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Scale 3241: "Dalimic"

Scale 3241: Dalimic, 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
Dalimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,5,7,10,11}
Forte Number6-Z48
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections2
Modes5
Prime?no
prime: 679
Deep Scaleno
Interval Vector232341
Interval Spectrump4m3n2s3d2t
Distribution Spectra<1> = {1,2,3}
<2> = {2,4,5}
<3> = {5,6,7}
<4> = {7,8,10}
<5> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[10]
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 TriadsD♯{3,7,10}121
Minor Triadscm{0,3,7}121
Augmented TriadsD♯+{3,7,11}210.67
Parsimonious Voice Leading Between Common Triads of Scale 3241. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ D# D# D#->D#+

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, D♯

Modes

Modes are the rotational transformation of this scale. Scale 3241 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 917
Scale 917: Dygimic, Ian Ring Music TheoryDygimic
3rd mode:
Scale 1253
Scale 1253: Zolimic, Ian Ring Music TheoryZolimic
4th mode:
Scale 1337
Scale 1337: Epogimic, Ian Ring Music TheoryEpogimic
5th mode:
Scale 679
Scale 679: Lanimic, Ian Ring Music TheoryLanimicThis is the prime mode
6th mode:
Scale 2387
Scale 2387: Paptimic, Ian Ring Music TheoryPaptimic

Prime

The prime form of this scale is Scale 679

Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic

Complement

The hexatonic modal family [3241, 917, 1253, 1337, 679, 2387] (Forte: 6-Z48) is the complement of the hexatonic modal family [427, 1379, 1421, 1589, 2261, 2737] (Forte: 6-Z26)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3241 is 679

Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic

Transformations:

T0 3241  T0I 679
T1 2387  T1I 1358
T2 679  T2I 2716
T3 1358  T3I 1337
T4 2716  T4I 2674
T5 1337  T5I 1253
T6 2674  T6I 2506
T7 1253  T7I 917
T8 2506  T8I 1834
T9 917  T9I 3668
T10 1834  T10I 3241
T11 3668  T11I 2387

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 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
Scale 3245Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
Scale 3233Scale 3233, Ian Ring Music Theory
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3249Scale 3249: Raga Tilang, Ian Ring Music TheoryRaga Tilang
Scale 3257Scale 3257: Mela Calanata, Ian Ring Music TheoryMela Calanata
Scale 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
Scale 3225Scale 3225: Ionalimic, Ian Ring Music TheoryIonalimic
Scale 3273Scale 3273: Raga Jivantini, Ian Ring Music TheoryRaga Jivantini
Scale 3305Scale 3305: Chromatic Hypophrygian, Ian Ring Music TheoryChromatic Hypophrygian
Scale 3113Scale 3113, Ian Ring Music Theory
Scale 3177Scale 3177: Rothimic, Ian Ring Music TheoryRothimic
Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic
Scale 3497Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian
Scale 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian
Scale 2217Scale 2217: Kagitonic, Ian Ring Music TheoryKagitonic
Scale 2729Scale 2729: Aeragimic, Ian Ring Music TheoryAeragimic
Scale 1193Scale 1193: Minor Pentatonic, Ian Ring Music TheoryMinor Pentatonic

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.