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Scale 3159: "Stocrian"

Scale 3159: Stocrian, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above.

Tonnetz Diagram

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Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Stocrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,6,10,11}
Forte Number7-9
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3399
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 351
Deep Scaleno
Interval Vector453432
Interval Spectrump3m4n3s5d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,5,6}
<3> = {3,4,5,6,7,8}
<4> = {4,5,6,7,8,9}
<5> = {6,7,8,9,10}
<6> = {8,10,11}
Spectra Variation3.429
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
Coherenceno
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 3159 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3627
Scale 3627: Kalian, Ian Ring Music TheoryKalian
3rd mode:
Scale 3861
Scale 3861: Phroptian, Ian Ring Music TheoryPhroptian
4th mode:
Scale 1989
Scale 1989: Dydian, Ian Ring Music TheoryDydian
5th mode:
Scale 1521
Scale 1521: Stanian, Ian Ring Music TheoryStanian
6th mode:
Scale 351
Scale 351: Epanian, Ian Ring Music TheoryEpanianThis is the prime mode
7th mode:
Scale 2223
Scale 2223: Konian, Ian Ring Music TheoryKonian

Prime

The prime form of this scale is Scale 351

Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian

Complement

The heptatonic modal family [3159, 3627, 3861, 1989, 1521, 351, 2223] (Forte: 7-9) is the complement of the pentatonic modal family [87, 1473, 1797, 2091, 3093] (Forte: 5-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3159 is 3399

Scale 3399Scale 3399: Zonian, Ian Ring Music TheoryZonian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3159 is chiral, and its enantiomorph is scale 3399

Scale 3399Scale 3399: Zonian, Ian Ring Music TheoryZonian

Transformations:

T0 3159  T0I 3399
T1 2223  T1I 2703
T2 351  T2I 1311
T3 702  T3I 2622
T4 1404  T4I 1149
T5 2808  T5I 2298
T6 1521  T6I 501
T7 3042  T7I 1002
T8 1989  T8I 2004
T9 3978  T9I 4008
T10 3861  T10I 3921
T11 3627  T11I 3747

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 3157Scale 3157: Zyptimic, Ian Ring Music TheoryZyptimic
Scale 3155Scale 3155: Ladimic, Ian Ring Music TheoryLadimic
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3167Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
Scale 3143Scale 3143: Polimic, Ian Ring Music TheoryPolimic
Scale 3151Scale 3151: Pacrian, Ian Ring Music TheoryPacrian
Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 3191Scale 3191: Bynyllic, Ian Ring Music TheoryBynyllic
Scale 3095Scale 3095, Ian Ring Music Theory
Scale 3127Scale 3127, Ian Ring Music Theory
Scale 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3287Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
Scale 2135Scale 2135, Ian Ring Music Theory
Scale 2647Scale 2647: Dadian, Ian Ring Music TheoryDadian
Scale 1111Scale 1111: Sycrimic, Ian Ring Music TheorySycrimic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, and MIDI playback by MIDI.js. Bibliography