# G-double-sharp half-diminished 7th chord

The Solution below shows the G-double-sharp half-diminished 7th chord in root position, 1st, 2nd, and 3rd inversions, on the piano, treble clef and bass clef.

The Lesson steps then explain how to construct this 7th chord using the 3rd, 5th and 7th note intervals, then finally how to construct the inverted chord variations.

For a quick summary of this topic, have a look at Seventh chord.

 Key C C# Db D D# Eb E E# Fb F F# Gb G G# Ab A A# Bb B B# Cb

## Solution - 4 parts

### 1. G-double-sharp half-diminished 7th chord

This step shows the G-double-sharp half-diminished 7th chord in root position on the piano, treble clef and bass clef.

The G-double-sharp half-diminished 7th chord contains 4 notes: G##, B#, D#, F##.

The chord spelling / formula relative to the G## major scale is:  1 b3 b5 b7.

G-double-sharp half-diminished 7th chord note names
Note no.Note intervalSpelling
/ formula
Note name#Semitones
from root
1root1The 1st note of the G-double-sharp half-diminished 7th chord is G##0
2G##-min-3rdb3The 2nd note of the G-double-sharp half-diminished 7th chord is B#3
3G##-dim-5thb5The 3rd note of the G-double-sharp half-diminished 7th chord is D#6
4G##-min-7thb7The 4th note of the G-double-sharp half-diminished 7th chord is F##10

Middle C (midi note 60) is shown with an orange line under the 2nd note on the piano diagram.

These note names are shown below on the treble clef followed by the bass clef.

The figured bass symbols for this chord in root position are 7/5/3.

The staff diagrams and audio files contain each note individually, ascending from the root, followed by the chord containing all 3 notes.

 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 2. G-double-sharp half-diminished 7th 1st inversion

This step shows the G-double-sharp half-diminished 7th 1st inversion on the piano, treble clef and bass clef.

The G-double-sharp half-diminished 7th 1st inversion contains 4 notes: B#, D#, F##, G##.

These note names are shown below on the treble clef followed by the bass clef.

The figured bass symbols for this chord in root position are 6/5/3, so the chord is said to be in six-five-three position.

 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 3. G-double-sharp half-diminished 7th 2nd inversion

This step shows the G-double-sharp half-diminished 7th 2nd inversion on the piano, treble clef and bass clef.

The G-double-sharp half-diminished 7th 2nd inversion contains 4 notes: D#, F##, G##, B#.

These note names are shown below on the treble clef followed by the bass clef.

The figured bass symbols for this chord in root position are 6/4/3, so the chord is said to be in six-four-three position.

 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 4. G-double-sharp half-diminished 7th 3rd inversion

This step shows the G-double-sharp half-diminished 7th 3rd inversion on the piano, treble clef and bass clef.

The G-double-sharp half-diminished 7th 3rd inversion contains 4 notes: F##, G##, B#, D#.

These note names are shown below on the treble clef followed by the bass clef.

The figured bass symbols for this chord in root position are 6/4/2, so the chord is said to be in six-four-two position.

 Bass Clef: Midi MP3 Treble Clef: Midi MP3

## Lesson steps

### 1. Piano key note names

This step shows the white and black note names on a piano keyboard so that the note names are familiar for later steps, and to show that the note names start repeating themselves after 12 notes.

The white keys are named using the alphabetic letters A, B, C, D, E, F, and G, which is a pattern that repeats up the piano keyboard.

Every white or black key could have a flat(b) or sharp(#) accidental name, depending on how that note is used. In a later step, if sharp or flat notes are used, the exact accidental names will be chosen.

The audio files below play every note shown on the piano above, so middle C (marked with an orange line at the bottom) is the 2nd note heard.

 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 2. G-double-sharp tonic note and one octave of notes

This step shows 1 octave of notes starting from note G##, to identify the start and end notes of the scale used to build this chord.

The numbered notes are those that might be used when building this chord.

Note 1 is the root note - the starting note of the chord - G##, and note 13 is the same note name but one octave higher.

