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Scale 2359: "Gadian"

Scale 2359: Gadian, 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
Gadian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,5,8,11}
Forte Number7-16
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3475
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 623
Deep Scaleno
Interval Vector435432
Interval Spectrump3m4n5s3d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,8,9,10}
<6> = {9,10,11}
Spectra Variation2.857
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 TriadsC♯{1,5,8}331.67
E{4,8,11}331.67
Minor Triadsc♯m{1,4,8}231.89
fm{5,8,0}331.67
Augmented TriadsC+{0,4,8}331.67
Diminished Triads{2,5,8}231.89
{5,8,11}231.89
g♯°{8,11,2}231.89
{11,2,5}232
Parsimonious Voice Leading Between Common Triads of Scale 2359. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm C# C# c#m->C# C#->d° C#->fm d°->b° E->f° g#° g#° E->g#° f°->fm 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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2359 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3227
Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
3rd mode:
Scale 3661
Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
4th mode:
Scale 1939
Scale 1939: Dathian, Ian Ring Music TheoryDathian
5th mode:
Scale 3017
Scale 3017: Gacrian, Ian Ring Music TheoryGacrian
6th mode:
Scale 889
Scale 889: Borian, Ian Ring Music TheoryBorian
7th mode:
Scale 623
Scale 623: Sycrian, Ian Ring Music TheorySycrianThis is the prime mode

Prime

The prime form of this scale is Scale 623

Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian

Complement

The heptatonic modal family [2359, 3227, 3661, 1939, 3017, 889, 623] (Forte: 7-16) is the complement of the pentatonic modal family [155, 865, 1555, 2125, 2825] (Forte: 5-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2359 is 3475

Scale 3475Scale 3475: Kylian, Ian Ring Music TheoryKylian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2359 is chiral, and its enantiomorph is scale 3475

Scale 3475Scale 3475: Kylian, Ian Ring Music TheoryKylian

Transformations:

T0 2359  T0I 3475
T1 623  T1I 2855
T2 1246  T2I 1615
T3 2492  T3I 3230
T4 889  T4I 2365
T5 1778  T5I 635
T6 3556  T6I 1270
T7 3017  T7I 2540
T8 1939  T8I 985
T9 3878  T9I 1970
T10 3661  T10I 3940
T11 3227  T11I 3785

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 2357Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana
Scale 2355Scale 2355: Raga Lalita, Ian Ring Music TheoryRaga Lalita
Scale 2363Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
Scale 2367Scale 2367: Laryllic, Ian Ring Music TheoryLaryllic
Scale 2343Scale 2343: Tharimic, Ian Ring Music TheoryTharimic
Scale 2351Scale 2351: Gynian, Ian Ring Music TheoryGynian
Scale 2327Scale 2327: Epalimic, Ian Ring Music TheoryEpalimic
Scale 2391Scale 2391: Molian, Ian Ring Music TheoryMolian
Scale 2423Scale 2423, Ian Ring Music Theory
Scale 2487Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic
Scale 2103Scale 2103, Ian Ring Music Theory
Scale 2231Scale 2231: Macrian, Ian Ring Music TheoryMacrian
Scale 2615Scale 2615: Thoptian, Ian Ring Music TheoryThoptian
Scale 2871Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
Scale 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
Scale 311Scale 311: Stagimic, Ian Ring Music TheoryStagimic
Scale 1335Scale 1335: Elephant Scale, Ian Ring Music TheoryElephant Scale

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.