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Scale 859: "Ultralocrian"

Scale 859: Ultralocrian, 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
Ultralocrian
Superlocrian Diminished
Superlocrian Double-Flat
Diminished Locrian
Western Altered
Mixolydian Sharp 1
Zeitler
Pathian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,6,8,9}
Forte Number7-32
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2905
Hemitonia3 (trihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes6
Prime?yes
Deep Scaleno
Interval Vector335442
Interval Spectrump4m4n5s3d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9}
<6> = {9,10,11}
Spectra Variation1.429
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
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 TriadsG♯{8,0,3}331.8
A{9,1,4}331.7
Minor Triadsc♯m{1,4,8}232
f♯m{6,9,1}331.8
am{9,0,4}431.6
Augmented TriadsC+{0,4,8}331.7
Diminished Triads{0,3,6}232
d♯°{3,6,9}232
f♯°{6,9,0}231.9
{9,0,3}231.9
Parsimonious Voice Leading Between Common Triads of Scale 859. Created by Ian Ring ©2019 d#° d#° c°->d#° G# G# c°->G# C+ C+ c#m c#m C+->c#m C+->G# am am C+->am A A c#m->A f#m f#m d#°->f#m f#° f#° f#°->f#m f#°->am f#m->A G#->a° a°->am am->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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 859 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2477
Scale 2477: Harmonic Minor, Ian Ring Music TheoryHarmonic Minor
3rd mode:
Scale 1643
Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6
4th mode:
Scale 2869
Scale 2869: Major Augmented, Ian Ring Music TheoryMajor Augmented
5th mode:
Scale 1741
Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
6th mode:
Scale 1459
Scale 1459: Phrygian Dominant, Ian Ring Music TheoryPhrygian Dominant
7th mode:
Scale 2777
Scale 2777: Aeolian Harmonic, Ian Ring Music TheoryAeolian Harmonic

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [859, 2477, 1643, 2869, 1741, 1459, 2777] (Forte: 7-32) is the complement of the pentatonic modal family [595, 665, 805, 1225, 2345] (Forte: 5-32)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 859 is 2905

Scale 2905Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 859 is chiral, and its enantiomorph is scale 2905

Scale 2905Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1

Transformations:

T0 859  T0I 2905
T1 1718  T1I 1715
T2 3436  T2I 3430
T3 2777  T3I 2765
T4 1459  T4I 1435
T5 2918  T5I 2870
T6 1741  T6I 1645
T7 3482  T7I 3290
T8 2869  T8I 2485
T9 1643  T9I 875
T10 3286  T10I 1750
T11 2477  T11I 3500

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 857Scale 857: Aeolydimic, Ian Ring Music TheoryAeolydimic
Scale 861Scale 861: Rylian, Ian Ring Music TheoryRylian
Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic
Scale 851Scale 851: Raga Hejjajji, Ian Ring Music TheoryRaga Hejjajji
Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian
Scale 843Scale 843: Molimic, Ian Ring Music TheoryMolimic
Scale 875Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7
Scale 891Scale 891: Ionilyllic, Ian Ring Music TheoryIonilyllic
Scale 795Scale 795: Aeologimic, Ian Ring Music TheoryAeologimic
Scale 827Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian
Scale 923Scale 923: Ultraphrygian, Ian Ring Music TheoryUltraphrygian
Scale 987Scale 987: Aeraptyllic, Ian Ring Music TheoryAeraptyllic
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian
Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic
Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian
Scale 1883Scale 1883, Ian Ring Music Theory
Scale 2907Scale 2907: Magen Abot 2, Ian Ring Music TheoryMagen Abot 2

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.