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Scale 2191: "Thydimic"

Scale 2191: Thydimic, 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
Thydimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,3,7,11}
Forte Number6-Z37
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes5
Prime?no
prime: 287
Deep Scaleno
Interval Vector432321
Interval Spectrump2m3n2s3d4t
Distribution Spectra<1> = {1,4}
<2> = {2,5,8}
<3> = {3,6,9}
<4> = {4,7,10}
<5> = {8,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.866
Myhill Propertyno
Balancedno
Ridge Tones[2]
ProprietyImproper
Heliotonicno

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{7,11,2}121
Minor Triadscm{0,3,7}121
Augmented TriadsD♯+{3,7,11}210.67
Parsimonious Voice Leading Between Common Triads of Scale 2191. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ Parsimonious Voice Leading Between Common Triads of Scale 2191. Created by Ian Ring ©2019 G D#+->G

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
Radius1
Self-Centeredno
Central VerticesD♯+
Peripheral Verticescm, G

Modes

Modes are the rotational transformation of this scale. Scale 2191 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3143
Scale 3143: Polimic, Ian Ring Music TheoryPolimic
3rd mode:
Scale 3619
Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
4th mode:
Scale 3857
Scale 3857: Ponimic, Ian Ring Music TheoryPonimic
5th mode:
Scale 497
Scale 497: Kadimic, Ian Ring Music TheoryKadimic
6th mode:
Scale 287
Scale 287: Gynimic, Ian Ring Music TheoryGynimicThis is the prime mode

Prime

The prime form of this scale is Scale 287

Scale 287Scale 287: Gynimic, Ian Ring Music TheoryGynimic

Complement

The hexatonic modal family [2191, 3143, 3619, 3857, 497, 287] (Forte: 6-Z37) is the complement of the hexatonic modal family [119, 1799, 2107, 2947, 3101, 3521] (Forte: 6-Z4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2191 is 3619

Scale 3619Scale 3619: Thanimic, Ian Ring Music TheoryThanimic

Transformations:

T0 2191  T0I 3619
T1 287  T1I 3143
T2 574  T2I 2191
T3 1148  T3I 287
T4 2296  T4I 574
T5 497  T5I 1148
T6 994  T6I 2296
T7 1988  T7I 497
T8 3976  T8I 994
T9 3857  T9I 1988
T10 3619  T10I 3976
T11 3143  T11I 3857

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 2189Scale 2189: Zagitonic, Ian Ring Music TheoryZagitonic
Scale 2187Scale 2187: Ionothitonic, Ian Ring Music TheoryIonothitonic
Scale 2183Scale 2183, Ian Ring Music Theory
Scale 2199Scale 2199: Dyptimic, Ian Ring Music TheoryDyptimic
Scale 2207Scale 2207: Mygian, Ian Ring Music TheoryMygian
Scale 2223Scale 2223: Konian, Ian Ring Music TheoryKonian
Scale 2255Scale 2255: Dylian, Ian Ring Music TheoryDylian
Scale 2063Scale 2063, Ian Ring Music Theory
Scale 2127Scale 2127, Ian Ring Music Theory
Scale 2319Scale 2319, Ian Ring Music Theory
Scale 2447Scale 2447: Thagian, Ian Ring Music TheoryThagian
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 3215Scale 3215: Katydian, Ian Ring Music TheoryKatydian
Scale 143Scale 143, Ian Ring Music Theory
Scale 1167Scale 1167: Aerodimic, Ian Ring Music TheoryAerodimic

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.