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Scale 3163: "Rogian"

Scale 3163: Rogian, 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. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

41161837294116105072918310504116183
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
Rogian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,6,10,11}
Forte Number7-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2887
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 367
Deep Scaleno
Interval Vector444342
Interval Spectrump4m3n4s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsF♯{6,10,1}231.4
B{11,3,6}231.4
Minor Triadsd♯m{3,6,10}221.2
Diminished Triads{0,3,6}142
a♯°{10,1,4}142
Parsimonious Voice Leading Between Common Triads of Scale 3163. Created by Ian Ring ©2019 B B c°->B d#m d#m F# F# d#m->F# d#m->B a#° a#° F#->a#°

view full size

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter4
Radius2
Self-Centeredno
Central Verticesd♯m
Peripheral Verticesc°, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 3163 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3629
Scale 3629: Boptian, Ian Ring Music TheoryBoptian
3rd mode:
Scale 1931
Scale 1931: Stogian, Ian Ring Music TheoryStogian
4th mode:
Scale 3013
Scale 3013: Thynian, Ian Ring Music TheoryThynian
5th mode:
Scale 1777
Scale 1777: Saptian, Ian Ring Music TheorySaptian
6th mode:
Scale 367
Scale 367: Aerodian, Ian Ring Music TheoryAerodianThis is the prime mode
7th mode:
Scale 2231
Scale 2231: Macrian, Ian Ring Music TheoryMacrian

Prime

The prime form of this scale is Scale 367

Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian

Complement

The heptatonic modal family [3163, 3629, 1931, 3013, 1777, 367, 2231] (Forte: 7-Z36) is the complement of the pentatonic modal family [151, 737, 1801, 2123, 3109] (Forte: 5-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3163 is 2887

Scale 2887Scale 2887: Gaptian, Ian Ring Music TheoryGaptian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3163 is chiral, and its enantiomorph is scale 2887

Scale 2887Scale 2887: Gaptian, Ian Ring Music TheoryGaptian

Transformations:

T0 3163  T0I 2887
T1 2231  T1I 1679
T2 367  T2I 3358
T3 734  T3I 2621
T4 1468  T4I 1147
T5 2936  T5I 2294
T6 1777  T6I 493
T7 3554  T7I 986
T8 3013  T8I 1972
T9 1931  T9I 3944
T10 3862  T10I 3793
T11 3629  T11I 3491

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 3161Scale 3161: Kodimic, Ian Ring Music TheoryKodimic
Scale 3165Scale 3165: Mylian, Ian Ring Music TheoryMylian
Scale 3167Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
Scale 3155Scale 3155: Ladimic, Ian Ring Music TheoryLadimic
Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
Scale 3147Scale 3147: Ryrimic, Ian Ring Music TheoryRyrimic
Scale 3179Scale 3179: Daptian, Ian Ring Music TheoryDaptian
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
Scale 3099Scale 3099, Ian Ring Music Theory
Scale 3131Scale 3131, Ian Ring Music Theory
Scale 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
Scale 3291Scale 3291: Lygyllic, Ian Ring Music TheoryLygyllic
Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 3675Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic
Scale 2139Scale 2139, Ian Ring Music Theory
Scale 2651Scale 2651: Panian, Ian Ring Music TheoryPanian
Scale 1115Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror

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, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.