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Scale 3665: "Stalimic"

Scale 3665: Stalimic, 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
Stalimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,4,6,9,10,11}
Forte Number6-Z41
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 335
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?no
prime: 335
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,4,5,6}
<3> = {3,5,6,7,9}
<4> = {6,7,8,10}
<5> = {8,9,10,11}
Spectra Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
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
Minor Triadsam{9,0,4}110.5
Diminished Triadsf♯°{6,9,0}110.5
Parsimonious Voice Leading Between Common Triads of Scale 3665. Created by Ian Ring ©2019 f#° f#° am am f#°->am

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3665 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 485
Scale 485: Stoptimic, Ian Ring Music TheoryStoptimic
3rd mode:
Scale 1145
Scale 1145: Zygimic, Ian Ring Music TheoryZygimic
4th mode:
Scale 655
Scale 655: Kataptimic, Ian Ring Music TheoryKataptimic
5th mode:
Scale 2375
Scale 2375: Aeolaptimic, Ian Ring Music TheoryAeolaptimic
6th mode:
Scale 3235
Scale 3235: Pothimic, Ian Ring Music TheoryPothimic

Prime

The prime form of this scale is Scale 335

Scale 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic

Complement

The hexatonic modal family [3665, 485, 1145, 655, 2375, 3235] (Forte: 6-Z41) is the complement of the hexatonic modal family [215, 1475, 1805, 2155, 2785, 3125] (Forte: 6-Z12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3665 is 335

Scale 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3665 is chiral, and its enantiomorph is scale 335

Scale 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic

Transformations:

T0 3665  T0I 335
T1 3235  T1I 670
T2 2375  T2I 1340
T3 655  T3I 2680
T4 1310  T4I 1265
T5 2620  T5I 2530
T6 1145  T6I 965
T7 2290  T7I 1930
T8 485  T8I 3860
T9 970  T9I 3625
T10 1940  T10I 3155
T11 3880  T11I 2215

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 3667Scale 3667: Kaptian, Ian Ring Music TheoryKaptian
Scale 3669Scale 3669: Mothian, Ian Ring Music TheoryMothian
Scale 3673Scale 3673: Ranian, Ian Ring Music TheoryRanian
Scale 3649Scale 3649, Ian Ring Music Theory
Scale 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
Scale 3681Scale 3681, Ian Ring Music Theory
Scale 3697Scale 3697: Ionarian, Ian Ring Music TheoryIonarian
Scale 3601Scale 3601, Ian Ring Music Theory
Scale 3633Scale 3633: Daptimic, Ian Ring Music TheoryDaptimic
Scale 3729Scale 3729: Starimic, Ian Ring Music TheoryStarimic
Scale 3793Scale 3793: Aeopian, Ian Ring Music TheoryAeopian
Scale 3921Scale 3921: Pythian, Ian Ring Music TheoryPythian
Scale 3153Scale 3153: Zathitonic, Ian Ring Music TheoryZathitonic
Scale 3409Scale 3409: Katanimic, Ian Ring Music TheoryKatanimic
Scale 2641Scale 2641: Raga Hindol, Ian Ring Music TheoryRaga Hindol
Scale 1617Scale 1617: Phronitonic, Ian Ring Music TheoryPhronitonic

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.