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Scale 3297

Scale 3297, 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).

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,5,6,7,10,11}
Forte Number6-Z6
Rotational Symmetrynone
Reflection Axes2.5
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes5
Prime?no
prime: 231
Deep Scaleno
Interval Vector421242
Interval Spectrump4m2ns2d4t2
Distribution Spectra<1> = {1,3,5}
<2> = {2,4,6}
<3> = {5,7}
<4> = {6,8,10}
<5> = {7,9,11}
Spectra Variation3
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tones[5]
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3297 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 231
Scale 231, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2163
Scale 2163, Ian Ring Music Theory
4th mode:
Scale 3129
Scale 3129, Ian Ring Music Theory
5th mode:
Scale 903
Scale 903, Ian Ring Music Theory
6th mode:
Scale 2499
Scale 2499, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 231

Scale 231Scale 231, Ian Ring Music Theory

Complement

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

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3297 is 231

Scale 231Scale 231, Ian Ring Music Theory

Transformations:

T0 3297  T0I 231
T1 2499  T1I 462
T2 903  T2I 924
T3 1806  T3I 1848
T4 3612  T4I 3696
T5 3129  T5I 3297
T6 2163  T6I 2499
T7 231  T7I 903
T8 462  T8I 1806
T9 924  T9I 3612
T10 1848  T10I 3129
T11 3696  T11I 2163

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 3299Scale 3299: Syptian, Ian Ring Music TheorySyptian
Scale 3301Scale 3301: Chromatic Mixolydian Inverse, Ian Ring Music TheoryChromatic Mixolydian Inverse
Scale 3305Scale 3305: Chromatic Hypophrygian, Ian Ring Music TheoryChromatic Hypophrygian
Scale 3313Scale 3313: Aeolacrian, Ian Ring Music TheoryAeolacrian
Scale 3265Scale 3265, Ian Ring Music Theory
Scale 3281Scale 3281: Raga Vijayavasanta, Ian Ring Music TheoryRaga Vijayavasanta
Scale 3233Scale 3233, Ian Ring Music Theory
Scale 3169Scale 3169, Ian Ring Music Theory
Scale 3425Scale 3425, Ian Ring Music Theory
Scale 3553Scale 3553, Ian Ring Music Theory
Scale 3809Scale 3809, Ian Ring Music Theory
Scale 2273Scale 2273, Ian Ring Music Theory
Scale 2785Scale 2785, Ian Ring Music Theory
Scale 1249Scale 1249, Ian Ring Music Theory

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.