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Scale 3775: "Loptyllian"

Scale 3775: Loptyllian, 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
Loptyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,4,5,7,9,10,11}
Forte Number10-2
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia7 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1535
Deep Scaleno
Interval Vector898884
Interval Spectrump8m8n8s9d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {7,8,9}
<8> = {8,9,10}
<9> = {10,11}
Spectra Variation1.6
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[2]
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}452.6
D♯{3,7,10}352.7
F{5,9,0}252.8
G{7,11,2}352.7
A{9,1,4}452.6
A♯{10,2,5}452.6
Minor Triadscm{0,3,7}352.7
dm{2,5,9}252.8
em{4,7,11}352.7
gm{7,10,2}452.6
am{9,0,4}452.6
a♯m{10,1,5}452.6
Augmented TriadsC♯+{1,5,9}452.6
D♯+{3,7,11}452.6
Diminished Triadsc♯°{1,4,7}252.8
{4,7,10}253
{7,10,1}252.8
{9,0,3}252.9
a♯°{10,1,4}252.8
{11,2,5}252.9
Parsimonious Voice Leading Between Common Triads of Scale 3775. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ cm->a° c#° c#° C->c#° em em C->em am am C->am A A c#°->A C#+ C#+ dm dm C#+->dm F F C#+->F C#+->A a#m a#m C#+->a#m A# A# dm->A# D# D# D#->D#+ D#->e° gm gm D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3775. Created by Ian Ring ©2019 G D#+->G e°->em F->am g°->gm g°->a#m gm->G gm->A# G->b° a°->am am->A a#° a#° A->a#° a#°->a#m a#m->A# A#->b°

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
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3775 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 3935
Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
3rd mode:
Scale 4015
Scale 4015: Phradyllian, Ian Ring Music TheoryPhradyllian
4th mode:
Scale 4055
Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian
5th mode:
Scale 4075
Scale 4075: Katyllian, Ian Ring Music TheoryKatyllian
6th mode:
Scale 4085
Scale 4085: Sydyllian, Ian Ring Music TheorySydyllian
7th mode:
Scale 2045
Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian
8th mode:
Scale 1535
Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllianThis is the prime mode
9th mode:
Scale 2815
Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian
10th mode:
Scale 3455
Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian

Prime

The prime form of this scale is Scale 1535

Scale 1535Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllian

Complement

The decatonic modal family [3775, 3935, 4015, 4055, 4075, 4085, 2045, 1535, 2815, 3455] (Forte: 10-2) is the complement of the modal family [5, 1025] (Forte: 2-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3775 is 4015

Scale 4015Scale 4015: Phradyllian, Ian Ring Music TheoryPhradyllian

Transformations:

T0 3775  T0I 4015
T1 3455  T1I 3935
T2 2815  T2I 3775
T3 1535  T3I 3455
T4 3070  T4I 2815
T5 2045  T5I 1535
T6 4090  T6I 3070
T7 4085  T7I 2045
T8 4075  T8I 4090
T9 4055  T9I 4085
T10 4015  T10I 4075
T11 3935  T11I 4055

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 3773Scale 3773: Raga Malgunji, Ian Ring Music TheoryRaga Malgunji
Scale 3771Scale 3771: Stophygic, Ian Ring Music TheoryStophygic
Scale 3767Scale 3767: Chromatic Bebop, Ian Ring Music TheoryChromatic Bebop
Scale 3759Scale 3759: Darygic, Ian Ring Music TheoryDarygic
Scale 3743Scale 3743: Thadygic, Ian Ring Music TheoryThadygic
Scale 3807Scale 3807: Bagyllian, Ian Ring Music TheoryBagyllian
Scale 3839Scale 3839: Mixolatic, Ian Ring Music TheoryMixolatic
Scale 3647Scale 3647: Eporygic, Ian Ring Music TheoryEporygic
Scale 3711Scale 3711: Dycryllian, Ian Ring Music TheoryDycryllian
Scale 3903Scale 3903: Aeogyllian, Ian Ring Music TheoryAeogyllian
Scale 4031Scale 4031: Godatic, Ian Ring Music TheoryGodatic
Scale 3263Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic
Scale 3519Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
Scale 2751Scale 2751: Sylygic, Ian Ring Music TheorySylygic
Scale 1727Scale 1727: Sydygic, Ian Ring Music TheorySydygic

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.