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Scale 2731: "Neapolitan Major"

Scale 2731: Neapolitan Major, 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

Western Modern
Neapolitan Major
Major Meapolitan
Lydian Major
Carnatic Mela
Mela Kokilapriya
Carnatic Raga
Raga Kokilaravam
Zeitler
Thydian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,5,7,9,11}
Forte Number7-33
Rotational Symmetrynone
Reflection Axes0
Palindromicyes
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections5
Modes6
Prime?no
prime: 1367
Deep Scaleno
Interval Vector262623
Interval Spectrump2m6n2s6d2t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9,10}
<6> = {10,11}
Spectra Variation1.429
Maximally Evenno
Maximal Area Setyes
Interior Area2.665
Myhill Propertyno
Balancedno
Ridge Tones[0]
ProprietyProper
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{5,9,0}231.4
Minor Triadscm{0,3,7}231.4
Augmented TriadsC♯+{1,5,9}142
D♯+{3,7,11}142
Diminished Triads{9,0,3}221.2
Parsimonious Voice Leading Between Common Triads of Scale 2731. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ cm->a° C#+ C#+ F F C#+->F F->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.

Diameter4
Radius2
Self-Centeredno
Central Vertices
Peripheral VerticesC♯+, D♯+

Modes

Modes are the rotational transformation of this scale. Scale 2731 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3413
Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
3rd mode:
Scale 1877
Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
4th mode:
Scale 1493
Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor
5th mode:
Scale 1397
Scale 1397: Major Locrian, Ian Ring Music TheoryMajor Locrian
6th mode:
Scale 1373
Scale 1373: Storian, Ian Ring Music TheoryStorian
7th mode:
Scale 1367
Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone InverseThis is the prime mode

Prime

The prime form of this scale is Scale 1367

Scale 1367Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone Inverse

Complement

The heptatonic modal family [2731, 3413, 1877, 1493, 1397, 1373, 1367] (Forte: 7-33) is the complement of the pentatonic modal family [341, 1109, 1301, 1349, 1361] (Forte: 5-33)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2731 is itself, because it is a palindromic scale!

Scale 2731Scale 2731: Neapolitan Major, Ian Ring Music TheoryNeapolitan Major

Transformations:

T0 2731  T0I 2731
T1 1367  T1I 1367
T2 2734  T2I 2734
T3 1373  T3I 1373
T4 2746  T4I 2746
T5 1397  T5I 1397
T6 2794  T6I 2794
T7 1493  T7I 1493
T8 2986  T8I 2986
T9 1877  T9I 1877
T10 3754  T10I 3754
T11 3413  T11I 3413

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 2729Scale 2729: Aeragimic, Ian Ring Music TheoryAeragimic
Scale 2733Scale 2733: Melodic Minor Ascending, Ian Ring Music TheoryMelodic Minor Ascending
Scale 2735Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
Scale 2723Scale 2723: Raga Jivantika, Ian Ring Music TheoryRaga Jivantika
Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati
Scale 2739Scale 2739: Mela Suryakanta, Ian Ring Music TheoryMela Suryakanta
Scale 2747Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
Scale 2699Scale 2699: Sythimic, Ian Ring Music TheorySythimic
Scale 2715Scale 2715: Kynian, Ian Ring Music TheoryKynian
Scale 2763Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
Scale 2795Scale 2795: Van der Horst Octatonic, Ian Ring Music TheoryVan der Horst Octatonic
Scale 2603Scale 2603: Gadimic, Ian Ring Music TheoryGadimic
Scale 2667Scale 2667: Byrian, Ian Ring Music TheoryByrian
Scale 2859Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
Scale 2987Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
Scale 2219Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic
Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
Scale 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 683Scale 683: Stogimic, Ian Ring Music TheoryStogimic
Scale 1707Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2

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. Special thanks to Richard Repp for helping with technical accuracy.