", fingers: "n14121n", fret: 2, capos: "115")[B-7]
#chart-chord-sharp(tabs: "xn323n", fingers: "n13241", fret: 3, capos: "115")[C△]
#chart-chord-sharp(tabs: "xn3n3n", fingers: "n13141", fret: 5, capos: "115")[D7]
#chart-chord-sharp(tabs: "xn3n2n", fingers: "n13121", fret: 7, capos: "115")[E-7]
#chart-chord-sharp(tabs: "x1212x", fingers: "n1324n", fret: 9)[F♯#super[ø]]
#chart-chord-sharp(tabs: "x1323x", fingers: "n1324n", fret: 10)[G△]
#chart-chord-sharp(tabs: "xn3n2n", fingers: "n13121", fret: 12, capos: "115")[A-7]

#figure( image("img/fig5-1-2.png", width: 100%) )

#line(length: 100%)
==== Root on 4#super[th] string // 7 chords
#chart-chord-sharp(tabs: "xx1322", fingers: "nn1423", fret: 2)[E-7]
#chart-chord-sharp(tabs: "xx1nnn", fingers: "nn1333", fret: 4, capos: "213")[F♯ø]
#chart-chord-sharp(tabs: "xx1nnn", fingers: "nn1333", fret: 5, capos: "313")[G△]
#chart-chord-sharp(tabs: "xx1322", fingers: "nn1423", fret: 7)[A-7]
#chart-chord-sharp(tabs: "xx1322", fingers: "nn1423", fret: 9)[B-7]
#chart-chord-sharp(tabs: "xx1nnn", fingers: "nn1333", fret: 10, capos: "313")[C△]
#chart-chord-sharp(tabs: "xx1323", fingers: "nn1324", fret: 12)[D7]

#line(length: 100%)

#pagebreak()
=== Scala di E minore armonica

#line(length: 100%)
==== Root on 6#super[th] string // 9 chords
#chart-chord-sharp(tabs: "1xnnnx", fingers: "1n333n", fret: 3, capos: "224")[G△#super[5+]]
#chart-chord-sharp(tabs: "1x111x", fingers: "2n333n", fret: 5, capos: "124")[A-7]
#chart-chord-sharp(tabs: "13121x", fingers: "13121n", fret: 7, capos: "126")[B7]
#chart-chord-sharp(tabs: "1n221x", fingers: "1n342n", fret: 8)[C△]
#chart-chord-sharp(tabs: "2n121x", fingers: "2n131n", fret: 10, capos:"124")[D♯#sym.degree]
#chart-chord-sharp(tabs: "1n211x", fingers: "1n211n", fret: 12, capos: "126")[E-△]
#chart-chord-sharp(tabs: "2n221x", fingers: "2n341n", fret: 14)[F♯#super[ø]]

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==== Root on 5#super[th] string // 10 chords

#chart-chord-sharp(tabs: "x13131", fingers: "n13141", fret: 2, capos: "115")[B7]
#chart-chord-sharp(tabs: "x1323x", fingers: "n1324n", fret: 3)[C△]
#chart-chord-sharp(tabs: "x2313x", fingers: "n2314n", fret: 5)[D♯#sym.degree]
#chart-chord-sharp(tabs: "x13221", fingers: "n14231", fret: 7, capos: "115")[E-△]
#chart-chord-sharp(tabs: "x1212x", fingers: "n1324n", fret: 9)[F♯#super[ø]]
#chart-chord-sharp(tabs: "x1423x", fingers: "n1423n", fret: 10)[G△#super[5+]]
#chart-chord-sharp(tabs: "x13121", fingers: "n13121", fret: 12, capos: "115")[A-7]

oppure

#chart-chord-sharp(tabs: "x4321x", fingers: "n4321n", fret: 7)[G△#super[5+]]

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==== Root on 4#super[th]  string // 11 chords
#chart-chord-sharp(tabs: "xx1332", fingers: "nn1342", fret: 2)[E-△]
#chart-chord-sharp(tabs: "xx1222", fingers: "nn1333", fret: 4, capos: "213")[F♯#super[ø]]
#chart-chord-sharp(tabs: "xx1433", fingers: "nn1423", fret: 5)[G△#super[5+]]
#chart-chord-sharp(tabs: "xx1322", fingers: "nn1423", fret: 7)[A-7]
#chart-chord-sharp(tabs: "xx1323", fingers: "nn1324", fret: 9)[B7]
#chart-chord-sharp(tabs: "xx1333", fingers: "nn1333", fret: 10, capos: "313")[C△]
#chart-chord-sharp(tabs: "xx1212", fingers: "nn1324")[D♯#sym.degree]

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=== G major chord shapes (5 voices) // 19 chords
\
#chart-chord-sharp(tabs: "324232", fingers: "214131", capos: "215")[G△9]
#chart-chord-sharp(tabs: "1x1113", fingers: "2n3334", fret: 5, capos: "124")[A-9]
#chart-chord-sharp(tabs: "134141", fingers: "123141", fret: 7, capos: "116")[B-7#super[(♭9)]]
#chart-chord-sharp(tabs: "213121", fingers: "214131", fret: 8, capos: "115")[C△9]
#chart-chord-sharp(tabs: "1n1213", fingers: "1n1214", fret: 10, capos: "126")[D9]
#chart-chord-sharp(tabs: "1x1113", fingers: "2n3334", fret: 12, capos: "124")[E-9]
#chart-chord-sharp(tabs: "2x2213", fingers: "nn2314", fret: 13)[F♯#super[ø(♭9)]]

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=== Diminished chord shapes // 17 chords
\
#chart-chord-sharp(tabs: "2xn2nx", fingers: "2n121n", capos: "124")[]
#chart-chord-sharp(tabs: "xx1212", fingers: "nn1324")[]
#chart-chord-sharp(tabs: "x3424x", fingers: "n2314n")[]

The same patterns can be repeated along the fretboard at intervals of minor thirds apart:

#chart-chord-sharp(tabs: "2x121x", fingers: "2n121n", fret: 3, capos: "124")[]
#chart-chord-sharp(tabs: "xx1212", fingers: "nn1324", fret: 3)[]
#chart-chord-sharp(tabs: "x3424x", fingers: "n2314n", fret: 3)[]

#chart-chord-sharp(tabs: "2x121x", fingers: "2n121n", fret: 6, capos: "124")[]
#chart-chord-sharp(tabs: "xx1212", fingers: "nn1324", fret: 6)[]
#chart-chord-sharp(tabs: "x3424x", fingers: "n2314n", fret: 6)[]

#chart-chord-sharp(tabs: "2x121x", fingers: "2n121n", fret: 9, capos: "124")[]
#chart-chord-sharp(tabs: "xx1212", fingers: "nn1324", fret: 9)[]
#chart-chord-sharp(tabs: "x3424x", fingers: "n2314n", fret: 9)[]

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#pagebreak()
#bibliography("music.bib"
  //, style: "iso-690-author-date"
  )