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Scale 1815: "Godian"

Scale 1815: Godian, 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
Godian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,8,9,10}
Forte Number7-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3357
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 375
Deep Scaleno
Interval Vector443532
Interval Spectrump3m5n3s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {4,6,7}
<4> = {5,6,8}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation2.857
Maximally Evenno
Maximal Area Setno
Interior Area2.299
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 TriadsA{9,1,4}321
Minor Triadsc♯m{1,4,8}221.2
am{9,0,4}221.2
Augmented TriadsC+{0,4,8}231.4
Diminished Triadsa♯°{10,1,4}131.6
Parsimonious Voice Leading Between Common Triads of Scale 1815. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m am am C+->am A A c#m->A am->A a#° a#° A->a#°

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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 Verticesc♯m, am, A
Peripheral VerticesC+, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 1815 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2955
Scale 2955: Thorian, Ian Ring Music TheoryThorian
3rd mode:
Scale 3525
Scale 3525: Zocrian, Ian Ring Music TheoryZocrian
4th mode:
Scale 1905
Scale 1905: Katacrian, Ian Ring Music TheoryKatacrian
5th mode:
Scale 375
Scale 375: Sodian, Ian Ring Music TheorySodianThis is the prime mode
6th mode:
Scale 2235
Scale 2235: Bathian, Ian Ring Music TheoryBathian
7th mode:
Scale 3165
Scale 3165: Mylian, Ian Ring Music TheoryMylian

Prime

The prime form of this scale is Scale 375

Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian

Complement

The heptatonic modal family [1815, 2955, 3525, 1905, 375, 2235, 3165] (Forte: 7-13) is the complement of the pentatonic modal family [279, 369, 1809, 2187, 3141] (Forte: 5-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1815 is 3357

Scale 3357Scale 3357: Phrodian, Ian Ring Music TheoryPhrodian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1815 is chiral, and its enantiomorph is scale 3357

Scale 3357Scale 3357: Phrodian, Ian Ring Music TheoryPhrodian

Transformations:

T0 1815  T0I 3357
T1 3630  T1I 2619
T2 3165  T2I 1143
T3 2235  T3I 2286
T4 375  T4I 477
T5 750  T5I 954
T6 1500  T6I 1908
T7 3000  T7I 3816
T8 1905  T8I 3537
T9 3810  T9I 2979
T10 3525  T10I 1863
T11 2955  T11I 3726

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 1813Scale 1813: Katothimic, Ian Ring Music TheoryKatothimic
Scale 1811Scale 1811: Kyptimic, Ian Ring Music TheoryKyptimic
Scale 1819Scale 1819: Pydian, Ian Ring Music TheoryPydian
Scale 1823Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic
Scale 1799Scale 1799, Ian Ring Music Theory
Scale 1807Scale 1807, Ian Ring Music Theory
Scale 1831Scale 1831: Pothian, Ian Ring Music TheoryPothian
Scale 1847Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic
Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
Scale 1943Scale 1943, Ian Ring Music Theory
Scale 1559Scale 1559, Ian Ring Music Theory
Scale 1687Scale 1687: Phralian, Ian Ring Music TheoryPhralian
Scale 1303Scale 1303: Epolimic, Ian Ring Music TheoryEpolimic
Scale 791Scale 791: Aeoloptimic, Ian Ring Music TheoryAeoloptimic
Scale 2839Scale 2839: Lyptian, Ian Ring Music TheoryLyptian
Scale 3863Scale 3863: Eparyllic, Ian Ring Music TheoryEparyllic

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.