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Scale 3295: "Phroptygic"

Scale 3295: Phroptygic, 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
Phroptygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,6,7,10,11}
Forte Number9-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3943
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}342.53
D♯{3,7,10}442.12
F♯{6,10,1}342.53
G{7,11,2}342.24
B{11,3,6}442.24
Minor Triadscm{0,3,7}342.35
d♯m{3,6,10}342.24
em{4,7,11}342.35
gm{7,10,2}442.24
bm{11,2,6}342.35
Augmented TriadsD+{2,6,10}442.24
D♯+{3,7,11}542
Diminished Triads{0,3,6}252.71
c♯°{1,4,7}242.76
{4,7,10}242.59
{7,10,1}252.71
a♯°{10,1,4}242.76
Parsimonious Voice Leading Between Common Triads of Scale 3295. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ c#° c#° C->c#° em em C->em a#° a#° c#°->a#° D+ D+ d#m d#m D+->d#m F# F# D+->F# gm gm D+->gm bm bm D+->bm D# D# d#m->D# d#m->B D#->D#+ D#->e° D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3295. Created by Ian Ring ©2019 G D#+->G D#+->B e°->em F#->g° F#->a#° g°->gm gm->G G->bm bm->B

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♯°, D+, d♯m, D♯, D♯+, e°, em, F♯, gm, G, a♯°, bm, B
Peripheral Verticesc°, g°

Modes

Modes are the rotational transformation of this scale. Scale 3295 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3695
Scale 3695: Kodygic, Ian Ring Music TheoryKodygic
3rd mode:
Scale 3895
Scale 3895: Eparygic, Ian Ring Music TheoryEparygic
4th mode:
Scale 3995
Scale 3995: Ionygic, Ian Ring Music TheoryIonygic
5th mode:
Scale 4045
Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic
6th mode:
Scale 2035
Scale 2035: Aerythygic, Ian Ring Music TheoryAerythygic
7th mode:
Scale 3065
Scale 3065: Zothygic, Ian Ring Music TheoryZothygic
8th mode:
Scale 895
Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygicThis is the prime mode
9th mode:
Scale 2495
Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic

Prime

The prime form of this scale is Scale 895

Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic

Complement

The nonatonic modal family [3295, 3695, 3895, 3995, 4045, 2035, 3065, 895, 2495] (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 3295 is 3943

Scale 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3295 is chiral, and its enantiomorph is scale 3943

Scale 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic

Transformations:

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

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 3293Scale 3293: Saryllic, Ian Ring Music TheorySaryllic
Scale 3291Scale 3291: Lygyllic, Ian Ring Music TheoryLygyllic
Scale 3287Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic
Scale 3279Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
Scale 3311Scale 3311: Mixodygic, Ian Ring Music TheoryMixodygic
Scale 3327Scale 3327: Madyllian, Ian Ring Music TheoryMadyllian
Scale 3231Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic
Scale 3263Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic
Scale 3167Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
Scale 3423Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
Scale 3551Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
Scale 3807Scale 3807: Bagyllian, Ian Ring Music TheoryBagyllian
Scale 2271Scale 2271: Poptyllic, Ian Ring Music TheoryPoptyllic
Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic
Scale 1247Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic

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.