Sheet 9 12

Sheet 9

LINEAR MODES

Sheet 9

OPEN MODES

Five-octave Modes

a)

& ?

Basic Mode of Fourth (a); module: perfect fourth; all modules are identical; Pattern: 32 Any of 5-tone segments of the Mode is a pentatonic scale! In this basic shape it can primarily be used for making chords or pentatonic-like melody; Look in After the Scent of the Blossomed Cherry, from p. 15 onward - Shiraame ni

w

Ï 2w

3

3

bÏ 2w

3

bw bÏ 2 w 3bÏ 2

bw#w Ï #w b Ï b w bÏ

Ï #w

Ï w .

Ï ÒÓ . w

Ï w

Ï w .

etc.

Ï ÒÓ D w Ï Ï w Ï # w Ï Ï Ï #w # . w #Ï Ï #Ï . . # w Ï . .D bw#w #Ï b Ï & D Ï b w D bÏ D D b) Ï b w bÏ D w Ï ? D . Ï w Ï b Ï 2 w 2 Ï b1 Ï 2 2 1 2 . etc. D w Ï 2 2 1 Homogenious Mode of Fourth made up of Dorian tetrachords only (b)

2

1

Ph Ó Ï Ò Ï w Ï w bÏ Ï w Ï Ï Ï # w w Ï .. . .Ph . bw#w Ï Ï #w Ï Ph & bÏ Ï Ph b b w bÏ Ph Ph Ï b Ph b w bÏ Ï b Ph ? w .Ï Ï w b Ï b Ï 2 w b1 Ï 2b Ï 2 1 2Ph 2 1. etc. 2 wb 2 1 1

d)

D

D

Homogenious Mode of Fourth made up of Phrygean tetrachords only (c)

c)

D

& ?

2

Ph

Ïn Ï w bÏ nÏ1bÏ 2bwb1. .etc. Ï b Ï nÏ b w .. bÏ 2 1 1 w b Ïn Ï Ï 2w b1Ï1nÏ1 2 1 1 1 1 1 1

Ph

w Ï#Ï Ï ÒwÓ Ï#Ï Ï w b ÏnÏ Ï w Ï Ï #Ï # w Ï #w Ï#Ï . ... . .. bw bÏnÏ bÏ bw#w Ï#Ï Ï

Homogenious Mode of Fourth made up of pentachords (1112) throughout the mode (d)

bÏ

Ph

2

LINEAR MODES

Sheet 10

Sheet 10

OPEN MODES The Mode of Fourth (cont.)

e)

& ?

Ï ÒÓ D w Ï Ï w Ï w Ï . . w #Ï Ï .D #w Ï Ï #w # Ï . Ï . b w Ï n bÏ #w Ï bÏ bw Ph

The Mode of Fourth; one of possible combinations of Dorian and Phrygean tetrachords in random order Ph D

Ph bÏ 2bw Ï Ï w bÏ . bÏ 1 . Ï w bÏ b Ï 2 w 1 2 2 2 Ï D w 2 1 2 D

2

1

D

D

etc.

Ph

The Mode of Fourth organized symmetrically - 24+1+24 tones; (acctually it might belong to the Sheet 12) homogeneus "wings"; left "wing" has pentachords (1211), while right "wing" has pentachors (1121); The central tone G# is tonic; it is surrounded by two semitones from each side (leading tones), what gives it a uniqe position and meaning in the Mode. Also it is the axis of symmetry

f)

& ?

&

bÏ n Ïbw n Ï #Ï.etc. Ï b w Ï Ï b n 1 1 1 2 1 1 w bÏ bÏn Ï w bÏ

. w b Ï2 Ï#Ï1 1

1

ÒÓ Ï b Ï b Ï ÏnÏ #Ï w Ïnw b b b Ï Ïnw b Ï bÏ Ï # w . Ï . . . . nw . .. . bÏ Ï#w Ï bÏ Ï Ï # w Ï # Ï Ï#w

1 2 1 1

Tonic

1 2 1

If we take only the central area - two modules on each side - we get a very interesting mode, with a range of less than two octaves and 17 tones [4+4 - 1 - 4+4]

Just for fun, we can take apart its constitutive parts - in fact: the root modes of fourth (I & II). I It should be noted that the mode I is on black keys while the mode II on the white ones. Look at Jeu a quatre, II/b from p.10-15

II

&

& &

#w #w

1

. #w Ï 2

. Ï

1

1

Ï #w

1

Ï #w 2

1

Ï #w

2

1

n Ï 1bw

2

Ï bw 1

Ï

Ï

Ï

Ï

bw

bw

bw

bw

#w

#w

#w Ï

1

Ï bw

1

1

#w

Ï bw

1

Ï

Ï

?

