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Scale 3727: "Tholyllic"

Scale 3727: Tholyllic, 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
Tholyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,7,9,10,11}
Forte Number8-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3631
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 383
Deep Scaleno
Interval Vector665542
Interval Spectrump4m5n5s6d6t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {6,7,9,10}
<7> = {8,10,11}
Spectra Variation3.25
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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 TriadsD♯{3,7,10}231.57
G{7,11,2}231.57
Minor Triadscm{0,3,7}241.86
gm{7,10,2}341.71
Augmented TriadsD♯+{3,7,11}331.43
Diminished Triads{7,10,1}152.43
{9,0,3}152.57
Parsimonious Voice Leading Between Common Triads of Scale 3727. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ cm->a° D# D# D#->D#+ gm gm D#->gm Parsimonious Voice Leading Between Common Triads of Scale 3727. Created by Ian Ring ©2019 G D#+->G g°->gm gm->G

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesD♯, D♯+, G
Peripheral Verticesg°, a°

Modes

Modes are the rotational transformation of this scale. Scale 3727 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3911
Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic
3rd mode:
Scale 4003
Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic
4th mode:
Scale 4049
Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic
5th mode:
Scale 509
Scale 509: Ionothyllic, Ian Ring Music TheoryIonothyllic
6th mode:
Scale 1151
Scale 1151: Mythyllic, Ian Ring Music TheoryMythyllic
7th mode:
Scale 2623
Scale 2623: Aerylyllic, Ian Ring Music TheoryAerylyllic
8th mode:
Scale 3359
Scale 3359: Bonyllic, Ian Ring Music TheoryBonyllic

Prime

The prime form of this scale is Scale 383

Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic

Complement

The octatonic modal family [3727, 3911, 4003, 4049, 509, 1151, 2623, 3359] (Forte: 8-2) is the complement of the tetratonic modal family [23, 1793, 2059, 3077] (Forte: 4-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3727 is 3631

Scale 3631Scale 3631: Gydyllic, Ian Ring Music TheoryGydyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3727 is chiral, and its enantiomorph is scale 3631

Scale 3631Scale 3631: Gydyllic, Ian Ring Music TheoryGydyllic

Transformations:

T0 3727  T0I 3631
T1 3359  T1I 3167
T2 2623  T2I 2239
T3 1151  T3I 383
T4 2302  T4I 766
T5 509  T5I 1532
T6 1018  T6I 3064
T7 2036  T7I 2033
T8 4072  T8I 4066
T9 4049  T9I 4037
T10 4003  T10I 3979
T11 3911  T11I 3863

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 3725Scale 3725: Kyrian, Ian Ring Music TheoryKyrian
Scale 3723Scale 3723: Myptian, Ian Ring Music TheoryMyptian
Scale 3719Scale 3719, Ian Ring Music Theory
Scale 3735Scale 3735, Ian Ring Music Theory
Scale 3743Scale 3743: Thadygic, Ian Ring Music TheoryThadygic
Scale 3759Scale 3759: Darygic, Ian Ring Music TheoryDarygic
Scale 3791Scale 3791: Stodygic, Ian Ring Music TheoryStodygic
Scale 3599Scale 3599, Ian Ring Music Theory
Scale 3663Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic
Scale 3855Scale 3855, Ian Ring Music Theory
Scale 3983Scale 3983: Thyptygic, Ian Ring Music TheoryThyptygic
Scale 3215Scale 3215: Katydian, Ian Ring Music TheoryKatydian
Scale 3471Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 1679Scale 1679: Kydian, Ian Ring Music TheoryKydian

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.