LAST       Costère Calculator       RESET


Center:        with target

Source Set:  

Offset:     

Costère Code:  

Density Tables:

   

1

1

1

1

1

1

1

1

1

1

1

1

  

C

C#

D

Eb

E

F

F#

G

G#

A

Bb

B

Cardinal:   

5

5

5

5

5

5

5

5

5

5

5

5

Tonal major:   

15

15

15

15

15

15

15

15

15

15

15

15

Tonal minor:   

15

15

15

15

15

15

15

15

15

15

15

15

Tonal inverse minor:   

15

15

15

15

15

15

15

15

15

15

15

15

   

 

 

 

 

 

 

 

 

 

 

 

 

   

T0

T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

Transpositional:   

60

60

60

60

60

60

60

60

60

60

60

60

   

 

 

 

 

 

 

 

 

 

 

 

 

   

T0I

T1I

T2I

T3I

T4I

T5I

T6I

T7I

T8I

T9I

T10I

T11I

Inversional:   

60

60

60

60

60

60

60

60

60

60

60

60


Normal form:    

{0 1 2 3 4 5 6 7 8 9 10 11}

InvNormal form:    

{0 1 2 3 4 5 6 7 8 9 10 11}

Tn type:    

(0 1 2 3 4 5 6 7 8 9 10 11)

Inv Tn type:    

(0 1 2 3 4 5 6 7 8 9 10 11)

Tn/TnI type:    

[0 1 2 3 4 5 6 7 8 9 10 11]

Interval Vector:    

±1

±2

±3

±4

±5

±6

12

12

12

12

12

6

index n:    

0

1

2

3

4

5

6

7

8

9

10

11

Tn invariance:    

12

12

12

12

12

12

12

12

12

12

12

12

TnI invariance:    

12

12

12

12

12

12

12

12

12

12

12

12

With multiple interval content
With limited transpositions
With limited inversions

Symmetrical to itself,
median axe at 0 = C (and its tritone)
with median note
relative = T0I


Cardinally Dense ( 60 >= 0 )
in cardinal equilibrium

Non-Transpositional

Tonal Binary-Mm Major-minor
Tonally Stable
Non-Tonic polytonal with binary components
M( 0-C , 1-C# , 2-D , 3-Eb , 4-E , 5-F , 6-F# , 7-G , 8-G# , 9-A , 10-Bb , 11-B)
m( 0-C , 1-C# , 2-D , 3-Eb , 4-E , 5-F , 6-F# , 7-G , 8-G# , 9-A , 10-Bb , 11-B)

partially modal-imitative
[ (0-Cm) (1-C#m) (2-Dm) (3-Ebm) (4-Em) (5-Fm) (6-F#m) (7-Gm) (8-G#m) (9-Am) (10-Bbm) (11-Bm) ]
[ (0-CM) (1-C#M) (2-DM) (3-EbM) (4-EM) (5-FM) (6-F#M) (7-GM) (8-G#M) (9-AM) (10-BbM) (11-BM) ]


Transpositional Properties:

  

common tones

density

collection

notes

T0

12

60

{ 0 1 2 3 4 5 6 7 8 9 10 11 }

{ C C# D Eb E F F# G G# A Bb B }

T1

12

60

{ 1 2 3 4 5 6 7 8 9 10 11 0 }

{ C# D Eb E F F# G G# A Bb B C }

T2

12

60

{ 2 3 4 5 6 7 8 9 10 11 0 1 }

{ D Eb E F F# G G# A Bb B C C# }

T3

12

60

{ 3 4 5 6 7 8 9 10 11 0 1 2 }

{ Eb E F F# G G# A Bb B C C# D }

T4

12

60

{ 4 5 6 7 8 9 10 11 0 1 2 3 }

{ E F F# G G# A Bb B C C# D Eb }

T5

12

60

{ 5 6 7 8 9 10 11 0 1 2 3 4 }

{ F F# G G# A Bb B C C# D Eb E }

T6

12

60

{ 6 7 8 9 10 11 0 1 2 3 4 5 }

{ F# G G# A Bb B C C# D Eb E F }

T7

12

60

{ 7 8 9 10 11 0 1 2 3 4 5 6 }

{ G G# A Bb B C C# D Eb E F F# }

T8

12

60

{ 8 9 10 11 0 1 2 3 4 5 6 7 }

{ G# A Bb B C C# D Eb E F F# G }

T9

12

60

{ 9 10 11 0 1 2 3 4 5 6 7 8 }

{ A Bb B C C# D Eb E F F# G G# }

T10

12

60

{ 10 11 0 1 2 3 4 5 6 7 8 9 }

{ Bb B C C# D Eb E F F# G G# A }

T11

12

60

{ 11 0 1 2 3 4 5 6 7 8 9 10 }

{ B C C# D Eb E F F# G G# A Bb }


Inversional Properties:

  

common tones

density

collection

notes

T0I

12

60

{ 1 2 3 4 5 6 7 8 9 10 11 0 }

{ C# D Eb E F F# G G# A Bb B C }

T1I

12

60

{ 2 3 4 5 6 7 8 9 10 11 0 1 }

{ D Eb E F F# G G# A Bb B C C# }

T2I

12

60

{ 3 4 5 6 7 8 9 10 11 0 1 2 }

{ Eb E F F# G G# A Bb B C C# D }

T3I

12

60

{ 4 5 6 7 8 9 10 11 0 1 2 3 }

{ E F F# G G# A Bb B C C# D Eb }

T4I

12

60

{ 5 6 7 8 9 10 11 0 1 2 3 4 }

{ F F# G G# A Bb B C C# D Eb E }

T5I

12

60

{ 6 7 8 9 10 11 0 1 2 3 4 5 }

{ F# G G# A Bb B C C# D Eb E F }

T6I

12

60

{ 7 8 9 10 11 0 1 2 3 4 5 6 }

{ G G# A Bb B C C# D Eb E F F# }

T7I

12

60

{ 8 9 10 11 0 1 2 3 4 5 6 7 }

{ G# A Bb B C C# D Eb E F F# G }

T8I

12

60

{ 9 10 11 0 1 2 3 4 5 6 7 8 }

{ A Bb B C C# D Eb E F F# G G# }

T9I

12

60

{ 10 11 0 1 2 3 4 5 6 7 8 9 }

{ Bb B C C# D Eb E F F# G G# A }

T10I

12

60

{ 11 0 1 2 3 4 5 6 7 8 9 10 }

{ B C C# D Eb E F F# G G# A Bb }

T11I

12

60

{ 0 1 2 3 4 5 6 7 8 9 10 11 }

{ C C# D Eb E F F# G G# A Bb B }


Notations:

T0

T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T0I

T1I

T2I

T3I

T4I

T5I

T6I

T7I

T8I

T9I

T10I

T11I



Copyright © 2010 – Marcus Bittencourt