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Scale 623: "Sycrian"

Scale 623: Sycrian, 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
Sycrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,5,6,9}
Forte Number7-16
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3785
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?yes
Deep Scaleno
Interval Vector435432
Interval Spectrump3m4n5s3d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,8,9,10}
<6> = {9,10,11}
Spectra Variation2.857
Maximally Evenno
Maximal Area Setno
Interior Area2.433
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 TriadsD{2,6,9}331.67
F{5,9,0}331.67
Minor Triadsdm{2,5,9}231.89
f♯m{6,9,1}331.67
Augmented TriadsC♯+{1,5,9}331.67
Diminished Triads{0,3,6}232
d♯°{3,6,9}231.89
f♯°{6,9,0}231.89
{9,0,3}231.89
Parsimonious Voice Leading Between Common Triads of Scale 623. Created by Ian Ring ©2019 d#° d#° c°->d#° c°->a° C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m D D dm->D D->d#° D->f#m f#° f#° F->f#° F->a° f#°->f#m

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 623 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2359
Scale 2359: Gadian, Ian Ring Music TheoryGadian
3rd mode:
Scale 3227
Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
4th mode:
Scale 3661
Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
5th mode:
Scale 1939
Scale 1939: Dathian, Ian Ring Music TheoryDathian
6th mode:
Scale 3017
Scale 3017: Gacrian, Ian Ring Music TheoryGacrian
7th mode:
Scale 889
Scale 889: Borian, Ian Ring Music TheoryBorian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [623, 2359, 3227, 3661, 1939, 3017, 889] (Forte: 7-16) is the complement of the pentatonic modal family [155, 865, 1555, 2125, 2825] (Forte: 5-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 623 is 3785

Scale 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 623 is chiral, and its enantiomorph is scale 3785

Scale 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian

Transformations:

T0 623  T0I 3785
T1 1246  T1I 3475
T2 2492  T2I 2855
T3 889  T3I 1615
T4 1778  T4I 3230
T5 3556  T5I 2365
T6 3017  T6I 635
T7 1939  T7I 1270
T8 3878  T8I 2540
T9 3661  T9I 985
T10 3227  T10I 1970
T11 2359  T11I 3940

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 621Scale 621: Pyramid Hexatonic, Ian Ring Music TheoryPyramid Hexatonic
Scale 619Scale 619: Double-Phrygian Hexatonic, Ian Ring Music TheoryDouble-Phrygian Hexatonic
Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic
Scale 631Scale 631: Zygian, Ian Ring Music TheoryZygian
Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic
Scale 591Scale 591: Gaptimic, Ian Ring Music TheoryGaptimic
Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian
Scale 559Scale 559: Lylimic, Ian Ring Music TheoryLylimic
Scale 687Scale 687: Aeolythian, Ian Ring Music TheoryAeolythian
Scale 751Scale 751, Ian Ring Music Theory
Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic
Scale 111Scale 111, Ian Ring Music Theory
Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian
Scale 1135Scale 1135: Katolian, Ian Ring Music TheoryKatolian
Scale 1647Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic
Scale 2671Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic

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.