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Scale 3995: "Ionygic"

Scale 3995: Ionygic, 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).

Common Names

Zeitler
Ionygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,3,4,7,8,9,10,11}
Forte Number9-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2879
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 895
Deep Scaleno
Interval Vector767763
Interval Spectrump6m7n7s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2.222
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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
Major TriadsC{0,4,7}442.12
D♯{3,7,10}342.53
E{4,8,11}342.24
G♯{8,0,3}442.24
A{9,1,4}342.53
Minor Triadscm{0,3,7}342.24
c♯m{1,4,8}342.35
em{4,7,11}442.24
g♯m{8,11,3}342.35
am{9,0,4}342.35
Augmented TriadsC+{0,4,8}542
D♯+{3,7,11}442.24
Diminished Triadsc♯°{1,4,7}242.59
{4,7,10}252.71
{7,10,1}242.76
{9,0,3}252.71
a♯°{10,1,4}242.76
Parsimonious Voice Leading Between Common Triads of Scale 3995. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E C+->G# am am C+->am c#°->c#m A A c#m->A D# D# D#->D#+ D#->e° D#->g° D#+->em g#m g#m D#+->g#m e°->em em->E E->g#m a#° a#° g°->a#° g#m->G# 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.

Diameter5
Radius4
Self-Centeredno
Central Verticescm, C, C+, c♯°, c♯m, D♯, D♯+, em, E, g°, g♯m, G♯, am, A, a♯°
Peripheral Verticese°, a°

Modes

Modes are the rotational transformation of this scale. Scale 3995 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 4045
Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic
3rd mode:
Scale 2035
Scale 2035: Aerythygic, Ian Ring Music TheoryAerythygic
4th mode:
Scale 3065
Scale 3065: Zothygic, Ian Ring Music TheoryZothygic
5th mode:
Scale 895
Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygicThis is the prime mode
6th mode:
Scale 2495
Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
7th mode:
Scale 3295
Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
8th mode:
Scale 3695
Scale 3695: Kodygic, Ian Ring Music TheoryKodygic
9th mode:
Scale 3895
Scale 3895: Eparygic, Ian Ring Music TheoryEparygic

Prime

The prime form of this scale is Scale 895

Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic

Complement

The nonatonic modal family [3995, 4045, 2035, 3065, 895, 2495, 3295, 3695, 3895] (Forte: 9-3) is the complement of the tritonic modal family [19, 769, 2057] (Forte: 3-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3995 is 2879

Scale 2879Scale 2879: Stadygic, Ian Ring Music TheoryStadygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3995 is chiral, and its enantiomorph is scale 2879

Scale 2879Scale 2879: Stadygic, Ian Ring Music TheoryStadygic

Transformations:

T0 3995  T0I 2879
T1 3895  T1I 1663
T2 3695  T2I 3326
T3 3295  T3I 2557
T4 2495  T4I 1019
T5 895  T5I 2038
T6 1790  T6I 4076
T7 3580  T7I 4057
T8 3065  T8I 4019
T9 2035  T9I 3943
T10 4070  T10I 3791
T11 4045  T11I 3487

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 3993Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic
Scale 3997Scale 3997: Dogygic, Ian Ring Music TheoryDogygic
Scale 3999Scale 3999: Dydyllian, Ian Ring Music TheoryDydyllian
Scale 3987Scale 3987: Loryllic, Ian Ring Music TheoryLoryllic
Scale 3991Scale 3991: Badygic, Ian Ring Music TheoryBadygic
Scale 3979Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic
Scale 4011Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
Scale 4027Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian
Scale 4059Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian
Scale 3867Scale 3867: Storyllic, Ian Ring Music TheoryStoryllic
Scale 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic
Scale 3739Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic
Scale 3483Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
Scale 2971Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
Scale 1947Scale 1947: Byptyllic, Ian Ring Music TheoryByptyllic

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.