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Scale 2967: "Madyllic"

Scale 2967: Madyllic, 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
Madyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,7,8,9,11}
Forte Number8-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3387
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes7
Prime?no
prime: 759
Deep Scaleno
Interval Vector555562
Interval Spectrump6m5n5s5d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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 TriadsC{0,4,7}331.7
E{4,8,11}331.7
G{7,11,2}252.5
A{9,1,4}252.5
Minor Triadsc♯m{1,4,8}341.9
em{4,7,11}341.9
am{9,0,4}242.1
Augmented TriadsC+{0,4,8}431.5
Diminished Triadsc♯°{1,4,7}242.1
g♯°{8,11,2}242.3
Parsimonious Voice Leading Between Common Triads of Scale 2967. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E am am C+->am c#°->c#m A A c#m->A em->E Parsimonious Voice Leading Between Common Triads of Scale 2967. Created by Ian Ring ©2019 G em->G g#° g#° E->g#° G->g#° am->A

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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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC, C+, E
Peripheral VerticesG, A

Modes

Modes are the rotational transformation of this scale. Scale 2967 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3531
Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri
3rd mode:
Scale 3813
Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
4th mode:
Scale 1977
Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic
5th mode:
Scale 759
Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllicThis is the prime mode
6th mode:
Scale 2427
Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
7th mode:
Scale 3261
Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
8th mode:
Scale 1839
Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic

Prime

The prime form of this scale is Scale 759

Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic

Complement

The octatonic modal family [2967, 3531, 3813, 1977, 759, 2427, 3261, 1839] (Forte: 8-14) is the complement of the tetratonic modal family [141, 417, 1059, 2577] (Forte: 4-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2967 is 3387

Scale 3387Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2967 is chiral, and its enantiomorph is scale 3387

Scale 3387Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic

Transformations:

T0 2967  T0I 3387
T1 1839  T1I 2679
T2 3678  T2I 1263
T3 3261  T3I 2526
T4 2427  T4I 957
T5 759  T5I 1914
T6 1518  T6I 3828
T7 3036  T7I 3561
T8 1977  T8I 3027
T9 3954  T9I 1959
T10 3813  T10I 3918
T11 3531  T11I 3741

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 2965Scale 2965: Darian, Ian Ring Music TheoryDarian
Scale 2963Scale 2963: Bygian, Ian Ring Music TheoryBygian
Scale 2971Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
Scale 2951Scale 2951, Ian Ring Music Theory
Scale 2959Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
Scale 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
Scale 3031Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic
Scale 2839Scale 2839: Lyptian, Ian Ring Music TheoryLyptian
Scale 2903Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic
Scale 2711Scale 2711: Stolian, Ian Ring Music TheoryStolian
Scale 2455Scale 2455: Bothian, Ian Ring Music TheoryBothian
Scale 3479Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
Scale 3991Scale 3991: Badygic, Ian Ring Music TheoryBadygic
Scale 919Scale 919: Chromatic Phrygian Inverse, Ian Ring Music TheoryChromatic Phrygian Inverse
Scale 1943Scale 1943, 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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.