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Scale 1821: "Aeradian"

Scale 1821: Aeradian, 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
Aeradian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,4,8,9,10}
Forte Number7-15
Rotational Symmetrynone
Reflection Axes0
Palindromicyes
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 471
Deep Scaleno
Interval Vector442443
Interval Spectrump4m4n2s4d4t3
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9,10}
<6> = {8,10,11}
Spectra Variation2.286
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tones[0]
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 TriadsG♯{8,0,3}221
Minor Triadsam{9,0,4}221
Augmented TriadsC+{0,4,8}221
Diminished Triads{9,0,3}221
Parsimonious Voice Leading Between Common Triads of Scale 1821. Created by Ian Ring ©2019 C+ C+ G# G# C+->G# am am C+->am G#->a° a°->am

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.

Diameter2
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1821 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1479
Scale 1479: Mela Jalarnava, Ian Ring Music TheoryMela Jalarnava
3rd mode:
Scale 2787
Scale 2787: Zyrian, Ian Ring Music TheoryZyrian
4th mode:
Scale 3441
Scale 3441: Thacrian, Ian Ring Music TheoryThacrian
5th mode:
Scale 471
Scale 471: Dodian, Ian Ring Music TheoryDodianThis is the prime mode
6th mode:
Scale 2283
Scale 2283: Aeolyptian, Ian Ring Music TheoryAeolyptian
7th mode:
Scale 3189
Scale 3189: Aeolonian, Ian Ring Music TheoryAeolonian

Prime

The prime form of this scale is Scale 471

Scale 471Scale 471: Dodian, Ian Ring Music TheoryDodian

Complement

The heptatonic modal family [1821, 1479, 2787, 3441, 471, 2283, 3189] (Forte: 7-15) is the complement of the pentatonic modal family [327, 453, 1137, 2211, 3153] (Forte: 5-15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1821 is itself, because it is a palindromic scale!

Scale 1821Scale 1821: Aeradian, Ian Ring Music TheoryAeradian

Transformations:

T0 1821  T0I 1821
T1 3642  T1I 3642
T2 3189  T2I 3189
T3 2283  T3I 2283
T4 471  T4I 471
T5 942  T5I 942
T6 1884  T6I 1884
T7 3768  T7I 3768
T8 3441  T8I 3441
T9 2787  T9I 2787
T10 1479  T10I 1479
T11 2958  T11I 2958

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 1823Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic
Scale 1817Scale 1817: Phrythimic, Ian Ring Music TheoryPhrythimic
Scale 1819Scale 1819: Pydian, Ian Ring Music TheoryPydian
Scale 1813Scale 1813: Katothimic, Ian Ring Music TheoryKatothimic
Scale 1805Scale 1805, Ian Ring Music Theory
Scale 1837Scale 1837: Dalian, Ian Ring Music TheoryDalian
Scale 1853Scale 1853: Maryllic, Ian Ring Music TheoryMaryllic
Scale 1885Scale 1885: Saptyllic, Ian Ring Music TheorySaptyllic
Scale 1949Scale 1949: Mathyllic, Ian Ring Music TheoryMathyllic
Scale 1565Scale 1565, Ian Ring Music Theory
Scale 1693Scale 1693: Dogian, Ian Ring Music TheoryDogian
Scale 1309Scale 1309: Pogimic, Ian Ring Music TheoryPogimic
Scale 797Scale 797: Katocrimic, Ian Ring Music TheoryKatocrimic
Scale 2845Scale 2845: Baptian, Ian Ring Music TheoryBaptian
Scale 3869Scale 3869: Bygyllic, Ian Ring Music TheoryBygyllic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.