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Scale 4039: "Ionogygic"

Scale 4039: Ionogygic, 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
Ionogygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,6,7,8,9,10,11}
Forte Number9-1
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia7 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 511
Deep Scaleno
Interval Vector876663
Interval Spectrump6m6n6s7d8t3
Distribution Spectra<1> = {1,4}
<2> = {2,5}
<3> = {3,6}
<4> = {4,7}
<5> = {5,8}
<6> = {6,9}
<7> = {7,10}
<8> = {8,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.433
Myhill Propertyyes
Balancedno
Ridge Tones[8]
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 4039 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 4067
Scale 4067: Aeolarygic, Ian Ring Music TheoryAeolarygic
3rd mode:
Scale 4081
Scale 4081: Manygic, Ian Ring Music TheoryManygic
4th mode:
Scale 511
Scale 511: Polygic, Ian Ring Music TheoryPolygicThis is the prime mode
5th mode:
Scale 2303
Scale 2303: Stanygic, Ian Ring Music TheoryStanygic
6th mode:
Scale 3199
Scale 3199: Thaptygic, Ian Ring Music TheoryThaptygic
7th mode:
Scale 3647
Scale 3647: Eporygic, Ian Ring Music TheoryEporygic
8th mode:
Scale 3871
Scale 3871: Aerynygic, Ian Ring Music TheoryAerynygic
9th mode:
Scale 3983
Scale 3983: Thyptygic, Ian Ring Music TheoryThyptygic

Prime

The prime form of this scale is Scale 511

Scale 511Scale 511: Polygic, Ian Ring Music TheoryPolygic

Complement

The nonatonic modal family [4039, 4067, 4081, 511, 2303, 3199, 3647, 3871, 3983] (Forte: 9-1) is the complement of the tritonic modal family [7, 2051, 3073] (Forte: 3-1)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4039 is 3199

Scale 3199Scale 3199: Thaptygic, Ian Ring Music TheoryThaptygic

Transformations:

T0 4039  T0I 3199
T1 3983  T1I 2303
T2 3871  T2I 511
T3 3647  T3I 1022
T4 3199  T4I 2044
T5 2303  T5I 4088
T6 511  T6I 4081
T7 1022  T7I 4067
T8 2044  T8I 4039
T9 4088  T9I 3983
T10 4081  T10I 3871
T11 4067  T11I 3647

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 4037Scale 4037: Ionyllic, Ian Ring Music TheoryIonyllic
Scale 4035Scale 4035, Ian Ring Music Theory
Scale 4043Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
Scale 4047Scale 4047: Thogyllian, Ian Ring Music TheoryThogyllian
Scale 4055Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian
Scale 4071Scale 4071: Rygyllian, Ian Ring Music TheoryRygyllian
Scale 3975Scale 3975, Ian Ring Music Theory
Scale 4007Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic
Scale 3911Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic
Scale 3783Scale 3783: Phrygyllic, Ian Ring Music TheoryPhrygyllic
Scale 3527Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
Scale 3015Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
Scale 1991Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.