Costère Calculator

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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:

Tn invariance:

TnI invariance:

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:

T10

T11

T0I

T1I

T2I

T3I

T4I

T5I

T6I

T7I

T8I

T9I

T10I

T11I