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Scale 4045: "Gyptygic"

Scale 4045: Gyptygic, 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
Gyptygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,6,7,8,9,10,11}
Forte Number9-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1663
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 895
Deep Scaleno
Interval Vector767763
Interval Spectrump6m7n7s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2.222
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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}342.53
D♯{3,7,10}342.24
G{7,11,2}442.24
G♯{8,0,3}342.53
B{11,3,6}442.12
Minor Triadscm{0,3,7}342.35
d♯m{3,6,10}442.24
gm{7,10,2}342.35
g♯m{8,11,3}342.35
bm{11,2,6}342.24
Augmented TriadsD+{2,6,10}442.24
D♯+{3,7,11}542
Diminished Triads{0,3,6}242.59
d♯°{3,6,9}252.71
f♯°{6,9,0}242.76
g♯°{8,11,2}252.71
{9,0,3}242.76
Parsimonious Voice Leading Between Common Triads of Scale 4045. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# D D D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° d#m d#m D+->d#m gm gm D+->gm bm bm D+->bm d#°->d#m D# D# d#m->D# d#m->B D#->D#+ D#->gm Parsimonious Voice Leading Between Common Triads of Scale 4045. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m D#+->B f#°->a° gm->G g#° g#° G->g#° G->bm g#°->g#m g#m->G# G#->a° bm->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.

Diameter5
Radius4
Self-Centeredno
Central Verticesc°, cm, D, D+, d♯m, D♯, D♯+, f♯°, gm, G, g♯m, G♯, a°, bm, B
Peripheral Verticesd♯°, g♯°

Modes

Modes are the rotational transformation of this scale. Scale 4045 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2035
Scale 2035: Aerythygic, Ian Ring Music TheoryAerythygic
3rd mode:
Scale 3065
Scale 3065: Zothygic, Ian Ring Music TheoryZothygic
4th mode:
Scale 895
Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygicThis is the prime mode
5th mode:
Scale 2495
Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
6th mode:
Scale 3295
Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
7th mode:
Scale 3695
Scale 3695: Kodygic, Ian Ring Music TheoryKodygic
8th mode:
Scale 3895
Scale 3895: Eparygic, Ian Ring Music TheoryEparygic
9th mode:
Scale 3995
Scale 3995: Ionygic, Ian Ring Music TheoryIonygic

Prime

The prime form of this scale is Scale 895

Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic

Complement

The nonatonic modal family [4045, 2035, 3065, 895, 2495, 3295, 3695, 3895, 3995] (Forte: 9-3) is the complement of the tritonic modal family [19, 769, 2057] (Forte: 3-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4045 is 1663

Scale 1663Scale 1663: Lydygic, Ian Ring Music TheoryLydygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 4045 is chiral, and its enantiomorph is scale 1663

Scale 1663Scale 1663: Lydygic, Ian Ring Music TheoryLydygic

Transformations:

T0 4045  T0I 1663
T1 3995  T1I 3326
T2 3895  T2I 2557
T3 3695  T3I 1019
T4 3295  T4I 2038
T5 2495  T5I 4076
T6 895  T6I 4057
T7 1790  T7I 4019
T8 3580  T8I 3943
T9 3065  T9I 3791
T10 2035  T10I 3487
T11 4070  T11I 2879

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 4047Scale 4047: Thogyllian, Ian Ring Music TheoryThogyllian
Scale 4041Scale 4041: Zaryllic, Ian Ring Music TheoryZaryllic
Scale 4043Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
Scale 4037Scale 4037: Ionyllic, Ian Ring Music TheoryIonyllic
Scale 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
Scale 4061Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
Scale 4077Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
Scale 3981Scale 3981: Phrycryllic, Ian Ring Music TheoryPhrycryllic
Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu
Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic
Scale 3789Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic
Scale 3533Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic
Scale 3021Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
Scale 1997Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.