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Scale 1613: "Thylimic"

Scale 1613: Thylimic, 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
Thylimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,6,9,10}
Forte Number6-Z28
Rotational Symmetrynone
Reflection Axes0
Palindromicyes
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 619
Deep Scaleno
Interval Vector224322
Interval Spectrump2m3n4s2d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,6}
<3> = {5,6,7}
<4> = {6,8,9}
<5> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[0]
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{2,6,9}331.43
Minor Triadsd♯m{3,6,10}331.43
Augmented TriadsD+{2,6,10}231.57
Diminished Triads{0,3,6}231.57
d♯°{3,6,9}231.57
f♯°{6,9,0}231.57
{9,0,3}231.71
Parsimonious Voice Leading Between Common Triads of Scale 1613. Created by Ian Ring ©2019 d#m d#m c°->d#m c°->a° D D D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° D+->d#m d#°->d#m f#°->a°

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1613 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1427
Scale 1427: Lolimic, Ian Ring Music TheoryLolimic
3rd mode:
Scale 2761
Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
4th mode:
Scale 857
Scale 857: Aeolydimic, Ian Ring Music TheoryAeolydimic
5th mode:
Scale 619
Scale 619: Double-Phrygian Hexatonic, Ian Ring Music TheoryDouble-Phrygian HexatonicThis is the prime mode
6th mode:
Scale 2357
Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana

Prime

The prime form of this scale is Scale 619

Scale 619Scale 619: Double-Phrygian Hexatonic, Ian Ring Music TheoryDouble-Phrygian Hexatonic

Complement

The hexatonic modal family [1613, 1427, 2761, 857, 619, 2357] (Forte: 6-Z28) is the complement of the hexatonic modal family [667, 869, 1241, 1619, 2381, 2857] (Forte: 6-Z49)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1613 is itself, because it is a palindromic scale!

Scale 1613Scale 1613: Thylimic, Ian Ring Music TheoryThylimic

Transformations:

T0 1613  T0I 1613
T1 3226  T1I 3226
T2 2357  T2I 2357
T3 619  T3I 619
T4 1238  T4I 1238
T5 2476  T5I 2476
T6 857  T6I 857
T7 1714  T7I 1714
T8 3428  T8I 3428
T9 2761  T9I 2761
T10 1427  T10I 1427
T11 2854  T11I 2854

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 1615Scale 1615: Sydian, Ian Ring Music TheorySydian
Scale 1609Scale 1609: Thyritonic, Ian Ring Music TheoryThyritonic
Scale 1611Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic
Scale 1605Scale 1605: Zanitonic, Ian Ring Music TheoryZanitonic
Scale 1621Scale 1621: Scriabin's Prometheus, Ian Ring Music TheoryScriabin's Prometheus
Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 1645Scale 1645: Dorian Flat 5, Ian Ring Music TheoryDorian Flat 5
Scale 1549Scale 1549, Ian Ring Music Theory
Scale 1581Scale 1581: Raga Bagesri, Ian Ring Music TheoryRaga Bagesri
Scale 1677Scale 1677: Raga Manavi, Ian Ring Music TheoryRaga Manavi
Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 1869Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
Scale 1101Scale 1101: Stothitonic, Ian Ring Music TheoryStothitonic
Scale 1357Scale 1357: Takemitsu Linea Mode 2, Ian Ring Music TheoryTakemitsu Linea Mode 2
Scale 589Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic
Scale 2637Scale 2637: Raga Ranjani, Ian Ring Music TheoryRaga Ranjani
Scale 3661Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian

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.