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Scale 3655: "Mathian"

Scale 3655: Mathian, 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
Mathian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,6,9,10,11}
Forte Number7-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3151
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 319
Deep Scaleno
Interval Vector544431
Interval Spectrump3m4n4s4d5t
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,5,7}
<3> = {3,5,6,8}
<4> = {4,6,7,9}
<5> = {5,7,8,10}
<6> = {8,9,11}
Spectra Variation3.714
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 3655 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3875
Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
3rd mode:
Scale 3985
Scale 3985: Thadian, Ian Ring Music TheoryThadian
4th mode:
Scale 505
Scale 505: Sanian, Ian Ring Music TheorySanian
5th mode:
Scale 575
Scale 575: Ionydian, Ian Ring Music TheoryIonydian
6th mode:
Scale 2335
Scale 2335: Epydian, Ian Ring Music TheoryEpydian
7th mode:
Scale 3215
Scale 3215: Katydian, Ian Ring Music TheoryKatydian

Prime

The prime form of this scale is Scale 319

Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian

Complement

The heptatonic modal family [3655, 3875, 3985, 505, 575, 2335, 3215] (Forte: 7-3) is the complement of the pentatonic modal family [55, 1795, 2075, 2945, 3085] (Forte: 5-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3655 is 3151

Scale 3151Scale 3151: Pacrian, Ian Ring Music TheoryPacrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3655 is chiral, and its enantiomorph is scale 3151

Scale 3151Scale 3151: Pacrian, Ian Ring Music TheoryPacrian

Transformations:

T0 3655  T0I 3151
T1 3215  T1I 2207
T2 2335  T2I 319
T3 575  T3I 638
T4 1150  T4I 1276
T5 2300  T5I 2552
T6 505  T6I 1009
T7 1010  T7I 2018
T8 2020  T8I 4036
T9 4040  T9I 3977
T10 3985  T10I 3859
T11 3875  T11I 3623

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 3653Scale 3653: Sathimic, Ian Ring Music TheorySathimic
Scale 3651Scale 3651, Ian Ring Music Theory
Scale 3659Scale 3659: Polian, Ian Ring Music TheoryPolian
Scale 3663Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic
Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
Scale 3687Scale 3687: Zonyllic, Ian Ring Music TheoryZonyllic
Scale 3591Scale 3591, Ian Ring Music Theory
Scale 3623Scale 3623: Aerocrian, Ian Ring Music TheoryAerocrian
Scale 3719Scale 3719, Ian Ring Music Theory
Scale 3783Scale 3783: Phrygyllic, Ian Ring Music TheoryPhrygyllic
Scale 3911Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic
Scale 3143Scale 3143: Polimic, Ian Ring Music TheoryPolimic
Scale 3399Scale 3399: Zonian, Ian Ring Music TheoryZonian
Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic
Scale 1607Scale 1607: Epytimic, Ian Ring Music TheoryEpytimic

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.