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Scale 2413: "Locrian Natural 2"

Scale 2413: Locrian Natural 2, 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

Western Altered
Locrian Natural 2
Zeitler
Phrydian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,5,6,8,11}
Forte Number7-31
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1747
Hemitonia3 (trihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes6
Prime?no
prime: 731
Deep Scaleno
Interval Vector336333
Interval Spectrump3m3n6s3d3t3
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9}
<6> = {9,10,11}
Spectra Variation1.714
Maximally Evenno
Maximal Area Setno
Interior Area2.549
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 TriadsG♯{8,0,3}331.7
B{11,3,6}331.7
Minor Triadsfm{5,8,0}331.8
g♯m{8,11,3}431.6
bm{11,2,6}331.8
Diminished Triads{0,3,6}232
{2,5,8}232
{5,8,11}231.9
g♯°{8,11,2}231.9
{11,2,5}232
Parsimonious Voice Leading Between Common Triads of Scale 2413. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B fm fm d°->fm d°->b° f°->fm g#m g#m f°->g#m fm->G# g#° g#° g#°->g#m bm bm g#°->bm g#m->G# g#m->B b°->bm bm->B

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2413 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1627
Scale 1627: Zyptian, Ian Ring Music TheoryZyptian
3rd mode:
Scale 2861
Scale 2861: Katothian, Ian Ring Music TheoryKatothian
4th mode:
Scale 1739
Scale 1739: Mela Sadvidhamargini, Ian Ring Music TheoryMela Sadvidhamargini
5th mode:
Scale 2917
Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
6th mode:
Scale 1753
Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
7th mode:
Scale 731
Scale 731: Ionorian, Ian Ring Music TheoryIonorianThis is the prime mode

Prime

The prime form of this scale is Scale 731

Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian

Complement

The heptatonic modal family [2413, 1627, 2861, 1739, 2917, 1753, 731] (Forte: 7-31) is the complement of the pentatonic modal family [587, 601, 713, 1609, 2341] (Forte: 5-31)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2413 is 1747

Scale 1747Scale 1747: Mela Ramapriya, Ian Ring Music TheoryMela Ramapriya

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2413 is chiral, and its enantiomorph is scale 1747

Scale 1747Scale 1747: Mela Ramapriya, Ian Ring Music TheoryMela Ramapriya

Transformations:

T0 2413  T0I 1747
T1 731  T1I 3494
T2 1462  T2I 2893
T3 2924  T3I 1691
T4 1753  T4I 3382
T5 3506  T5I 2669
T6 2917  T6I 1243
T7 1739  T7I 2486
T8 3478  T8I 877
T9 2861  T9I 1754
T10 1627  T10I 3508
T11 3254  T11I 2921

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 2415Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
Scale 2409Scale 2409: Zacrimic, Ian Ring Music TheoryZacrimic
Scale 2411Scale 2411: Aeolorian, Ian Ring Music TheoryAeolorian
Scale 2405Scale 2405: Katalimic, Ian Ring Music TheoryKatalimic
Scale 2421Scale 2421: Malian, Ian Ring Music TheoryMalian
Scale 2429Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
Scale 2381Scale 2381: Takemitsu Linea Mode 1, Ian Ring Music TheoryTakemitsu Linea Mode 1
Scale 2397Scale 2397: Stagian, Ian Ring Music TheoryStagian
Scale 2349Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana
Scale 2477Scale 2477: Harmonic Minor, Ian Ring Music TheoryHarmonic Minor
Scale 2541Scale 2541: Algerian, Ian Ring Music TheoryAlgerian
Scale 2157Scale 2157, Ian Ring Music Theory
Scale 2285Scale 2285: Aerogian, Ian Ring Music TheoryAerogian
Scale 2669Scale 2669: Jeths' Mode, Ian Ring Music TheoryJeths' Mode
Scale 2925Scale 2925: Diminished, Ian Ring Music TheoryDiminished
Scale 3437Scale 3437, Ian Ring Music Theory
Scale 365Scale 365: Marimic, Ian Ring Music TheoryMarimic
Scale 1389Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian

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.