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Scale 2987: "Neapolitan Major and Minor Mixed"

Scale 2987: Neapolitan Major and Minor Mixed, 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

Western Mixed
Neapolitan Major and Minor Mixed
Zeitler
Thanyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,5,7,8,9,11}
Forte Number8-24
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 1399
Deep Scaleno
Interval Vector464743
Interval Spectrump4m7n4s6d4t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.5
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tones[8]
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♯{1,5,8}242.1
F{5,9,0}341.9
G♯{8,0,3}431.5
Minor Triadscm{0,3,7}242.1
fm{5,8,0}431.5
g♯m{8,11,3}341.9
Augmented TriadsC♯+{1,5,9}252.5
D♯+{3,7,11}252.5
Diminished Triads{5,8,11}231.9
{9,0,3}231.9
Parsimonious Voice Leading Between Common Triads of Scale 2987. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# C# C# C#+ C#+ C#->C#+ fm fm C#->fm F F C#+->F g#m g#m D#+->g#m f°->fm f°->g#m fm->F fm->G# F->a° g#m->G# G#->a°

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
Radius3
Self-Centeredno
Central Verticesf°, fm, G♯, a°
Peripheral VerticesC♯+, D♯+

Modes

Modes are the rotational transformation of this scale. Scale 2987 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3541
Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
3rd mode:
Scale 1909
Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
4th mode:
Scale 1501
Scale 1501: Stygyllic, Ian Ring Music TheoryStygyllic
5th mode:
Scale 1399
Scale 1399: Syryllic, Ian Ring Music TheorySyryllicThis is the prime mode
6th mode:
Scale 2747
Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
7th mode:
Scale 3421
Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
8th mode:
Scale 1879
Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic

Prime

The prime form of this scale is Scale 1399

Scale 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic

Complement

The octatonic modal family [2987, 3541, 1909, 1501, 1399, 2747, 3421, 1879] (Forte: 8-24) is the complement of the tetratonic modal family [277, 337, 1093, 1297] (Forte: 4-24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2987 is 2747

Scale 2747Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic

Transformations:

T0 2987  T0I 2747
T1 1879  T1I 1399
T2 3758  T2I 2798
T3 3421  T3I 1501
T4 2747  T4I 3002
T5 1399  T5I 1909
T6 2798  T6I 3818
T7 1501  T7I 3541
T8 3002  T8I 2987
T9 1909  T9I 1879
T10 3818  T10I 3758
T11 3541  T11I 3421

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 2985Scale 2985: Epacrian, Ian Ring Music TheoryEpacrian
Scale 2989Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
Scale 2991Scale 2991: Zanygic, Ian Ring Music TheoryZanygic
Scale 2979Scale 2979: Gyptian, Ian Ring Music TheoryGyptian
Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
Scale 2995Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra
Scale 3003Scale 3003: Genus Chromaticum, Ian Ring Music TheoryGenus Chromaticum
Scale 2955Scale 2955: Thorian, Ian Ring Music TheoryThorian
Scale 2971Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
Scale 3019Scale 3019, Ian Ring Music Theory
Scale 3051Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
Scale 2859Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
Scale 2923Scale 2923: Baryllic, Ian Ring Music TheoryBaryllic
Scale 2731Scale 2731: Neapolitan Major, Ian Ring Music TheoryNeapolitan Major
Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel
Scale 4011Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
Scale 939Scale 939: Mela Senavati, Ian Ring Music TheoryMela Senavati
Scale 1963Scale 1963: Epocryllic, Ian Ring Music TheoryEpocryllic

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.