 No. Note 1 2 3 4 5 6 7 8 9 10 11 12 13 G## A# / Bb B C C# / Db D D# / Eb E F F# / Gb G G# / Ab G##
 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 3. G-double-sharp major scale note interval positions

This step describes the G## major scale , whose note intervals are used to define the chord in a later step.

The major scale uses the  W-W-H-W-W-W-H  note counting rule to identify the scale note positions.

To count up a Whole tone, count up by two physical piano keys, either white or black.

To count up a Half-tone (semitone), count up from the last note up by one physical piano key, either white or black.

The tonic note (shown as *) is the starting point and is always the 1st note in the major scale.

Again, the final 8th note is the octave note, having the same name as the tonic note.
 No. Note 1 2 3 4 5 6 7 8 G## B C# / Db D E F# / Gb G# / Ab G##
 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 4. G-double-sharp major scale note interval numbers

This step identifies the note interval numbers of each scale note, which are used to calculate the chord note names in a later step.

To identify the note interval numbers for this major scale, just assign each note position from the previous step, with numbers ascending from 1 to 8.

 No. Note 1 2 3 4 5 6 7 8 G## A## B## C## D## E## F### G##

To understand why the note names of this major scale have these specific sharp and flat names, have a look at the G## major scale page.

Both the note interval numbers and note names from the piano diagram above will be used in later steps to calculate the chord note names.

### 5. 7th chord qualities

This step defines a seventh chord, names the 7th chord qualities and identifies the notes that vary between them.

#### 7th chord definition

Whereas a triad chord contains 3 notes, a 7th chord contains 4 notes that are played together or overlapping.

#### 7th chord qualities

7th chords exist in eight different chord qualities, which are diminished, half-diminished, minor, minor-major , dominant, major, augmented, and augmented-major.

Each chord quality name is the name of the entire chord as a whole, not its individual notes (which will be covered later).

#### Triad chord qualities using the 1st, 3rd, 5th and 7th scale notes

All of these 7th chord qualities are based on the 1st, 3rd, 5th and 7th notes of the major scale piano diagram above.

Depending on the chord quality, the 3rd, 5th and 7th scale note names of the major scale above might need to be adjusted up or down by one or more half-notes / semitones / piano keys.

It is these variations of the 3rd, 5th and 7th notes that give each one a distinctive sound for any given key (eg. C-flat, E etc).

In fact, these 7th chords are based on triad chords - the first 3 notes of any 7th chord are identical to a specific triad chord quality, with one extra note added to make it a 7th chord.

#### Suspended 7th chords - using the 2nd or 4th scale notes

A suspended chord is known in music theory as an altered chord because it takes one of the above chord qualities and modifies it in some way.

Unlike all of the above qualities, Suspended triad chords do not use the 3rd note of the major scale (at all) to build the chord.

The 3rd note is suspended, ie. removed completely, and replaced by either the 2nd note of the major scale - a suspended 2nd, or more commonly by the 4th note of the major scale - a suspended 4th.

Musically, this is interesting, since it is usually the 3rd note of the scale that defines the overall character of the chord as being major (typically described as 'happy') or minor ('sad').

Without this 3rd note, suspended chords tend to have an open and ambiguous sound.

The steps below will detail the half-diminished 7th triad chord quality in the key of G##.

### 6. 7th chord note intervals

This step defines the note intervals for each chord quality, including the intervals for the G-double-sharp half-diminished 7th 7th chord. It also shows how the 7th chord qualities are related to the triad chord qualities they are based on.

Each individual note in a 7th chord can be represented in music theory using a note interval, which is used to express the relationship between the first note of the chord (the root note), and the note in question.

The root note is always the 1st note (note interval 1 in the above diagram) of the major scale diagram above. ie. the tonic of the major scale.

Then there is one note interval to describe the 2nd note, and another to describe the 3rd note of the chord, and finally another interval for the 4th chord note.

In the same way that the entire chord itself has a chord quality, the intervals representing the individual notes within that chord each have their own quality.

These note interval qualities are diminished, minor, major, perfect and augmented.

Below is a table showing the note interval qualities for all 7th chords, together with the interval short names / abbrevations in brackets.

