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Scale 3015: "Laptyllic"

Scale 3015: Laptyllic, 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
Laptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,6,7,8,9,11}
Forte Number8-6
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 495
Deep Scaleno
Interval Vector654463
Interval Spectrump6m4n4s5d6t3
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {3,4,6}
<4> = {5,7}
<5> = {6,8,9}
<6> = {7,9,10}
<7> = {8,10,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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 TriadsD{2,6,9}231.5
G{7,11,2}241.83
Minor Triadsf♯m{6,9,1}241.83
bm{11,2,6}231.5
Diminished Triadsf♯°{6,9,0}152.5
g♯°{8,11,2}152.5
Parsimonious Voice Leading Between Common Triads of Scale 3015. Created by Ian Ring ©2019 D D f#m f#m D->f#m bm bm D->bm f#° f#° f#°->f#m Parsimonious Voice Leading Between Common Triads of Scale 3015. Created by Ian Ring ©2019 G g#° g#° G->g#° G->bm

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, bm
Peripheral Verticesf♯°, g♯°

Modes

Modes are the rotational transformation of this scale. Scale 3015 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3555
Scale 3555: Pylyllic, Ian Ring Music TheoryPylyllic
3rd mode:
Scale 3825
Scale 3825: Pynyllic, Ian Ring Music TheoryPynyllic
4th mode:
Scale 495
Scale 495: Bocryllic, Ian Ring Music TheoryBocryllicThis is the prime mode
5th mode:
Scale 2295
Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic
6th mode:
Scale 3195
Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
7th mode:
Scale 3645
Scale 3645: Zycryllic, Ian Ring Music TheoryZycryllic
8th mode:
Scale 1935
Scale 1935: Mycryllic, Ian Ring Music TheoryMycryllic

Prime

The prime form of this scale is Scale 495

Scale 495Scale 495: Bocryllic, Ian Ring Music TheoryBocryllic

Complement

The octatonic modal family [3015, 3555, 3825, 495, 2295, 3195, 3645, 1935] (Forte: 8-6) is the complement of the tetratonic modal family [135, 225, 2115, 3105] (Forte: 4-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3015 is 3195

Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic

Transformations:

T0 3015  T0I 3195
T1 1935  T1I 2295
T2 3870  T2I 495
T3 3645  T3I 990
T4 3195  T4I 1980
T5 2295  T5I 3960
T6 495  T6I 3825
T7 990  T7I 3555
T8 1980  T8I 3015
T9 3960  T9I 1935
T10 3825  T10I 3870
T11 3555  T11I 3645

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 3013Scale 3013: Thynian, Ian Ring Music TheoryThynian
Scale 3011Scale 3011, Ian Ring Music Theory
Scale 3019Scale 3019, Ian Ring Music Theory
Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic
Scale 3031Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic
Scale 3047Scale 3047: Panygic, Ian Ring Music TheoryPanygic
Scale 2951Scale 2951, Ian Ring Music Theory
Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
Scale 2887Scale 2887: Gaptian, Ian Ring Music TheoryGaptian
Scale 2759Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani
Scale 2503Scale 2503: Mela Jhalavarali, Ian Ring Music TheoryMela Jhalavarali
Scale 3527Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
Scale 4039Scale 4039: Ionogygic, Ian Ring Music TheoryIonogygic
Scale 967Scale 967: Mela Salaga, Ian Ring Music TheoryMela Salaga
Scale 1991Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic

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.