3

LINEAR MODES

Sheet 11

Sheet 11

OPEN MODES

The Mode of Fifth (7-octave) This mode is called The Mode of Fifth, since it has the module of perfect fifth; pattern (a - 25) or (b - 52). In its root shape it is mostly used to make harmonic ground or a certain type of melody - look at Jeu a quatre, p. 25 Though it is possible, there isn't much sence to fill its modules in with smaller intervals (as it was done with the Mode of Fourth).

a)

& ?

w Ô Ò

b)

2

. w Ï 5

2

Ï w 5

2

.Ï w 5

2

Ï w 5

#Ï w etc.

& ?

w Ô Ò

5

Ï w 2

5

Ï

2

w

5

Possible harmonic progression:

4 &4 ?4 4

úúúú ú

úúú úú

# úú úúú

Ï w 2

5

#ú ###úúú

Ï w 2

Ï w

#Ï .

#w

Ï #w

#Ï #w

Ï #w

#Ï #w

#Ï #w

#Ï # w .

#Ï # w .

etc.

#ú ### úúú

###úúúú

#úúú ú

úúúú ú

##úúú ú

ÒÓ # Ï bw Ï w . #w . .

ÒÓ bÏ w #Ï # wbw . .

Ï w .

Ï w .

4 4 4 4

4

Sheet 12

CENTRALLY-ORIENTED MODES

Sheet 12

SYMMETRICAL MODES Gravitationonal Mode

Symmetrical Gravitational Mode with the unique ton G# (tonic). 18 +1 +18 = 37 tones All modules contain five tones (pentachords); they gradually expand their range (dim. 4, perfect 4, aug. 4, perf. 5, min. 6) looking from the center - simmetrically - towards both ends (up and down). Tone G# is the tonic with two leading tones from both sides; it is also the axis of symmetry. Look at Jeu a quatre, p.p. 23, 24 and elsewhere

& ?

ÒÓ w Ï Ï # w bÏ . . Ï w Ï Ï perf. 4 # #Ï Ï Ï b w 2 2 bw Ï #Ï Ï . 1 1 2. 3 2 1 2 1 Ï 1# Ï 1 Ï 2 #w Ï #Ý Ï #w 1 1 1 1 min. 6 perf. 4 1 1 1

perf. 5 1 2 1

3 #Ï w 2Ï b1Ï 1n Ï 2# w b Ï n Ï w w 3 Ï 2 Ï 1b Ï 2 augm. 4 min. 6

extreme lower section

middle lower section

1

perf. 5 2 1 3

augm. 4

dim. 4 axis of symmetry

extreme upper section

middle upper section

central section Compare with the central section of the Mode (f) on Sheet 10

"Harmonization" of the mode. All tones (in order) are in outer voices. Chords are made by using every other tone of the mode.

ÒÏÓ Ï ÏÏ #Ï ÏÏ #Ï Ï n Ï # Ï b Ï Ï & #Ï nÏÏ #bÏÏÏÏ #bnÏÏÏÏÏ b# nÏÏÏÏ #Ï Ï # Ï ? bÏÏÏÏ #bnÏÏÏÏ #bÏnÏÏÏÏ #bnÏÏÏÏ # bÏnÏÏÏÏ ÏÏ b ÏÏ Ï bÏ

bÏ nbnÏÏÏÏÏ #b #ÏÏÏÏÏ nnbÏÏÏÏÏ #b #ÏÏÏÏ nnÏÏÏÏ #b #ÏÏÏ bÏ Ï bÏ Ï bÏ Ï #Ï # Ï nb#nÏÏÏÏÏÏ ## bÏnÏÏÏÏ nn#ÏÏÏÏÏ ##b ÏÏÏÏ & Ï ÏÏÏÏ #b# ÏÏÏÏ

nnÏÏÏÏ #bÏbÏÏ Ï #Ï nn ÏÏÏ ## ÏÏ

nÏÏÏ

bbÏÏ

ÏÏ

bÏ

Ï

#w

nÏÏÏ ##ÏÏ

ÏÏ

#Ï

Ï

#w