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
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)
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)
