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Scale 3225: "Ionalimic"

Scale 3225: Ionalimic, 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
Ionalimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,4,7,10,11}
Forte Number6-Z44
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 807
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 615
Deep Scaleno
Interval Vector313431
Interval Spectrump3m4n3sd3t
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {5,7}
<4> = {6,8,10}
<5> = {9,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.25
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}231.5
D♯{3,7,10}231.5
Minor Triadscm{0,3,7}231.5
em{4,7,11}321.17
Augmented TriadsD♯+{3,7,11}321.17
Diminished Triads{4,7,10}231.5
Parsimonious Voice Leading Between Common Triads of Scale 3225. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ em em C->em D# D# D#->D#+ D#->e° D#+->em e°->em

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
Radius2
Self-Centeredno
Central VerticesD♯+, em
Peripheral Verticescm, C, D♯, e°

Modes

Modes are the rotational transformation of this scale. Scale 3225 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 915
Scale 915: Raga Kalagada, Ian Ring Music TheoryRaga Kalagada
3rd mode:
Scale 2505
Scale 2505: Mydimic, Ian Ring Music TheoryMydimic
4th mode:
Scale 825
Scale 825: Thyptimic, Ian Ring Music TheoryThyptimic
5th mode:
Scale 615
Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimicThis is the prime mode
6th mode:
Scale 2355
Scale 2355: Raga Lalita, Ian Ring Music TheoryRaga Lalita

Prime

The prime form of this scale is Scale 615

Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic

Complement

The hexatonic modal family [3225, 915, 2505, 825, 615, 2355] (Forte: 6-Z44) is the complement of the hexatonic modal family [411, 867, 1587, 2253, 2481, 2841] (Forte: 6-Z19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3225 is 807

Scale 807Scale 807: Raga Suddha Mukhari, Ian Ring Music TheoryRaga Suddha Mukhari

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3225 is chiral, and its enantiomorph is scale 807

Scale 807Scale 807: Raga Suddha Mukhari, Ian Ring Music TheoryRaga Suddha Mukhari

Transformations:

T0 3225  T0I 807
T1 2355  T1I 1614
T2 615  T2I 3228
T3 1230  T3I 2361
T4 2460  T4I 627
T5 825  T5I 1254
T6 1650  T6I 2508
T7 3300  T7I 921
T8 2505  T8I 1842
T9 915  T9I 3684
T10 1830  T10I 3273
T11 3660  T11I 2451

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 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
Scale 3229Scale 3229: Aeolaptian, Ian Ring Music TheoryAeolaptian
Scale 3217Scale 3217: Molitonic, Ian Ring Music TheoryMolitonic
Scale 3221Scale 3221: Bycrimic, Ian Ring Music TheoryBycrimic
Scale 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
Scale 3241Scale 3241: Dalimic, Ian Ring Music TheoryDalimic
Scale 3257Scale 3257: Mela Calanata, Ian Ring Music TheoryMela Calanata
Scale 3289Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6
Scale 3097Scale 3097, Ian Ring Music Theory
Scale 3161Scale 3161: Kodimic, Ian Ring Music TheoryKodimic
Scale 3353Scale 3353: Phraptimic, Ian Ring Music TheoryPhraptimic
Scale 3481Scale 3481: Katathian, Ian Ring Music TheoryKatathian
Scale 3737Scale 3737: Phrocrian, Ian Ring Music TheoryPhrocrian
Scale 2201Scale 2201: Ionagitonic, Ian Ring Music TheoryIonagitonic
Scale 2713Scale 2713: Porimic, Ian Ring Music TheoryPorimic
Scale 1177Scale 1177: Garitonic, Ian Ring Music TheoryGaritonic

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.