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Scale 2903: "Gothyllic"

Scale 2903: Gothyllic, 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
Gothyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,6,8,9,11}
Forte Number8-22
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3419
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 1391
Deep Scaleno
Interval Vector465562
Interval Spectrump6m5n5s6d4t2
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.75
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
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}242.1
E{4,8,11}242.1
A{9,1,4}341.9
Minor Triadsc♯m{1,4,8}242.1
f♯m{6,9,1}341.9
am{9,0,4}341.9
bm{11,2,6}242.3
Augmented TriadsC+{0,4,8}341.9
Diminished Triadsf♯°{6,9,0}242.1
g♯°{8,11,2}242.3
Parsimonious Voice Leading Between Common Triads of Scale 2903. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E am am C+->am A A c#m->A D D f#m f#m D->f#m bm bm D->bm g#° g#° E->g#° f#° f#° f#°->f#m f#°->am f#m->A g#°->bm am->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2903 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3499
Scale 3499: Hamel, Ian Ring Music TheoryHamel
3rd mode:
Scale 3797
Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic
4th mode:
Scale 1973
Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
5th mode:
Scale 1517
Scale 1517: Sagyllic, Ian Ring Music TheorySagyllic
6th mode:
Scale 1403
Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale
7th mode:
Scale 2749
Scale 2749: Katagyllic, Ian Ring Music TheoryKatagyllic
8th mode:
Scale 1711
Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh

Prime

The prime form of this scale is Scale 1391

Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic

Complement

The octatonic modal family [2903, 3499, 3797, 1973, 1517, 1403, 2749, 1711] (Forte: 8-22) is the complement of the tetratonic modal family [149, 673, 1061, 1289] (Forte: 4-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2903 is 3419

Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2903 is chiral, and its enantiomorph is scale 3419

Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1

Transformations:

T0 2903  T0I 3419
T1 1711  T1I 2743
T2 3422  T2I 1391
T3 2749  T3I 2782
T4 1403  T4I 1469
T5 2806  T5I 2938
T6 1517  T6I 1781
T7 3034  T7I 3562
T8 1973  T8I 3029
T9 3946  T9I 1963
T10 3797  T10I 3926
T11 3499  T11I 3757

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 2901Scale 2901: Lydian Augmented, Ian Ring Music TheoryLydian Augmented
Scale 2899Scale 2899: Kagian, Ian Ring Music TheoryKagian
Scale 2907Scale 2907: Magen Abot 2, Ian Ring Music TheoryMagen Abot 2
Scale 2911Scale 2911: Katygic, Ian Ring Music TheoryKatygic
Scale 2887Scale 2887: Gaptian, Ian Ring Music TheoryGaptian
Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
Scale 2935Scale 2935: Modygic, Ian Ring Music TheoryModygic
Scale 2839Scale 2839: Lyptian, Ian Ring Music TheoryLyptian
Scale 2871Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
Scale 2967Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
Scale 3031Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic
Scale 2647Scale 2647: Dadian, Ian Ring Music TheoryDadian
Scale 2775Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
Scale 2391Scale 2391: Molian, Ian Ring Music TheoryMolian
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
Scale 3927Scale 3927: Monygic, Ian Ring Music TheoryMonygic
Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian
Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic

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.