Intro
The 4 important subgroups in music are whole tone, diminished, augmented, and tritones.
This of course works best with horizontal instruments like the piano. As we discussed in the guitar theory notes, guitar is both vertical and horizontal which makes it hard to directly apply the following tricks.
We will modify these tricks for guitar and redefine them in the guitar theory notes.
Deriving The 4 Subgroups: Whole, Diminished, Augmented, Tritones
Original Reference:
Here is the diagram that derives the 3 subgroups, diminished, augmented, tritone.
This like the guitar alphabet should be internalized and memorized by heart.
Chromatic
C Db D Eb E F Gb G Ab A Bb B -> 12/12 = 1 Chromatic Scale
Whole Tone
C D E Gb Ab Bb Db Eb F G A B -> 12/6 = 2 Whole Tone scales
Diminished
C Eb Gb A Db E G Bb D F Ab B -> 12/4 = 3 Diminished Chords
Augmented
C E Ab Db F A D Gb Bb Eb G B -> 12/3 = 4 Augmented Chords
Tritone
C Gb Db G D Ab Eb A E Bb F B -> 12/2 = 6 Tritones
Whole Tone: Riding And Surrounding Black Keys
Intro
The 2 whole tone scales are separated by a step. One starting on C, the other on C# or Db. From there, you follow this pattern.
Whole Tone
C D E Gb Ab Bb || Db Eb F G A B -> 12/6 = 2 Whole Tone scales
The 'Why' Of Whole Tone: Surrounding And Riding
The trick to remember, is you either surround the 2 pair of black keys, or you ride them, and for the 3 pairs of black keys you do the reverse.
(surround + ride)
C Group: C D E, Gb Ab Bb
The C, D, E, surround the group of 2 black keys.
The Gb, Ab, B, ride the group of 3 black keys.
(ride + surround)
Db Group: Db Eb F G A B
The Db, Eb, ride the group of 2 black keys
The F, G, A, B, surround the group of 3 black keys
Solfege Deriving The 2 Whole Tone Scales: 2 Groups In Major and Minor Do
Do Major
Whole Tone Group 1: Do Re Mi 4/5 5/6 6/7
--->
^ ^ ^
4 5 6 4 5 6
- - - Do Re Mi - - -
5 6 7 5 6 7
v v v
--->
Whole Tone Group 2: Fa Sol La Ti 1/2 2/3
--->
^ ^
1 2 1 2
- - Fa Sol La Ti - -
2 3 2 3
v v
--->
Do Minor
Whole Tone Group 1: Me Fa Sol 6/7 7/1 1/2
--->
^ ^ ^
6 7 1 6 7 1
- - - Me Fa Sol - - -
7 1 2 7 1 2
v v v
--->
Whole Tone Group 2: La Te Do Re 3/4 4/5
--->
^ ^
3 4 3 4
- - La Te Do Re - -
4 5 4 5
v v
--->
Diminished: 2 Couples + Modified 7th
Intro
The 3 diminished tone scales are separated by a step. One starting on C, the other on C# or Db, and the last one on D. From there you build minor 3rd triads until you arrive at the original note.
Diminished
C Eb Gb A || Db E G Bb || D F Ab B -> 12/4 = 3 Diminished Chords
The 'Why' Of Diminished: Couples
The trick to remember, is to remember the solfege modifications.
Start with: Do Re Mi Fa Sol La Ti Do.
2 of the pairs of these letters, Do Re, Re Mi, Mi Fa, etc. are a half step away from each other, while the other 5 are a whole step away from each other.
Specifically:
- 2 Pairs Half Step Away: (Mi <-> Fa), (Ti <-> Do)
- 5 Pairs Whole Step Away: (Do <-> Re), (Re <-> Mi), (Fa <-> Sol), (Sol <-> La), (La <-> Ti)
A cute analogy to remember, is that sometimes couples need time and space from each other. The couples of course being the group with pairs a half step away, Mi Fa, Ti Do.
If we apply the analogy of space away from each other we get:
Couple 1:
(Mi <-> Fa) => (Me <-> Fi)
Couple 2:
(Ti <-> Do) => (Te <-> Di)
These new groups actually make up 2 of our diminished scales:
Couple 1:
Do Mi Sol La -> Do Me Fi La
Couple 2:
Do Mi Sol La -> Di Mi Sol Te
Now for the third group, this one I haven't come up with a funny analogy, but its easier than the others because its based on the 7th degree which is just a diminished chord. To generate the diminished chord, you just add an extra note.
7th Degree Chord + Extra Note
Ti Re Fa. -> Ti Re Fa Le
This last one leads into the separate trick of generating these 3 chords on the fly and not relying entirely on the couple trick, which is more of a 'why' explanation as to why we can just make diminished chords and where they come from. Again, 2 of them come from the 2 half step groups, the 3rd one comes from the diminished chord prevalent in major scales, the 7th degree.
