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Scale 2011: "Raphygic"

Scale 2011: Raphygic, 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
Raphygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,3,4,6,7,8,9,10}
Forte Number9-10
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1759
Deep Scaleno
Interval Vector668664
Interval Spectrump6m6n8s6d6t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tones[4]
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 TriadsC{0,4,7}442.37
D♯{3,7,10}442.37
F♯{6,10,1}442.42
G♯{8,0,3}342.47
A{9,1,4}442.32
Minor Triadscm{0,3,7}442.32
c♯m{1,4,8}342.47
d♯m{3,6,10}442.42
f♯m{6,9,1}442.37
am{9,0,4}442.37
Augmented TriadsC+{0,4,8}442.32
Diminished Triads{0,3,6}242.58
c♯°{1,4,7}242.74
d♯°{3,6,9}242.63
{4,7,10}242.63
f♯°{6,9,0}242.63
{7,10,1}242.63
{9,0,3}242.74
a♯°{10,1,4}242.58
Parsimonious Voice Leading Between Common Triads of Scale 2011. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° C->e° c#m c#m C+->c#m C+->G# am am C+->am c#°->c#m A A c#m->A d#° d#° d#°->d#m f#m f#m d#°->f#m d#m->D# F# F# d#m->F# D#->e° D#->g° f#° f#° f#°->f#m f#°->am f#m->F# f#m->A F#->g° a#° a#° F#->a#° G#->a° a°->am am->A A->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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2011 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3053
Scale 3053: Zycrygic, Ian Ring Music TheoryZycrygic
3rd mode:
Scale 1787
Scale 1787: Mycrygic, Ian Ring Music TheoryMycrygic
4th mode:
Scale 2941
Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic
5th mode:
Scale 1759
Scale 1759: Pylygic, Ian Ring Music TheoryPylygicThis is the prime mode
6th mode:
Scale 2927
Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
7th mode:
Scale 3511
Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
8th mode:
Scale 3803
Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
9th mode:
Scale 3949
Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic

Prime

The prime form of this scale is Scale 1759

Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic

Complement

The nonatonic modal family [2011, 3053, 1787, 2941, 1759, 2927, 3511, 3803, 3949] (Forte: 9-10) is the complement of the tritonic modal family [73, 521, 577] (Forte: 3-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2011 is 2941

Scale 2941Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic

Transformations:

T0 2011  T0I 2941
T1 4022  T1I 1787
T2 3949  T2I 3574
T3 3803  T3I 3053
T4 3511  T4I 2011
T5 2927  T5I 4022
T6 1759  T6I 3949
T7 3518  T7I 3803
T8 2941  T8I 3511
T9 1787  T9I 2927
T10 3574  T10I 1759
T11 3053  T11I 3518

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 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic
Scale 2015Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 2003Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic
Scale 2007Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
Scale 1995Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic
Scale 2027Scale 2027: Boptygic, Ian Ring Music TheoryBoptygic
Scale 2043Scale 2043: Maqam Tarzanuyn, Ian Ring Music TheoryMaqam Tarzanuyn
Scale 1947Scale 1947: Byptyllic, Ian Ring Music TheoryByptyllic
Scale 1979Scale 1979: Aeradygic, Ian Ring Music TheoryAeradygic
Scale 1883Scale 1883, Ian Ring Music Theory
Scale 1755Scale 1755: Octatonic, Ian Ring Music TheoryOctatonic
Scale 1499Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian
Scale 987Scale 987: Aeraptyllic, Ian Ring Music TheoryAeraptyllic
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 4059Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian

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.