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Scale 1405: "Goryllic"

Scale 1405: Goryllic, 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).

Common Names

Zeitler
Goryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,5,6,8,10}
Forte Number8-21
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 1375
Deep Scaleno
Interval Vector474643
Interval Spectrump4m6n4s7d4t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
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}242
A♯{10,2,5}242
Minor Triadsd♯m{3,6,10}242
fm{5,8,0}242
Augmented TriadsC+{0,4,8}242
D+{2,6,10}242
Diminished Triads{0,3,6}242
{2,5,8}242
Parsimonious Voice Leading Between Common Triads of Scale 1405. Created by Ian Ring ©2019 d#m d#m c°->d#m G# G# c°->G# C+ C+ fm fm C+->fm C+->G# d°->fm A# A# d°->A# D+ D+ D+->d#m D+->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1405 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1375
Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllicThis is the prime mode
3rd mode:
Scale 2735
Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
4th mode:
Scale 3415
Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
5th mode:
Scale 3755
Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
6th mode:
Scale 3925
Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
7th mode:
Scale 2005
Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
8th mode:
Scale 1525
Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic

Prime

The prime form of this scale is Scale 1375

Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic

Complement

The octatonic modal family [1405, 1375, 2735, 3415, 3755, 3925, 2005, 1525] (Forte: 8-21) is the complement of the tetratonic modal family [85, 1045, 1285, 1345] (Forte: 4-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1405 is 2005

Scale 2005Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic

Transformations:

T0 1405  T0I 2005
T1 2810  T1I 4010
T2 1525  T2I 3925
T3 3050  T3I 3755
T4 2005  T4I 3415
T5 4010  T5I 2735
T6 3925  T6I 1375
T7 3755  T7I 2750
T8 3415  T8I 1405
T9 2735  T9I 2810
T10 1375  T10I 1525
T11 2750  T11I 3050

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 1407Scale 1407: Tharygic, Ian Ring Music TheoryTharygic
Scale 1401Scale 1401: Pagian, Ian Ring Music TheoryPagian
Scale 1403Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale
Scale 1397Scale 1397: Major Locrian, Ian Ring Music TheoryMajor Locrian
Scale 1389Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian
Scale 1373Scale 1373: Storian, Ian Ring Music TheoryStorian
Scale 1341Scale 1341: Madian, Ian Ring Music TheoryMadian
Scale 1469Scale 1469: Epiryllic, Ian Ring Music TheoryEpiryllic
Scale 1533Scale 1533: Katycrygic, Ian Ring Music TheoryKatycrygic
Scale 1149Scale 1149: Bydian, Ian Ring Music TheoryBydian
Scale 1277Scale 1277: Zadyllic, Ian Ring Music TheoryZadyllic
Scale 1661Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
Scale 1917Scale 1917: Thydyllian, Ian Ring Music TheoryThydyllian
Scale 381Scale 381: Kogian, Ian Ring Music TheoryKogian
Scale 893Scale 893: Dadyllic, Ian Ring Music TheoryDadyllic
Scale 2429Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
Scale 3453Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic

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.