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Scale 3373: "Lodian"

Scale 3373: Lodian, 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
Lodian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,5,8,10,11}
Forte Number7-25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1687
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 733
Deep Scaleno
Interval Vector345342
Interval Spectrump4m3n5s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {9,10,11}
Spectra Variation2.286
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
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}231.75
A♯{10,2,5}231.88
Minor Triadsfm{5,8,0}331.63
g♯m{8,11,3}331.63
Diminished Triads{2,5,8}231.75
{5,8,11}231.75
g♯°{8,11,2}231.75
{11,2,5}231.88
Parsimonious Voice Leading Between Common Triads of Scale 3373. Created by Ian Ring ©2019 fm fm d°->fm A# A# d°->A# f°->fm g#m g#m f°->g#m G# G# fm->G# g#° g#° g#°->g#m g#°->b° g#m->G# A#->b°

view full size

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3373 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1867
Scale 1867: Solian, Ian Ring Music TheorySolian
3rd mode:
Scale 2981
Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
4th mode:
Scale 1769
Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
5th mode:
Scale 733
Scale 733: Donian, Ian Ring Music TheoryDonianThis is the prime mode
6th mode:
Scale 1207
Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian
7th mode:
Scale 2651
Scale 2651: Panian, Ian Ring Music TheoryPanian

Prime

The prime form of this scale is Scale 733

Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian

Complement

The heptatonic modal family [3373, 1867, 2981, 1769, 733, 1207, 2651] (Forte: 7-25) is the complement of the pentatonic modal family [301, 721, 1099, 1673, 2597] (Forte: 5-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3373 is 1687

Scale 1687Scale 1687: Phralian, Ian Ring Music TheoryPhralian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3373 is chiral, and its enantiomorph is scale 1687

Scale 1687Scale 1687: Phralian, Ian Ring Music TheoryPhralian

Transformations:

T0 3373  T0I 1687
T1 2651  T1I 3374
T2 1207  T2I 2653
T3 2414  T3I 1211
T4 733  T4I 2422
T5 1466  T5I 749
T6 2932  T6I 1498
T7 1769  T7I 2996
T8 3538  T8I 1897
T9 2981  T9I 3794
T10 1867  T10I 3493
T11 3734  T11I 2891

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 3375Scale 3375, Ian Ring Music Theory
Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic
Scale 3371Scale 3371: Aeolylian, Ian Ring Music TheoryAeolylian
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian
Scale 3389Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
Scale 3341Scale 3341, Ian Ring Music Theory
Scale 3357Scale 3357: Phrodian, Ian Ring Music TheoryPhrodian
Scale 3405Scale 3405: Stynian, Ian Ring Music TheoryStynian
Scale 3437Scale 3437, Ian Ring Music Theory
Scale 3501Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
Scale 3117Scale 3117, Ian Ring Music Theory
Scale 3245Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
Scale 3629Scale 3629: Boptian, Ian Ring Music TheoryBoptian
Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
Scale 2349Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana
Scale 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian
Scale 1325Scale 1325: Phradimic, Ian Ring Music TheoryPhradimic

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.