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Scale 2231: "Macrian"

Scale 2231: Macrian, 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

Zeitler
Macrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,5,7,11}
Forte Number7-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3491
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 367
Deep Scaleno
Interval Vector444342
Interval Spectrump4m3n4s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
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{0,4,7}231.4
G{7,11,2}231.4
Minor Triadsem{4,7,11}221.2
Diminished Triadsc♯°{1,4,7}142
b°{11,2,5}142
Parsimonious Voice Leading Between Common Triads of Scale 2231. Created by Ian Ring ©2019 C C c#° c#° C->c#° em em C->em Parsimonious Voice Leading Between Common Triads of Scale 2231. Created by Ian Ring ©2019 G em->G b° b° G->b°

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 Verticesem
Peripheral Verticesc♯°, b°

Modes

Modes are the rotational transformation of this scale. Scale 2231 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3163		Scale 3163: Rogian, Ian Ring Music TheoryRogian
3rd mode:
Scale 3629		Scale 3629: Boptian, Ian Ring Music TheoryBoptian
4th mode:
Scale 1931		Scale 1931: Stogian, Ian Ring Music TheoryStogian
5th mode:
Scale 3013		Scale 3013: Thynian, Ian Ring Music TheoryThynian
6th mode:
Scale 1777		Scale 1777: Saptian, Ian Ring Music TheorySaptian
7th mode:
Scale 367		Scale 367: Aerodian, Ian Ring Music TheoryAerodianThis is the prime mode

Prime

The prime form of this scale is Scale 367

Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian

Complement

The heptatonic modal family [2231, 3163, 3629, 1931, 3013, 1777, 367] (Forte: 7-Z36) is the complement of the pentatonic modal family [151, 737, 1801, 2123, 3109] (Forte: 5-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2231 is 3491

Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2231 is chiral, and its enantiomorph is scale 3491

Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian

Transformations:

T0 2231  T0I 3491
T1 367  T1I 2887
T2 734  T2I 1679
T3 1468  T3I 3358
T4 2936  T4I 2621
T5 1777  T5I 1147
T6 3554  T6I 2294
T7 3013  T7I 493
T8 1931  T8I 986
T9 3862  T9I 1972
T10 3629  T10I 3944
T11 3163  T11I 3793

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 2229Scale 2229: Raga Nalinakanti, Ian Ring Music TheoryRaga Nalinakanti
Scale 2227Scale 2227: Raga Gaula, Ian Ring Music TheoryRaga Gaula
Scale 2235Scale 2235: Bathian, Ian Ring Music TheoryBathian
Scale 2239Scale 2239: Dacryllic, Ian Ring Music TheoryDacryllic
Scale 2215Scale 2215: Ranimic, Ian Ring Music TheoryRanimic
Scale 2223Scale 2223: Konian, Ian Ring Music TheoryKonian
Scale 2199Scale 2199: Dyptimic, Ian Ring Music TheoryDyptimic
Scale 2263Scale 2263: Lycrian, Ian Ring Music TheoryLycrian
Scale 2295Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic
Scale 2103Scale 2103, Ian Ring Music Theory
Scale 2167Scale 2167, Ian Ring Music Theory
Scale 2359Scale 2359: Gadian, Ian Ring Music TheoryGadian
Scale 2487Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic
Scale 2743Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic
Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
Scale 183Scale 183, Ian Ring Music Theory
Scale 1207Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian

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.