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Scale 2887: "Gaptian"

Scale 2887: Gaptian, 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
Gaptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,6,8,9,11}
Forte Number7-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3163
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 367
Deep Scaleno
Interval Vector444342
Interval Spectrump4m3n4s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
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 TriadsD{2,6,9}221.2
Minor Triadsf♯m{6,9,1}231.4
bm{11,2,6}231.4
Diminished Triadsf♯°{6,9,0}142
g♯°{8,11,2}142
Parsimonious Voice Leading Between Common Triads of Scale 2887. Created by Ian Ring ©2019 D D f#m f#m D->f#m bm bm D->bm f#° f#° f#°->f#m g#° g#° g#°->bm

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
Peripheral Verticesf♯°, g♯°

Modes

Modes are the rotational transformation of this scale. Scale 2887 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3491
Scale 3491: Tharian, Ian Ring Music TheoryTharian
3rd mode:
Scale 3793
Scale 3793: Aeopian, Ian Ring Music TheoryAeopian
4th mode:
Scale 493
Scale 493: Rygian, Ian Ring Music TheoryRygian
5th mode:
Scale 1147
Scale 1147: Epynian, Ian Ring Music TheoryEpynian
6th mode:
Scale 2621
Scale 2621: Ionogian, Ian Ring Music TheoryIonogian
7th mode:
Scale 1679
Scale 1679: Kydian, Ian Ring Music TheoryKydian

Prime

The prime form of this scale is Scale 367

Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian

Complement

The heptatonic modal family [2887, 3491, 3793, 493, 1147, 2621, 1679] (Forte: 7-Z36) is the complement of the pentatonic modal family [151, 737, 1801, 2123, 3109] (Forte: 5-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2887 is 3163

Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2887 is chiral, and its enantiomorph is scale 3163

Scale 3163Scale 3163: Rogian, Ian Ring Music TheoryRogian

Transformations:

T0 2887  T0I 3163
T1 1679  T1I 2231
T2 3358  T2I 367
T3 2621  T3I 734
T4 1147  T4I 1468
T5 2294  T5I 2936
T6 493  T6I 1777
T7 986  T7I 3554
T8 1972  T8I 3013
T9 3944  T9I 1931
T10 3793  T10I 3862
T11 3491  T11I 3629

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 2885Scale 2885: Byrimic, Ian Ring Music TheoryByrimic
Scale 2883Scale 2883, Ian Ring Music Theory
Scale 2891Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian
Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 2903Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
Scale 2823Scale 2823, Ian Ring Music Theory
Scale 2855Scale 2855: Epocrain, Ian Ring Music TheoryEpocrain
Scale 2951Scale 2951, Ian Ring Music Theory
Scale 3015Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
Scale 2631Scale 2631: Macrimic, Ian Ring Music TheoryMacrimic
Scale 2759Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani
Scale 2375Scale 2375: Aeolaptimic, Ian Ring Music TheoryAeolaptimic
Scale 3399Scale 3399: Zonian, Ian Ring Music TheoryZonian
Scale 3911Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic
Scale 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic
Scale 1863Scale 1863: Pycrian, Ian Ring Music TheoryPycrian

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.