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Scale 1873: "Dathimic"

Scale 1873: Dathimic, 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
Dathimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,4,6,8,9,10}
Forte Number6-21
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 349
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections5
Modes5
Prime?no
prime: 349
Deep Scaleno
Interval Vector242412
Interval Spectrumpm4n2s4d2t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,6}
<3> = {4,5,7,8}
<4> = {6,8,9,10}
<5> = {8,10,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.232
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
Minor Triadsam{9,0,4}210.67
Augmented TriadsC+{0,4,8}121
Diminished Triadsf♯°{6,9,0}121
Parsimonious Voice Leading Between Common Triads of Scale 1873. Created by Ian Ring ©2019 C+ C+ am am C+->am f#° f#° f#°->am

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
Radius1
Self-Centeredno
Central Verticesam
Peripheral VerticesC+, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 1873 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 373
Scale 373: Epagimic, Ian Ring Music TheoryEpagimic
3rd mode:
Scale 1117
Scale 1117: Raptimic, Ian Ring Music TheoryRaptimic
4th mode:
Scale 1303
Scale 1303: Epolimic, Ian Ring Music TheoryEpolimic
5th mode:
Scale 2699
Scale 2699: Sythimic, Ian Ring Music TheorySythimic
6th mode:
Scale 3397
Scale 3397: Sydimic, Ian Ring Music TheorySydimic

Prime

The prime form of this scale is Scale 349

Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic

Complement

The hexatonic modal family [1873, 373, 1117, 1303, 2699, 3397] (Forte: 6-21) is the complement of the hexatonic modal family [349, 1111, 1489, 1861, 2603, 3349] (Forte: 6-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1873 is 349

Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1873 is chiral, and its enantiomorph is scale 349

Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic

Transformations:

T0 1873  T0I 349
T1 3746  T1I 698
T2 3397  T2I 1396
T3 2699  T3I 2792
T4 1303  T4I 1489
T5 2606  T5I 2978
T6 1117  T6I 1861
T7 2234  T7I 3722
T8 373  T8I 3349
T9 746  T9I 2603
T10 1492  T10I 1111
T11 2984  T11I 2222

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 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1881Scale 1881: Katorian, Ian Ring Music TheoryKatorian
Scale 1857Scale 1857, Ian Ring Music Theory
Scale 1865Scale 1865: Thagimic, Ian Ring Music TheoryThagimic
Scale 1889Scale 1889, Ian Ring Music Theory
Scale 1905Scale 1905: Katacrian, Ian Ring Music TheoryKatacrian
Scale 1809Scale 1809: Ranitonic, Ian Ring Music TheoryRanitonic
Scale 1841Scale 1841: Thogimic, Ian Ring Music TheoryThogimic
Scale 1937Scale 1937: Galimic, Ian Ring Music TheoryGalimic
Scale 2001Scale 2001: Gydian, Ian Ring Music TheoryGydian
Scale 1617Scale 1617: Phronitonic, Ian Ring Music TheoryPhronitonic
Scale 1745Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
Scale 1361Scale 1361: Bolitonic, Ian Ring Music TheoryBolitonic
Scale 849Scale 849: Aerynitonic, Ian Ring Music TheoryAerynitonic
Scale 2897Scale 2897: Rycrimic, Ian Ring Music TheoryRycrimic
Scale 3921Scale 3921: Pythian, Ian Ring Music TheoryPythian

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.