The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 585: "Diminished Seventh"

Scale 585: Diminished Seventh, 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).

Common Names

Diminished Seventh


Cardinality4 (tetratonic)
Pitch Class Set{0,3,6,9}
Forte Number4-28
Rotational Symmetry3, 6, 9 semitones
Reflection Axes0, 1.5, 3, 4.5
Hemitonia0 (anhemitonic)
Cohemitonia0 (ancohemitonic)
Deep Scaleno
Interval Vector004002
Interval Spectrumn4t2
Distribution Spectra<1> = {3}
<2> = {6}
<3> = {9}
Spectra Variation0
Maximally Evenyes
Maximal Area Setyes
Interior Area2
Myhill Propertyno
Ridge Tones[0,3,6,9]
ProprietyStrictly Proper

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
Diminished Triads{0,3,6}221
Parsimonious Voice Leading Between Common Triads of Scale 585. Created by Ian Ring ©2019 d#° d#° c°->d#° c°->a° f#° f#° d#°->f#° f#°->a°

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.



Modes are the rotational transformation of this scale. This scale has no modes, becaue any rotation of this scale will produce another copy of itself.


This is the prime form of this scale.


The tetratonic modal family [585] (Forte: 4-28) is the complement of the octatonic modal family [1755, 2925] (Forte: 8-28)


The inverse of a scale is a reflection using the root as its axis. The inverse of 585 is itself, because it is a palindromic scale!

Scale 585Scale 585: Diminished Seventh, Ian Ring Music TheoryDiminished Seventh


T0 585  T0I 585
T1 1170  T1I 1170
T2 2340  T2I 2340
T3 585  T3I 585
T4 1170  T4I 1170
T5 2340  T5I 2340
T6 585  T6I 585
T7 1170  T7I 1170
T8 2340  T8I 2340
T9 585  T9I 585
T10 1170  T10I 1170
T11 2340  T11I 2340

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 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic
Scale 589Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic
Scale 577Scale 577, Ian Ring Music Theory
Scale 581Scale 581: Eporic 2, Ian Ring Music TheoryEporic 2
Scale 593Scale 593: Saric, Ian Ring Music TheorySaric
Scale 601Scale 601: Bycritonic, Ian Ring Music TheoryBycritonic
Scale 617Scale 617: Katycritonic, Ian Ring Music TheoryKatycritonic
Scale 521Scale 521, Ian Ring Music Theory
Scale 553Scale 553: Rothic 2, Ian Ring Music TheoryRothic 2
Scale 649Scale 649: Byptic, Ian Ring Music TheoryByptic
Scale 713Scale 713: Thoptitonic, Ian Ring Music TheoryThoptitonic
Scale 841Scale 841: Phrothitonic, Ian Ring Music TheoryPhrothitonic
Scale 73Scale 73, Ian Ring Music Theory
Scale 329Scale 329: Mynic 2, Ian Ring Music TheoryMynic 2
Scale 1097Scale 1097: Aeraphic, Ian Ring Music TheoryAeraphic
Scale 1609Scale 1609: Thyritonic, Ian Ring Music TheoryThyritonic
Scale 2633Scale 2633: Bartók Beta Chord, Ian Ring Music TheoryBartók Beta Chord

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.