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Scale 313: "Goritonic"

Scale 313: Goritonic, 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
Goritonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,3,4,5,8}
Forte Number5-Z37
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes4
Prime?yes
Deep Scaleno
Interval Vector212320
Interval Spectrump2m3n2sd2
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,7}
<3> = {5,8,10}
<4> = {8,9,11}
Spectra Variation3.2
Maximally Evenno
Maximal Area Setno
Interior Area1.933
Myhill Propertyno
Balancedno
Ridge Tones[8]
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}121
Minor Triadsfm{5,8,0}121
Augmented TriadsC+{0,4,8}210.67
Parsimonious Voice Leading Between Common Triads of Scale 313. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm G# G# C+->G#

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 VerticesC+
Peripheral Verticesfm, G♯

Modes

Modes are the rotational transformation of this scale. Scale 313 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 551
Scale 551: Aeoloditonic, Ian Ring Music TheoryAeoloditonic
3rd mode:
Scale 2323
Scale 2323: Doptitonic, Ian Ring Music TheoryDoptitonic
4th mode:
Scale 3209
Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
5th mode:
Scale 913
Scale 913: Aeolyritonic, Ian Ring Music TheoryAeolyritonic

Prime

This is the prime form of this scale.

Complement

The pentatonic modal family [313, 551, 2323, 3209, 913] (Forte: 5-Z37) is the complement of the heptatonic modal family [443, 1591, 1891, 2269, 2843, 2993, 3469] (Forte: 7-Z37)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 313 is 913

Scale 913Scale 913: Aeolyritonic, Ian Ring Music TheoryAeolyritonic

Transformations:

T0 313  T0I 913
T1 626  T1I 1826
T2 1252  T2I 3652
T3 2504  T3I 3209
T4 913  T4I 2323
T5 1826  T5I 551
T6 3652  T6I 1102
T7 3209  T7I 2204
T8 2323  T8I 313
T9 551  T9I 626
T10 1102  T10I 1252
T11 2204  T11I 2504

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 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic
Scale 317Scale 317: Korimic, Ian Ring Music TheoryKorimic
Scale 305Scale 305: Gonic, Ian Ring Music TheoryGonic
Scale 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic
Scale 297Scale 297: Mynic, Ian Ring Music TheoryMynic
Scale 281Scale 281: Lanic, Ian Ring Music TheoryLanic
Scale 345Scale 345: Gylitonic, Ian Ring Music TheoryGylitonic
Scale 377Scale 377: Kathimic, Ian Ring Music TheoryKathimic
Scale 441Scale 441: Thycrimic, Ian Ring Music TheoryThycrimic
Scale 57Scale 57, Ian Ring Music Theory
Scale 185Scale 185, Ian Ring Music Theory
Scale 569Scale 569: Mothitonic, Ian Ring Music TheoryMothitonic
Scale 825Scale 825: Thyptimic, Ian Ring Music TheoryThyptimic
Scale 1337Scale 1337: Epogimic, Ian Ring Music TheoryEpogimic
Scale 2361Scale 2361: Docrimic, Ian Ring Music TheoryDocrimic

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.