Scale 585: "Diminished Seventh"

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

Western: Diminished Seventh

Zeitler: Phrynic

Analysis

Cardinality	4 (tetratonic)
Pitch Class Set	{0,3,6,9}
Forte Number	4-28
Rotational Symmetry	3, 6, 9 semitones
Reflection Axes	0, 1.5, 3, 4.5
Palindromic	yes
Chirality	no
Hemitonia	0 (anhemitonic)
Cohemitonia	0 (ancohemitonic)
Imperfections	4
Modes	0
Prime?	yes
Deep Scale	no
Interval Vector	004002
Interval Spectrum	n⁴t²
Distribution Spectra	<1> = {3} <2> = {6} <3> = {9}
Spectra Variation	0
Maximally Even	yes
Maximal Area Set	yes
Interior Area	2
Myhill Property	no
Balanced	yes
Ridge Tones	[0,3,6,9]
Propriety	Strictly Proper
Heliotonic	no

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 Type	Triad^*	Pitch Classes	Degree	Eccentricity	Closeness Centrality
Diminished Triads	c°	{0,3,6}	2	2	1
	d♯°	{3,6,9}	2	2	1
	f♯°	{6,9,0}	2	2	1
	a°	{9,0,3}	2	2	1

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.

Diameter	2
Radius	2
Self-Centered	yes

Modes

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.

Prime

This is the prime form of this scale.

Complement

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

Inverse

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 585

Diminished Seventh

Transformations:

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 587				Pathitonic
Scale 589				Ionalitonic
Scale 577
Scale 581				Eporic 2
Scale 593				Saric
Scale 601				Bycritonic
Scale 617				Katycritonic
Scale 521
Scale 553				Rothic 2
Scale 649				Byptic
Scale 713				Thoptitonic
Scale 841				Phrothitonic
Scale 73
Scale 329				Mynic 2
Scale 1097				Aeraphic
Scale 1609				Thyritonic
Scale 2633				Bartók 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 (http://allthescales.org) 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.