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Scale 1947: "Byptyllic"

Scale 1947: Byptyllic, 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
Byptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,7,8,9,10}
Forte Number8-18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2877
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 879
Deep Scaleno
Interval Vector546553
Interval Spectrump5m5n6s4d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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}441.92
D♯{3,7,10}342.23
G♯{8,0,3}342.08
A{9,1,4}342.15
Minor Triadscm{0,3,7}342
c♯m{1,4,8}342.08
am{9,0,4}342.08
Augmented TriadsC+{0,4,8}441.85
Diminished Triadsc♯°{1,4,7}242.31
{4,7,10}242.31
{7,10,1}242.46
{9,0,3}242.46
a♯°{10,1,4}242.38
Parsimonious Voice Leading Between Common Triads of Scale 1947. Created by Ian Ring ©2019 cm cm C C cm->C D# D# cm->D# G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° C->e° c#m c#m C+->c#m C+->G# am am C+->am c#°->c#m A A c#m->A D#->e° D#->g° a#° a#° g°->a#° G#->a° a°->am am->A A->a#°

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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 1947 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3021
Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
3rd mode:
Scale 1779
Scale 1779: Zynyllic, Ian Ring Music TheoryZynyllic
4th mode:
Scale 2937
Scale 2937: Phragyllic, Ian Ring Music TheoryPhragyllic
5th mode:
Scale 879
Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllicThis is the prime mode
6th mode:
Scale 2487
Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic
7th mode:
Scale 3291
Scale 3291: Lygyllic, Ian Ring Music TheoryLygyllic
8th mode:
Scale 3693
Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic

Prime

The prime form of this scale is Scale 879

Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic

Complement

The octatonic modal family [1947, 3021, 1779, 2937, 879, 2487, 3291, 3693] (Forte: 8-18) is the complement of the tetratonic modal family [147, 609, 777, 2121] (Forte: 4-18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1947 is 2877

Scale 2877Scale 2877: Phrylyllic, Ian Ring Music TheoryPhrylyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1947 is chiral, and its enantiomorph is scale 2877

Scale 2877Scale 2877: Phrylyllic, Ian Ring Music TheoryPhrylyllic

Transformations:

T0 1947  T0I 2877
T1 3894  T1I 1659
T2 3693  T2I 3318
T3 3291  T3I 2541
T4 2487  T4I 987
T5 879  T5I 1974
T6 1758  T6I 3948
T7 3516  T7I 3801
T8 2937  T8I 3507
T9 1779  T9I 2919
T10 3558  T10I 1743
T11 3021  T11I 3486

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 1945Scale 1945: Zarian, Ian Ring Music TheoryZarian
Scale 1949Scale 1949: Mathyllic, Ian Ring Music TheoryMathyllic
Scale 1951Scale 1951: Marygic, Ian Ring Music TheoryMarygic
Scale 1939Scale 1939: Dathian, Ian Ring Music TheoryDathian
Scale 1943Scale 1943, Ian Ring Music Theory
Scale 1931Scale 1931: Stogian, Ian Ring Music TheoryStogian
Scale 1963Scale 1963: Epocryllic, Ian Ring Music TheoryEpocryllic
Scale 1979Scale 1979: Aeradygic, Ian Ring Music TheoryAeradygic
Scale 2011Scale 2011: Raphygic, Ian Ring Music TheoryRaphygic
Scale 1819Scale 1819: Pydian, Ian Ring Music TheoryPydian
Scale 1883Scale 1883, Ian Ring Music Theory
Scale 1691Scale 1691: Kathian, Ian Ring Music TheoryKathian
Scale 1435Scale 1435: Makam Huzzam, Ian Ring Music TheoryMakam Huzzam
Scale 923Scale 923: Ultraphrygian, Ian Ring Music TheoryUltraphrygian
Scale 2971Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
Scale 3995Scale 3995: Ionygic, Ian Ring Music TheoryIonygic

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.