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Scale 3147: "Ryrimic"

Scale 3147: Ryrimic, 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
Ryrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,6,10,11}
Forte Number6-Z40
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2631
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?no
prime: 303
Deep Scaleno
Interval Vector333231
Interval Spectrump3m2n3s3d3t
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,5,7}
<3> = {3,4,6,8,9}
<4> = {5,7,9,10}
<5> = {8,9,10,11}
Spectra Variation3.667
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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}131.5
B{11,3,6}221
Minor Triadsd♯m{3,6,10}221
Diminished Triads{0,3,6}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3147. Created by Ian Ring ©2019 B B c°->B d#m d#m F# F# d#m->F# d#m->B

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.

Diameter3
Radius2
Self-Centeredno
Central Verticesd♯m, B
Peripheral Verticesc°, F♯

Modes

Modes are the rotational transformation of this scale. Scale 3147 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3621
Scale 3621: Gylimic, Ian Ring Music TheoryGylimic
3rd mode:
Scale 1929
Scale 1929: Aeolycrimic, Ian Ring Music TheoryAeolycrimic
4th mode:
Scale 753
Scale 753: Aeronimic, Ian Ring Music TheoryAeronimic
5th mode:
Scale 303
Scale 303: Golimic, Ian Ring Music TheoryGolimicThis is the prime mode
6th mode:
Scale 2199
Scale 2199: Dyptimic, Ian Ring Music TheoryDyptimic

Prime

The prime form of this scale is Scale 303

Scale 303Scale 303: Golimic, Ian Ring Music TheoryGolimic

Complement

The hexatonic modal family [3147, 3621, 1929, 753, 303, 2199] (Forte: 6-Z40) is the complement of the hexatonic modal family [183, 1761, 1803, 2139, 2949, 3117] (Forte: 6-Z11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3147 is 2631

Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3147 is chiral, and its enantiomorph is scale 2631

Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic

Transformations:

T0 3147  T0I 2631
T1 2199  T1I 1167
T2 303  T2I 2334
T3 606  T3I 573
T4 1212  T4I 1146
T5 2424  T5I 2292
T6 753  T6I 489
T7 1506  T7I 978
T8 3012  T8I 1956
T9 1929  T9I 3912
T10 3858  T10I 3729
T11 3621  T11I 3363

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 3145Scale 3145: Stolitonic, Ian Ring Music TheoryStolitonic
Scale 3149Scale 3149: Phrycrimic, Ian Ring Music TheoryPhrycrimic
Scale 3151Scale 3151: Pacrian, Ian Ring Music TheoryPacrian
Scale 3139Scale 3139, Ian Ring Music Theory
Scale 3143Scale 3143: Polimic, Ian Ring Music TheoryPolimic
Scale 3155Scale 3155: Ladimic, Ian Ring Music TheoryLadimic
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3179Scale 3179: Daptian, Ian Ring Music TheoryDaptian
Scale 3083Scale 3083, Ian Ring Music Theory
Scale 3115Scale 3115, Ian Ring Music Theory
Scale 3211Scale 3211: Epacrimic, Ian Ring Music TheoryEpacrimic
Scale 3275Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani
Scale 3403Scale 3403: Bylian, Ian Ring Music TheoryBylian
Scale 3659Scale 3659: Polian, Ian Ring Music TheoryPolian
Scale 2123Scale 2123, Ian Ring Music Theory
Scale 2635Scale 2635: Gocrimic, Ian Ring Music TheoryGocrimic
Scale 1099Scale 1099: Dyritonic, Ian Ring Music TheoryDyritonic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.