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Scale 3417: "Golian"

Scale 3417: Golian, 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
Golian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,4,6,8,10,11}
Forte Number7-30
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 855
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 855
Deep Scaleno
Interval Vector343542
Interval Spectrump4m5n3s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9,10}
<6> = {9,10,11}
Spectra Variation1.714
Maximally Evenno
Maximal Area Setno
Interior Area2.549
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 TriadsE{4,8,11}231.71
G♯{8,0,3}331.43
B{11,3,6}331.43
Minor Triadsd♯m{3,6,10}142.14
g♯m{8,11,3}321.29
Augmented TriadsC+{0,4,8}241.86
Diminished Triads{0,3,6}231.57
Parsimonious Voice Leading Between Common Triads of Scale 3417. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ E E C+->E C+->G# d#m d#m d#m->B g#m g#m E->g#m g#m->G# g#m->B

view full size

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.

Diameter4
Radius2
Self-Centeredno
Central Verticesg♯m
Peripheral VerticesC+, d♯m

Modes

Modes are the rotational transformation of this scale. Scale 3417 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 939
Scale 939: Mela Senavati, Ian Ring Music TheoryMela Senavati
3rd mode:
Scale 2517
Scale 2517: Harmonic Lydian, Ian Ring Music TheoryHarmonic Lydian
4th mode:
Scale 1653
Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
5th mode:
Scale 1437
Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending
6th mode:
Scale 1383
Scale 1383: Pynian, Ian Ring Music TheoryPynian
7th mode:
Scale 2739
Scale 2739: Mela Suryakanta, Ian Ring Music TheoryMela Suryakanta

Prime

The prime form of this scale is Scale 855

Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian

Complement

The heptatonic modal family [3417, 939, 2517, 1653, 1437, 1383, 2739] (Forte: 7-30) is the complement of the pentatonic modal family [339, 789, 1221, 1329, 2217] (Forte: 5-30)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3417 is 855

Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3417 is chiral, and its enantiomorph is scale 855

Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian

Transformations:

T0 3417  T0I 855
T1 2739  T1I 1710
T2 1383  T2I 3420
T3 2766  T3I 2745
T4 1437  T4I 1395
T5 2874  T5I 2790
T6 1653  T6I 1485
T7 3306  T7I 2970
T8 2517  T8I 1845
T9 939  T9I 3690
T10 1878  T10I 3285
T11 3756  T11I 2475

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 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 3421Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
Scale 3409Scale 3409: Katanimic, Ian Ring Music TheoryKatanimic
Scale 3413Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
Scale 3401Scale 3401: Palimic, Ian Ring Music TheoryPalimic
Scale 3433Scale 3433: Thonian, Ian Ring Music TheoryThonian
Scale 3449Scale 3449: Bacryllic, Ian Ring Music TheoryBacryllic
Scale 3353Scale 3353: Phraptimic, Ian Ring Music TheoryPhraptimic
Scale 3385Scale 3385: Chromatic Phrygian, Ian Ring Music TheoryChromatic Phrygian
Scale 3481Scale 3481: Katathian, Ian Ring Music TheoryKatathian
Scale 3545Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic
Scale 3161Scale 3161: Kodimic, Ian Ring Music TheoryKodimic
Scale 3289Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6
Scale 3673Scale 3673: Ranian, Ian Ring Music TheoryRanian
Scale 3929Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
Scale 2393Scale 2393: Zathimic, Ian Ring Music TheoryZathimic
Scale 2905Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1
Scale 1369Scale 1369: Boptimic, Ian Ring Music TheoryBoptimic

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.