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Scale 541

Scale 541, 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).

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,2,3,4,9}
Forte Number5-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1801
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes4
Prime?no
prime: 151
Deep Scaleno
Interval Vector222121
Interval Spectrump2mn2s2d2t
Distribution Spectra<1> = {1,2,3,5}
<2> = {2,3,5,6,8}
<3> = {4,6,7,9,10}
<4> = {7,9,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.683
Myhill Propertyno
Balancedno
Ridge Tonesnone
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
Minor Triadsam{9,0,4}110.5
Diminished Triads{9,0,3}110.5
Parsimonious Voice Leading Between Common Triads of Scale 541. Created by Ian Ring ©2019 am am a°->am

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 541 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1159
Scale 1159, Ian Ring Music Theory
3rd mode:
Scale 2627
Scale 2627, Ian Ring Music Theory
4th mode:
Scale 3361
Scale 3361, Ian Ring Music Theory
5th mode:
Scale 233
Scale 233, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 151

Scale 151Scale 151, Ian Ring Music Theory

Complement

The pentatonic modal family [541, 1159, 2627, 3361, 233] (Forte: 5-Z36) is the complement of the heptatonic modal family [367, 1777, 1931, 2231, 3013, 3163, 3629] (Forte: 7-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 541 is 1801

Scale 1801Scale 1801, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 541 is chiral, and its enantiomorph is scale 1801

Scale 1801Scale 1801, Ian Ring Music Theory

Transformations:

T0 541  T0I 1801
T1 1082  T1I 3602
T2 2164  T2I 3109
T3 233  T3I 2123
T4 466  T4I 151
T5 932  T5I 302
T6 1864  T6I 604
T7 3728  T7I 1208
T8 3361  T8I 2416
T9 2627  T9I 737
T10 1159  T10I 1474
T11 2318  T11I 2948

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 543Scale 543, Ian Ring Music Theory
Scale 537Scale 537, Ian Ring Music Theory
Scale 539Scale 539, Ian Ring Music Theory
Scale 533Scale 533, Ian Ring Music Theory
Scale 525Scale 525, Ian Ring Music Theory
Scale 557Scale 557: Raga Abhogi, Ian Ring Music TheoryRaga Abhogi
Scale 573Scale 573: Saptimic, Ian Ring Music TheorySaptimic
Scale 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic
Scale 669Scale 669: Gycrimic, Ian Ring Music TheoryGycrimic
Scale 797Scale 797: Katocrimic, Ian Ring Music TheoryKatocrimic
Scale 29Scale 29, Ian Ring Music Theory
Scale 285Scale 285: Zaritonic, Ian Ring Music TheoryZaritonic
Scale 1053Scale 1053, Ian Ring Music Theory
Scale 1565Scale 1565, Ian Ring Music Theory
Scale 2589Scale 2589, Ian Ring Music Theory

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.