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Scale 2395: "Zoptian"

Scale 2395: Zoptian, 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
Zoptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,6,8,11}
Forte Number7-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2899
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections2
Modes6
Prime?no
prime: 695
Deep Scaleno
Interval Vector344451
Interval Spectrump5m4n4s4d3t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.286
Maximally Evenno
Maximal Area Setno
Interior Area2.549
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 TriadsE{4,8,11}231.57
G♯{8,0,3}321.29
B{11,3,6}241.86
Minor Triadsc♯m{1,4,8}142.14
g♯m{8,11,3}331.43
Augmented TriadsC+{0,4,8}331.43
Diminished Triads{0,3,6}231.71
Parsimonious Voice Leading Between Common Triads of Scale 2395. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E C+->G# g#m g#m E->g#m g#m->G# g#m->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.

Diameter4
Radius2
Self-Centeredno
Central VerticesG♯
Peripheral Verticesc♯m, B

Modes

Modes are the rotational transformation of this scale. Scale 2395 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3245
Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
3rd mode:
Scale 1835
Scale 1835: Byptian, Ian Ring Music TheoryByptian
4th mode:
Scale 2965
Scale 2965: Darian, Ian Ring Music TheoryDarian
5th mode:
Scale 1765
Scale 1765: Lonian, Ian Ring Music TheoryLonian
6th mode:
Scale 1465
Scale 1465: Mela Ragavardhani, Ian Ring Music TheoryMela Ragavardhani
7th mode:
Scale 695
Scale 695: Sarian, Ian Ring Music TheorySarianThis is the prime mode

Prime

The prime form of this scale is Scale 695

Scale 695Scale 695: Sarian, Ian Ring Music TheorySarian

Complement

The heptatonic modal family [2395, 3245, 1835, 2965, 1765, 1465, 695] (Forte: 7-27) is the complement of the pentatonic modal family [299, 689, 1417, 1573, 2197] (Forte: 5-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2395 is 2899

Scale 2899Scale 2899: Kagian, Ian Ring Music TheoryKagian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2395 is chiral, and its enantiomorph is scale 2899

Scale 2899Scale 2899: Kagian, Ian Ring Music TheoryKagian

Transformations:

T0 2395  T0I 2899
T1 695  T1I 1703
T2 1390  T2I 3406
T3 2780  T3I 2717
T4 1465  T4I 1339
T5 2930  T5I 2678
T6 1765  T6I 1261
T7 3530  T7I 2522
T8 2965  T8I 949
T9 1835  T9I 1898
T10 3670  T10I 3796
T11 3245  T11I 3497

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 2393Scale 2393: Zathimic, Ian Ring Music TheoryZathimic
Scale 2397Scale 2397: Stagian, Ian Ring Music TheoryStagian
Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 2387Scale 2387: Paptimic, Ian Ring Music TheoryPaptimic
Scale 2391Scale 2391: Molian, Ian Ring Music TheoryMolian
Scale 2379Scale 2379: Raga Gurjari Todi, Ian Ring Music TheoryRaga Gurjari Todi
Scale 2411Scale 2411: Aeolorian, Ian Ring Music TheoryAeolorian
Scale 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
Scale 2331Scale 2331: Dylimic, Ian Ring Music TheoryDylimic
Scale 2363Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
Scale 2459Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian
Scale 2523Scale 2523: Mirage Scale, Ian Ring Music TheoryMirage Scale
Scale 2139Scale 2139, Ian Ring Music Theory
Scale 2267Scale 2267: Padian, Ian Ring Music TheoryPadian
Scale 2651Scale 2651: Panian, Ian Ring Music TheoryPanian
Scale 2907Scale 2907: Magen Abot 2, Ian Ring Music TheoryMagen Abot 2
Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic
Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian

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.