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Scale 1327: "Zalian"

Scale 1327: Zalian, 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

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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
Zalian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,5,8,10}
Forte Number7-23
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3733
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes6
Prime?no
prime: 701
Deep Scaleno
Interval Vector354351
Interval Spectrump5m3n4s5d3t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.549
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}321.17
G♯{8,0,3}142.17
A♯{10,2,5}241.83
Minor Triadsfm{5,8,0}231.5
a♯m{10,1,5}231.5
Diminished Triads{2,5,8}231.5
Parsimonious Voice Leading Between Common Triads of Scale 1327. Created by Ian Ring ©2019 C# C# C#->d° fm fm C#->fm a#m a#m C#->a#m A# A# d°->A# G# G# fm->G# a#m->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.

Diameter4
Radius2
Self-Centeredno
Central VerticesC♯
Peripheral VerticesG♯, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1327 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2711
Scale 2711: Stolian, Ian Ring Music TheoryStolian
3rd mode:
Scale 3403
Scale 3403: Bylian, Ian Ring Music TheoryBylian
4th mode:
Scale 3749
Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
5th mode:
Scale 1961
Scale 1961: Soptian, Ian Ring Music TheorySoptian
6th mode:
Scale 757
Scale 757: Ionyptian, Ian Ring Music TheoryIonyptian
7th mode:
Scale 1213
Scale 1213: Gyrian, Ian Ring Music TheoryGyrian

Prime

The prime form of this scale is Scale 701

Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian

Complement

The heptatonic modal family [1327, 2711, 3403, 3749, 1961, 757, 1213] (Forte: 7-23) is the complement of the pentatonic modal family [173, 1067, 1441, 1669, 2581] (Forte: 5-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1327 is 3733

Scale 3733Scale 3733: Gycrian, Ian Ring Music TheoryGycrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1327 is chiral, and its enantiomorph is scale 3733

Scale 3733Scale 3733: Gycrian, Ian Ring Music TheoryGycrian

Transformations:

T0 1327  T0I 3733
T1 2654  T1I 3371
T2 1213  T2I 2647
T3 2426  T3I 1199
T4 757  T4I 2398
T5 1514  T5I 701
T6 3028  T6I 1402
T7 1961  T7I 2804
T8 3922  T8I 1513
T9 3749  T9I 3026
T10 3403  T10I 1957
T11 2711  T11I 3914

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 1325Scale 1325: Phradimic, Ian Ring Music TheoryPhradimic
Scale 1323Scale 1323: Ritsu, Ian Ring Music TheoryRitsu
Scale 1319Scale 1319: Phronimic, Ian Ring Music TheoryPhronimic
Scale 1335Scale 1335: Elephant Scale, Ian Ring Music TheoryElephant Scale
Scale 1343Scale 1343: Zalyllic, Ian Ring Music TheoryZalyllic
Scale 1295Scale 1295, Ian Ring Music Theory
Scale 1311Scale 1311: Bynian, Ian Ring Music TheoryBynian
Scale 1359Scale 1359: Aerygian, Ian Ring Music TheoryAerygian
Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic
Scale 1455Scale 1455: Phrygiolian, Ian Ring Music TheoryPhrygiolian
Scale 1071Scale 1071, Ian Ring Music Theory
Scale 1199Scale 1199: Magian, Ian Ring Music TheoryMagian
Scale 1583Scale 1583: Salian, Ian Ring Music TheorySalian
Scale 1839Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic
Scale 303Scale 303: Golimic, Ian Ring Music TheoryGolimic
Scale 815Scale 815: Bolian, Ian Ring Music TheoryBolian
Scale 2351Scale 2351: Gynian, Ian Ring Music TheoryGynian
Scale 3375Scale 3375, Ian Ring Music Theory

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.