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Scale 3487: "Byptygic"

Scale 3487: Byptygic, 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

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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
Byptygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,7,8,10,11}
Forte Number9-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3895
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 895
Deep Scaleno
Interval Vector767763
Interval Spectrump6m7n7s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2.222
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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}442.24
D♯{3,7,10}342.35
E{4,8,11}342.24
G{7,11,2}342.35
G♯{8,0,3}342.35
Minor Triadscm{0,3,7}342.24
c♯m{1,4,8}342.53
em{4,7,11}442.12
gm{7,10,2}342.53
g♯m{8,11,3}442.24
Augmented TriadsC+{0,4,8}442.24
D♯+{3,7,11}542
Diminished Triadsc♯°{1,4,7}252.71
{4,7,10}242.59
{7,10,1}242.76
g♯°{8,11,2}252.71
a♯°{10,1,4}242.76
Parsimonious Voice Leading Between Common Triads of Scale 3487. 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#° em em C->em c#m c#m C+->c#m E E C+->E C+->G# c#°->c#m a#° a#° c#m->a#° D# D# D#->D#+ D#->e° gm gm D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3487. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m e°->em em->E E->g#m g°->gm g°->a#° gm->G g#° g#° G->g#° g#°->g#m g#m->G#

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.

Diameter5
Radius4
Self-Centeredno
Central Verticescm, C, C+, c♯m, D♯, D♯+, e°, em, E, g°, gm, G, g♯m, G♯, a♯°
Peripheral Verticesc♯°, g♯°

Modes

Modes are the rotational transformation of this scale. Scale 3487 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3791
Scale 3791: Stodygic, Ian Ring Music TheoryStodygic
3rd mode:
Scale 3943
Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
4th mode:
Scale 4019
Scale 4019: Lonygic, Ian Ring Music TheoryLonygic
5th mode:
Scale 4057
Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
6th mode:
Scale 1019
Scale 1019: Aeranygic, Ian Ring Music TheoryAeranygic
7th mode:
Scale 2557
Scale 2557: Dothygic, Ian Ring Music TheoryDothygic
8th mode:
Scale 1663
Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
9th mode:
Scale 2879
Scale 2879: Stadygic, Ian Ring Music TheoryStadygic

Prime

The prime form of this scale is Scale 895

Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic

Complement

The nonatonic modal family [3487, 3791, 3943, 4019, 4057, 1019, 2557, 1663, 2879] (Forte: 9-3) is the complement of the tritonic modal family [19, 769, 2057] (Forte: 3-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3487 is 3895

Scale 3895Scale 3895: Eparygic, Ian Ring Music TheoryEparygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3487 is chiral, and its enantiomorph is scale 3895

Scale 3895Scale 3895: Eparygic, Ian Ring Music TheoryEparygic

Transformations:

T0 3487  T0I 3895
T1 2879  T1I 3695
T2 1663  T2I 3295
T3 3326  T3I 2495
T4 2557  T4I 895
T5 1019  T5I 1790
T6 2038  T6I 3580
T7 4076  T7I 3065
T8 4057  T8I 2035
T9 4019  T9I 4070
T10 3943  T10I 4045
T11 3791  T11I 3995

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 3485Scale 3485: Sabach, Ian Ring Music TheorySabach
Scale 3483Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
Scale 3479Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
Scale 3471Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic
Scale 3503Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
Scale 3519Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
Scale 3551Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
Scale 3359Scale 3359: Bonyllic, Ian Ring Music TheoryBonyllic
Scale 3423Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
Scale 3231Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic
Scale 3743Scale 3743: Thadygic, Ian Ring Music TheoryThadygic
Scale 3999Scale 3999: Dydyllian, Ian Ring Music TheoryDydyllian
Scale 2463Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic
Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
Scale 1439Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.