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Scale 1805

Scale 1805, 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).

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,8,9,10}
Forte Number6-Z12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1565
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 215
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,4,6}
<3> = {4,5,7,8}
<4> = {6,8,9,10}
<5> = {7,10,11}
Spectra Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area1.866
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 TriadsG♯{8,0,3}110.5
Diminished Triads{9,0,3}110.5
Parsimonious Voice Leading Between Common Triads of Scale 1805. Created by Ian Ring ©2019 G# G# G#->a°

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1805 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1475
Scale 1475, Ian Ring Music Theory
3rd mode:
Scale 2785
Scale 2785, Ian Ring Music Theory
4th mode:
Scale 215
Scale 215, Ian Ring Music TheoryThis is the prime mode
5th mode:
Scale 2155
Scale 2155, Ian Ring Music Theory
6th mode:
Scale 3125
Scale 3125, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 215

Scale 215Scale 215, Ian Ring Music Theory

Complement

The hexatonic modal family [1805, 1475, 2785, 215, 2155, 3125] (Forte: 6-Z12) is the complement of the hexatonic modal family [335, 965, 1265, 2215, 3155, 3625] (Forte: 6-Z41)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1805 is 1565

Scale 1565Scale 1565, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1805 is chiral, and its enantiomorph is scale 1565

Scale 1565Scale 1565, Ian Ring Music Theory

Transformations:

T0 1805  T0I 1565
T1 3610  T1I 3130
T2 3125  T2I 2165
T3 2155  T3I 235
T4 215  T4I 470
T5 430  T5I 940
T6 860  T6I 1880
T7 1720  T7I 3760
T8 3440  T8I 3425
T9 2785  T9I 2755
T10 1475  T10I 1415
T11 2950  T11I 2830

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 1807Scale 1807, Ian Ring Music Theory
Scale 1801Scale 1801, Ian Ring Music Theory
Scale 1803Scale 1803, Ian Ring Music Theory
Scale 1797Scale 1797, Ian Ring Music Theory
Scale 1813Scale 1813: Katothimic, Ian Ring Music TheoryKatothimic
Scale 1821Scale 1821: Aeradian, Ian Ring Music TheoryAeradian
Scale 1837Scale 1837: Dalian, Ian Ring Music TheoryDalian
Scale 1869Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
Scale 1933Scale 1933: Mocrian, Ian Ring Music TheoryMocrian
Scale 1549Scale 1549, Ian Ring Music Theory
Scale 1677Scale 1677: Raga Manavi, Ian Ring Music TheoryRaga Manavi
Scale 1293Scale 1293, Ian Ring Music Theory
Scale 781Scale 781, Ian Ring Music Theory
Scale 2829Scale 2829, Ian Ring Music Theory
Scale 3853Scale 3853, Ian Ring Music Theory

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.