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8/14/2019 Sheet 1 8
1/8
MEDIAEVAL TRETACHORDS
&
Sheet 1
2
Lydian L
2
2
Mixolydian M
2
2
1
2
Dorian D
1
2
Phrygean P
1
2
2
Sheet 1
&Lydian mode
L
1
M
. Hypolydian mode
M
L
Characteristic interval
Lyd. 4
& .Ionian mode
M
2
M . .Hypoionian mode
M
. . M
Characteristic interval
None
&Mixolydian mode
M
2
D
Hypomixolydian mode
D
M
Characteristic interval
Mixolyd. 7
&Dorian mode
D
2
D
. .Hypodorian mode
D
. D
Characteristic interval
Dorian 6
& .
Aeolian mode
.
D .
2
Ph
Hypoionian mode
Ph
D
Characteristic interval
None
&Phrygean mode
Ph
2
Ph
. .Hypophrygean mode
Ph
Ph
Characteristic interval
Phrygean 2
& .Locrian mode
.Ph
1
L
Hypolocrian mode
L
Ph Characteristic interval . None
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8/14/2019 Sheet 1 8
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MESSIAEN'S MODES
&
Sheet 2
1st. Mode (6 tones); pattern: 2-2-2-2-2-2
.
###
b
1 possible transposition
b b
Sheet 2
&2nd Mode (8 tones); pattern: 12-12-12-12
.bb n# b # . 2 possible transpositions
bbn# bbbn
& .3rd Mode (9 tones); pattern: 211-211-211
bn#bbn# .#3 possible transpositions
bn# betc.... b#etc....
& .4th Mode (8 tones); pattern: 1131-1131
bn#bn # .5 possible transpositions
##etc.... b etc.... #etc.... betc.... # ...etc.
&5th Mode (6 tones); pattern: 141-141
. b# # .5 possible transpositions
# b #b etc.... ##etc.... etc....bb
&.6th Mode (8 tones); pattern: 2211-2211
###bb5 possible transpositions
bnetc.... #etc.... b etc.... ##etc.... etc....
&.7th Mode (10 tones); pattern: 11121-11121
# .b#bn# .5 possible transpositions
## etc.... # etc....# etc.... betc.... #
etc....
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PENTATONIC SCALE
&
Sheet 3
2
3
Module of perfect 4th; pattern: 23. The Mode is made of two
moduls tied on sinaphe.Between the second module and next (octave)
transposition is a whole-tone diazeuxis
2 3
the whole-tonediazeuxis
2
3
2 .3
.
Sheet 3
&some typical chords of pentatonic mode
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ANTIQUE MAJOR SCALE
& . 2 .Mixolydian mode
M
2 . 1 .2 M
2 1 2 M
2 1bAeolian mode2
M
2
1
b2
M
2
1
b .
UNUSUAL COMBINATIONSof mediaeval tetrachords
&This tone row can be found in melodic g-minor,
but differently treated. Here the tonic is A andE and F# are
stable and quite normal.
.1b"Phrigo-dorian" mode
.2
.2
2
2#
1
2
2
The 2nd Messiaen's mode; pattern: 212-1-212-1
Two dorian (or minor) tetrachords with a semitonediazeuxis - in
fact make the 2nd Messiaen's mode!
1
2
1#
2#
1
2#
1
&The same tone row as upper "Phrigo-dorian" mode, butwith
different tonic - E not A
"Dori-lydian" mode; pattern: 212-1-222
2# 1 2 1b 2 2 2
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ONE-OCTAVE MODES
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Sheet 4
(Re-shaped 3rd Messiaen's Mode)One-octave mode of 9 tones;
module - maj 3; three different tetrachords: 211-121-112The mode is
symetrical in relation to non-existent tone f#;or if it is expanded
to two octaves, the symetry exists in relation to c2
. 2 1#1The axis of symmetrywithin an octave
1 2 1b1n
The axis of symmetrywithin two octaves
1b
LINEAR MODES
2 2 1#1 1 21b .1n .
1b .2 .
Sheet 4
&
"Harmozation" of the mode; in outer voices are both "wings" of
the mode.Chords are made by using every other tone of the mode.
bbb nn bb n b n b w& bbb nn bb nn bb n bb n b w
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8/14/2019 Sheet 1 8
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SEMI-CLOSED MODESTwo-octaves Modes
&
Sheet 5
Two-octaves mode; 12 diferent tones; modul - min. 6Three
identical pentachords (on sinaphe); pattern: 3212The Mode is
symmetrical towards the axis situated between a and bTon a as the
central tone of the Mode can be regarded as tonic (ex. a, b, c)
but it is more interesting to see tones a and b as double
tonic!ali je mnogo zanimljivije videti tonove a i b kao dvosrtruku
toniku! (ex. d)
# . 3 . 2 # . 1 2
LINEAR MODES
3b
2
"double tonic"
Axis of symmetry
1b2
b
3b2 1b2b .
