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Scale 3427: "Zacrian"

Scale 3427: Zacrian, 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
Zacrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,5,6,8,10,11}
Forte Number7-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2263
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes6
Prime?no
prime: 431
Deep Scaleno
Interval Vector443352
Interval Spectrump5m3n3s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {8,10,11}
Spectra Variation2.857
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♯{1,5,8}221.2
F♯{6,10,1}142
Minor Triadsfm{5,8,0}231.4
a♯m{10,1,5}231.4
Diminished Triadsf°{5,8,11}142
Parsimonious Voice Leading Between Common Triads of Scale 3427. Created by Ian Ring ©2019 C# C# fm fm C#->fm a#m a#m C#->a#m f° f° f°->fm F# F# F#->a#m

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 VerticesC♯
Peripheral Verticesf°, F♯

Modes

Modes are the rotational transformation of this scale. Scale 3427 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3761		Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri
3rd mode:
Scale 491		Scale 491: Aeolyrian, Ian Ring Music TheoryAeolyrian
4th mode:
Scale 2293		Scale 2293: Gorian, Ian Ring Music TheoryGorian
5th mode:
Scale 1597		Scale 1597: Aeolodian, Ian Ring Music TheoryAeolodian
6th mode:
Scale 1423		Scale 1423: Doptian, Ian Ring Music TheoryDoptian
7th mode:
Scale 2759		Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani

Prime

The prime form of this scale is Scale 431

Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian

Complement

The heptatonic modal family [3427, 3761, 491, 2293, 1597, 1423, 2759] (Forte: 7-14) is the complement of the pentatonic modal family [167, 901, 1249, 2131, 3113] (Forte: 5-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3427 is 2263

Scale 2263Scale 2263: Lycrian, Ian Ring Music TheoryLycrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3427 is chiral, and its enantiomorph is scale 2263

Scale 2263Scale 2263: Lycrian, Ian Ring Music TheoryLycrian

Transformations:

T0 3427  T0I 2263
T1 2759  T1I 431
T2 1423  T2I 862
T3 2846  T3I 1724
T4 1597  T4I 3448
T5 3194  T5I 2801
T6 2293  T6I 1507
T7 491  T7I 3014
T8 982  T8I 1933
T9 1964  T9I 3866
T10 3928  T10I 3637
T11 3761  T11I 3179

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 3425Scale 3425, Ian Ring Music Theory
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 3431Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
Scale 3435Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
Scale 3443Scale 3443: Verdi's Scala Enigmatica, Ian Ring Music TheoryVerdi's Scala Enigmatica
Scale 3395Scale 3395, Ian Ring Music Theory
Scale 3411Scale 3411: Enigmatic, Ian Ring Music TheoryEnigmatic
Scale 3363Scale 3363: Rogimic, Ian Ring Music TheoryRogimic
Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian
Scale 3555Scale 3555: Pylyllic, Ian Ring Music TheoryPylyllic
Scale 3171Scale 3171: Zythimic, Ian Ring Music TheoryZythimic
Scale 3299Scale 3299: Syptian, Ian Ring Music TheorySyptian
Scale 3683Scale 3683: Dycrian, Ian Ring Music TheoryDycrian
Scale 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
Scale 2403Scale 2403: Lycrimic, Ian Ring Music TheoryLycrimic
Scale 2915Scale 2915: Aeolydian, Ian Ring Music TheoryAeolydian
Scale 1379Scale 1379: Kycrimic, Ian Ring Music TheoryKycrimic

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.