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Scale 1157

Scale 1157, 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{0,2,7,10}
Forte Number4-22
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1061
Hemitonia0 (anhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections2
Modes3
Prime?no
prime: 149
Deep Scaleno
Interval Vector021120
Interval Spectrump2mns2
Distribution Spectra<1> = {2,3,5}
<2> = {4,5,7,8}
<3> = {7,9,10}
Spectra Variation2.5
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1157 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 1313
Scale 1313, Ian Ring Music Theory
3rd mode:
Scale 169
Scale 169: Vietnamese Tetratonic, Ian Ring Music TheoryVietnamese Tetratonic
4th mode:
Scale 533
Scale 533, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 149

Scale 149Scale 149: Eskimo Tetratonic, Ian Ring Music TheoryEskimo Tetratonic

Complement

The tetratonic modal family [1157, 1313, 169, 533] (Forte: 4-22) is the complement of the octatonic modal family [1391, 1469, 1781, 1963, 2743, 3029, 3419, 3757] (Forte: 8-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1157 is 1061

Scale 1061Scale 1061, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1157 is chiral, and its enantiomorph is scale 1061

Scale 1061Scale 1061, Ian Ring Music Theory

Transformations:

T0 1157  T0I 1061
T1 2314  T1I 2122
T2 533  T2I 149
T3 1066  T3I 298
T4 2132  T4I 596
T5 169  T5I 1192
T6 338  T6I 2384
T7 676  T7I 673
T8 1352  T8I 1346
T9 2704  T9I 2692
T10 1313  T10I 1289
T11 2626  T11I 2578

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 1159Scale 1159, Ian Ring Music Theory
Scale 1153Scale 1153, Ian Ring Music Theory
Scale 1155Scale 1155, Ian Ring Music Theory
Scale 1161Scale 1161: Bi Yu, Ian Ring Music TheoryBi Yu
Scale 1165Scale 1165: Gycritonic, Ian Ring Music TheoryGycritonic
Scale 1173Scale 1173: Dominant Pentatonic, Ian Ring Music TheoryDominant Pentatonic
Scale 1189Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic
Scale 1221Scale 1221: Epyritonic, Ian Ring Music TheoryEpyritonic
Scale 1029Scale 1029, Ian Ring Music Theory
Scale 1093Scale 1093: Lydic, Ian Ring Music TheoryLydic
Scale 1285Scale 1285, Ian Ring Music Theory
Scale 1413Scale 1413, Ian Ring Music Theory
Scale 1669Scale 1669: Raga Matha Kokila, Ian Ring Music TheoryRaga Matha Kokila
Scale 133Scale 133, Ian Ring Music Theory
Scale 645Scale 645, Ian Ring Music Theory
Scale 2181Scale 2181, Ian Ring Music Theory
Scale 3205Scale 3205, 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.