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Scale 2615: "Thoptian"

Scale 2615: Thoptian, 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
Thoptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,5,9,11}
Forte Number7-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3467
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 379
Deep Scaleno
Interval Vector444441
Interval Spectrump4m4n4s4d4t
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,7}
<4> = {5,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.299
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 TriadsF{5,9,0}231.5
A{9,1,4}231.5
Minor Triadsdm{2,5,9}231.5
am{9,0,4}241.83
Augmented TriadsC♯+{1,5,9}321.17
Diminished Triads{11,2,5}142.17
Parsimonious Voice Leading Between Common Triads of Scale 2615. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F A A C#+->A dm->b° am am F->am 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
Radius2
Self-Centeredno
Central VerticesC♯+
Peripheral Verticesam, b°

Modes

Modes are the rotational transformation of this scale. Scale 2615 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3355
Scale 3355: Bagian, Ian Ring Music TheoryBagian
3rd mode:
Scale 3725
Scale 3725: Kyrian, Ian Ring Music TheoryKyrian
4th mode:
Scale 1955
Scale 1955: Sonian, Ian Ring Music TheorySonian
5th mode:
Scale 3025
Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian
6th mode:
Scale 445
Scale 445: Gocrian, Ian Ring Music TheoryGocrian
7th mode:
Scale 1135
Scale 1135: Katolian, Ian Ring Music TheoryKatolian

Prime

The prime form of this scale is Scale 379

Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian

Complement

The heptatonic modal family [2615, 3355, 3725, 1955, 3025, 445, 1135] (Forte: 7-11) is the complement of the pentatonic modal family [157, 929, 1063, 2579, 3337] (Forte: 5-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2615 is 3467

Scale 3467Scale 3467: Katonian, Ian Ring Music TheoryKatonian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2615 is chiral, and its enantiomorph is scale 3467

Scale 3467Scale 3467: Katonian, Ian Ring Music TheoryKatonian

Transformations:

T0 2615  T0I 3467
T1 1135  T1I 2839
T2 2270  T2I 1583
T3 445  T3I 3166
T4 890  T4I 2237
T5 1780  T5I 379
T6 3560  T6I 758
T7 3025  T7I 1516
T8 1955  T8I 3032
T9 3910  T9I 1969
T10 3725  T10I 3938
T11 3355  T11I 3781

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 2613Scale 2613: Raga Hamsa Vinodini, Ian Ring Music TheoryRaga Hamsa Vinodini
Scale 2611Scale 2611: Raga Vasanta, Ian Ring Music TheoryRaga Vasanta
Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian
Scale 2623Scale 2623: Aerylyllic, Ian Ring Music TheoryAerylyllic
Scale 2599Scale 2599: Malimic, Ian Ring Music TheoryMalimic
Scale 2607Scale 2607: Aerolian, Ian Ring Music TheoryAerolian
Scale 2583Scale 2583, Ian Ring Music Theory
Scale 2647Scale 2647: Dadian, Ian Ring Music TheoryDadian
Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic
Scale 2743Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic
Scale 2871Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
Scale 2103Scale 2103, Ian Ring Music Theory
Scale 2359Scale 2359: Gadian, Ian Ring Music TheoryGadian
Scale 3127Scale 3127, Ian Ring Music Theory
Scale 3639Scale 3639: Paptyllic, Ian Ring Music TheoryPaptyllic
Scale 567Scale 567: Aeoladimic, Ian Ring Music TheoryAeoladimic
Scale 1591Scale 1591: Rodian, Ian Ring Music TheoryRodian

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.