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Scale 3545: "Thyptyllic"

Scale 3545: Thyptyllic, 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
Thyptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,3,4,6,7,8,10,11}
Forte Number8-19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 887
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 887
Deep Scaleno
Interval Vector545752
Interval Spectrump5m7n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.75
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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 TriadsC{0,4,7}342
D♯{3,7,10}342.08
E{4,8,11}342.15
G♯{8,0,3}342.15
B{11,3,6}342.08
Minor Triadscm{0,3,7}431.77
d♯m{3,6,10}252.62
em{4,7,11}431.77
g♯m{8,11,3}331.92
Augmented TriadsC+{0,4,8}352.38
D♯+{3,7,11}531.54
Diminished Triads{0,3,6}242.31
{4,7,10}242.31
Parsimonious Voice Leading Between Common Triads of Scale 3545. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ em em C->em E E C+->E C+->G# d#m d#m D# D# d#m->D# d#m->B D#->D#+ D#->e° D#+->em g#m g#m D#+->g#m D#+->B e°->em em->E E->g#m g#m->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 Verticescm, D♯+, em, g♯m
Peripheral VerticesC+, d♯m

Modes

Modes are the rotational transformation of this scale. Scale 3545 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 955
Scale 955: Ionogyllic, Ian Ring Music TheoryIonogyllic
3rd mode:
Scale 2525
Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic
4th mode:
Scale 1655
Scale 1655: Katygyllic, Ian Ring Music TheoryKatygyllic
5th mode:
Scale 2875
Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic
6th mode:
Scale 3485
Scale 3485: Sabach, Ian Ring Music TheorySabach
7th mode:
Scale 1895
Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
8th mode:
Scale 2995
Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra

Prime

The prime form of this scale is Scale 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Complement

The octatonic modal family [3545, 955, 2525, 1655, 2875, 3485, 1895, 2995] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3545 is 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3545 is chiral, and its enantiomorph is scale 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Transformations:

T0 3545  T0I 887
T1 2995  T1I 1774
T2 1895  T2I 3548
T3 3790  T3I 3001
T4 3485  T4I 1907
T5 2875  T5I 3814
T6 1655  T6I 3533
T7 3310  T7I 2971
T8 2525  T8I 1847
T9 955  T9I 3694
T10 1910  T10I 3293
T11 3820  T11I 2491

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 3547Scale 3547: Sadygic, Ian Ring Music TheorySadygic
Scale 3549Scale 3549: Messiaen Mode 3 Inverse, Ian Ring Music TheoryMessiaen Mode 3 Inverse
Scale 3537Scale 3537: Katogian, Ian Ring Music TheoryKatogian
Scale 3541Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
Scale 3529Scale 3529: Stalian, Ian Ring Music TheoryStalian
Scale 3561Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic
Scale 3577Scale 3577: Loptygic, Ian Ring Music TheoryLoptygic
Scale 3481Scale 3481: Katathian, Ian Ring Music TheoryKatathian
Scale 3513Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic
Scale 3417Scale 3417: Golian, Ian Ring Music TheoryGolian
Scale 3289Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6
Scale 3801Scale 3801: Maptyllic, Ian Ring Music TheoryMaptyllic
Scale 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
Scale 2521Scale 2521: Mela Dhatuvardhani, Ian Ring Music TheoryMela Dhatuvardhani
Scale 3033Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic
Scale 1497Scale 1497: Mela Jyotisvarupini, Ian Ring Music TheoryMela Jyotisvarupini

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.