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Scale 3041

Scale 3041, 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).

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,5,6,7,8,9,11}
Forte Number7-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 251
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 223
Deep Scaleno
Interval Vector544332
Interval Spectrump3m3n4s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7,8}
<4> = {4,5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.714
Maximally Evenno
Maximal Area Setno
Interior Area1.933
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
Major TriadsF{5,9,0}221
Minor Triadsfm{5,8,0}221
Diminished Triads{5,8,11}131.5
f♯°{6,9,0}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3041. Created by Ian Ring ©2019 fm fm f°->fm F F fm->F f#° f#° F->f#°

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.

Diameter3
Radius2
Self-Centeredno
Central Verticesfm, F
Peripheral Verticesf°, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 3041 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 223
Scale 223, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2159
Scale 2159, Ian Ring Music Theory
4th mode:
Scale 3127
Scale 3127, Ian Ring Music Theory
5th mode:
Scale 3611
Scale 3611, Ian Ring Music Theory
6th mode:
Scale 3853
Scale 3853, Ian Ring Music Theory
7th mode:
Scale 1987
Scale 1987, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 223

Scale 223Scale 223, Ian Ring Music Theory

Complement

The heptatonic modal family [3041, 223, 2159, 3127, 3611, 3853, 1987] (Forte: 7-4) is the complement of the pentatonic modal family [79, 961, 2087, 3091, 3593] (Forte: 5-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3041 is 251

Scale 251Scale 251, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3041 is chiral, and its enantiomorph is scale 251

Scale 251Scale 251, Ian Ring Music Theory

Transformations:

T0 3041  T0I 251
T1 1987  T1I 502
T2 3974  T2I 1004
T3 3853  T3I 2008
T4 3611  T4I 4016
T5 3127  T5I 3937
T6 2159  T6I 3779
T7 223  T7I 3463
T8 446  T8I 2831
T9 892  T9I 1567
T10 1784  T10I 3134
T11 3568  T11I 2173

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 3043Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
Scale 3045Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic
Scale 3049Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
Scale 3057Scale 3057: Phroryllic, Ian Ring Music TheoryPhroryllic
Scale 3009Scale 3009, Ian Ring Music Theory
Scale 3025Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian
Scale 2977Scale 2977, Ian Ring Music Theory
Scale 2913Scale 2913, Ian Ring Music Theory
Scale 2785Scale 2785, Ian Ring Music Theory
Scale 2529Scale 2529, Ian Ring Music Theory
Scale 3553Scale 3553, Ian Ring Music Theory
Scale 4065Scale 4065, Ian Ring Music Theory
Scale 993Scale 993, Ian Ring Music Theory
Scale 2017Scale 2017, 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.