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Scale 1557

Scale 1557, 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

Cardinality5 (pentatonic)
Pitch Class Set{0,2,4,9,10}
Forte Number5-24
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1293
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes4
Prime?no
prime: 171
Deep Scaleno
Interval Vector131221
Interval Spectrump2m2ns3dt
Distribution Spectra<1> = {1,2,5}
<2> = {3,4,6,7}
<3> = {5,6,8,9}
<4> = {7,10,11}
Spectra Variation3.2
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1557 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1413
Scale 1413, Ian Ring Music Theory
3rd mode:
Scale 1377
Scale 1377, Ian Ring Music Theory
4th mode:
Scale 171
Scale 171, Ian Ring Music TheoryThis is the prime mode
5th mode:
Scale 2133
Scale 2133: Raga Kumurdaki, Ian Ring Music TheoryRaga Kumurdaki

Prime

The prime form of this scale is Scale 171

Scale 171Scale 171, Ian Ring Music Theory

Complement

The pentatonic modal family [1557, 1413, 1377, 171, 2133] (Forte: 5-24) is the complement of the heptatonic modal family [687, 1401, 1509, 1941, 2391, 3243, 3669] (Forte: 7-24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1557 is 1293

Scale 1293Scale 1293, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1557 is chiral, and its enantiomorph is scale 1293

Scale 1293Scale 1293, Ian Ring Music Theory

Transformations:

T0 1557  T0I 1293
T1 3114  T1I 2586
T2 2133  T2I 1077
T3 171  T3I 2154
T4 342  T4I 213
T5 684  T5I 426
T6 1368  T6I 852
T7 2736  T7I 1704
T8 1377  T8I 3408
T9 2754  T9I 2721
T10 1413  T10I 1347
T11 2826  T11I 2694

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 1559Scale 1559, Ian Ring Music Theory
Scale 1553Scale 1553, Ian Ring Music Theory
Scale 1555Scale 1555, Ian Ring Music Theory
Scale 1561Scale 1561, Ian Ring Music Theory
Scale 1565Scale 1565, Ian Ring Music Theory
Scale 1541Scale 1541, Ian Ring Music Theory
Scale 1549Scale 1549, Ian Ring Music Theory
Scale 1573Scale 1573: Raga Guhamanohari, Ian Ring Music TheoryRaga Guhamanohari
Scale 1589Scale 1589: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 1621Scale 1621: Scriabin's Prometheus, Ian Ring Music TheoryScriabin's Prometheus
Scale 1685Scale 1685: Zeracrimic, Ian Ring Music TheoryZeracrimic
Scale 1813Scale 1813: Katothimic, Ian Ring Music TheoryKatothimic
Scale 1045Scale 1045, Ian Ring Music Theory
Scale 1301Scale 1301: Koditonic, Ian Ring Music TheoryKoditonic
Scale 533Scale 533, Ian Ring Music Theory
Scale 2581Scale 2581: Raga Neroshta, Ian Ring Music TheoryRaga Neroshta
Scale 3605Scale 3605, 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.