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Scale 2523: "Mirage Scale"

Scale 2523: Mirage Scale, 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

Western Modern
Mirage Scale
Zeitler
Rygyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,6,7,8,11}
Forte Number8-20
Rotational Symmetrynone
Reflection Axes3.5
Palindromicno
Chiralityno
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 951
Deep Scaleno
Interval Vector545662
Interval Spectrump6m6n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5}
<4> = {5,6,7}
<5> = {7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tones[7]
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 TriadsC{0,4,7}431.67
E{4,8,11}342
G♯{8,0,3}331.83
B{11,3,6}252.5
Minor Triadscm{0,3,7}431.67
c♯m{1,4,8}252.5
em{4,7,11}331.83
g♯m{8,11,3}342
Augmented TriadsC+{0,4,8}441.83
D♯+{3,7,11}441.83
Diminished Triads{0,3,6}242.33
c♯°{1,4,7}242.33
Parsimonious Voice Leading Between Common Triads of Scale 2523. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E C+->G# c#°->c#m D#+->em g#m g#m D#+->g#m D#+->B em->E E->g#m g#m->G#

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
Radius3
Self-Centeredno
Central Verticescm, C, em, G♯
Peripheral Verticesc♯m, B

Modes

Modes are the rotational transformation of this scale. Scale 2523 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3309
Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic
3rd mode:
Scale 1851
Scale 1851: Zacryllic, Ian Ring Music TheoryZacryllic
4th mode:
Scale 2973
Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
5th mode:
Scale 1767
Scale 1767: Dyryllic, Ian Ring Music TheoryDyryllic
6th mode:
Scale 2931
Scale 2931: Zathyllic, Ian Ring Music TheoryZathyllic
7th mode:
Scale 3513
Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic
8th mode:
Scale 951
Scale 951: Thogyllic, Ian Ring Music TheoryThogyllicThis is the prime mode

Prime

The prime form of this scale is Scale 951

Scale 951Scale 951: Thogyllic, Ian Ring Music TheoryThogyllic

Complement

The octatonic modal family [2523, 3309, 1851, 2973, 1767, 2931, 3513, 951] (Forte: 8-20) is the complement of the tetratonic modal family [291, 393, 561, 2193] (Forte: 4-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2523 is 2931

Scale 2931Scale 2931: Zathyllic, Ian Ring Music TheoryZathyllic

Transformations:

T0 2523  T0I 2931
T1 951  T1I 1767
T2 1902  T2I 3534
T3 3804  T3I 2973
T4 3513  T4I 1851
T5 2931  T5I 3702
T6 1767  T6I 3309
T7 3534  T7I 2523
T8 2973  T8I 951
T9 1851  T9I 1902
T10 3702  T10I 3804
T11 3309  T11I 3513

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 2521Scale 2521: Mela Dhatuvardhani, Ian Ring Music TheoryMela Dhatuvardhani
Scale 2525Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic
Scale 2527Scale 2527: Phradygic, Ian Ring Music TheoryPhradygic
Scale 2515Scale 2515: Chromatic Hypolydian, Ian Ring Music TheoryChromatic Hypolydian
Scale 2519Scale 2519: Dathyllic, Ian Ring Music TheoryDathyllic
Scale 2507Scale 2507: Todi That, Ian Ring Music TheoryTodi That
Scale 2539Scale 2539: Half-Diminished Bebop, Ian Ring Music TheoryHalf-Diminished Bebop
Scale 2555Scale 2555: Bythygic, Ian Ring Music TheoryBythygic
Scale 2459Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian
Scale 2491Scale 2491: Layllic, Ian Ring Music TheoryLayllic
Scale 2395Scale 2395: Zoptian, Ian Ring Music TheoryZoptian
Scale 2267Scale 2267: Padian, Ian Ring Music TheoryPadian
Scale 2779Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 3547Scale 3547: Sadygic, Ian Ring Music TheorySadygic
Scale 475Scale 475: Aeolygian, Ian Ring Music TheoryAeolygian
Scale 1499Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian

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.