When we say pentachords we mean the pentachords as defined in post 225 (see also post 203 and 214 and 262).
The pentachord is not considered restricted in a single octave, therefore power-5 chords, waves are created as defined in the post 217.
For such rotational improvisations, string instruments tuned by octaves (strings at the same note but different octave see post 210 about octave tuning) are very convenient.
In addition for every such chord or chord transition we may have a morphological rhythmic pattern E.g. A1 B1 B2 B3 or A1 A2 A3 B1 , which shows how the melodic theme is repeated or varied by translation inversion and rotation-mutation.
We refresh here the enumeration of all 20 pentachords with their chords
The pentachord is not considered restricted in a single octave, therefore power-5 chords, waves are created as defined in the post 217.
Although we mention here 3 chords (major minor or diminished mainly) as underlying chords, they can be substituted with a single power-5 chord that power-5 chord which is defined by the end-notes of the pentachord. In addition, if we apply the 3 chords mentioned as underlying chords, it need not be the chords contained in the pentachord, but the chords 1-4-5 of the diatonic scale that the (diatonic family) pentachord belongs. For the case of pentachord of the chromatic or enharmonian family more discussion is required.
If the improvisational rotation in the pentachord
starts from the lower end and ends in it it is called UPPER CYCLIC (NEUTRAL/SAD)
If it starts from the upper end and ends in it it is called LOWER CYCLIC (NEUTRAL HAPPY)
If it starts from the upper end and ends at the lower end it is called DESCENDING (SAD)
If it starts from the lower end and ends at the upper end it is called ASCENDING (HAPPY)
If the improvisational rotation in the pentachord
starts from the lower end and ends in it it is called UPPER CYCLIC (NEUTRAL/SAD)
If it starts from the upper end and ends in it it is called LOWER CYCLIC (NEUTRAL HAPPY)
If it starts from the upper end and ends at the lower end it is called DESCENDING (SAD)
If it starts from the lower end and ends at the upper end it is called ASCENDING (HAPPY)
For such rotational improvisations, string instruments tuned by octaves (strings at the same note but different octave see post 210 about octave tuning) are very convenient.
In addition for every such chord or chord transition we may have a morphological rhythmic pattern E.g. A1 B1 B2 B3 or A1 A2 A3 B1 , which shows how the melodic theme is repeated or varied by translation inversion and rotation-mutation.
We refresh here the enumeration of all 20 pentachords with their chords
ALL 20 PENTACHORDS (also called vector intervals of 5ths)
All pentachords contain a single power-5 chord that power-5 chord which is defined by the end-notes of the pentachord.
DIATONIC FAMILY
(containing only 2, and 1)
2-2-2-1 Major Lydian Contains a major chord (known also as Natzi/Zaouil)
2-2-1-2 Major Ionian/Mixolydian Contains a major chord.(known also as Rast/Mahour)
2-1-2-2 Minor Dorian Contains a minor chord (known also as Bousselik/Nichavent)
1-2-2-2 Minor Frygian/Aeolian Contains a minor chord (known also as Qourdi)
CHROMATIC FAMILY
(containing 3 )
1-1-3-2
1-1-2-3
1-3-2-1 Contains a major chord and a diminished chord
1-2-3-1 Contains a minor chord and a diminished chord
1-2-1-3 Contains a minor chord and a diminished chord
1-3-1-2 Contains a major chord and a diminished chord (known also as Hijaz)
3-2-1-1 Contains a diminished chord
2-3-1-1
3-1-2-1 Contains a major chord and a diminished chord
2-1-3-1 Contains a minor chord and a diminished chord (known also as Nevesser/Nikriz)
3-1-1-2 Contains a major chord (known also as Saz-kar)
2-1-1-3 Contains a minor chord (known also as Samba)
ENHARMONIAN FAMILY
(containing 4 )
1-1-1-4 Contains a minor chord
1-1-4-1
1-4-1-1
4-1-1-1 Contains a major chord
