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Scale 1667

Scale 1667, 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{0,1,7,9,10}
Forte Number5-10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2093
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?no
prime: 91
Deep Scaleno
Interval Vector223111
Interval Spectrumpmn3s2d2t
Distribution Spectra<1> = {1,2,6}
<2> = {3,7,8}
<3> = {4,5,9}
<4> = {6,10,11}
Spectra Variation4
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1667 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2881
Scale 2881, Ian Ring Music Theory
3rd mode:
Scale 109
Scale 109, Ian Ring Music Theory
4th mode:
Scale 1051
Scale 1051, Ian Ring Music Theory
5th mode:
Scale 2573
Scale 2573, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 91

Scale 91Scale 91, Ian Ring Music Theory

Complement

The pentatonic modal family [1667, 2881, 109, 1051, 2573] (Forte: 5-10) is the complement of the heptatonic modal family [607, 761, 1993, 2351, 3223, 3659, 3877] (Forte: 7-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1667 is 2093

Scale 2093Scale 2093, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1667 is chiral, and its enantiomorph is scale 2093

Scale 2093Scale 2093, Ian Ring Music Theory

Transformations:

T0 1667  T0I 2093
T1 3334  T1I 91
T2 2573  T2I 182
T3 1051  T3I 364
T4 2102  T4I 728
T5 109  T5I 1456
T6 218  T6I 2912
T7 436  T7I 1729
T8 872  T8I 3458
T9 1744  T9I 2821
T10 3488  T10I 1547
T11 2881  T11I 3094

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 1665Scale 1665, Ian Ring Music Theory
Scale 1669Scale 1669: Raga Matha Kokila, Ian Ring Music TheoryRaga Matha Kokila
Scale 1671Scale 1671, Ian Ring Music Theory
Scale 1675Scale 1675: Raga Salagavarali, Ian Ring Music TheoryRaga Salagavarali
Scale 1683Scale 1683: Raga Malayamarutam, Ian Ring Music TheoryRaga Malayamarutam
Scale 1699Scale 1699: Raga Rasavali, Ian Ring Music TheoryRaga Rasavali
Scale 1731Scale 1731, Ian Ring Music Theory
Scale 1539Scale 1539, Ian Ring Music Theory
Scale 1603Scale 1603, Ian Ring Music Theory
Scale 1795Scale 1795, Ian Ring Music Theory
Scale 1923Scale 1923, Ian Ring Music Theory
Scale 1155Scale 1155, Ian Ring Music Theory
Scale 1411Scale 1411, Ian Ring Music Theory
Scale 643Scale 643, Ian Ring Music Theory
Scale 2691Scale 2691, Ian Ring Music Theory
Scale 3715Scale 3715, 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.