Solfege Deriving The 3 Diminished Scales: 3 Groups In Major and Minor Do
Do Major
Diminished Scale Group 1: La Do 2/3 4/5
Group 1:
--->
^ ^
2 4 2 4
- - La Do - -
3 5 3 5
v v
--->
Diminished Scale Group 2: Mi Sol 6/7 1/2
Group 2:
--->
^ ^
6 1 6 1
- - Mi Sol - -
7 2 7 2
v v
---> Diminished Scale Group 3: Ti Re Fa 5/6
Group 3:
--->
^
5 5
- Ti Re Fa -
6 6
v
---> Do Minor
Minor Version Group 1: Do Me 4/5 6/7
Minor Version Group 2: Sol Te 1/2 3/4
Minor Version Group 3: Re Fa Le 7/1
Augmented: 3 Modified Major Chords + Modified ii
Intro
Augmented Triads come from the 3 Major chords in a major key as well as the least modified diminished chord, Ti Re Fa Si/Le.
Augmented
C E Ab || Db F A || D Gb Bb || Eb G B -> 12/3 = 4 Augmented Chords
The 'Why' Of Augmented: 3 Modified Major Chords + Modified ii chord
Group 1: Major I
Do Mi Sol -> Do Mi Si
Group 2: Modified ii
Re Fa La -> Re Fi Li
Group 3: Major IV
Fa La Do -> Fa La Di
Group 4: Major V
Sol Ti Re -> Sol Ti Ri
And grouped by number of solfege modifications.
1 Note Modified:
Group 1: Major I
Do Mi Sol -> Do Mi Si
Group 3: Major IV
Fa La Do -> Fa La Di
Group 4: Major V
Sol Ti Re -> Sol Ti Ri
2 Note Modified:
Group 2: Modified ii
Re Fa La -> Re Fi Li
Solfege Deriving The 4 Augmented Scales
Do Major
Group 1: Do Mi 5/6
--->
^
5 5
- Do Mi -
6 6
v
--->Group 2: Re 4/5 6/7
--->
^ ^
4 6 4 6
- - Re - -
5 7 5 7
v v
--->Group 3: Fa La 1/2
--->
^
1 1
- Fa La -
2 2
v
--->Group 4: Sol Ti 2/3
--->
^
2 2
- Sol Ti -
3 3
v
--->Do Minor
Group 1: Mi Sol 7/1
--->
^
7 7
- Mi Sol -
1 1
v
--->Group 2: Fa 6/7 1/2
--->
^ ^
6 1 6 1
- - Fa - -
7 2 7 2
v v
--->Group 3: Le Do 3/4
--->
^
3 3
- Le Do -
4 4
v
--->Group 4: Te Re 4/5
--->
^
4 4
- Te Re -
5 5
v
--->Tritone: Fi/Se
Intro
Tritones is the group with the least funny story as there are only 2 notes per group.
Tritone
C Gb || Db G || D Ab || Eb A || E Bb || F B -> 12/2 = 6 TritonesThe 'Why' Of Tritones: Full Solfege, Halfsies, And The Lovers
The trick is to just remember that in jazz a popular transition is to do a Sol Do Sol, Fi Do Fi, Fa Do Fa, Mi Re Do. Sing it and you will probably recognize it.
This is all thanks to our friend the tritone, the note between the 4th and 5th degree of a major scale: Fi/Se.
Tritone memorization will force you to memorize the relative 4th and 5th scale degree for any key, and to get the tritone, just raise or lower the note, depending on whether you are singing the 4th or 5th.
Everybody Has A 5th Because Triads, Except The 7th
Full Solfege Modification: Do, Re, Mi, Sol, La
The easiest way to generate this on the fly, is to thing of the triad and go a 5th up, then a half step down.
Ex:
Do -> Sol -> Se
Re -> La -> Le
Mi -> The exception is the 7th degree, which just needs to go to its 5th
Ex:
Ti -> FaTritones From Halfsies: 1/2, 2/3, 4/5, 5/6, 6/7
The halfsies, or black keys in C major, are a the same but just in reverse.
Take the current halfsy, move it up half a step, then go down a fifth or up a 4th
Ex:
1/2 -> 2 -> 5
2/3 -> 3 -> 6
4/5 -> 5 -> 1
5/6 -> 6 -> 2
6/7 -> 7 -> 3Tritone Lovers
This is the exception pair, that is composed of 2 Full Solfege notes and no halfsies.
Fa -> Ti, Ti -> Fa
Doing Down
Going down is the same but just the steps in reverse.
Solfege Deriving The 6 Tritones: Group of 7 and 5
Do Major
Group 1: Do 4/5
Do -> 5 -> 4/5
or
4/5 -> 5 -> 1
Group 2: Re 5/6
Re -> 6 -> 5/6
or
5/6 -> 6 -> Re
Group 3: Mi 6/7
Mi -> 7 -> 6/7
or
6/7 -> 7 -> Mi
Group 4: Fa Ti
Fa -> Ti
or
Ti -> Fa
Group 5: 1/2 Sol
Sol -> 2 -> 1/2
or
1/2 -> 2 -> 5
Group 6: 2/3 La
La -> 3 -> 2/3
or
2/3 -> 3 -> La
Do Minor
Group 1: Me 6/7
Do -> 5 -> 4/5
or
4/5 -> 5 -> 1
Group 2: Fa 7/1
Re -> 6 -> 5/6
or
5/6 -> 6 -> Re
Group 3: Sol 1/2
Mi -> 7 -> 6/7
or
6/7 -> 7 -> Mi
Group 4: Le Re
Fa -> Ti
or
Ti -> Fa
Group 5: 3/4 Te
Sol -> 2 -> 1/2
or
1/2 -> 2 -> 5
Group 6: 4/5 Do
La -> 3 -> 2/3
or
2/3 -> 3 -> La