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Scale 2479: "Harmonic and Neapolitan Minor Mixed"

Scale 2479: Harmonic and Neapolitan 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
Harmonic and Neapolitan Minor Mixed
Zeitler
Rycryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,5,7,8,11}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3763
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 863
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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♯{1,5,8}242.27
G{7,11,2}342
G♯{8,0,3}341.91
Minor Triadscm{0,3,7}242.18
fm{5,8,0}342
g♯m{8,11,3}441.82
Augmented TriadsD♯+{3,7,11}341.91
Diminished Triads{2,5,8}242.36
{5,8,11}242.09
g♯°{8,11,2}242.09
{11,2,5}242.27
Parsimonious Voice Leading Between Common Triads of Scale 2479. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# C# C# C#->d° fm fm C#->fm d°->b° Parsimonious Voice Leading Between Common Triads of Scale 2479. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m f°->fm f°->g#m fm->G# g#° g#° G->g#° G->b° g#°->g#m g#m->G#

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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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2479 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3287
Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic
3rd mode:
Scale 3691
Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
4th mode:
Scale 3893
Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
5th mode:
Scale 1997
Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani
6th mode:
Scale 1523
Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic
7th mode:
Scale 2809
Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
8th mode:
Scale 863
Scale 863: Pyryllic, Ian Ring Music TheoryPyryllicThis is the prime mode

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [2479, 3287, 3691, 3893, 1997, 1523, 2809, 863] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2479 is 3763

Scale 3763Scale 3763: Modyllic, Ian Ring Music TheoryModyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2479 is chiral, and its enantiomorph is scale 3763

Scale 3763Scale 3763: Modyllic, Ian Ring Music TheoryModyllic

Transformations:

T0 2479  T0I 3763
T1 863  T1I 3431
T2 1726  T2I 2767
T3 3452  T3I 1439
T4 2809  T4I 2878
T5 1523  T5I 1661
T6 3046  T6I 3322
T7 1997  T7I 2549
T8 3994  T8I 1003
T9 3893  T9I 2006
T10 3691  T10I 4012
T11 3287  T11I 3929

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 2477Scale 2477: Harmonic Minor, Ian Ring Music TheoryHarmonic Minor
Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
Scale 2471Scale 2471: Mela Ganamurti, Ian Ring Music TheoryMela Ganamurti
Scale 2487Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic
Scale 2495Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
Scale 2447Scale 2447: Thagian, Ian Ring Music TheoryThagian
Scale 2463Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic
Scale 2511Scale 2511: Aeroptyllic, Ian Ring Music TheoryAeroptyllic
Scale 2543Scale 2543: Dydygic, Ian Ring Music TheoryDydygic
Scale 2351Scale 2351: Gynian, Ian Ring Music TheoryGynian
Scale 2415Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
Scale 2223Scale 2223: Konian, Ian Ring Music TheoryKonian
Scale 2735Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
Scale 2991Scale 2991: Zanygic, Ian Ring Music TheoryZanygic
Scale 3503Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian
Scale 1455Scale 1455: Phrygiolian, Ian Ring Music TheoryPhrygiolian

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.