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Scale 1961: "Soptian"

Scale 1961: Soptian, 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

Zeitler
Soptian

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

{0,3,5,7,8,9,10}

Forte Number

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

7-23

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: 701

Hemitonia

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

3 (trihemitonic)

Cohemitonia

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

2 (dicohemitonic)

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.

6

Prime Form

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

no
prime: 701

Deep Scale

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

no

Interval Formula

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

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

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.

<3, 5, 4, 3, 5, 1>

Interval Spectrum

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

p5m3n4s5d3t

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

Spectra Variation

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

2.571

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.

2.549

Polygon Perimeter

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

5.967

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

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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}142.17
F{5,9,0}241.83
G♯{8,0,3}321.17
Minor Triadscm{0,3,7}231.5
fm{5,8,0}231.5
Diminished Triads{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 1961. Created by Ian Ring ©2019 cm cm D# D# cm->D# G# G# cm->G# fm fm F F fm->F fm->G# F->a° G#->a°

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.

Diameter4
Radius2
Self-Centeredno
Central VerticesG♯
Peripheral VerticesD♯, F

Modes

Modes are the rotational transformation of this scale. Scale 1961 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 757
Scale 757: Ionyptian, Ian Ring Music TheoryIonyptian
3rd mode:
Scale 1213
Scale 1213: Gyrian, Ian Ring Music TheoryGyrian
4th mode:
Scale 1327
Scale 1327: Zalian, Ian Ring Music TheoryZalian
5th mode:
Scale 2711
Scale 2711: Stolian, Ian Ring Music TheoryStolian
6th mode:
Scale 3403
Scale 3403: Bylian, Ian Ring Music TheoryBylian
7th mode:
Scale 3749
Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati

Prime

The prime form of this scale is Scale 701

Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian

Complement

The heptatonic modal family [1961, 757, 1213, 1327, 2711, 3403, 3749] (Forte: 7-23) is the complement of the pentatonic modal family [173, 1067, 1441, 1669, 2581] (Forte: 5-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1961 is 701

Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1961 is chiral, and its enantiomorph is scale 701

Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian

Transformations:

T0 1961  T0I 701
T1 3922  T1I 1402
T2 3749  T2I 2804
T3 3403  T3I 1513
T4 2711  T4I 3026
T5 1327  T5I 1957
T6 2654  T6I 3914
T7 1213  T7I 3733
T8 2426  T8I 3371
T9 757  T9I 2647
T10 1514  T10I 1199
T11 3028  T11I 2398

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 1963Scale 1963: Epocryllic, Ian Ring Music TheoryEpocryllic
Scale 1965Scale 1965: Raga Mukhari, Ian Ring Music TheoryRaga Mukhari
Scale 1953Scale 1953, Ian Ring Music Theory
Scale 1957Scale 1957: Pyrian, Ian Ring Music TheoryPyrian
Scale 1969Scale 1969: Stylian, Ian Ring Music TheoryStylian
Scale 1977Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic
Scale 1929Scale 1929: Aeolycrimic, Ian Ring Music TheoryAeolycrimic
Scale 1945Scale 1945: Zarian, Ian Ring Music TheoryZarian
Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
Scale 2025Scale 2025, Ian Ring Music Theory
Scale 1833Scale 1833: Ionacrimic, Ian Ring Music TheoryIonacrimic
Scale 1897Scale 1897: Ionopian, Ian Ring Music TheoryIonopian
Scale 1705Scale 1705: Raga Manohari, Ian Ring Music TheoryRaga Manohari
Scale 1449Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
Scale 937Scale 937: Stothimic, Ian Ring Music TheoryStothimic
Scale 2985Scale 2985: Epacrian, Ian Ring Music TheoryEpacrian
Scale 4009Scale 4009: Phranyllic, Ian Ring Music TheoryPhranyllic

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. 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.