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Scale 2663: "Lalian"

Scale 2663: Lalian, 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
Lalian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,5,6,9,11}
Forte Number7-Z18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3275
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 755
Deep Scaleno
Interval Vector434442
Interval Spectrump4m4n4s3d4t2
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 Area2.433
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 TriadsD{2,6,9}331.5
F{5,9,0}242
Minor Triadsdm{2,5,9}331.5
f♯m{6,9,1}331.5
bm{11,2,6}242
Augmented TriadsC♯+{1,5,9}331.5
Diminished Triadsf♯°{6,9,0}242
{11,2,5}242
Parsimonious Voice Leading Between Common Triads of Scale 2663. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m D D dm->D dm->b° D->f#m bm bm D->bm f#° f#° F->f#° f#°->f#m b°->bm

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
Radius3
Self-Centeredno
Central VerticesC♯+, dm, D, f♯m
Peripheral VerticesF, f♯°, b°, bm

Modes

Modes are the rotational transformation of this scale. Scale 2663 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3379
Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending
3rd mode:
Scale 3737
Scale 3737: Phrocrian, Ian Ring Music TheoryPhrocrian
4th mode:
Scale 979
Scale 979: Mela Dhavalambari, Ian Ring Music TheoryMela Dhavalambari
5th mode:
Scale 2537
Scale 2537: Laptian, Ian Ring Music TheoryLaptian
6th mode:
Scale 829
Scale 829: Lygian, Ian Ring Music TheoryLygian
7th mode:
Scale 1231
Scale 1231: Logian, Ian Ring Music TheoryLogian

Prime

The prime form of this scale is Scale 755

Scale 755Scale 755: Phrythian, Ian Ring Music TheoryPhrythian

Complement

The heptatonic modal family [2663, 3379, 3737, 979, 2537, 829, 1231] (Forte: 7-Z18) is the complement of the pentatonic modal family [179, 779, 1633, 2137, 2437] (Forte: 5-Z18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2663 is 3275

Scale 3275Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2663 is chiral, and its enantiomorph is scale 3275

Scale 3275Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani

Transformations:

T0 2663  T0I 3275
T1 1231  T1I 2455
T2 2462  T2I 815
T3 829  T3I 1630
T4 1658  T4I 3260
T5 3316  T5I 2425
T6 2537  T6I 755
T7 979  T7I 1510
T8 1958  T8I 3020
T9 3916  T9I 1945
T10 3737  T10I 3890
T11 3379  T11I 3685

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 2661Scale 2661: Stydimic, Ian Ring Music TheoryStydimic
Scale 2659Scale 2659: Katynimic, Ian Ring Music TheoryKatynimic
Scale 2667Scale 2667: Byrian, Ian Ring Music TheoryByrian
Scale 2671Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic
Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic
Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic
Scale 2647Scale 2647: Dadian, Ian Ring Music TheoryDadian
Scale 2599Scale 2599: Malimic, Ian Ring Music TheoryMalimic
Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati
Scale 2791Scale 2791: Mixothyllic, Ian Ring Music TheoryMixothyllic
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
Scale 2151Scale 2151, Ian Ring Music Theory
Scale 2407Scale 2407: Zylian, Ian Ring Music TheoryZylian
Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 3687Scale 3687: Zonyllic, Ian Ring Music TheoryZonyllic
Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic
Scale 1639Scale 1639: Aeolothian, Ian Ring Music TheoryAeolothian

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.