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Scale 3017: "Gacrian"

Scale 3017: Gacrian, 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
Gacrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,6,7,8,9,11}
Forte Number7-16
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 635
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 623
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
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}331.67
B{11,3,6}331.67
Minor Triadscm{0,3,7}331.67
g♯m{8,11,3}231.89
Augmented TriadsD♯+{3,7,11}331.67
Diminished Triads{0,3,6}231.89
d♯°{3,6,9}231.89
f♯°{6,9,0}232
{9,0,3}231.89
Parsimonious Voice Leading Between Common Triads of Scale 3017. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# d#° d#° f#° f#° d#°->f#° d#°->B g#m g#m D#+->g#m D#+->B f#°->a° g#m->G# G#->a°

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 3017 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 889
Scale 889: Borian, Ian Ring Music TheoryBorian
3rd mode:
Scale 623
Scale 623: Sycrian, Ian Ring Music TheorySycrianThis is the prime mode
4th mode:
Scale 2359
Scale 2359: Gadian, Ian Ring Music TheoryGadian
5th mode:
Scale 3227
Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
6th mode:
Scale 3661
Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
7th mode:
Scale 1939
Scale 1939: Dathian, Ian Ring Music TheoryDathian

Prime

The prime form of this scale is Scale 623

Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian

Complement

The heptatonic modal family [3017, 889, 623, 2359, 3227, 3661, 1939] (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 3017 is 635

Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3017 is chiral, and its enantiomorph is scale 635

Scale 635Scale 635: Epolian, Ian Ring Music TheoryEpolian

Transformations:

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

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 3019Scale 3019, Ian Ring Music Theory
Scale 3021Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
Scale 3009Scale 3009, Ian Ring Music Theory
Scale 3013Scale 3013: Thynian, Ian Ring Music TheoryThynian
Scale 3025Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian
Scale 3033Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic
Scale 3049Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
Scale 2953Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic
Scale 2985Scale 2985: Epacrian, Ian Ring Music TheoryEpacrian
Scale 2889Scale 2889: Thoptimic, Ian Ring Music TheoryThoptimic
Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
Scale 2505Scale 2505: Mydimic, Ian Ring Music TheoryMydimic
Scale 3529Scale 3529: Stalian, Ian Ring Music TheoryStalian
Scale 4041Scale 4041: Zaryllic, Ian Ring Music TheoryZaryllic
Scale 969Scale 969: Ionogimic, Ian Ring Music TheoryIonogimic
Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian

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.