The final column shows the triad chord quality that the 7th chord is based on, so the 2nd and 3rd note quality columns are the same as the triad table for the same key.

seventh chord note interval qualities
7th chord quality2nd note quality3rd note quality4th note qualityBased on triad quality
diminishedminor (m3)diminished (d5)diminished (d7)diminished
half-diminishedminor (m3)diminished (d5)minor (m7)diminished
minorminor (m3)perfect (P5)minor (m7)minor
minor majorminor (m3)perfect (P5)major (M7)minor
dominantmajor (M3)perfect (P5)minor (m7)major
majormajor (M3)perfect (P5)major (M7)major
augmentedmajor (M3)augmented (A5)minor (m7)augmented
augmented-majormajor (M3)augmented (A5)major (M7)augmented
major suspended
(2nd/4th)
major (M2) or
perfect (P4)
perfect (P5)major (M7)suspended
(2nd/4th)
dominant
suspended 4th
perfect (P4)perfect (P5)minor (m7)suspended 4th

The numbers in brackets are the note interval number (ie the scale note number) shown in the previous step.

Looking at the table above, the note intervals for the chord quality we are interested in (half-diminished 7th), in the key of G## are G##-min-3rd, G##-dim-5th, and G##-min-7th.

The links above explain in detail the meaning of these qualities, the short abbrevations in brackets, and how to calculate the interval note names based on the scale note names from the previous step.

### 7. G-double-sharp half-diminished 7th chord in root position

This step shows the G-double-sharp half-diminished 7th chord note interval names and note positions on a piano diagram.

#### Note name adjustments

Each note interval quality (diminished, minor, major, perfect, augmented) expresses a possible adjustment ie. a possible increase or decrease in the note pitch from the major scale notes in step 4.

If an adjustment in the pitch occurs, the note name given in the major scale in step 4 is modified, so that sharp or flat accidentals will be added or removed.

But crucially, for all interval qualities, the starting point from which accidentals need to be added or removed are the major scale note names in step 4.

For this chord, this is explained in detail in G##-min-3rd, G##-dim-5th and G##-min-7th, but the relevant adjustments for this half-diminished 7th chord quality are shown below:

G##-3rd: The 3rd note quality of the major scale is major, and the note interval quality needed is minor, so the 3rd note scale note name - B##, is adjusted 1 half-note / semitone down to B#. The chord note spelling reflects this note flattening: b3.

G##-5th: The 5th note quality of the major scale is perfect, and the note interval quality needed is diminished, so the 5th note scale note name - D##, is adjusted 1 half-note / semitone down to D#. The chord note spelling reflects this note flattening: b5.

G##-7th: The 7th note quality of the major scale is major, and the note interval quality needed is minor, so the 7th note scale note name - F###, is adjusted 1 half-tone / semitone down to F##. The chord note spelling reflects this note flattening: b7.

If it is still not clear why the interval qualities are organised / related as they are, please refer to each of the interval links above.

#### G-double-sharp half-diminished 7th seventh chord note names

The final chord note names and note interval links are shown in the table below.

Note Interval No. Interval def Spelling 1 3 5 7 G## B# D# F## root G##-min-3rd G##-dim-5th G##-min-7th 1 b3 b5 b7 0 3 6 10

The piano diagram below shows the interval short names, the note positions and the final note names of this triad chord.

In music theory, this 7th chord as it stands is said to be in root position because the root of the chord - note G##, is the note with the lowest pitch of all the chord notes.

The note order of this chord can also be changed, so that the root is no longer the lowest note, in which case the chord is no longer in root position, and will be called an inverted 7th chord instead.

For 7th chords, there are 3 possible inverted variations as described below.

#### Figured bass notation

The figured bass notation for a 7th chord in root position is 7/5/3, with the 7 placed above the 5, and the 5 above the 3.

These numbers represent the interval between the lowest note of the chord and the note in question.

So another name for this inversion would be G-double-sharp half-diminished 7th triad in seven-five-three position.

For example, the 7 represents note F##, from the G##-7th interval, since the chord root, G##, is the lowest note of the chord (as it is not inverted). .

