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Scale 3179: "Daptian"

Scale 3179: Daptian, 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
Daptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,5,6,10,11}
Forte Number7-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2759
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes6
Prime?no
prime: 431
Deep Scaleno
Interval Vector443352
Interval Spectrump5m3n3s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {8,10,11}
Spectra Variation2.857
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsF♯{6,10,1}231.4
B{11,3,6}231.4
Minor Triadsd♯m{3,6,10}221.2
a♯m{10,1,5}142
Diminished Triads{0,3,6}142
Parsimonious Voice Leading Between Common Triads of Scale 3179. Created by Ian Ring ©2019 B B c°->B d#m d#m F# F# d#m->F# d#m->B a#m a#m F#->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
Radius2
Self-Centeredno
Central Verticesd♯m
Peripheral Verticesc°, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 3179 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3637
Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
3rd mode:
Scale 1933
Scale 1933: Mocrian, Ian Ring Music TheoryMocrian
4th mode:
Scale 1507
Scale 1507: Zynian, Ian Ring Music TheoryZynian
5th mode:
Scale 2801
Scale 2801: Zogian, Ian Ring Music TheoryZogian
6th mode:
Scale 431
Scale 431: Epyrian, Ian Ring Music TheoryEpyrianThis is the prime mode
7th mode:
Scale 2263
Scale 2263: Lycrian, Ian Ring Music TheoryLycrian

Prime

The prime form of this scale is Scale 431

Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian

Complement

The heptatonic modal family [3179, 3637, 1933, 1507, 2801, 431, 2263] (Forte: 7-14) is the complement of the pentatonic modal family [167, 901, 1249, 2131, 3113] (Forte: 5-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3179 is 2759

Scale 2759Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3179 is chiral, and its enantiomorph is scale 2759

Scale 2759Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani

Transformations:

T0 3179  T0I 2759
T1 2263  T1I 1423
T2 431  T2I 2846
T3 862  T3I 1597
T4 1724  T4I 3194
T5 3448  T5I 2293
T6 2801  T6I 491
T7 1507  T7I 982
T8 3014  T8I 1964
T9 1933  T9I 3928
T10 3866  T10I 3761
T11 3637  T11I 3427

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 3177Scale 3177: Rothimic, Ian Ring Music TheoryRothimic
Scale 3181Scale 3181: Rolian, Ian Ring Music TheoryRolian
Scale 3183Scale 3183: Mixonyllic, Ian Ring Music TheoryMixonyllic
Scale 3171Scale 3171: Zythimic, Ian Ring Music TheoryZythimic
Scale 3175Scale 3175: Eponian, Ian Ring Music TheoryEponian
Scale 3187Scale 3187: Koptian, Ian Ring Music TheoryKoptian
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
Scale 3147Scale 3147: Ryrimic, Ian Ring Music TheoryRyrimic
Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian
Scale 3115Scale 3115, Ian Ring Music Theory
Scale 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
Scale 3307Scale 3307: Boptyllic, Ian Ring Music TheoryBoptyllic
Scale 3435Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
Scale 2155Scale 2155, Ian Ring Music Theory
Scale 2667Scale 2667: Byrian, Ian Ring Music TheoryByrian
Scale 1131Scale 1131: Honchoshi Plagal Form, Ian Ring Music TheoryHonchoshi Plagal Form

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.