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Scale 1115: "Superlocrian Hexamirror"

Scale 1115: Superlocrian Hexamirror, 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 Modern
Superlocrian Hexamirror
Zeitler
Locrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,4,6,10}
Forte Number6-Z23
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 365
Deep Scaleno
Interval Vector234222
Interval Spectrump2m2n4s3d2t2
Distribution Spectra<1> = {1,2,4}
<2> = {3,6}
<3> = {4,5,7,8}
<4> = {6,9}
<5> = {8,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.232
Myhill Propertyno
Balancedno
Ridge Tones[4]
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}221
Minor Triadsd♯m{3,6,10}221
Diminished Triadsc°{0,3,6}131.5
a♯°{10,1,4}131.5
Parsimonious Voice Leading Between Common Triads of Scale 1115. Created by Ian Ring ©2019 c° c° d#m d#m c°->d#m F# F# d#m->F# a#° a#° F#->a#°

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, F♯
Peripheral Verticesc°, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 1115 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2605		Scale 2605: Rylimic, Ian Ring Music TheoryRylimic
3rd mode:
Scale 1675		Scale 1675: Raga Salagavarali, Ian Ring Music TheoryRaga Salagavarali
4th mode:
Scale 2885		Scale 2885: Byrimic, Ian Ring Music TheoryByrimic
5th mode:
Scale 1745		Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
6th mode:
Scale 365		Scale 365: Marimic, Ian Ring Music TheoryMarimicThis is the prime mode

Prime

The prime form of this scale is Scale 365

Scale 365Scale 365: Marimic, Ian Ring Music TheoryMarimic

Complement

The hexatonic modal family [1115, 2605, 1675, 2885, 1745, 365] (Forte: 6-Z23) is the complement of the hexatonic modal family [605, 745, 1175, 1865, 2635, 3365] (Forte: 6-Z45)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1115 is 2885

Scale 2885Scale 2885: Byrimic, Ian Ring Music TheoryByrimic

Transformations:

T0 1115  T0I 2885
T1 2230  T1I 1675
T2 365  T2I 3350
T3 730  T3I 2605
T4 1460  T4I 1115
T5 2920  T5I 2230
T6 1745  T6I 365
T7 3490  T7I 730
T8 2885  T8I 1460
T9 1675  T9I 2920
T10 3350  T10I 1745
T11 2605  T11I 3490

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 1113Scale 1113: Locrian Pentatonic 2, Ian Ring Music TheoryLocrian Pentatonic 2
Scale 1117Scale 1117: Raptimic, Ian Ring Music TheoryRaptimic
Scale 1119Scale 1119: Rarian, Ian Ring Music TheoryRarian
Scale 1107Scale 1107: Mogitonic, Ian Ring Music TheoryMogitonic
Scale 1111Scale 1111: Sycrimic, Ian Ring Music TheorySycrimic
Scale 1099Scale 1099: Dyritonic, Ian Ring Music TheoryDyritonic
Scale 1131Scale 1131: Honchoshi Plagal Form, Ian Ring Music TheoryHonchoshi Plagal Form
Scale 1147Scale 1147: Epynian, Ian Ring Music TheoryEpynian
Scale 1051Scale 1051, Ian Ring Music Theory
Scale 1083Scale 1083, Ian Ring Music Theory
Scale 1179Scale 1179: Sonimic, Ian Ring Music TheorySonimic
Scale 1243Scale 1243: Epylian, Ian Ring Music TheoryEpylian
Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian
Scale 1627Scale 1627: Zyptian, Ian Ring Music TheoryZyptian
Scale 91Scale 91, Ian Ring Music Theory
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 2139Scale 2139, Ian Ring Music Theory
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian

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.