Music Theory
Choosing tempo when Changing Time Signature
The operation of choosing a new tempo when the time signature is changed from simple to compound time appears straightforward, but it is easy to get confused. For example, the forum on this link tries to thrash out this issue (with various solutions - some right, some wrong).
When changing the time signature the tempo can be left as-is. The click will change to be quavers sounding at twice the rate of the click on the 4/4 section.
Most likely, the tempo will need adjusted to sound right musically the 6/8 section.
Here is an example of how to change from 4/4 to 6/8:
In 4/4 at 120 bpm each note duration is 0.5s, so there is 2s per bar.
At the change to 6/8 the click in a sequencer changes to quavers, but the beat is still referenced to crotchets.
Therefore each quaver has a duration of 0.25s, so the total bar time is 1.5s.
To match the tempo of the 6/8 section to that of the 4/4 it is therefore necessary to multiply the tempo by 3/4 (a fraction, not a time sig.)
So, 0.75(120) = 90 bpm.
However...
6/8 time breaks into a count of 1,2 (ie 2 dotted crotchets per bar), and if we want this count to be at the same tempo as the 4/4 section the 6/8 section must be speed-up.
To do this: multiply the 4/4 tempo by 1.5
eg 1.5(120) = 180 bpm.
To go from 6/8 to 4/4 multiply the tempo by 2/3.
Scales
Scale Pattern
1. MAJOR T T S T T T S
(IONIAN)
2. NATURAL MINOR
(AEOLIAN) T S T T S T T
3. MELODIC MINOR (up) T S T T T T S
MELODIC MINOR (down) T T S T T S T
(Same as Aeolian)
4. HARMONIC MINOR TSTTSm3S
5. WHOLE TONE TTTTTT
6. CHROMATIC SSSSSSSSSSSS
7. PENTATONIC (Major) T T m3 T m3
8. BLUES m3 T S S m3 T
1. MAJOR T T S T T T S
(IONIAN)
2. NATURAL MINOR
(AEOLIAN) T S T T S T T
3. MELODIC MINOR (up) T S T T T T S
MELODIC MINOR (down) T T S T T S T
(Same as Aeolian)
4. HARMONIC MINOR TSTTSm3S
5. WHOLE TONE TTTTTT
6. CHROMATIC SSSSSSSSSSSS
7. PENTATONIC (Major) T T m3 T m3
8. BLUES m3 T S S m3 T
Intervals
The 12 possible steps (semitones) of a scale can be related to the tonic as intervals.
They are called (from bottom to top):
unison Tonic
minor 2nd
Major 2nd Supertonic
minor 3rd
Major 3rd Mediant
Perfect 4th Subdominant
Tritone (tt) : this equals an augmented 4th
or a diminished 5th
Perfect 5th Dominant
minor 6th
Major 6th Submediant
minor 7th
Major 7th Leading Note
Perfect 8th (octave)
They are called (from bottom to top):
unison Tonic
minor 2nd
Major 2nd Supertonic
minor 3rd
Major 3rd Mediant
Perfect 4th Subdominant
Tritone (tt) : this equals an augmented 4th
or a diminished 5th
Perfect 5th Dominant
minor 6th
Major 6th Submediant
minor 7th
Major 7th Leading Note
Perfect 8th (octave)
Melodic Motifs
| motifs.pdf |
Chords
The patterns for chords in root position is as follows (from bottom to top):
Triads:
Major - M3 , m3
Minor - m3 , M3
Augmented - M3 , M3
Diminished - m3 , m3
Chords of the 7th (basic set):
Major 7th - M3 , m3 , M3
Minor 7th - m3 , M3 , m3
(Dominant) 7th - M3 , m3 , m3
Diminished 7th - m3 , m3, m3
The rest of the 7ths family
Half Diminished 7th (m7th b5th ) - m3 , m3 , M3
Major minor 7th - m3 , M3 , M3
Augmented 7th - M3 , M3 , m3
The combination M3 , M3 , M3 is not a 7th chord (it is the Augmented triad).
Major minor 7th - m3 , M3 , M3
Augmented 7th - M3 , M3 , m3
The combination M3 , M3 , M3 is not a 7th chord (it is the Augmented triad).
Inversions
Triads have 1st and 2nd inversions eg C Major inversions are EGC, and GCE respectively.
7th chords also have a 3rd inversion eg CM7 inversions would be EGBC (1st ) , GBCE (2nd ) , and BCEG (3rd ).
Open chords: these are where the sequence of notes is broken eg CM7 sounded as CEBG. Commonly used on guitar due to fingering limitations, they add interest to the chord’s tone.
7th chords also have a 3rd inversion eg CM7 inversions would be EGBC (1st ) , GBCE (2nd ) , and BCEG (3rd ).
Open chords: these are where the sequence of notes is broken eg CM7 sounded as CEBG. Commonly used on guitar due to fingering limitations, they add interest to the chord’s tone.
6th Chords
Major 6th - A Major triad with the submediant added
Minor 6th - A minor triad with the submediant added
Minor 6th - A minor triad with the submediant added
Altered Chords
Where additional note(s) are added to a chord:
Suspended Chord (*sus) - The mediant is replaced by the subdominant in a Major triad. It usually resolves.
Added 2nd - adding the supertonic to a Major triad.
Six Nine - a major 6th plus the 9th note. The 5th is usually omitted.
Altered bass note - eg C/D
Suspended Chord (*sus) - The mediant is replaced by the subdominant in a Major triad. It usually resolves.
Added 2nd - adding the supertonic to a Major triad.
Six Nine - a major 6th plus the 9th note. The 5th is usually omitted.
Altered bass note - eg C/D
Analysis of Time Signature Choice
| analysis_of_time_signature_choice.pdf |
Chords II - Jazz Chords
Much of the flavour of Jazz is to do with the chords used. Some common ones are:
Major 9th - M3 , m3 , M3 , m3
Minor 9th - m3 , M3 , m3 , M3
(Dominant) 9th - M3 , m3 , m3 , M3
Minor 11th - m3 , M3 , m3 , M3 , m3
(Dominant) 11th - M3 , [m3] , m3 , M3 , m3
The mediant is omitted because it clashes with the 11th note.
(Dominant) 13th sus - M3 , [m3] , (m3) , M3 , m3 , M3
The mediant (and sometimes the dominant) are omitted.
(Dominant) 13th - M3 , [m3] , (m3) , M3 , M2 , P4
An altered chord (to make it more musically useful).
(Dominant) 13th b9th - M3 , [m3] , m3 , m3 , M3 , M3
By the time we get to here and consider altered chords and inversions you can see that Jazz has a vast collection of chords. 15th chords, anyone? they don’t really exist because we have worked our way back to the tonic (up two octaves).
Avant Garde
Poly chords - where two chords (usually triads) are played simultaneously eg C and F# would give the notes CEGF#A#C#, which don’t fit any stack of 3rds.
Clusters - more of a dischord, really. It is a group of notes close together eg CEFF#G. or GBCDE (CM9).
Chameleons (my name)
Many inversions morph into another chord (usually an altered chord). A clear example however is the 1st inversion of Am7, which is exactly the same chord as C6. The ambiguity is corrected by also stating the tonic as a bass note.