The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 4035

Scale 4035, 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{0,1,6,7,8,9,10,11}
Forte Number8-1
Rotational Symmetrynone
Reflection Axes3.5
Hemitonia7 (multihemitonic)
Cohemitonia6 (multicohemitonic)
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
Maximal Area Setno
Interior Area2
Myhill Propertyyes
Ridge Tones[7]

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsF♯{6,10,1}221
Minor Triadsf♯m{6,9,1}221
Diminished Triadsf♯°{6,9,0}131.5
Parsimonious Voice Leading Between Common Triads of Scale 4035. Created by Ian Ring ©2019 f#° f#° f#m f#m f#°->f#m F# F# f#m->F# F#->g°

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Central Verticesf♯m, F♯
Peripheral Verticesf♯°, g°


Modes are the rotational transformation of this scale. Scale 4035 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 4065
Scale 4065, Ian Ring Music Theory
3rd mode:
Scale 255
Scale 255, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2175
Scale 2175, Ian Ring Music Theory
5th mode:
Scale 3135
Scale 3135, Ian Ring Music Theory
6th mode:
Scale 3615
Scale 3615, Ian Ring Music Theory
7th mode:
Scale 3855
Scale 3855, Ian Ring Music Theory
8th mode:
Scale 3975
Scale 3975, Ian Ring Music Theory


The prime form of this scale is Scale 255

Scale 255Scale 255, Ian Ring Music Theory


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


The inverse of a scale is a reflection using the root as its axis. The inverse of 4035 is 2175

Scale 2175Scale 2175, Ian Ring Music Theory


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

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 4033Scale 4033, Ian Ring Music Theory
Scale 4037Scale 4037: Ionyllic, Ian Ring Music TheoryIonyllic
Scale 4039Scale 4039: Ionogygic, Ian Ring Music TheoryIonogygic
Scale 4043Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
Scale 4051Scale 4051: Ionilygic, Ian Ring Music TheoryIonilygic
Scale 4067Scale 4067: Aeolarygic, Ian Ring Music TheoryAeolarygic
Scale 3971Scale 3971, Ian Ring Music Theory
Scale 4003Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic
Scale 3907Scale 3907, Ian Ring Music Theory
Scale 3779Scale 3779, Ian Ring Music Theory
Scale 3523Scale 3523, Ian Ring Music Theory
Scale 3011Scale 3011, Ian Ring Music Theory
Scale 1987Scale 1987, 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, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler ( used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.