In the same way, the figured bass 5 symbol represents note D#, from the G##-5th interval, and the 3 symbol represents note B#, from the G##-3rd interval

Since figured bass notation works within the context of a key, we don't need to indicate in the figured bass symbols whether eg. the 3rd is a major, minor etc. The key is assumed from the key signature.

Often, for a 7th chord in root position, only the 7 symbol is shown, since it is assumed that the chord is shown in root position (ie not inverted), unless otherwise indicated as shown below.

 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 8. G-double-sharp half-diminished 7th 1st inversion

This step shows the first inversion of the G-double-sharp half-diminished 7th.

To invert a chord, simply take the first note of the chord to be inverted (the lowest in pitch) and move it up an octave to the end of the chord.

So for a 1st inversion, take the root of the 7th chord in root position from the step above - note G##, and move it up one octave (12 notes) so it is the last (highest) note in the chord.

The second note of the original 7th chord (in root position) - note B# is now the note with the lowest pitch.

#### Figured bass notation

The figured bass notation for this chord in 1st inversion is 6/5/3, with the 6 placed above the 5, and the 5 placed above the 3 on a staff diagram.

Based on this numbering scheme, another name for this inversion would be G-double-sharp half-diminished 7th triad in six-five-three position.

These numbers represent the interval between the lowest note of the chord (not necessarily the original chord root!), and the note in question.

For example, the 6 represents note G##, from the B#-6th interval, since the lowest (bass) note of the chord - now inverted, is B#.

In the same way, the figured bass 5 symbol represents note F##, from the B#-5th interval, and the 3 symbol represents note D#, from the B#-3rd interval

In 1st inversion, often the 3 symbol is not shown at all, as it is assumed.

 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 9. G-double-sharp half-diminished 7th 2nd inversion

This step shows the second inversion of the G-double-sharp half-diminished 7th.

For a 2nd inversion, take the first note of the 1st inversion above - B#, and move it to the end of the chord.

So the second note of the 1st inversion - note D# is now the note with the lowest pitch for the 2nd inversion.

Or put another way, the third note of the original 7th chord (in root position) is now the note with the lowest pitch.

#### Figured bass notation

The figured bass notation for this chord in 2nd inversion is 6/4/3, with the 6 placed above the 4, and the 4 placed above the 3 on a staff diagram.

Based on this numbering scheme, another name for this inversion would be G-double-sharp half-diminished 7th triad in six-four-three position.

These numbers represent the interval between the lowest note of the chord (not necessarily the original chord root!), and the note in question.

For example, the 6 represents note B#, from the D#-6th interval, since the lowest (bass) note of the chord - now inverted, is D#.

In the same way, the figured bass 4 symbol represents note G##, from the D#-4th interval, and the 3 symbol represents note F##, from the D#-3rd interval

In 2nd inversion, often the 6 symbol is not shown at all, as it is assumed.

 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 10. G-double-sharp half-diminished 7th 3rd inversion

This step shows the third inversion of the G-double-sharp half-diminished 7th.

For a 3rd inversion, take the first note of the 2nd inversion above - D#, and move it to the end of the chord.

So the second note of the 2nd inversion - note F## is now the note with the lowest pitch for the 3rd inversion.

Or put another way, the fourth note of the original 7th chord (in root position) is now the note with the lowest pitch.

#### Figured bass notation

The figured bass notation for this chord in 3rd inversion is 6/4/2, with the 6 placed above the 4, and the 4 placed above the 2 on a staff diagram.

Based on this numbering scheme, another name for this inversion would be G-double-sharp half-diminished 7th triad in six-four-two position.

These numbers represent the interval between the lowest note of the chord (not necessarily the original chord root!), and the note in question.

For example, the 6 represents note D#, from the F##-6th interval, since the lowest (bass) note of the chord - now inverted, is F##.

In the same way, the figured bass 4 symbol represents note B#, from the F##-4th interval, and the 2 symbol represents note G##, from the F##-2nd interval

In 3rd inversion, often the 6 symbol is not shown at all, as it is assumed.

 Bass Clef: Midi MP3 Treble Clef: Midi MP3