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Scale 1413

Scale 1413, 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{0,2,7,8,10}
Forte Number5-24
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1077
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 1413 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1377
Scale 1377, Ian Ring Music Theory
3rd mode:
Scale 171
Scale 171, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2133
Scale 2133: Raga Kumurdaki, Ian Ring Music TheoryRaga Kumurdaki
5th mode:
Scale 1557
Scale 1557, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 171

Scale 171Scale 171, Ian Ring Music Theory

Complement

The pentatonic modal family [1413, 1377, 171, 2133, 1557] (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 1413 is 1077

Scale 1077Scale 1077, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1413 is chiral, and its enantiomorph is scale 1077

Scale 1077Scale 1077, Ian Ring Music Theory

Transformations:

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

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 1415Scale 1415, Ian Ring Music Theory
Scale 1409Scale 1409, Ian Ring Music Theory
Scale 1411Scale 1411, Ian Ring Music Theory
Scale 1417Scale 1417: Raga Shailaja, Ian Ring Music TheoryRaga Shailaja
Scale 1421Scale 1421: Raga Trimurti, Ian Ring Music TheoryRaga Trimurti
Scale 1429Scale 1429: Bythimic, Ian Ring Music TheoryBythimic
Scale 1445Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari
Scale 1477Scale 1477: Raga Jaganmohanam, Ian Ring Music TheoryRaga Jaganmohanam
Scale 1285Scale 1285, Ian Ring Music Theory
Scale 1349Scale 1349: Tholitonic, Ian Ring Music TheoryTholitonic
Scale 1157Scale 1157, Ian Ring Music Theory
Scale 1669Scale 1669: Raga Matha Kokila, Ian Ring Music TheoryRaga Matha Kokila
Scale 1925Scale 1925, Ian Ring Music Theory
Scale 389Scale 389, Ian Ring Music Theory
Scale 901Scale 901, Ian Ring Music Theory
Scale 2437Scale 2437, Ian Ring Music Theory
Scale 3461Scale 3461, 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.