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Scale 3217: "Molitonic"

Scale 3217: Molitonic, 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
Molitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,4,7,10,11}
Forte Number5-Z38
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 295
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes4
Prime?no
prime: 295
Deep Scaleno
Interval Vector212221
Interval Spectrump2m2n2sd2t
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,5,6,7}
<3> = {5,6,7,8,10}
<4> = {8,9,11}
Spectra Variation3.2
Maximally Evenno
Maximal Area Setno
Interior Area1.933
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
Major TriadsC{0,4,7}121
Minor Triadsem{4,7,11}210.67
Diminished Triads{4,7,10}121
Parsimonious Voice Leading Between Common Triads of Scale 3217. Created by Ian Ring ©2019 C C em em C->em e°->em

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.

Diameter2
Radius1
Self-Centeredno
Central Verticesem
Peripheral VerticesC, e°

Modes

Modes are the rotational transformation of this scale. Scale 3217 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 457
Scale 457: Staptitonic, Ian Ring Music TheoryStaptitonic
3rd mode:
Scale 569
Scale 569: Mothitonic, Ian Ring Music TheoryMothitonic
4th mode:
Scale 583
Scale 583: Aeritonic, Ian Ring Music TheoryAeritonic
5th mode:
Scale 2339
Scale 2339: Raga Kshanika, Ian Ring Music TheoryRaga Kshanika

Prime

The prime form of this scale is Scale 295

Scale 295Scale 295: Gyritonic, Ian Ring Music TheoryGyritonic

Complement

The pentatonic modal family [3217, 457, 569, 583, 2339] (Forte: 5-Z38) is the complement of the heptatonic modal family [439, 1763, 1819, 2267, 2929, 2957, 3181] (Forte: 7-Z38)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3217 is 295

Scale 295Scale 295: Gyritonic, Ian Ring Music TheoryGyritonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3217 is chiral, and its enantiomorph is scale 295

Scale 295Scale 295: Gyritonic, Ian Ring Music TheoryGyritonic

Transformations:

T0 3217  T0I 295
T1 2339  T1I 590
T2 583  T2I 1180
T3 1166  T3I 2360
T4 2332  T4I 625
T5 569  T5I 1250
T6 1138  T6I 2500
T7 2276  T7I 905
T8 457  T8I 1810
T9 914  T9I 3620
T10 1828  T10I 3145
T11 3656  T11I 2195

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 3219Scale 3219: Ionaphimic, Ian Ring Music TheoryIonaphimic
Scale 3221Scale 3221: Bycrimic, Ian Ring Music TheoryBycrimic
Scale 3225Scale 3225: Ionalimic, Ian Ring Music TheoryIonalimic
Scale 3201Scale 3201, Ian Ring Music Theory
Scale 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
Scale 3233Scale 3233, Ian Ring Music Theory
Scale 3249Scale 3249: Raga Tilang, Ian Ring Music TheoryRaga Tilang
Scale 3281Scale 3281: Raga Vijayavasanta, Ian Ring Music TheoryRaga Vijayavasanta
Scale 3089Scale 3089, Ian Ring Music Theory
Scale 3153Scale 3153: Zathitonic, Ian Ring Music TheoryZathitonic
Scale 3345Scale 3345: Zylitonic, Ian Ring Music TheoryZylitonic
Scale 3473Scale 3473: Lathimic, Ian Ring Music TheoryLathimic
Scale 3729Scale 3729: Starimic, Ian Ring Music TheoryStarimic
Scale 2193Scale 2193: Thaptic, Ian Ring Music TheoryThaptic
Scale 2705Scale 2705: Raga Mamata, Ian Ring Music TheoryRaga Mamata
Scale 1169Scale 1169: Raga Mahathi, Ian Ring Music TheoryRaga Mahathi

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.