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Scale 605: "Dycrimic"

Scale 605: Dycrimic, 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
Dycrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,4,6,9}
Forte Number6-Z45
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes5
Prime?yes
Deep Scaleno
Interval Vector234222
Interval Spectrump2m2n4s3d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5,6}
<3> = {4,6,8}
<4> = {6,7,9,10}
<5> = {9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[6]
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{2,6,9}231.5
Minor Triadsam{9,0,4}231.5
Diminished Triads{0,3,6}231.5
d♯°{3,6,9}231.5
f♯°{6,9,0}231.5
{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 605. Created by Ian Ring ©2019 d#° d#° c°->d#° c°->a° D D D->d#° f#° f#° D->f#° am am f#°->am a°->am

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 605 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1175
Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic
3rd mode:
Scale 2635
Scale 2635: Gocrimic, Ian Ring Music TheoryGocrimic
4th mode:
Scale 3365
Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
5th mode:
Scale 1865
Scale 1865: Thagimic, Ian Ring Music TheoryThagimic
6th mode:
Scale 745
Scale 745: Kolimic, Ian Ring Music TheoryKolimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [605, 1175, 2635, 3365, 1865, 745] (Forte: 6-Z45) is the complement of the hexatonic modal family [365, 1115, 1675, 1745, 2605, 2885] (Forte: 6-Z23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 605 is 1865

Scale 1865Scale 1865: Thagimic, Ian Ring Music TheoryThagimic

Transformations:

T0 605  T0I 1865
T1 1210  T1I 3730
T2 2420  T2I 3365
T3 745  T3I 2635
T4 1490  T4I 1175
T5 2980  T5I 2350
T6 1865  T6I 605
T7 3730  T7I 1210
T8 3365  T8I 2420
T9 2635  T9I 745
T10 1175  T10I 1490
T11 2350  T11I 2980

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 607Scale 607: Kadian, Ian Ring Music TheoryKadian
Scale 601Scale 601: Bycritonic, Ian Ring Music TheoryBycritonic
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 597Scale 597: Kung, Ian Ring Music TheoryKung
Scale 589Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic
Scale 621Scale 621: Pyramid Hexatonic, Ian Ring Music TheoryPyramid Hexatonic
Scale 637Scale 637: Debussy's Heptatonic, Ian Ring Music TheoryDebussy's Heptatonic
Scale 541Scale 541, Ian Ring Music Theory
Scale 573Scale 573: Saptimic, Ian Ring Music TheorySaptimic
Scale 669Scale 669: Gycrimic, Ian Ring Music TheoryGycrimic
Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian
Scale 861Scale 861: Rylian, Ian Ring Music TheoryRylian
Scale 93Scale 93, Ian Ring Music Theory
Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic
Scale 1117Scale 1117: Raptimic, Ian Ring Music TheoryRaptimic
Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 2653Scale 2653: Sygian, Ian Ring Music TheorySygian

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.