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Scale 1131: "Honchoshi Plagal Form"

Scale 1131: Honchoshi Plagal Form, 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

Japanese
Honchoshi Plagal Form
Zeitler
Thocrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,5,6,10}
Forte Number6-Z25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2757
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections2
Modes5
Prime?no
prime: 363
Deep Scaleno
Interval Vector233241
Interval Spectrump4m2n3s3d2t
Distribution Spectra<1> = {1,2,4}
<2> = {3,4,5,6}
<3> = {5,7}
<4> = {6,7,8,9}
<5> = {8,10,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.232
Myhill Propertyno
Balancedno
Ridge Tonesnone
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
a♯m{10,1,5}131.5
Diminished Triads{0,3,6}131.5
Parsimonious Voice Leading Between Common Triads of Scale 1131. Created by Ian Ring ©2019 d#m d#m c°->d#m F# F# d#m->F# a#m a#m F#->a#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.

Diameter3
Radius2
Self-Centeredno
Central Verticesd♯m, F♯
Peripheral Verticesc°, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 1131 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2613
Scale 2613: Raga Hamsa Vinodini, Ian Ring Music TheoryRaga Hamsa Vinodini
3rd mode:
Scale 1677
Scale 1677: Raga Manavi, Ian Ring Music TheoryRaga Manavi
4th mode:
Scale 1443
Scale 1443: Raga Phenadyuti, Ian Ring Music TheoryRaga Phenadyuti
5th mode:
Scale 2769
Scale 2769: Dyrimic, Ian Ring Music TheoryDyrimic
6th mode:
Scale 429
Scale 429: Koptimic, Ian Ring Music TheoryKoptimic

Prime

The prime form of this scale is Scale 363

Scale 363Scale 363: Soptimic, Ian Ring Music TheorySoptimic

Complement

The hexatonic modal family [1131, 2613, 1677, 1443, 2769, 429] (Forte: 6-Z25) is the complement of the hexatonic modal family [663, 741, 1209, 1833, 2379, 3237] (Forte: 6-Z47)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1131 is 2757

Scale 2757Scale 2757: Raga Nishadi, Ian Ring Music TheoryRaga Nishadi

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1131 is chiral, and its enantiomorph is scale 2757

Scale 2757Scale 2757: Raga Nishadi, Ian Ring Music TheoryRaga Nishadi

Transformations:

T0 1131  T0I 2757
T1 2262  T1I 1419
T2 429  T2I 2838
T3 858  T3I 1581
T4 1716  T4I 3162
T5 3432  T5I 2229
T6 2769  T6I 363
T7 1443  T7I 726
T8 2886  T8I 1452
T9 1677  T9I 2904
T10 3354  T10I 1713
T11 2613  T11I 3426

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 1129Scale 1129: Raga Jayakauns, Ian Ring Music TheoryRaga Jayakauns
Scale 1133Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
Scale 1135Scale 1135: Katolian, Ian Ring Music TheoryKatolian
Scale 1123Scale 1123: Iwato, Ian Ring Music TheoryIwato
Scale 1127Scale 1127: Eparimic, Ian Ring Music TheoryEparimic
Scale 1139Scale 1139: Aerygimic, Ian Ring Music TheoryAerygimic
Scale 1147Scale 1147: Epynian, Ian Ring Music TheoryEpynian
Scale 1099Scale 1099: Dyritonic, Ian Ring Music TheoryDyritonic
Scale 1115Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror
Scale 1067Scale 1067, Ian Ring Music Theory
Scale 1195Scale 1195: Raga Gandharavam, Ian Ring Music TheoryRaga Gandharavam
Scale 1259Scale 1259: Stadian, Ian Ring Music TheoryStadian
Scale 1387Scale 1387: Locrian, Ian Ring Music TheoryLocrian
Scale 1643Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6
Scale 107Scale 107, Ian Ring Music Theory
Scale 619Scale 619: Double-Phrygian Hexatonic, Ian Ring Music TheoryDouble-Phrygian Hexatonic
Scale 2155Scale 2155, Ian Ring Music Theory
Scale 3179Scale 3179: Daptian, Ian Ring Music TheoryDaptian

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.