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Scale 667: "Rodimic"

Scale 667: Rodimic, 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
Rodimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,4,7,9}
Forte Number6-Z49
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?yes
Deep Scaleno
Interval Vector224322
Interval Spectrump2m3n4s2d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {4,6,8}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[4]
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 TriadsC{0,4,7}321.17
A{9,1,4}231.5
Minor Triadscm{0,3,7}231.5
am{9,0,4}321.17
Diminished Triadsc♯°{1,4,7}231.5
{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 667. Created by Ian Ring ©2019 cm cm C C cm->C cm->a° c#° c#° C->c#° am am C->am A A c#°->A a°->am am->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.

Diameter3
Radius2
Self-Centeredno
Central VerticesC, am
Peripheral Verticescm, c♯°, a°, A

Modes

Modes are the rotational transformation of this scale. Scale 667 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2381
Scale 2381: Takemitsu Linea Mode 1, Ian Ring Music TheoryTakemitsu Linea Mode 1
3rd mode:
Scale 1619
Scale 1619: Prometheus Neapolitan, Ian Ring Music TheoryPrometheus Neapolitan
4th mode:
Scale 2857
Scale 2857: Stythimic, Ian Ring Music TheoryStythimic
5th mode:
Scale 869
Scale 869: Kothimic, Ian Ring Music TheoryKothimic
6th mode:
Scale 1241
Scale 1241: Pygimic, Ian Ring Music TheoryPygimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [667, 2381, 1619, 2857, 869, 1241] (Forte: 6-Z49) is the complement of the hexatonic modal family [619, 857, 1427, 1613, 2357, 2761] (Forte: 6-Z28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 667 is 2857

Scale 2857Scale 2857: Stythimic, Ian Ring Music TheoryStythimic

Transformations:

T0 667  T0I 2857
T1 1334  T1I 1619
T2 2668  T2I 3238
T3 1241  T3I 2381
T4 2482  T4I 667
T5 869  T5I 1334
T6 1738  T6I 2668
T7 3476  T7I 1241
T8 2857  T8I 2482
T9 1619  T9I 869
T10 3238  T10I 1738
T11 2381  T11I 3476

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 665Scale 665: Raga Mohanangi, Ian Ring Music TheoryRaga Mohanangi
Scale 669Scale 669: Gycrimic, Ian Ring Music TheoryGycrimic
Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian
Scale 659Scale 659: Raga Rasika Ranjani, Ian Ring Music TheoryRaga Rasika Ranjani
Scale 663Scale 663: Phrynimic, Ian Ring Music TheoryPhrynimic
Scale 651Scale 651: Golitonic, Ian Ring Music TheoryGolitonic
Scale 683Scale 683: Stogimic, Ian Ring Music TheoryStogimic
Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian
Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian
Scale 539Scale 539, Ian Ring Music Theory
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 795Scale 795: Aeologimic, Ian Ring Music TheoryAeologimic
Scale 923Scale 923: Ultraphrygian, Ian Ring Music TheoryUltraphrygian
Scale 155Scale 155, Ian Ring Music Theory
Scale 411Scale 411: Lygimic, Ian Ring Music TheoryLygimic
Scale 1179Scale 1179: Sonimic, Ian Ring Music TheorySonimic
Scale 1691Scale 1691: Kathian, Ian Ring Music TheoryKathian
Scale 2715Scale 2715: Kynian, Ian Ring Music TheoryKynian

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.