Working out the four Japanese modes, they each start with an interval:
- Yoh is an ascending major 2nd interval.
- In is a descending minor 2nd interval.
- Ritsu/Ryo is a descending major 2nd interval.
- and Ryukyu is an ascending minor 2nd.
With a stopping note of A, we get:
X:1
T:Four intervals
L:1/4
V:Y clef=treble name="Yoh"
GA
V:I clef=treble name="In"
_BA
V:RR clef=treble name="Ritsu/Ryo"
BA
V:R clef=treble name="Ryukyu"
^GA
Notes are added at the beginning to build a perfect 4th, we then have:
X:1
T:Four tetrachords
L:1/4
V:Y clef=treble name="Yoh"
EGA
V:I clef=treble name="In"
d_BA
V:RR clef=treble name="Ritsu/Ryo"
dBA
V:R clef=treble name="Ryukyu"
E^GA
Since the perfect 4th interval is counted from the bottom note, we add an E for the ascending intervals, and a D for the descending intervals.
Next, we want to build a three-note “tetrachord” backwards from A, using that as the starting note instead. So get this:
X:1
T:Four modes
L:1/4
V:Y clef=treble name="Yoh"
EGA | Acd
V:I clef=treble name="In"
d_BA | AFE
V:RR clef=treble name="Ritsu/Ryo"
dBA | A^FE
V:R clef=treble name="Ryukyu"
E^GA | Ac^d
We get 2 new stopping notes, D for ascending, and E for descending (the opposite of the starting notes for the first chord).
If we “jump” these chords to the beginning, shifting them an octave, we get the pentatonic scales:
X:1
T:Four scales
L:1/4
V:Y clef=treble name="Yoh"
A,CD EGA
V:I clef=treble name="In"
afe d_BA
V:RR clef=treble name="Ritsu/Ryo"
a^fe dBA
V:R clef=treble name="Ryukyu"
A,C^,D E^GA