The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3947: "Ryptygic"

Scale 3947: Ryptygic, 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
Ryptygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,3,5,6,8,9,10,11}
Forte Number9-7
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2783
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections2
Modes8
Prime?no
prime: 1471
Deep Scaleno
Interval Vector677673
Interval Spectrump7m6n7s7d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.778
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♯{1,5,8}242.38
F{5,9,0}442.13
F♯{6,10,1}342.44
G♯{8,0,3}442.31
B{11,3,6}342.44
Minor Triadsd♯m{3,6,10}342.44
fm{5,8,0}442.19
f♯m{6,9,1}442.31
g♯m{8,11,3}342.44
a♯m{10,1,5}242.56
Augmented TriadsC♯+{1,5,9}442.19
Diminished Triads{0,3,6}242.56
d♯°{3,6,9}242.56
{5,8,11}242.56
f♯°{6,9,0}242.44
{9,0,3}242.44
Parsimonious Voice Leading Between Common Triads of Scale 3947. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C# C# C#+ C#+ C#->C#+ fm fm C#->fm F F C#+->F f#m f#m C#+->f#m a#m a#m C#+->a#m d#° d#° d#m d#m d#°->d#m d#°->f#m F# F# d#m->F# d#m->B f°->fm g#m g#m f°->g#m fm->F fm->G# f#° f#° F->f#° F->a° f#°->f#m f#m->F# F#->a#m g#m->G# g#m->B 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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3947 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 4021
Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
3rd mode:
Scale 2029
Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
4th mode:
Scale 1531
Scale 1531: Styptygic, Ian Ring Music TheoryStyptygic
5th mode:
Scale 2813
Scale 2813: Zolygic, Ian Ring Music TheoryZolygic
6th mode:
Scale 1727
Scale 1727: Sydygic, Ian Ring Music TheorySydygic
7th mode:
Scale 2911
Scale 2911: Katygic, Ian Ring Music TheoryKatygic
8th mode:
Scale 3503
Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
9th mode:
Scale 3799
Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic

Prime

The prime form of this scale is Scale 1471

Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic

Complement

The nonatonic modal family [3947, 4021, 2029, 1531, 2813, 1727, 2911, 3503, 3799] (Forte: 9-7) is the complement of the tritonic modal family [37, 641, 1033] (Forte: 3-7)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3947 is 2783

Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3947 is chiral, and its enantiomorph is scale 2783

Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic

Transformations:

T0 3947  T0I 2783
T1 3799  T1I 1471
T2 3503  T2I 2942
T3 2911  T3I 1789
T4 1727  T4I 3578
T5 3454  T5I 3061
T6 2813  T6I 2027
T7 1531  T7I 4054
T8 3062  T8I 4013
T9 2029  T9I 3931
T10 4058  T10I 3767
T11 4021  T11I 3439

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 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
Scale 3951Scale 3951: Mathyllian, Ian Ring Music TheoryMathyllian
Scale 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
Scale 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
Scale 3963Scale 3963: Aeoryllian, Ian Ring Music TheoryAeoryllian
Scale 3915Scale 3915, Ian Ring Music Theory
Scale 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic
Scale 3883Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic
Scale 4011Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
Scale 4075Scale 4075: Katyllian, Ian Ring Music TheoryKatyllian
Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
Scale 3819Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic
Scale 3435Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
Scale 2923Scale 2923: Baryllic, Ian Ring Music TheoryBaryllic
Scale 1899Scale 1899: Moptyllic, Ian Ring Music TheoryMoptyllic

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.