# A-double-flat 2nd intervals

The Solution below shows the 2nd note intervals above note Abb, and their inversions on the piano, treble clef and bass clef.

The Lesson steps then explain how to calculate each note interval name, number, spelling and quality. The final lesson step explains how to invert each interval.

For a quick summary of this topic, and to see the important interval table used to calculate the number of semitones in each interval, have a look at Note interval.

 Key Interval no C C# Db D D# Eb E E# Fb F F# Gb G G# Ab A A# Bb B B# Cb [1st] 2nd 3rd 4th 5th 6th 7th 8th

## Solution

### 1. A-double-flat dim2-min2-maj2-aug2 intervals

This step shows the A-double-flat second intervals on the piano, treble clef and bass clef.

#### 2nd intervals above note A-double-flat

A-double-flat dim2-min2-maj2-aug2 intervals
ShortMediumSpelling
/ formula
Intervals 'above' statement#Semitones
d2dim2bb2The Abb to Bbbbb interval is diminished 2nd0
m2min2b2The Abb to Bbbb interval is minor 2nd1
M2maj22The Abb to Bbb interval is major 2nd2
A2aug2#2The Abb to Bb interval is augmented 2nd3

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

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

#### Inverted intervals identifying note A-double-flat

This table inverts the above intervals, so that each link in the last column leads to note A-double-flat.

A-double-flat 2nd inverted intervals
ShortMediumLongNote nameLink to inverted
interval
d2Abbdim2A-double-flat diminished 2ndBbbbb<-(!?)->  G-aug-7th
m2Abbmin2A-double-flat minor 2ndBbbb<-(!?)->  Ab-maj-7th
M2Abbmaj2A-double-flat major 2ndBbb<-(!?)->  A-min-7th
A2Abbaug2A-double-flat augmented 2ndBb<-(!?)->  Bb-dim-7th

#### 2nd intervals below note A-double-flat

Intervals below
ShortMediumIntervals 'below' statement
d2dim2The diminished 2nd interval below Bbbbb is Abb
m2min2The minor 2nd interval below Bbbb is Abb
M2maj2The major 2nd interval below Bbb is Abb
A2aug2The augmented 2nd interval below Bb is Abb
 Bass Clef: Midi MP3 Treble Clef: Midi MP3

# Be the musician who sees a I-IV-V major progression..

## 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. A-double-flat major note interval positions

This step constructs the A-double-flat major scale, which is necessary because all interval names in this key are calculated using this major scale as starting point.

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 - Abb ,shown with an asterisk (*), is the starting point and is always the 1st note in the major scale.

The tonic is also the note from which intervals will be calculated in later steps - ie. all calculated intervals will have higher note pitches than the tonic.

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 Abb A B C D E F# / Gb Abb
 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 3. A-double-flat major interval qualities

This step identifies the interval quality and formula / spelling for each note in the major scale, then identifies the second note of the major scale, and decides whether the interval quality is either perfect or major.

The table and piano diagram below show the 8 notes (7 scale major notes + octave note) in the Abb major scale together with the interval quality for each.

#### Perfect or major?

The interval quality for each note in this major scale is always perfect or major. So the 1st, 4th, 5th and 8th are always perfect, and the rest are always major. This rule is fixed all major scales in all keys, so you will never see a perfect 3rd or a major 4th interval.

The difference between the perfect and major intervals is that perfect interval notes sound more perfect / pleasing to the ear than major intervals - ie. are more consonant / less disonant, when played together (harmonic interval) with, or alongside(melodic interval) the tonic note.

 No. Note #Semitones Quality Spelling/ formula 1 2 3 4 5 6 7 8 Abb Bbb Cb Dbb Ebb Fb Gb Abb 0 2 4 5 7 9 11 12 perfect major major perfect perfect major major perfect 1 2 3 4 5 6 7 8

#### Interval spelling / formula

In music theory, note intervals can also be expressed using using a spelling or formula, which mean the same thing. You may have seen a chord expressed as 1 b3 5, for example.

The spelling of the interval qualities in the above table will always be shown without any sharp(#) or flat(b) symbols, since these extra symbols represent the difference of the note from the major scale. And since the above table shows the intervals of the major scale, no sharp / flat adjustments are needed.

Using just the notes we have in the major scale above, a chord spelling of 1 3 5 uses the 1st, 3rd and 5th notes as they are, ie. the Abb major chord. Or a 1 3 5 7 chord adds the extra 7th note, ie. the uses the 1st, 3rd and 5th notes as they are, ie. the Abb maj 7 chord.

This rest of this page will focus on the relationship between the tonic note - Abb, and the intervals surrounding the 2nd major scale note - Bbb, whose interval quality is major. So we will definitely see extra sharp or flat spelling symbols there.

### 4. A-double-flat 2nd interval pitches

This step identifies the note positions of the A-double-flat 2nd intervals on a piano keyboard.

