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Scale 2463: "Ionathyllic"

Scale 2463: Ionathyllic, 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

Zeitler
Ionathyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,7,8,11}
Forte Number8-7
Rotational Symmetrynone
Reflection Axes1.5
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 831
Deep Scaleno
Interval Vector645652
Interval Spectrump5m6n5s4d6t2
Distribution Spectra<1> = {1,3}
<2> = {2,4}
<3> = {3,5,7}
<4> = {4,6,8}
<5> = {5,7,9}
<6> = {8,10}
<7> = {9,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.5
Myhill Propertyno
Balancedno
Ridge Tones[3]
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{0,4,7}441.83
E{4,8,11}331.83
G{7,11,2}252.5
G♯{8,0,3}331.83
Minor Triadscm{0,3,7}331.83
c♯m{1,4,8}252.5
em{4,7,11}331.83
g♯m{8,11,3}441.83
Augmented TriadsC+{0,4,8}441.83
D♯+{3,7,11}441.83
Diminished Triadsc♯°{1,4,7}252.5
g♯°{8,11,2}252.5
Parsimonious Voice Leading Between Common Triads of Scale 2463. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E C+->G# c#°->c#m D#+->em Parsimonious Voice Leading Between Common Triads of Scale 2463. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m em->E E->g#m g#° g#° G->g#° 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.

Diameter5
Radius3
Self-Centeredno
Central Verticescm, em, E, G♯
Peripheral Verticesc♯°, c♯m, G, g♯°

Modes

Modes are the rotational transformation of this scale. Scale 2463 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3279
Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
3rd mode:
Scale 3687
Scale 3687: Zonyllic, Ian Ring Music TheoryZonyllic
4th mode:
Scale 3891
Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
5th mode:
Scale 3993
Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic
6th mode:
Scale 1011
Scale 1011: Kycryllic, Ian Ring Music TheoryKycryllic
7th mode:
Scale 2553
Scale 2553: Aeolaptyllic, Ian Ring Music TheoryAeolaptyllic
8th mode:
Scale 831
Scale 831: Rodyllic, Ian Ring Music TheoryRodyllicThis is the prime mode

Prime

The prime form of this scale is Scale 831

Scale 831Scale 831: Rodyllic, Ian Ring Music TheoryRodyllic

Complement

The octatonic modal family [2463, 3279, 3687, 3891, 3993, 1011, 2553, 831] (Forte: 8-7) is the complement of the tetratonic modal family [51, 771, 2073, 2433] (Forte: 4-7)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2463 is 3891

Scale 3891Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic

Transformations:

T0 2463  T0I 3891
T1 831  T1I 3687
T2 1662  T2I 3279
T3 3324  T3I 2463
T4 2553  T4I 831
T5 1011  T5I 1662
T6 2022  T6I 3324
T7 4044  T7I 2553
T8 3993  T8I 1011
T9 3891  T9I 2022
T10 3687  T10I 4044
T11 3279  T11I 3993

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 2461Scale 2461: Sagian, Ian Ring Music TheorySagian
Scale 2459Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian
Scale 2455Scale 2455: Bothian, Ian Ring Music TheoryBothian
Scale 2447Scale 2447: Thagian, Ian Ring Music TheoryThagian
Scale 2479Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed
Scale 2495Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
Scale 2527Scale 2527: Phradygic, Ian Ring Music TheoryPhradygic
Scale 2335Scale 2335: Epydian, Ian Ring Music TheoryEpydian
Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 2207Scale 2207: Mygian, Ian Ring Music TheoryMygian
Scale 2719Scale 2719: Zocryllic, Ian Ring Music TheoryZocryllic
Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
Scale 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
Scale 415Scale 415: Aeoladian, Ian Ring Music TheoryAeoladian
Scale 1439Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic

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.