The Exciting Universe Of Music Theory

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Scale 4005

Scale 4005, 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

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).


Cardinality8 (octatonic)
Pitch Class Set{0,2,5,7,8,9,10,11}
Forte Number8-10
Rotational Symmetrynone
Reflection Axes3.5
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
prime: 765
Deep Scaleno
Interval Vector566452
Interval Spectrump5m4n6s6d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {7,9,10}
<7> = {9,10,11}
Spectra Variation2.75
Maximally Evenno
Myhill Propertyno
Ridge Tones[7]


Modes are the rotational transformation of this scale. Scale 4005 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2025
Scale 2025, Ian Ring Music Theory
3rd mode:
Scale 765
Scale 765, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 1215
Scale 1215, Ian Ring Music Theory
5th mode:
Scale 2655
Scale 2655, Ian Ring Music Theory
6th mode:
Scale 3375
Scale 3375, Ian Ring Music Theory
7th mode:
Scale 3735
Scale 3735, Ian Ring Music Theory
8th mode:
Scale 3915
Scale 3915, Ian Ring Music Theory


The prime form of this scale is Scale 765

Scale 765Scale 765, Ian Ring Music Theory


The octatonic modal family [4005, 2025, 765, 1215, 2655, 3375, 3735, 3915] (Forte: 8-10) is the complement of the tetratonic modal family [45, 1035, 1665, 2565] (Forte: 4-10)


The inverse of a scale is a reflection using the root as its axis. The inverse of 4005 is 1215

Scale 1215Scale 1215, Ian Ring Music Theory


T0 4005  T0I 1215
T1 3915  T1I 2430
T2 3735  T2I 765
T3 3375  T3I 1530
T4 2655  T4I 3060
T5 1215  T5I 2025
T6 2430  T6I 4050
T7 765  T7I 4005
T8 1530  T8I 3915
T9 3060  T9I 3735
T10 2025  T10I 3375
T11 4050  T11I 2655

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 4007Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic
Scale 4001Scale 4001, Ian Ring Music Theory
Scale 4003Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic
Scale 4009Scale 4009: Phranyllic, Ian Ring Music TheoryPhranyllic
Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu
Scale 4021Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
Scale 3973Scale 3973, Ian Ring Music Theory
Scale 3989Scale 3989: Sythyllic, Ian Ring Music TheorySythyllic
Scale 4037Scale 4037: Ionyllic, Ian Ring Music TheoryIonyllic
Scale 4069Scale 4069: Starygic, Ian Ring Music TheoryStarygic
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 3941Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
Scale 3749Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 2981Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
Scale 1957Scale 1957: Pyrian, Ian Ring Music TheoryPyrian

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 ( Peruse this Bibliography.