The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 871: "Locrian Double-flat 3 Double-flat 7"

Scale 871: Locrian Double-flat 3 Double-flat 7, 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 Double-flat 3 Double-flat 7
Zeitler
Epadian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,5,6,8,9}
Forte Number7-22
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?yes
Deep Scaleno
Interval Vector424542
Interval Spectrump4m5n4s2d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9,10}
<6> = {9,10,11}
Spectra Variation1.714
Maximally Evenno
Maximal Area Setno
Interior Area2.433
Myhill Propertyno
Balancedyes
Ridge Tones[2]
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 TriadsC♯{1,5,8}331.67
D{2,6,9}242
F{5,9,0}331.67
Minor Triadsdm{2,5,9}331.67
fm{5,8,0}242
f♯m{6,9,1}331.67
Augmented TriadsC♯+{1,5,9}421.33
Diminished Triads{2,5,8}242
f♯°{6,9,0}242
Parsimonious Voice Leading Between Common Triads of Scale 871. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m d°->dm D D dm->D D->f#m fm->F f#° f#° F->f#° f#°->f#m

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 VerticesC♯+
Peripheral Verticesd°, D, fm, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 871 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2483
Scale 2483: Double Harmonic, Ian Ring Music TheoryDouble Harmonic
3rd mode:
Scale 3289
Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6
4th mode:
Scale 923
Scale 923: Ultraphrygian, Ian Ring Music TheoryUltraphrygian
5th mode:
Scale 2509
Scale 2509: Double Harmonic Minor, Ian Ring Music TheoryDouble Harmonic Minor
6th mode:
Scale 1651
Scale 1651: Asian, Ian Ring Music TheoryAsian
7th mode:
Scale 2873
Scale 2873: Ionian Augmented Sharp 2, Ian Ring Music TheoryIonian Augmented Sharp 2

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [871, 2483, 3289, 923, 2509, 1651, 2873] (Forte: 7-22) is the complement of the pentatonic modal family [403, 611, 793, 2249, 2353] (Forte: 5-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 871 is 3289

Scale 3289Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6

Transformations:

T0 871  T0I 3289
T1 1742  T1I 2483
T2 3484  T2I 871
T3 2873  T3I 1742
T4 1651  T4I 3484
T5 3302  T5I 2873
T6 2509  T6I 1651
T7 923  T7I 3302
T8 1846  T8I 2509
T9 3692  T9I 923
T10 3289  T10I 1846
T11 2483  T11I 3692

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 869Scale 869: Kothimic, Ian Ring Music TheoryKothimic
Scale 867Scale 867: Phrocrimic, Ian Ring Music TheoryPhrocrimic
Scale 875Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7
Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic
Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic
Scale 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic
Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian
Scale 807Scale 807: Raga Suddha Mukhari, Ian Ring Music TheoryRaga Suddha Mukhari
Scale 935Scale 935: Chromatic Dorian, Ian Ring Music TheoryChromatic Dorian
Scale 999Scale 999: Ionodyllic, Ian Ring Music TheoryIonodyllic
Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic
Scale 743Scale 743: Chromatic Hypophrygian Inverse, Ian Ring Music TheoryChromatic Hypophrygian Inverse
Scale 359Scale 359: Bothimic, Ian Ring Music TheoryBothimic
Scale 1383Scale 1383: Pynian, Ian Ring Music TheoryPynian
Scale 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic

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.