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Scale 1211: "Zadian"

Scale 1211: Zadian, 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
Zadian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,5,7,10}
Forte Number7-25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2981
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 733
Deep Scaleno
Interval Vector345342
Interval Spectrump4m3n5s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {9,10,11}
Spectra Variation2.286
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{0,4,7}331.63
D♯{3,7,10}331.63
Minor Triadscm{0,3,7}231.75
a♯m{10,1,5}231.88
Diminished Triadsc♯°{1,4,7}231.75
{4,7,10}231.75
{7,10,1}231.75
a♯°{10,1,4}231.88
Parsimonious Voice Leading Between Common Triads of Scale 1211. Created by Ian Ring ©2019 cm cm C C cm->C D# D# cm->D# c#° c#° C->c#° C->e° a#° a#° c#°->a#° D#->e° D#->g° a#m a#m g°->a#m a#°->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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1211 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2653
Scale 2653: Sygian, Ian Ring Music TheorySygian
3rd mode:
Scale 1687
Scale 1687: Phralian, Ian Ring Music TheoryPhralian
4th mode:
Scale 2891
Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian
5th mode:
Scale 3493
Scale 3493: Rathian, Ian Ring Music TheoryRathian
6th mode:
Scale 1897
Scale 1897: Ionopian, Ian Ring Music TheoryIonopian
7th mode:
Scale 749
Scale 749: Aeologian, Ian Ring Music TheoryAeologian

Prime

The prime form of this scale is Scale 733

Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian

Complement

The heptatonic modal family [1211, 2653, 1687, 2891, 3493, 1897, 749] (Forte: 7-25) is the complement of the pentatonic modal family [301, 721, 1099, 1673, 2597] (Forte: 5-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1211 is 2981

Scale 2981Scale 2981: Ionolian, Ian Ring Music TheoryIonolian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1211 is chiral, and its enantiomorph is scale 2981

Scale 2981Scale 2981: Ionolian, Ian Ring Music TheoryIonolian

Transformations:

T0 1211  T0I 2981
T1 2422  T1I 1867
T2 749  T2I 3734
T3 1498  T3I 3373
T4 2996  T4I 2651
T5 1897  T5I 1207
T6 3794  T6I 2414
T7 3493  T7I 733
T8 2891  T8I 1466
T9 1687  T9I 2932
T10 3374  T10I 1769
T11 2653  T11I 3538

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 1209Scale 1209: Raga Bhanumanjari, Ian Ring Music TheoryRaga Bhanumanjari
Scale 1213Scale 1213: Gyrian, Ian Ring Music TheoryGyrian
Scale 1215Scale 1215, Ian Ring Music Theory
Scale 1203Scale 1203: Pagimic, Ian Ring Music TheoryPagimic
Scale 1207Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian
Scale 1195Scale 1195: Raga Gandharavam, Ian Ring Music TheoryRaga Gandharavam
Scale 1179Scale 1179: Sonimic, Ian Ring Music TheorySonimic
Scale 1243Scale 1243: Epylian, Ian Ring Music TheoryEpylian
Scale 1275Scale 1275: Stagyllic, Ian Ring Music TheoryStagyllic
Scale 1083Scale 1083, Ian Ring Music Theory
Scale 1147Scale 1147: Epynian, Ian Ring Music TheoryEpynian
Scale 1339Scale 1339: Kycrian, Ian Ring Music TheoryKycrian
Scale 1467Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish Phrygian
Scale 1723Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic
Scale 187Scale 187, Ian Ring Music Theory
Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian
Scale 2235Scale 2235: Bathian, Ian Ring Music TheoryBathian
Scale 3259Scale 3259, 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.