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Scale 553: "Rothic"

Scale 553: Rothic, 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
Rothic

Analysis

Cardinality4 (tetratonic)
Pitch Class Set{0,3,5,9}
Forte Number4-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 649
Hemitonia0 (anhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes3
Prime?no
prime: 293
Deep Scaleno
Interval Vector012111
Interval Spectrumpmn2st
Distribution Spectra<1> = {2,3,4}
<2> = {5,6,7}
<3> = {8,9,10}
Spectra Variation1.5
Maximally Evenno
Maximal Area Setno
Interior Area1.866
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyStrictly Proper
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 TriadsF{5,9,0}110.5
Diminished Triads{9,0,3}110.5
Parsimonious Voice Leading Between Common Triads of Scale 553. Created by Ian Ring ©2019 F F F->a°

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 553 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 581
Scale 581: Eporic, Ian Ring Music TheoryEporic
3rd mode:
Scale 1169
Scale 1169: Raga Mahathi, Ian Ring Music TheoryRaga Mahathi
4th mode:
Scale 329
Scale 329: Mynic, Ian Ring Music TheoryMynic

Prime

The prime form of this scale is Scale 293

Scale 293Scale 293: Raga Haripriya, Ian Ring Music TheoryRaga Haripriya

Complement

The tetratonic modal family [553, 581, 1169, 329] (Forte: 4-27) is the complement of the octatonic modal family [1463, 1757, 1771, 1883, 2779, 2933, 2989, 3437] (Forte: 8-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 553 is 649

Scale 649Scale 649: Byptic, Ian Ring Music TheoryByptic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 553 is chiral, and its enantiomorph is scale 649

Scale 649Scale 649: Byptic, Ian Ring Music TheoryByptic

Transformations:

T0 553  T0I 649
T1 1106  T1I 1298
T2 2212  T2I 2596
T3 329  T3I 1097
T4 658  T4I 2194
T5 1316  T5I 293
T6 2632  T6I 586
T7 1169  T7I 1172
T8 2338  T8I 2344
T9 581  T9I 593
T10 1162  T10I 1186
T11 2324  T11I 2372

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 555Scale 555: Aeolycritonic, Ian Ring Music TheoryAeolycritonic
Scale 557Scale 557: Raga Abhogi, Ian Ring Music TheoryRaga Abhogi
Scale 545Scale 545, Ian Ring Music Theory
Scale 549Scale 549: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 561Scale 561: Phratic, Ian Ring Music TheoryPhratic
Scale 569Scale 569: Mothitonic, Ian Ring Music TheoryMothitonic
Scale 521Scale 521, Ian Ring Music Theory
Scale 537Scale 537, Ian Ring Music Theory
Scale 585Scale 585: Diminished Seventh, Ian Ring Music TheoryDiminished Seventh
Scale 617Scale 617: Katycritonic, Ian Ring Music TheoryKatycritonic
Scale 681Scale 681: Kyemyonjo, Ian Ring Music TheoryKyemyonjo
Scale 809Scale 809: Dogitonic, Ian Ring Music TheoryDogitonic
Scale 41Scale 41: Vietnamese Tritonic, Ian Ring Music TheoryVietnamese Tritonic
Scale 297Scale 297: Mynic, Ian Ring Music TheoryMynic
Scale 1065Scale 1065, Ian Ring Music Theory
Scale 1577Scale 1577: Raga Chandrakauns (Kafi), Ian Ring Music TheoryRaga Chandrakauns (Kafi)
Scale 2601Scale 2601: Raga Chandrakauns, Ian Ring Music TheoryRaga Chandrakauns

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.