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Scale 3155: "Ladimic"

Scale 3155: Ladimic, 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

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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
Ladimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,4,6,10,11}
Forte Number6-Z41
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2375
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?no
prime: 335
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,4,5,6}
<3> = {3,5,6,7,9}
<4> = {6,7,8,10}
<5> = {8,9,10,11}
Spectra Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
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 TriadsF♯{6,10,1}110.5
Diminished Triadsa♯°{10,1,4}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3155. Created by Ian Ring ©2019 F# F# a#° a#° F#->a#°

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3155 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3625
Scale 3625: Podimic, Ian Ring Music TheoryPodimic
3rd mode:
Scale 965
Scale 965: Ionothimic, Ian Ring Music TheoryIonothimic
4th mode:
Scale 1265
Scale 1265: Pynimic, Ian Ring Music TheoryPynimic
5th mode:
Scale 335
Scale 335: Zanimic, Ian Ring Music TheoryZanimicThis is the prime mode
6th mode:
Scale 2215
Scale 2215: Ranimic, Ian Ring Music TheoryRanimic

Prime

The prime form of this scale is Scale 335

Scale 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic

Complement

The hexatonic modal family [3155, 3625, 965, 1265, 335, 2215] (Forte: 6-Z41) is the complement of the hexatonic modal family [215, 1475, 1805, 2155, 2785, 3125] (Forte: 6-Z12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3155 is 2375

Scale 2375Scale 2375: Aeolaptimic, Ian Ring Music TheoryAeolaptimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3155 is chiral, and its enantiomorph is scale 2375

Scale 2375Scale 2375: Aeolaptimic, Ian Ring Music TheoryAeolaptimic

Transformations:

T0 3155  T0I 2375
T1 2215  T1I 655
T2 335  T2I 1310
T3 670  T3I 2620
T4 1340  T4I 1145
T5 2680  T5I 2290
T6 1265  T6I 485
T7 2530  T7I 970
T8 965  T8I 1940
T9 1930  T9I 3880
T10 3860  T10I 3665
T11 3625  T11I 3235

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 3153Scale 3153: Zathitonic, Ian Ring Music TheoryZathitonic
Scale 3157Scale 3157: Zyptimic, Ian Ring Music TheoryZyptimic
Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3139Scale 3139, Ian Ring Music Theory
Scale 3147Scale 3147: Ryrimic, Ian Ring Music TheoryRyrimic
Scale 3171Scale 3171: Zythimic, Ian Ring Music TheoryZythimic
Scale 3187Scale 3187: Koptian, Ian Ring Music TheoryKoptian
Scale 3091Scale 3091, Ian Ring Music Theory
Scale 3123Scale 3123, Ian Ring Music Theory
Scale 3219Scale 3219: Ionaphimic, Ian Ring Music TheoryIonaphimic
Scale 3283Scale 3283: Mela Visvambhari, Ian Ring Music TheoryMela Visvambhari
Scale 3411Scale 3411: Enigmatic, Ian Ring Music TheoryEnigmatic
Scale 3667Scale 3667: Kaptian, Ian Ring Music TheoryKaptian
Scale 2131Scale 2131, Ian Ring Music Theory
Scale 2643Scale 2643: Raga Hamsanandi, Ian Ring Music TheoryRaga Hamsanandi
Scale 1107Scale 1107: Mogitonic, Ian Ring Music TheoryMogitonic

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.