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Scale 3171: "Zythimic"

Scale 3171: Zythimic, 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
Zythimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,5,6,10,11}
Forte Number6-Z38
Rotational Symmetrynone
Reflection Axes5.5
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes5
Prime?no
prime: 399
Deep Scaleno
Interval Vector421242
Interval Spectrump4m2ns2d4t2
Distribution Spectra<1> = {1,4}
<2> = {2,5}
<3> = {3,6,9}
<4> = {7,10}
<5> = {8,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area1.866
Myhill Propertyno
Balancedno
Ridge Tones[11]
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3171 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3633
Scale 3633: Daptimic, Ian Ring Music TheoryDaptimic
3rd mode:
Scale 483
Scale 483: Kygimic, Ian Ring Music TheoryKygimic
4th mode:
Scale 2289
Scale 2289: Mocrimic, Ian Ring Music TheoryMocrimic
5th mode:
Scale 399
Scale 399: Zynimic, Ian Ring Music TheoryZynimicThis is the prime mode
6th mode:
Scale 2247
Scale 2247: Raga Vijayasri, Ian Ring Music TheoryRaga Vijayasri

Prime

The prime form of this scale is Scale 399

Scale 399Scale 399: Zynimic, Ian Ring Music TheoryZynimic

Complement

The hexatonic modal family [3171, 3633, 483, 2289, 399, 2247] (Forte: 6-Z38) is the complement of the hexatonic modal family [231, 903, 2163, 2499, 3129, 3297] (Forte: 6-Z6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3171 is 2247

Scale 2247Scale 2247: Raga Vijayasri, Ian Ring Music TheoryRaga Vijayasri

Transformations:

T0 3171  T0I 2247
T1 2247  T1I 399
T2 399  T2I 798
T3 798  T3I 1596
T4 1596  T4I 3192
T5 3192  T5I 2289
T6 2289  T6I 483
T7 483  T7I 966
T8 966  T8I 1932
T9 1932  T9I 3864
T10 3864  T10I 3633
T11 3633  T11I 3171

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 3169Scale 3169, Ian Ring Music Theory
Scale 3173Scale 3173: Zarimic, Ian Ring Music TheoryZarimic
Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 3179Scale 3179: Daptian, Ian Ring Music TheoryDaptian
Scale 3187Scale 3187: Koptian, Ian Ring Music TheoryKoptian
Scale 3139Scale 3139, Ian Ring Music Theory
Scale 3155Scale 3155: Ladimic, Ian Ring Music TheoryLadimic
Scale 3107Scale 3107, Ian Ring Music Theory
Scale 3235Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
Scale 3299Scale 3299: Syptian, Ian Ring Music TheorySyptian
Scale 3427Scale 3427: Zacrian, Ian Ring Music TheoryZacrian
Scale 3683Scale 3683: Dycrian, Ian Ring Music TheoryDycrian
Scale 2147Scale 2147, Ian Ring Music Theory
Scale 2659Scale 2659: Katynimic, Ian Ring Music TheoryKatynimic
Scale 1123Scale 1123: Iwato, Ian Ring Music TheoryIwato

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.