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Scale 2425: "Rorian"

Scale 2425: Rorian, 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
Rorian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,4,5,6,8,11}
Forte Number7-Z18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 979
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 755
Deep Scaleno
Interval Vector434442
Interval Spectrump4m4n4s3d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.433
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}331.5
G♯{8,0,3}331.5
B{11,3,6}242
Minor Triadsfm{5,8,0}242
g♯m{8,11,3}331.5
Augmented TriadsC+{0,4,8}331.5
Diminished Triads{0,3,6}242
{5,8,11}242
Parsimonious Voice Leading Between Common Triads of Scale 2425. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ E E C+->E fm fm C+->fm C+->G# E->f° g#m g#m E->g#m f°->fm 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
Radius3
Self-Centeredno
Central VerticesC+, E, g♯m, G♯
Peripheral Verticesc°, f°, fm, B

Modes

Modes are the rotational transformation of this scale. Scale 2425 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 815
Scale 815: Bolian, Ian Ring Music TheoryBolian
3rd mode:
Scale 2455
Scale 2455: Bothian, Ian Ring Music TheoryBothian
4th mode:
Scale 3275
Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani
5th mode:
Scale 3685
Scale 3685: Kodian, Ian Ring Music TheoryKodian
6th mode:
Scale 1945
Scale 1945: Zarian, Ian Ring Music TheoryZarian
7th mode:
Scale 755
Scale 755: Phrythian, Ian Ring Music TheoryPhrythianThis is the prime mode

Prime

The prime form of this scale is Scale 755

Scale 755Scale 755: Phrythian, Ian Ring Music TheoryPhrythian

Complement

The heptatonic modal family [2425, 815, 2455, 3275, 3685, 1945, 755] (Forte: 7-Z18) is the complement of the pentatonic modal family [179, 779, 1633, 2137, 2437] (Forte: 5-Z18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2425 is 979

Scale 979Scale 979: Mela Dhavalambari, Ian Ring Music TheoryMela Dhavalambari

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2425 is chiral, and its enantiomorph is scale 979

Scale 979Scale 979: Mela Dhavalambari, Ian Ring Music TheoryMela Dhavalambari

Transformations:

T0 2425  T0I 979
T1 755  T1I 1958
T2 1510  T2I 3916
T3 3020  T3I 3737
T4 1945  T4I 3379
T5 3890  T5I 2663
T6 3685  T6I 1231
T7 3275  T7I 2462
T8 2455  T8I 829
T9 815  T9I 1658
T10 1630  T10I 3316
T11 3260  T11I 2537

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 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
Scale 2429Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
Scale 2417Scale 2417: Kanimic, Ian Ring Music TheoryKanimic
Scale 2421Scale 2421: Malian, Ian Ring Music TheoryMalian
Scale 2409Scale 2409: Zacrimic, Ian Ring Music TheoryZacrimic
Scale 2393Scale 2393: Zathimic, Ian Ring Music TheoryZathimic
Scale 2361Scale 2361: Docrimic, Ian Ring Music TheoryDocrimic
Scale 2489Scale 2489: Mela Gangeyabhusani, Ian Ring Music TheoryMela Gangeyabhusani
Scale 2553Scale 2553: Aeolaptyllic, Ian Ring Music TheoryAeolaptyllic
Scale 2169Scale 2169, Ian Ring Music Theory
Scale 2297Scale 2297: Thylian, Ian Ring Music TheoryThylian
Scale 2681Scale 2681: Aerycrian, Ian Ring Music TheoryAerycrian
Scale 2937Scale 2937: Phragyllic, Ian Ring Music TheoryPhragyllic
Scale 3449Scale 3449: Bacryllic, Ian Ring Music TheoryBacryllic
Scale 377Scale 377: Kathimic, Ian Ring Music TheoryKathimic
Scale 1401Scale 1401: Pagian, Ian Ring Music TheoryPagian

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.