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Scale 3455: "Ryptyllian"

Scale 3455: Ryptyllian, 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
Ryptyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,4,5,6,8,10,11}
Forte Number10-2
Rotational Symmetrynone
Reflection Axes2
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[4]
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♯{1,5,8}452.6
E{4,8,11}352.7
F♯{6,10,1}252.8
G♯{8,0,3}352.7
A♯{10,2,5}452.6
B{11,3,6}452.6
Minor Triadsc♯m{1,4,8}352.7
d♯m{3,6,10}252.8
fm{5,8,0}352.7
g♯m{8,11,3}452.6
a♯m{10,1,5}452.6
bm{11,2,6}452.6
Augmented TriadsC+{0,4,8}452.6
D+{2,6,10}452.6
Diminished Triads{0,3,6}252.9
{2,5,8}252.8
{5,8,11}253
g♯°{8,11,2}252.8
a♯°{10,1,4}252.9
{11,2,5}252.8
Parsimonious Voice Leading Between Common Triads of Scale 3455. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm C+->G# C# C# c#m->C# a#° a#° c#m->a#° C#->d° C#->fm a#m a#m C#->a#m A# A# d°->A# D+ D+ d#m d#m D+->d#m F# F# D+->F# D+->A# bm bm D+->bm d#m->B E->f° g#m g#m E->g#m f°->fm F#->a#m g#° g#° g#°->g#m g#°->bm g#m->G# g#m->B a#°->a#m a#m->A# A#->b° b°->bm bm->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 3455 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 3775
Scale 3775: Loptyllian, Ian Ring Music TheoryLoptyllian
3rd mode:
Scale 3935
Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
4th mode:
Scale 4015
Scale 4015: Phradyllian, Ian Ring Music TheoryPhradyllian
5th mode:
Scale 4055
Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian
6th mode:
Scale 4075
Scale 4075: Katyllian, Ian Ring Music TheoryKatyllian
7th mode:
Scale 4085
Scale 4085: Sydyllian, Ian Ring Music TheorySydyllian
8th mode:
Scale 2045
Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian
9th mode:
Scale 1535
Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllianThis is the prime mode
10th mode:
Scale 2815
Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian

Prime

The prime form of this scale is Scale 1535

Scale 1535Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllian

Complement

The decatonic modal family [3455, 3775, 3935, 4015, 4055, 4075, 4085, 2045, 1535, 2815] (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 3455 is 4055

Scale 4055Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian

Transformations:

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

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 3453Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
Scale 3451Scale 3451: Garygic, Ian Ring Music TheoryGarygic
Scale 3447Scale 3447: Kynygic, Ian Ring Music TheoryKynygic
Scale 3439Scale 3439: Lythygic, Ian Ring Music TheoryLythygic
Scale 3423Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
Scale 3391Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic
Scale 3519Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
Scale 3583Scale 3583: Zylatic, Ian Ring Music TheoryZylatic
Scale 3199Scale 3199: Thaptygic, Ian Ring Music TheoryThaptygic
Scale 3327Scale 3327: Madyllian, Ian Ring Music TheoryMadyllian
Scale 3711Scale 3711: Dycryllian, Ian Ring Music TheoryDycryllian
Scale 3967Scale 3967: Soratic, Ian Ring Music TheorySoratic
Scale 2431Scale 2431: Gythygic, Ian Ring Music TheoryGythygic
Scale 2943Scale 2943: Dathyllian, Ian Ring Music TheoryDathyllian
Scale 1407Scale 1407: Tharygic, Ian Ring Music TheoryTharygic

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.