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Scale 4065

Scale 4065, 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

Cardinality8 (octatonic)
Pitch Class Set{0,5,6,7,8,9,10,11}
Forte Number8-1
Rotational Symmetrynone
Reflection Axes2.5
Palindromicno
Chiralityno
Hemitonia7 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 255
Deep Scaleno
Interval Vector765442
Interval Spectrump4m4n5s6d7t2
Distribution Spectra<1> = {1,5}
<2> = {2,6}
<3> = {3,7}
<4> = {4,8}
<5> = {5,9}
<6> = {6,10}
<7> = {7,11}
Spectra Variation3.5
Maximally Evenno
Myhill Propertyyes
Balancedno
Ridge Tones[5]
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 4065 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 255
Scale 255, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2175
Scale 2175, Ian Ring Music Theory
4th mode:
Scale 3135
Scale 3135, Ian Ring Music Theory
5th mode:
Scale 3615
Scale 3615, Ian Ring Music Theory
6th mode:
Scale 3855
Scale 3855, Ian Ring Music Theory
7th mode:
Scale 3975
Scale 3975, Ian Ring Music Theory
8th mode:
Scale 4035
Scale 4035, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 255

Scale 255Scale 255, Ian Ring Music Theory

Complement

The octatonic modal family [4065, 255, 2175, 3135, 3615, 3855, 3975, 4035] (Forte: 8-1) is the complement of the tetratonic modal family [15, 2055, 3075, 3585] (Forte: 4-1)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4065 is 255

Scale 255Scale 255, Ian Ring Music Theory

Transformations:

T0 4065  T0I 255
T1 4035  T1I 510
T2 3975  T2I 1020
T3 3855  T3I 2040
T4 3615  T4I 4080
T5 3135  T5I 4065
T6 2175  T6I 4035
T7 255  T7I 3975
T8 510  T8I 3855
T9 1020  T9I 3615
T10 2040  T10I 3135
T11 4080  T11I 2175

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 4067Scale 4067: Aeolarygic, Ian Ring Music TheoryAeolarygic
Scale 4069Scale 4069: Starygic, Ian Ring Music TheoryStarygic
Scale 4073Scale 4073: Sathygic, Ian Ring Music TheorySathygic
Scale 4081Scale 4081: Manygic, Ian Ring Music TheoryManygic
Scale 4033Scale 4033, Ian Ring Music Theory
Scale 4049Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic
Scale 4001Scale 4001, Ian Ring Music Theory
Scale 3937Scale 3937, Ian Ring Music Theory
Scale 3809Scale 3809, Ian Ring Music Theory
Scale 3553Scale 3553, Ian Ring Music Theory
Scale 3041Scale 3041, Ian Ring Music Theory
Scale 2017Scale 2017, 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.