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Scale 3771: "Stophygic"

Scale 3771: Stophygic, 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
Stophygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,3,4,5,7,9,10,11}
Forte Number9-8
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2991
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1503
Deep Scaleno
Interval Vector676764
Interval Spectrump6m7n6s7d6t4
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.556
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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 TriadsC{0,4,7}442.07
D♯{3,7,10}342.47
F{5,9,0}242.47
A{9,1,4}442.2
Minor Triadscm{0,3,7}342.33
em{4,7,11}342.33
am{9,0,4}442.07
a♯m{10,1,5}342.47
Augmented TriadsC♯+{1,5,9}342.4
D♯+{3,7,11}342.4
Diminished Triadsc♯°{1,4,7}242.33
{4,7,10}242.67
{7,10,1}242.53
{9,0,3}242.47
a♯°{10,1,4}242.53
Parsimonious Voice Leading Between Common Triads of Scale 3771. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ cm->a° c#° c#° C->c#° em em C->em am am C->am A A c#°->A C#+ C#+ F F C#+->F C#+->A a#m a#m C#+->a#m D# D# D#->D#+ D#->e° D#->g° D#+->em e°->em F->am g°->a#m a°->am am->A a#° a#° A->a#° a#°->a#m

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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3771 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3933
Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
3rd mode:
Scale 2007
Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
4th mode:
Scale 3051
Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
5th mode:
Scale 3573
Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
6th mode:
Scale 1917
Scale 1917: Sacrygic, Ian Ring Music TheorySacrygic
7th mode:
Scale 1503
Scale 1503: Padygic, Ian Ring Music TheoryPadygicThis is the prime mode
8th mode:
Scale 2799
Scale 2799: Epilygic, Ian Ring Music TheoryEpilygic
9th mode:
Scale 3447
Scale 3447: Kynygic, Ian Ring Music TheoryKynygic

Prime

The prime form of this scale is Scale 1503

Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic

Complement

The nonatonic modal family [3771, 3933, 2007, 3051, 3573, 1917, 1503, 2799, 3447] (Forte: 9-8) is the complement of the tritonic modal family [69, 321, 1041] (Forte: 3-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3771 is 2991

Scale 2991Scale 2991: Zanygic, Ian Ring Music TheoryZanygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3771 is chiral, and its enantiomorph is scale 2991

Scale 2991Scale 2991: Zanygic, Ian Ring Music TheoryZanygic

Transformations:

T0 3771  T0I 2991
T1 3447  T1I 1887
T2 2799  T2I 3774
T3 1503  T3I 3453
T4 3006  T4I 2811
T5 1917  T5I 1527
T6 3834  T6I 3054
T7 3573  T7I 2013
T8 3051  T8I 4026
T9 2007  T9I 3957
T10 4014  T10I 3819
T11 3933  T11I 3543

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 3769Scale 3769: Eponyllic, Ian Ring Music TheoryEponyllic
Scale 3773Scale 3773: Raga Malgunji, Ian Ring Music TheoryRaga Malgunji
Scale 3775Scale 3775: Loptyllian, Ian Ring Music TheoryLoptyllian
Scale 3763Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
Scale 3767Scale 3767: Chromatic Bebop, Ian Ring Music TheoryChromatic Bebop
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 3739Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic
Scale 3803Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
Scale 3835Scale 3835: Katodyllian, Ian Ring Music TheoryKatodyllian
Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
Scale 3707Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
Scale 3899Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic
Scale 4027Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian
Scale 3259Scale 3259, Ian Ring Music Theory
Scale 3515Scale 3515: Moorish Phrygian, Ian Ring Music TheoryMoorish Phrygian
Scale 2747Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
Scale 1723Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic

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.