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Scale 1397: "Major Locrian"

Scale 1397: Major Locrian, 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

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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

Western Modern
Major Locrian
Exoticisms
Arabian (b)
Zeitler
Gothian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,4,5,6,8,10}
Forte Number7-33
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections5
Modes6
Prime?no
prime: 1367
Deep Scaleno
Interval Vector262623
Interval Spectrump2m6n2s6d2t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9,10}
<6> = {10,11}
Spectra Variation1.429
Maximally Evenno
Maximal Area Setyes
Interior Area2.665
Myhill Propertyno
Balancedno
Ridge Tones[10]
ProprietyProper
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 TriadsA♯{10,2,5}231.4
Minor Triadsfm{5,8,0}231.4
Augmented TriadsC+{0,4,8}142
D+{2,6,10}142
Diminished Triads{2,5,8}221.2
Parsimonious Voice Leading Between Common Triads of Scale 1397. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm d°->fm A# A# d°->A# D+ D+ D+->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 Vertices
Peripheral VerticesC+, D+

Modes

Modes are the rotational transformation of this scale. Scale 1397 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1373
Scale 1373: Storian, Ian Ring Music TheoryStorian
3rd mode:
Scale 1367
Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone InverseThis is the prime mode
4th mode:
Scale 2731
Scale 2731: Neapolitan Major, Ian Ring Music TheoryNeapolitan Major
5th mode:
Scale 3413
Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
6th mode:
Scale 1877
Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
7th mode:
Scale 1493
Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor

Prime

The prime form of this scale is Scale 1367

Scale 1367Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone Inverse

Complement

The heptatonic modal family [1397, 1373, 1367, 2731, 3413, 1877, 1493] (Forte: 7-33) is the complement of the pentatonic modal family [341, 1109, 1301, 1349, 1361] (Forte: 5-33)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1397 is 1493

Scale 1493Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor

Transformations:

T0 1397  T0I 1493
T1 2794  T1I 2986
T2 1493  T2I 1877
T3 2986  T3I 3754
T4 1877  T4I 3413
T5 3754  T5I 2731
T6 3413  T6I 1367
T7 2731  T7I 2734
T8 1367  T8I 1373
T9 2734  T9I 2746
T10 1373  T10I 1397
T11 2746  T11I 2794

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 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic
Scale 1393Scale 1393: Mycrimic, Ian Ring Music TheoryMycrimic
Scale 1395Scale 1395: Asian (a), Ian Ring Music TheoryAsian (a)
Scale 1401Scale 1401: Pagian, Ian Ring Music TheoryPagian
Scale 1405Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic
Scale 1381Scale 1381: Padimic, Ian Ring Music TheoryPadimic
Scale 1389Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian
Scale 1365Scale 1365: Whole Tone, Ian Ring Music TheoryWhole Tone
Scale 1333Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic
Scale 1461Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
Scale 1525Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic
Scale 1141Scale 1141: Rynimic, Ian Ring Music TheoryRynimic
Scale 1269Scale 1269: Katythian, Ian Ring Music TheoryKatythian
Scale 1653Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
Scale 1909Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
Scale 373Scale 373: Epagimic, Ian Ring Music TheoryEpagimic
Scale 885Scale 885: Sathian, Ian Ring Music TheorySathian
Scale 2421Scale 2421: Malian, Ian Ring Music TheoryMalian
Scale 3445Scale 3445: Messiaen Mode 6 Inverse, Ian Ring Music TheoryMessiaen Mode 6 Inverse

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.