Having established that the major 2nd interval of the Abb major scale is note Bbb, this step will explore the other 2nd intervals next this note.

A major interval always has 3 other intervals grouped around it - one higher and two lower:

> One half-tone / semitone up from the major interval is the augmented interval.

> One half-tone / semitone down from the major interval is the minor interval.

> One half-tone / semitone down from the minor interval is the diminished interval.

The interval number (2nd) is added to the end, resulting in interval names going from the lowest note pitch to the highest:

2nd interval quality Names
ShortMediumLongSpelling
/ formula
#Semitones
d2dim2diminished 2ndbb20
m2min2minor 2ndb21
M2maj2major 2nd22
A2aug2augmented 2nd#23

#### Interval spelling / formula

Each interval has a spelling that represents its position relative to the major interval.

Flat signs (b) are used for intervals lower, and sharp (#) for intervals higher.

#### Interval short and medium names

Each interval name also has short and medium abbreviations, which are just different names for the same interval that you might see.

The short names are used in the piano diagram below to show the exact interval positions, with the orange number 0 representing the major interval, and the other orange numbers showing the number of half-tones / semitones up or down relative to that major interval.

The exact note names, including sharps and flats, of each of these intervals will be covered in the next step.

 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 5. A-double-flat 2nd intervals

This step identifies the note names of the A-double-flat 2nd intervals on a piano keyboard.

To calculate the correct interval names, just like the previous step, the major 2nd note is used as the starting point for working out interval information around it.

The major 2nd note name is Bbb, and so all intervals around it must start with the note name B, ie. be a variation of that name, with either sharps or flats used describe the interval difference in half-tones / semitones from any given interval note to the major 2nd.

Sharps or flats will be added or cancelled to force all interval names to start with B. Even if that involves using double and triple-sharps and flats.

A-double-flat 2nd intervals
ShortMediumLongSpelling
/ formula
Note name#Semitones
d2Abbdim2A-double-flat diminished 2ndbb2Bbbbb0
m2Abbmin2A-double-flat minor 2ndb2Bbbb1
M2Abbmaj2A-double-flat major 2nd2Bbb2
A2Abbaug2A-double-flat augmented 2nd#2Bb3

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

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

But why is this done ? To get the missing piece of the puzzle, we need to return to the interval number - the 2nd.

Not only does this number describe the note number of the major interval in the major scale, but it also describes the number of either lines or spaces on the staff between the tonic note and all intervals sharing that number - 2nd, be they called diminished, minor, major, perfect or augmented.

On either the treble or bass clef above, count the number of lines and spaces - starting from 1 at the tonic note (the lowest note), and ending on a given interval, and the last line or space having the interval you want will be 2nd line or space.

So this naming system forces all related 2nd intervals to share the same treble / bass clef line or space, as ultimately they are all 2nds, but each interval having different interval quality names (major, minor, diminished etc).

However, this explanation does not hold for intervals that are measured starting from double sharps or flats, but is useful in other cases.

 Bass Clef: Midi MP3 Treble Clef: Midi MP3

### 6. A-double-flat 2nd inverted intervals

This step explains how to invert note intervals, then identifies the A-double-flat 2nd inverted note intervals shown in previous steps.

#### Note interval inversion

An inverted interval is just an interval that is turned upside down.

For example, in the steps above, one of the intervals we measured was a major 2nd above Abb, which is note Bbb.

In contrast, an inverted interval specifies the distance from Bbb to Abb - ie. note Abb is above note Bbb.

A set of fixed rules exist to help us calculate the new quality name and interval number:

#### Note interval quality inversion rules

> A major interval always inverts to a minor interval.

> A minor interval always inverts to a major interval.

> A perfect interval always inverts to a perfect interval - no change.

> A diminished interval always inverts to a augmented interval.

> An augmented interval always inverts to a diminished interval.

#### Note interval number inversion rules

Simply subtract the original interval number from 9, resulting in the inverted interval number.

#### A-double-flat 2nd interval inversions

Taking the above rules into account, below is the table shown in the previous step, but with an extra column at the end for the link to the inverted interval quality in each case.

A-double-flat 2nd inverted intervals
ShortMediumLongNote nameLink to inverted
interval
d2Abbdim2A-double-flat diminished 2ndBbbbb<-(!?)->  G-aug-7th
m2Abbmin2A-double-flat minor 2ndBbbb<-(!?)->  Ab-maj-7th
M2Abbmaj2A-double-flat major 2ndBbb<-(!?)->  A-min-7th
A2Abbaug2A-double-flat augmented 2ndBb<-(!?)->  Bb-dim-7th

One or more of the inverted intervals in the last column are marked <-(!?)->, meaning that the note from which the inverted interval would be measured is not common, and so an enharmonic (simpler) note is given.

The note pitches, interval number and quality do not change.