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Scale 731: "Ionorian"

Scale 731: Ionorian, 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
Ionorian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,6,7,9}
Forte Number7-31
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2921
Hemitonia3 (trihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes6
Prime?yes
Deep Scaleno
Interval Vector336333
Interval Spectrump3m3n6s3d3t3
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9}
<6> = {9,10,11}
Spectra Variation1.714
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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
A{9,1,4}331.7
Minor Triadscm{0,3,7}331.8
f♯m{6,9,1}331.8
am{9,0,4}431.6
Diminished Triads{0,3,6}232
c♯°{1,4,7}232
d♯°{3,6,9}232
f♯°{6,9,0}231.9
{9,0,3}231.9
Parsimonious Voice Leading Between Common Triads of Scale 731. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° C C cm->C cm->a° c#° c#° C->c#° am am C->am A A c#°->A f#m f#m d#°->f#m f#° f#° f#°->f#m f#°->am f#m->A a°->am am->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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 731 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2413
Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2
3rd mode:
Scale 1627
Scale 1627: Zyptian, Ian Ring Music TheoryZyptian
4th mode:
Scale 2861
Scale 2861: Katothian, Ian Ring Music TheoryKatothian
5th mode:
Scale 1739
Scale 1739: Mela Sadvidhamargini, Ian Ring Music TheoryMela Sadvidhamargini
6th mode:
Scale 2917
Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
7th mode:
Scale 1753
Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [731, 2413, 1627, 2861, 1739, 2917, 1753] (Forte: 7-31) is the complement of the pentatonic modal family [587, 601, 713, 1609, 2341] (Forte: 5-31)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 731 is 2921

Scale 2921Scale 2921: Pogian, Ian Ring Music TheoryPogian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 731 is chiral, and its enantiomorph is scale 2921

Scale 2921Scale 2921: Pogian, Ian Ring Music TheoryPogian

Transformations:

T0 731  T0I 2921
T1 1462  T1I 1747
T2 2924  T2I 3494
T3 1753  T3I 2893
T4 3506  T4I 1691
T5 2917  T5I 3382
T6 1739  T6I 2669
T7 3478  T7I 1243
T8 2861  T8I 2486
T9 1627  T9I 877
T10 3254  T10I 1754
T11 2413  T11I 3508

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 729Scale 729: Stygimic, Ian Ring Music TheoryStygimic
Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian
Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic
Scale 723Scale 723: Ionadimic, Ian Ring Music TheoryIonadimic
Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian
Scale 715Scale 715: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2
Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian
Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic
Scale 667Scale 667: Rodimic, Ian Ring Music TheoryRodimic
Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian
Scale 987Scale 987: Aeraptyllic, Ian Ring Music TheoryAeraptyllic
Scale 219Scale 219: Istrian, Ian Ring Music TheoryIstrian
Scale 475Scale 475: Aeolygian, Ian Ring Music TheoryAeolygian
Scale 1243Scale 1243: Epylian, Ian Ring Music TheoryEpylian
Scale 1755Scale 1755: Octatonic, Ian Ring Music TheoryOctatonic
Scale 2779Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich

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.