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Scale 4085: "Sydyllian"

Scale 4085: Sydyllian, 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
Sydyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,2,4,5,6,7,8,9,10,11}
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{0,4,7}252.8
D{2,6,9}352.7
E{4,8,11}452.6
F{5,9,0}452.6
G{7,11,2}452.6
A♯{10,2,5}352.7
Minor Triadsdm{2,5,9}452.6
em{4,7,11}452.6
fm{5,8,0}452.6
gm{7,10,2}352.7
am{9,0,4}252.8
bm{11,2,6}352.7
Augmented TriadsC+{0,4,8}452.6
D+{2,6,10}452.6
Diminished Triads{2,5,8}252.8
{4,7,10}252.9
{5,8,11}252.8
f♯°{6,9,0}252.9
g♯°{8,11,2}252.8
{11,2,5}253
Parsimonious Voice Leading Between Common Triads of Scale 4085. Created by Ian Ring ©2019 C C C+ C+ C->C+ em em C->em E E C+->E fm fm C+->fm am am C+->am dm dm d°->dm d°->fm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° gm gm D+->gm D+->A# bm bm D+->bm e°->em e°->gm em->E Parsimonious Voice Leading Between Common Triads of Scale 4085. Created by Ian Ring ©2019 G em->G E->f° g#° g#° E->g#° f°->fm fm->F F->f#° F->am gm->G G->g#° G->bm A#->b° b°->bm

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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 4085 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 2045
Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian
3rd mode:
Scale 1535
Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllianThis is the prime mode
4th mode:
Scale 2815
Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian
5th mode:
Scale 3455
Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
6th mode:
Scale 3775
Scale 3775: Loptyllian, Ian Ring Music TheoryLoptyllian
7th mode:
Scale 3935
Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
8th mode:
Scale 4015
Scale 4015: Phradyllian, Ian Ring Music TheoryPhradyllian
9th mode:
Scale 4055
Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian
10th mode:
Scale 4075
Scale 4075: Katyllian, Ian Ring Music TheoryKatyllian

Prime

The prime form of this scale is Scale 1535

Scale 1535Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllian

Complement

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

Scale 1535Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllian

Transformations:

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

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 4087Scale 4087: Aeolatic, Ian Ring Music TheoryAeolatic
Scale 4081Scale 4081: Manygic, Ian Ring Music TheoryManygic
Scale 4083Scale 4083: Bathyllian, Ian Ring Music TheoryBathyllian
Scale 4089Scale 4089: Katoryllian, Ian Ring Music TheoryKatoryllian
Scale 4093Scale 4093: Aerycratic, Ian Ring Music TheoryAerycratic
Scale 4069Scale 4069: Starygic, Ian Ring Music TheoryStarygic
Scale 4077Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
Scale 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
Scale 4021Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic
Scale 3829Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
Scale 3573Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
Scale 3061Scale 3061: Apinygic, Ian Ring Music TheoryApinygic
Scale 2037Scale 2037: Sythygic, Ian Ring Music TheorySythygic

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.