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Scale 3599: "Heptatonic Chromatic 4"

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 Modern: Heptatonic Chromatic 4

Dozenal: WIKIAN

Analysis

Cardinality Cardinality is the count of how many pitches are in the scale.	7 (heptatonic)
Pitch Class Set The tones in this scale, expressed as numbers from 0 to 11	{0,1,2,3,9,10,11}
Forte Number A code assigned by theorist Alan Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.	7-1
Rotational Symmetry Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.	none
Reflection Axes If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.	[0]
Palindromicity A palindromic scale has the same pattern of intervals both ascending and descending.	yes
Chirality A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.	no
Hemitonia A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.	6 (multihemitonic)
Cohemitonia A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.	5 (multicohemitonic)
Imperfections An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.	5
Modes Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.	6
Prime Form Describes if this scale is in prime form, using the Rahn/Ring formula.	no prime: 127
Deep Scale A deep scale is one where the interval vector has 6 different digits.	yes
Interval Vector Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.	[6, 5, 4, 3, 2, 1]
Interval Spectrum The same as the Interval Vector, but expressed in a syntax used by Howard Hansen.	p²m³n⁴s⁵d⁶t
Distribution Spectra Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.	<1> = {1,6} <2> = {2,7} <3> = {3,8} <4> = {4,9} <5> = {5,10} <6> = {6,11}
Spectra Variation Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.	4.286
Maximally Even A scale is maximally even if the tones are optimally spaced apart from each other.	no
Maximal Area Set A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.	no
Interior Area Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.	1.5
Polygon Perimeter Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.	5.106
Myhill Property A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.	yes
Balanced A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.	no
Ridge Tones Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.	[0]
Propriety Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".	Improper

Harmonic Chords

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	a°	{9,0,3}	0	0	0

The following pitch classes are not present in any of the common triads: {1,2,10,11}

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 3599 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 3847	Heptatonic Chromatic 5
3rd mode: Scale 3971	Heptatonic Chromatic 6
4th mode: Scale 4033	Heptatonic Chromatic Descending
5th mode: Scale 127	Heptatonic Chromatic	This is the prime mode
6th mode: Scale 2111	Heptatonic Chromatic 2
7th mode: Scale 3103	Heptatonic Chromatic 3

Prime

The prime form of this scale is Scale 127

Scale 127

Heptatonic Chromatic

Complement

The heptatonic modal family [3599, 3847, 3971, 4033, 127, 2111, 3103] (Forte: 7-1) is the complement of the pentatonic modal family [31, 2063, 3079, 3587, 3841] (Forte: 5-1)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3599 is itself, because it is a palindromic scale!

Scale 3599

Heptatonic Chromatic 4

Transformations:

T₀	3599	T₀I	3599
T₁	3103	T₁I	3103
T₂	2111	T₂I	2111
T₃	127	T₃I	127
T₄	254	T₄I	254
T₅	508	T₅I	508
T₆	1016	T₆I	1016
T₇	2032	T₇I	2032
T₈	4064	T₈I	4064
T₉	4033	T₉I	4033
T₁₀	3971	T₁₀I	3971
T₁₁	3847	T₁₁I	3847

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 3597				WIJIAN
Scale 3595				WIHIAN
Scale 3591				WIFIAN
Scale 3607				WOPIAN
Scale 3615				Octatonic Chromatic 4
Scale 3631				Gydyllic
Scale 3663				Sonyllic
Scale 3727				Tholyllic
Scale 3855				Octatonic Chromatic 5
Scale 3087				Hexatonic Chromatic 3
Scale 3343				VAJIAN
Scale 2575				PUMIAN
Scale 1551				JORIAN

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.