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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

41161837294116105072918310504116183
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

Cardinality7 (heptatonic)
Pitch Class Set{0,3,5,7,8,9,10}
Forte Number7-23
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 701
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes6
Prime?no
prime: 701
Deep Scaleno
Interval Vector354351
Interval Spectrump5m3n4s5d3t
Distribution Spectra<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 Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

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 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. 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.