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Scale 3575: "Symmetrical Decatonic"

Scale 3575: Symmetrical Decatonic, 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

Western Modern
Symmetrical Decatonic

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,4,5,6,7,8,10,11}
Forte Number10-6
Rotational Symmetry6 semitones
Reflection Axes0, 3
Palindromicyes
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes4
Prime?no
prime: 2015
Deep Scaleno
Interval Vector888885
Interval Spectrump8m8n8s8d8t5
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4}
<4> = {4,5}
<5> = {6}
<6> = {7,8}
<7> = {8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation0.8
Maximally Evenyes
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedyes
Ridge Tones[0,6]
ProprietyProper
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}352.77
C♯{1,5,8}452.59
E{4,8,11}452.68
F♯{6,10,1}352.77
G{7,11,2}452.59
A♯{10,2,5}452.68
Minor Triadsc♯m{1,4,8}452.68
em{4,7,11}452.59
fm{5,8,0}352.77
gm{7,10,2}452.68
a♯m{10,1,5}452.59
bm{11,2,6}352.77
Augmented TriadsC+{0,4,8}452.68
D+{2,6,10}452.68
Diminished Triadsc♯°{1,4,7}253.05
{2,5,8}252.86
{4,7,10}252.86
{5,8,11}253.05
{7,10,1}253.05
g♯°{8,11,2}252.86
a♯°{10,1,4}252.86
{11,2,5}253.05
Parsimonious Voice Leading Between Common Triads of Scale 3575. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E fm fm C+->fm c#°->c#m 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+ 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 3575. Created by Ian Ring ©2019 G em->G E->f° g#° g#° E->g#° f°->fm F#->g° F#->a#m g°->gm gm->G G->g#° G->bm a#°->a#m a#m->A# A#->b° b°->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
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3575 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 3835
Scale 3835, Ian Ring Music Theory
3rd mode:
Scale 3965
Scale 3965: Messiaen Mode 7 Inverse, Ian Ring Music TheoryMessiaen Mode 7 Inverse
4th mode:
Scale 2015
Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7This is the prime mode
5th mode:
Scale 3055
Scale 3055: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7

Prime

The prime form of this scale is Scale 2015

Scale 2015Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7

Complement

The decatonic modal family [3575, 3835, 3965, 2015, 3055] (Forte: 10-6) is the complement of the modal family [65] (Forte: 2-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3575 is itself, because it is a palindromic scale!

Scale 3575Scale 3575: Symmetrical Decatonic, Ian Ring Music TheorySymmetrical Decatonic

Transformations:

T0 3575  T0I 3575
T1 3055  T1I 3055
T2 2015  T2I 2015
T3 4030  T3I 4030
T4 3965  T4I 3965
T5 3835  T5I 3835
T6 3575  T6I 3575
T7 3055  T7I 3055
T8 2015  T8I 2015
T9 4030  T9I 4030
T10 3965  T10I 3965
T11 3835  T11I 3835

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 3573Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
Scale 3571Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
Scale 3579Scale 3579: Zyphyllian, Ian Ring Music TheoryZyphyllian
Scale 3583Scale 3583: Zylatic, Ian Ring Music TheoryZylatic
Scale 3559Scale 3559: Thophygic, Ian Ring Music TheoryThophygic
Scale 3567Scale 3567: Epityllian, Ian Ring Music TheoryEpityllian
Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
Scale 3511Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
Scale 3447Scale 3447: Mogyllian, Ian Ring Music TheoryMogyllian
Scale 3319Scale 3319: Tholygic, Ian Ring Music TheoryTholygic
Scale 3831Scale 3831: Ionyllian, Ian Ring Music TheoryIonyllian
Scale 4087Scale 4087: Aeolatic, Ian Ring Music TheoryAeolatic
Scale 2551Scale 2551: Thocrygic, Ian Ring Music TheoryThocrygic
Scale 3063Scale 3063: Solyllian, Ian Ring Music TheorySolyllian
Scale 1527Scale 1527: Aeolyrigic, Ian Ring Music TheoryAeolyrigic

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.