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Scale 369: "Laditonic"

Scale 369: Laditonic, 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
Laditonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,4,5,6,8}
Forte Number5-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 465
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes4
Prime?no
prime: 279
Deep Scaleno
Interval Vector221311
Interval Spectrumpm3ns2d2t
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6,8}
<3> = {4,6,7,9,10}
<4> = {8,10,11}
Spectra Variation3.6
Maximally Evenno
Maximal Area Setno
Interior Area1.799
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
Minor Triadsfm{5,8,0}110.5
Augmented TriadsC+{0,4,8}110.5
Parsimonious Voice Leading Between Common Triads of Scale 369. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm

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 369 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 279
Scale 279: Poditonic, Ian Ring Music TheoryPoditonicThis is the prime mode
3rd mode:
Scale 2187
Scale 2187: Ionothitonic, Ian Ring Music TheoryIonothitonic
4th mode:
Scale 3141
Scale 3141: Kanitonic, Ian Ring Music TheoryKanitonic
5th mode:
Scale 1809
Scale 1809: Ranitonic, Ian Ring Music TheoryRanitonic

Prime

The prime form of this scale is Scale 279

Scale 279Scale 279: Poditonic, Ian Ring Music TheoryPoditonic

Complement

The pentatonic modal family [369, 279, 2187, 3141, 1809] (Forte: 5-13) is the complement of the heptatonic modal family [375, 1815, 1905, 2235, 2955, 3165, 3525] (Forte: 7-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 369 is 465

Scale 465Scale 465: Zoditonic, Ian Ring Music TheoryZoditonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 369 is chiral, and its enantiomorph is scale 465

Scale 465Scale 465: Zoditonic, Ian Ring Music TheoryZoditonic

Transformations:

T0 369  T0I 465
T1 738  T1I 930
T2 1476  T2I 1860
T3 2952  T3I 3720
T4 1809  T4I 3345
T5 3618  T5I 2595
T6 3141  T6I 1095
T7 2187  T7I 2190
T8 279  T8I 285
T9 558  T9I 570
T10 1116  T10I 1140
T11 2232  T11I 2280

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 371Scale 371: Rythimic, Ian Ring Music TheoryRythimic
Scale 373Scale 373: Epagimic, Ian Ring Music TheoryEpagimic
Scale 377Scale 377: Kathimic, Ian Ring Music TheoryKathimic
Scale 353Scale 353, Ian Ring Music Theory
Scale 361Scale 361: Bocritonic, Ian Ring Music TheoryBocritonic
Scale 337Scale 337: Koptic, Ian Ring Music TheoryKoptic
Scale 305Scale 305: Gonic, Ian Ring Music TheoryGonic
Scale 433Scale 433: Raga Zilaf, Ian Ring Music TheoryRaga Zilaf
Scale 497Scale 497: Kadimic, Ian Ring Music TheoryKadimic
Scale 113Scale 113, Ian Ring Music Theory
Scale 241Scale 241, Ian Ring Music Theory
Scale 625Scale 625: Ionyptitonic, Ian Ring Music TheoryIonyptitonic
Scale 881Scale 881: Aerothimic, Ian Ring Music TheoryAerothimic
Scale 1393Scale 1393: Mycrimic, Ian Ring Music TheoryMycrimic
Scale 2417Scale 2417: Kanimic, Ian Ring Music TheoryKanimic

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.