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Showing posts with label 95. SYMMETRIC SCALES OF MESSIAEN AND MORE. Show all posts
Showing posts with label 95. SYMMETRIC SCALES OF MESSIAEN AND MORE. Show all posts

Sunday, June 3, 2018

95. SYMMETRIC SCALES OF MESSIAEN AND MORE

Although we have  classified in many ways many known and unknown scales, we mention here , the symmetric scales , without constraint if they are 4 notes 5 notes, 6 notes , 7 notes , 8 notes etc

As a start some already known symmetric scales, on the whole tone pan-flute. The musical composer Oliver Messiaen has enumerated the first 7 of them.

https://www.youtube.com/watch?v=VRO14-jiE0Y&t=82s

1) 2-2-2-2-2-2 (all chords augmented)
2) 2-1-2-1-2-1-2-1 (diminished scale ,all chords diminsihed,nice sounding to make a 8-notes  flute for it))
3) 2-1-1-2-1-1-2-1-1
4) 1-1-3-1-1-1-3-1 (nice sounding to make a 8-notes  flute for it)
5) 1-4-1-1-4-1 (nice sounding to makea  flute for it)
6) 2-2-1-1-2-2-1-1
7) 1-1-1-2-1-1-1-1-2-1
8) 3-1-3-1-3-1 (augmented scale. nice sounding to make a 6-notes  flute for it .E.G. D F F# A Bb C# D, which is a subscale of the 8-notes Samba scale D E F F# A Bb C C# D)
9) 5-1-5-1
10) 3-2-1-3-2-1 (nice sounding to make a 6-notes  flute for it)
11) 3-1-2-3-1-2 (nice sounding to make a 6-notes  flute for it)
12) 1-1-1-1-1-1-1-1-1-1-1-1

Some more are

13) 4-2-4-2
14) 3-3-3-3
16) 4-4-4


Semi-symmetric may be considered the next
The pentatonic may count also as one
1) 2-3-2-3-2
Also alternating 2nd 3rds

2) 2-3-2-4-1 or
3) 4-1-4-1-2 or
4) 1-4-2-3-2
etc



2-OCTAVES HARMONIC SCALES (NON-CHROMATIC) WITH MANY CHORDS

Notice that if we allow for range larger than an octave then as in the post 79, there are more symmetric scale e.g.

1) the -4-3-4-3-3-4-3-  which is the melodic minor scale when reduced to a single octave 
and other are the next


2) 3-3-4-4-3-3-4=24 This scale has obviously successive diminished minor , major and augmented chords.

3) 3-3-3-4-4-4-3=24

4) 3-5-3-5-3-5=24

5) 3-3-3-5-5-5=24

6) 3-4-3-4-7-7=24

7) 3-7-3-7-4=24

8) 3-3-7-7-4=24

9) 4-5-4-5-4-2=24

10) 4-5-4-5-4-2=24

11) 4-4-5-5-4-2=24

12) 4-4-4-5-5-5-2=24

13) 4-4-4-5-2-5=24

14) 5-7-5-7=24

15) 3-4-5-3-4-5=24

16) 3-4-3-4-5-5=24

17) 3-3-5-4-4=24


18) 4-5-7-4-4=24

19) 3-5-7-3-4-7=24

etc

Also in more than 2 octaves

3-octaves

5-5-5-5-5-5-6-=36

and 4-octaves

7-7-7-7-7-7-6-=48

The last one is close to how one can derive a diatonic scale by exact 5ths (Here the 5ths of 7-semitones are not exact, so the Pythagorean comma becomes a whole semitone)

etc.



(This post has not been completely yet)