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Scale 1565

Scale 1565, 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

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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{0,2,3,4,9,10}
Forte Number6-Z12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1805
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 215
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,4,6}
<3> = {4,5,7,8}
<4> = {6,8,9,10}
<5> = {7,10,11}
Spectra Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area1.866
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1565 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1415
Scale 1415, Ian Ring Music Theory
3rd mode:
Scale 2755
Scale 2755, Ian Ring Music Theory
4th mode:
Scale 3425
Scale 3425, Ian Ring Music Theory
5th mode:
Scale 235
Scale 235, Ian Ring Music Theory
6th mode:
Scale 2165
Scale 2165, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 215

Scale 215Scale 215, Ian Ring Music Theory

Complement

The hexatonic modal family [1565, 1415, 2755, 3425, 235, 2165] (Forte: 6-Z12) is the complement of the hexatonic modal family [335, 965, 1265, 2215, 3155, 3625] (Forte: 6-Z41)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1565 is 1805

Scale 1805Scale 1805, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1565 is chiral, and its enantiomorph is scale 1805

Scale 1805Scale 1805, Ian Ring Music Theory

Transformations:

T0 1565  T0I 1805
T1 3130  T1I 3610
T2 2165  T2I 3125
T3 235  T3I 2155
T4 470  T4I 215
T5 940  T5I 430
T6 1880  T6I 860
T7 3760  T7I 1720
T8 3425  T8I 3440
T9 2755  T9I 2785
T10 1415  T10I 1475
T11 2830  T11I 2950

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 1567Scale 1567, Ian Ring Music Theory
Scale 1561Scale 1561, Ian Ring Music Theory
Scale 1563Scale 1563, Ian Ring Music Theory
Scale 1557Scale 1557, Ian Ring Music Theory
Scale 1549Scale 1549, Ian Ring Music Theory
Scale 1581Scale 1581: Raga Bagesri, Ian Ring Music TheoryRaga Bagesri
Scale 1597Scale 1597: Aeolodian, Ian Ring Music TheoryAeolodian
Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 1693Scale 1693: Dogian, Ian Ring Music TheoryDogian
Scale 1821Scale 1821: Aeradian, Ian Ring Music TheoryAeradian
Scale 1053Scale 1053, Ian Ring Music Theory
Scale 1309Scale 1309: Pogimic, Ian Ring Music TheoryPogimic
Scale 541Scale 541, Ian Ring Music Theory
Scale 2589Scale 2589, Ian Ring Music Theory
Scale 3613Scale 3613, 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.