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Scale 3531: "Neveseri"

Scale 3531: Neveseri, 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

Unknown / Unsorted
Neveseri
Dozenal
Watian
Zeitler
Dycryllic

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

8 (octatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,1,3,6,7,8,10,11}

Forte Number

A code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

8-14

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.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 2679

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

5 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

3 (tricohemitonic)

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.

2

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.

7

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 759

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Structure

Defines the scale as the sequence of intervals between one tone and the next.

[1, 2, 3, 1, 1, 2, 1, 1]

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.

<5, 5, 5, 5, 6, 2>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hanson.

p6m5n5s5d5t2

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> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2.25

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.

2.616

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

6.002

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

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.

none

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

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(34, 56, 136)

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 TriadsD♯{3,7,10}331.7
F♯{6,10,1}252.5
G♯{8,0,3}252.5
B{11,3,6}331.7
Minor Triadscm{0,3,7}341.9
d♯m{3,6,10}341.9
g♯m{8,11,3}242.1
Augmented TriadsD♯+{3,7,11}431.5
Diminished Triads{0,3,6}242.1
{7,10,1}242.3
Parsimonious Voice Leading Between Common Triads of Scale 3531. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# d#m d#m D# D# d#m->D# F# F# d#m->F# d#m->B D#->D#+ D#->g° g#m g#m D#+->g#m D#+->B F#->g° g#m->G#

view full size

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesD♯, D♯+, B
Peripheral VerticesF♯, G♯

Modes

Modes are the rotational transformation of this scale. Scale 3531 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3813
Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
3rd mode:
Scale 1977
Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic
4th mode:
Scale 759
Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllicThis is the prime mode
5th mode:
Scale 2427
Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
6th mode:
Scale 3261
Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
7th mode:
Scale 1839
Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic
8th mode:
Scale 2967
Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic

Prime

The prime form of this scale is Scale 759

Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic

Complement

The octatonic modal family [3531, 3813, 1977, 759, 2427, 3261, 1839, 2967] (Forte: 8-14) is the complement of the tetratonic modal family [141, 417, 1059, 2577] (Forte: 4-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3531 is 2679

Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3531 is chiral, and its enantiomorph is scale 2679

Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic

Transformations:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 3531       T0I <11,0> 2679
T1 <1,1> 2967      T1I <11,1> 1263
T2 <1,2> 1839      T2I <11,2> 2526
T3 <1,3> 3678      T3I <11,3> 957
T4 <1,4> 3261      T4I <11,4> 1914
T5 <1,5> 2427      T5I <11,5> 3828
T6 <1,6> 759      T6I <11,6> 3561
T7 <1,7> 1518      T7I <11,7> 3027
T8 <1,8> 3036      T8I <11,8> 1959
T9 <1,9> 1977      T9I <11,9> 3918
T10 <1,10> 3954      T10I <11,10> 3741
T11 <1,11> 3813      T11I <11,11> 3387
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2301      T0MI <7,0> 2019
T1M <5,1> 507      T1MI <7,1> 4038
T2M <5,2> 1014      T2MI <7,2> 3981
T3M <5,3> 2028      T3MI <7,3> 3867
T4M <5,4> 4056      T4MI <7,4> 3639
T5M <5,5> 4017      T5MI <7,5> 3183
T6M <5,6> 3939      T6MI <7,6> 2271
T7M <5,7> 3783      T7MI <7,7> 447
T8M <5,8> 3471      T8MI <7,8> 894
T9M <5,9> 2847      T9MI <7,9> 1788
T10M <5,10> 1599      T10MI <7,10> 3576
T11M <5,11> 3198      T11MI <7,11> 3057

The transformations that map this set to itself are: T0

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 3529Scale 3529: Stalian, Ian Ring Music TheoryStalian
Scale 3533Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic
Scale 3535Scale 3535: Mylygic, Ian Ring Music TheoryMylygic
Scale 3523Scale 3523, Ian Ring Music Theory
Scale 3527Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
Scale 3539Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 3547Scale 3547: Sadygic, Ian Ring Music TheorySadygic
Scale 3563Scale 3563: Ionoptygic, Ian Ring Music TheoryIonoptygic
Scale 3467Scale 3467: Katonian, Ian Ring Music TheoryKatonian
Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel
Scale 3403Scale 3403: Bylian, Ian Ring Music TheoryBylian
Scale 3275Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani
Scale 3787Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
Scale 4043Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
Scale 2507Scale 2507: Todi That, Ian Ring Music TheoryTodi That
Scale 3019Scale 3019: Subian, Ian Ring Music TheorySubian
Scale 1483Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. All other diagrams and visualizations are © Ian Ring. 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, and George Howlett for assistance with the Carnatic ragas.