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Scale 897

Scale 897, 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

Cardinality4 (tetratonic)
Pitch Class Set{0,7,8,9}
Forte Number4-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 57
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes3
Prime?no
prime: 39
Deep Scaleno
Interval Vector211110
Interval Spectrumpmnsd2
Distribution Spectra<1> = {1,3,7}
<2> = {2,4,8,10}
<3> = {5,9,11}
Spectra Variation5
Maximally Evenno
Maximal Area Setno
Interior Area0.75
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.

Modes

Modes are the rotational transformation of this scale. Scale 897 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 39
Scale 39, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2067
Scale 2067, Ian Ring Music Theory
4th mode:
Scale 3081
Scale 3081, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 39

Scale 39Scale 39, Ian Ring Music Theory

Complement

The tetratonic modal family [897, 39, 2067, 3081] (Forte: 4-4) is the complement of the octatonic modal family [447, 2019, 2271, 3057, 3183, 3639, 3867, 3981] (Forte: 8-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 897 is 57

Scale 57Scale 57, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 897 is chiral, and its enantiomorph is scale 57

Scale 57Scale 57, Ian Ring Music Theory

Transformations:

T0 897  T0I 57
T1 1794  T1I 114
T2 3588  T2I 228
T3 3081  T3I 456
T4 2067  T4I 912
T5 39  T5I 1824
T6 78  T6I 3648
T7 156  T7I 3201
T8 312  T8I 2307
T9 624  T9I 519
T10 1248  T10I 1038
T11 2496  T11I 2076

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 899Scale 899, Ian Ring Music Theory
Scale 901Scale 901, Ian Ring Music Theory
Scale 905Scale 905: Bylitonic, Ian Ring Music TheoryBylitonic
Scale 913Scale 913: Aeolyritonic, Ian Ring Music TheoryAeolyritonic
Scale 929Scale 929, Ian Ring Music Theory
Scale 961Scale 961, Ian Ring Music Theory
Scale 769Scale 769, Ian Ring Music Theory
Scale 833Scale 833, Ian Ring Music Theory
Scale 641Scale 641, Ian Ring Music Theory
Scale 385Scale 385, Ian Ring Music Theory
Scale 1409Scale 1409, Ian Ring Music Theory
Scale 1921Scale 1921, Ian Ring Music Theory
Scale 2945Scale 2945, 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, 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. Special thanks to Richard Repp for helping with technical accuracy.