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Scale 3037: "Nine Tone Scale"

Scale 3037: Nine Tone Scale, 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
Nine Tone Scale
Zeitler
Staptygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,4,6,7,8,9,11}
Forte Number9-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1915
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes8
Prime?no
prime: 1775
Deep Scaleno
Interval Vector667773
Interval Spectrump7m7n7s6d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {5,6}
<5> = {6,7}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.111
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tonesnone
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}342.44
D{2,6,9}342.67
E{4,8,11}342.44
G{7,11,2}342.39
G♯{8,0,3}442.22
B{11,3,6}442.28
Minor Triadscm{0,3,7}442.17
em{4,7,11}342.39
g♯m{8,11,3}442.17
am{9,0,4}342.56
bm{11,2,6}342.5
Augmented TriadsC+{0,4,8}442.33
D♯+{3,7,11}542
Diminished Triads{0,3,6}242.56
d♯°{3,6,9}242.72
f♯°{6,9,0}242.72
g♯°{8,11,2}242.67
{9,0,3}242.67
Parsimonious Voice Leading Between Common Triads of Scale 3037. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ em em C->em E E C+->E C+->G# am am C+->am D D d#° d#° D->d#° f#° f#° D->f#° bm bm D->bm d#°->B D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3037. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m D#+->B em->E E->g#m f#°->am g#° g#° G->g#° G->bm g#°->g#m g#m->G# G#->a° a°->am 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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3037 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1783
Scale 1783: Youlan Scale, Ian Ring Music TheoryYoulan Scale
3rd mode:
Scale 2939
Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
4th mode:
Scale 3517
Scale 3517: Epocrygic, Ian Ring Music TheoryEpocrygic
5th mode:
Scale 1903
Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic
6th mode:
Scale 2999
Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
7th mode:
Scale 3547
Scale 3547: Sadygic, Ian Ring Music TheorySadygic
8th mode:
Scale 3821
Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic
9th mode:
Scale 1979
Scale 1979: Aeradygic, Ian Ring Music TheoryAeradygic

Prime

The prime form of this scale is Scale 1775

Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic

Complement

The nonatonic modal family [3037, 1783, 2939, 3517, 1903, 2999, 3547, 3821, 1979] (Forte: 9-11) is the complement of the tritonic modal family [137, 289, 529] (Forte: 3-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3037 is 1915

Scale 1915Scale 1915: Thydygic, Ian Ring Music TheoryThydygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3037 is chiral, and its enantiomorph is scale 1915

Scale 1915Scale 1915: Thydygic, Ian Ring Music TheoryThydygic

Transformations:

T0 3037  T0I 1915
T1 1979  T1I 3830
T2 3958  T2I 3565
T3 3821  T3I 3035
T4 3547  T4I 1975
T5 2999  T5I 3950
T6 1903  T6I 3805
T7 3806  T7I 3515
T8 3517  T8I 2935
T9 2939  T9I 1775
T10 1783  T10I 3550
T11 3566  T11I 3005

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 3039Scale 3039: Godyllian, Ian Ring Music TheoryGodyllian
Scale 3033Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 3029Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
Scale 3021Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
Scale 3053Scale 3053: Zycrygic, Ian Ring Music TheoryZycrygic
Scale 3069Scale 3069: Maqam Shawq Afza, Ian Ring Music TheoryMaqam Shawq Afza
Scale 2973Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
Scale 3005Scale 3005: Gycrygic, Ian Ring Music TheoryGycrygic
Scale 2909Scale 2909: Mocryllic, Ian Ring Music TheoryMocryllic
Scale 2781Scale 2781: Gycryllic, Ian Ring Music TheoryGycryllic
Scale 2525Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic
Scale 3549Scale 3549: Messiaen Mode 3 Inverse, Ian Ring Music TheoryMessiaen Mode 3 Inverse
Scale 4061Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
Scale 989Scale 989: Phrolyllic, Ian Ring Music TheoryPhrolyllic
Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic

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.