&a) Multy-voice progression, from 1 to 7 tones; center
(tonic): a
b bb #
bbb
#b#
bbb
# bb b w
&b)
Four-voice progression; center (tonic): a
bb # bb b## bb # bb wwww
&c)
1
#Another harmonic progression - from 1 to 6 different tones;
center (tonic): a
2
#3
###4
##5
nb bbb bb 2
b w
? # # ### # ## &6
nn5
#4
3
1
w
&d)
bHarmonic progression - from 2 to 8 (10) different tones;
"double tonic": a-b
bb bbb b bbb bbb ### bbb bbb b bbb bb wb
&2
2
4
4
6
#6
6
##8
# (10)
###8
#6
##6
6
#4
4
2
2
w
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SEMI-CLOSED MODESTwo-octave Modes (3)
Sheet 7
B
The same mode as the previous one but divided into six moduls of
maj. 3
There are three different tretrachords: 211 - 121 - 112 (each
shows up twice)All of them are symetrically situated towards
central tone (tonic) - g#
Look at the sheet 4: one-octave mode and its "two-octave
variant"In fact, this is the same mode, transposed from c to g#
Two-octave mode; 19 tones; modul - min. 6; lower part is
identical as in mode A (sheet 6)The mode is symetrical towards the
central tone (tonic) g #. There are leading tones from both
sides.There are 3 different heptachords on sinaphe; The first and
the third are mutually symetrical,while the second one is
symetrical in itself; pattern: 211121 - 211112 - 121112
/ 2# . 1 .
1
.1# .2#1
LINEAR MODES
2#
1
Axis of symetry
1#
1
1b
21 #2#1 1 1b
Sheet 7
2b /Skippedtones
.
B1
/ 2# . 1 . 1 . 1# .2#1
2# 1Axis of symetry 1#1
1
b2
1#2#1 1
1b2b /Skippedtones
.
Two-octave Modes - "unregular"
A2 /
Modul of perfect 5. Three different hexachords with one
semitone-diazeuxis and one wholetone.Pattern: 21112 - 1 - 21211 - 2
- 11212
2# . 1 . 1 .1# /2#12
#1
2
1
b1
n2#1 1b 2 1b2b
/ Skippedtones
b .
&.
N.B.! Lower, hexachordal "wing" combines Phrigean mode
and whole-tone scale, while in the upper pentachordal "wing"a
segment of Messiaen's Second mode can be seen as well asmixolydian
(major) tetrachord. Only they are differently marked.
Example of "unregular" and non-periodic mode; from "After the
Scent of the Blossomed Cherry" (five haiku)
. # . n .b .
2
b .bb 2
# b Naturally, this example, as many others,can be understood as
polymodality, if wetake every modul as a particular mode.In either
way the register change should
be noted
. b . b . .
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SEMI-CLOSED MODESTwo-octave Modes (3)
Sheet 7
B
The same mode as the previous one but divided into six modules
of maj. 3There are three different tretrachords: 211 - 121 - 112
(each shows up twice)All of them are symetrically situated towards
central tone (tonic) - g#
Look at the sheet 4: one-octave mode and its "two-octave
variant"In fact, this is the same mode, transposed from c to g#
Two-octave mode; 19 tones; module - min. 6; lower part is
identical as in mode A (sheet 6)The mode is symetrical towards the
central tone (tonic) g #. There are leading tones from both
sides.There are three different heptachords on sinaphe; The first
and the third are mutually symetrical,while the second one is
symetrical in itself; pattern: 211121 - 211112 - 121112
In this case and some other cases later, ton G# is taken as the
axis of symmetry since piano keyboardis symmetrical related to
it
/2
# .1
.1
.1# .2#1
LINEAR MODES
2#
1
Axis of symmetry
1#
1
1b
21 #2#1 1 1b
Sheet 7
2b /Skippedtones
.
B1 / 2# . 1 .
1 . 1# .2#1 2# 1
Axis of symetry
1#1 1b2 1 #2#1 1
1
b2
b /
Skippedtones
.
Two-octave Modes - "irregular"
A2 /
Module of perfect 5. Three different hexachords with one
semitone-diazeuxis and one wholetone.Pattern: 21112 - 1 - 21211 - 2
- 11212
2# .
1 .
1
.1# /2#1
2#1 2 1 b1n2#1 1b 2 1b2b /
Skippedtones
b .
&.
N.B.! Lower, hexachordal "wing" combines Phrigean mode
and whole-tone scale, while in the upper pentachordal "wing"a
segment of Messiaen's Second mode can be seen as well asmixolydian
(major) tetrachord. Only they are differently marked.
Example of "irregular" and non-periodic mode; from "After the
Scent of the Blossomed Cherry" - Taoraruru
. # . n .b .
2
b .bb 2
# b Naturally, this example, as many others,can be understood as
polymodality, if wetake every module as a particular mode.In either
way the register change should
be noted
. b . b . .?
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SEMI-CLOSED MODESThree-octave Modes
&
Sheet 8
Lower Tritonante
The three-octave mode (21 tones); four identical modules of
maj.6; Pattern: 32112
Lower Mediante
LINEAR MODES
Tonic
/
b# bn#
Sheet 8
?###3
2
1
1#
2## # b
Tonic
/Upper Mediante
Upper Tritonante
&4-tone chords made up of every other tone of the mode
wb #b n #b wwwn? wwww### ## ##
b##n ## wwwb## # b# n w
&wwwn # bn #n #bwwww #b n #b#
nn# wwww###
? Note! The chords on Tonic, both Mediantes and Tritonantes have
identical "consonant", fourth-fifth structure (5-7-12)
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