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Scale 3173: "Zarimic"

Scale 3173: Zarimic, 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
Zarimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,5,6,10,11}
Forte Number6-Z17
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1223
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 407
Deep Scaleno
Interval Vector322332
Interval Spectrump3m3n2s2d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5}
<3> = {4,6,8}
<4> = {7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.116
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 TriadsA♯{10,2,5}221
Minor Triadsbm{11,2,6}221
Augmented TriadsD+{2,6,10}221
Diminished Triadsb°{11,2,5}221
Parsimonious Voice Leading Between Common Triads of Scale 3173. Created by Ian Ring ©2019 D+ D+ A# A# D+->A# bm bm D+->bm b° b° A#->b° b°->bm

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.

Diameter2
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3173 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1817		Scale 1817: Phrythimic, Ian Ring Music TheoryPhrythimic
3rd mode:
Scale 739		Scale 739: Rorimic, Ian Ring Music TheoryRorimic
4th mode:
Scale 2417		Scale 2417: Kanimic, Ian Ring Music TheoryKanimic
5th mode:
Scale 407		Scale 407: Zylimic, Ian Ring Music TheoryZylimicThis is the prime mode
6th mode:
Scale 2251		Scale 2251: Zodimic, Ian Ring Music TheoryZodimic

Prime

The prime form of this scale is Scale 407

Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic

Complement

The hexatonic modal family [3173, 1817, 739, 2417, 407, 2251] (Forte: 6-Z17) is the complement of the hexatonic modal family [359, 907, 1649, 2227, 2501, 3161] (Forte: 6-Z43)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3173 is 1223

Scale 1223Scale 1223: Phryptimic, Ian Ring Music TheoryPhryptimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3173 is chiral, and its enantiomorph is scale 1223

Scale 1223Scale 1223: Phryptimic, Ian Ring Music TheoryPhryptimic

Transformations:

T0 3173  T0I 1223
T1 2251  T1I 2446
T2 407  T2I 797
T3 814  T3I 1594
T4 1628  T4I 3188
T5 3256  T5I 2281
T6 2417  T6I 467
T7 739  T7I 934
T8 1478  T8I 1868
T9 2956  T9I 3736
T10 1817  T10I 3377
T11 3634  T11I 2659

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 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 3169Scale 3169, Ian Ring Music Theory
Scale 3171Scale 3171: Zythimic, Ian Ring Music TheoryZythimic
Scale 3177Scale 3177: Rothimic, Ian Ring Music TheoryRothimic
Scale 3181Scale 3181: Rolian, Ian Ring Music TheoryRolian
Scale 3189Scale 3189: Aeolonian, Ian Ring Music TheoryAeolonian
Scale 3141Scale 3141: Kanitonic, Ian Ring Music TheoryKanitonic
Scale 3157Scale 3157: Zyptimic, Ian Ring Music TheoryZyptimic
Scale 3109Scale 3109, Ian Ring Music Theory
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3301Scale 3301: Chromatic Mixolydian Inverse, Ian Ring Music TheoryChromatic Mixolydian Inverse
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 3685Scale 3685: Kodian, Ian Ring Music TheoryKodian
Scale 2149Scale 2149, Ian Ring Music Theory
Scale 2661Scale 2661: Stydimic, Ian Ring Music TheoryStydimic
Scale 1125Scale 1125: Ionaritonic, Ian Ring Music TheoryIonaritonic

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.