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Scale 1469: "Epiryllic"

Scale 1469: Epiryllic, 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
Epiryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,5,7,8,10}
Forte Number8-22
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1973
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 1391
Deep Scaleno
Interval Vector465562
Interval Spectrump6m5n5s6d4t2
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.75
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
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{0,4,7}341.9
D♯{3,7,10}341.9
G♯{8,0,3}242.1
A♯{10,2,5}242.3
Minor Triadscm{0,3,7}341.9
fm{5,8,0}242.1
gm{7,10,2}242.1
Augmented TriadsC+{0,4,8}341.9
Diminished Triads{2,5,8}242.3
{4,7,10}242.1
Parsimonious Voice Leading Between Common Triads of Scale 1469. Created by Ian Ring ©2019 cm cm C C cm->C D# D# cm->D# G# G# cm->G# C+ C+ C->C+ C->e° fm fm C+->fm C+->G# d°->fm A# A# d°->A# D#->e° gm gm D#->gm gm->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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1469 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1391
Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllicThis is the prime mode
3rd mode:
Scale 2743
Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic
4th mode:
Scale 3419
Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
5th mode:
Scale 3757
Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
6th mode:
Scale 1963
Scale 1963: Epocryllic, Ian Ring Music TheoryEpocryllic
7th mode:
Scale 3029
Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
8th mode:
Scale 1781
Scale 1781: Gocryllic, Ian Ring Music TheoryGocryllic

Prime

The prime form of this scale is Scale 1391

Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic

Complement

The octatonic modal family [1469, 1391, 2743, 3419, 3757, 1963, 3029, 1781] (Forte: 8-22) is the complement of the tetratonic modal family [149, 673, 1061, 1289] (Forte: 4-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1469 is 1973

Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1469 is chiral, and its enantiomorph is scale 1973

Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic

Transformations:

T0 1469  T0I 1973
T1 2938  T1I 3946
T2 1781  T2I 3797
T3 3562  T3I 3499
T4 3029  T4I 2903
T5 1963  T5I 1711
T6 3926  T6I 3422
T7 3757  T7I 2749
T8 3419  T8I 1403
T9 2743  T9I 2806
T10 1391  T10I 1517
T11 2782  T11I 3034

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 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic
Scale 1465Scale 1465: Mela Ragavardhani, Ian Ring Music TheoryMela Ragavardhani
Scale 1467Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish Phrygian
Scale 1461Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
Scale 1453Scale 1453: Aeolian, Ian Ring Music TheoryAeolian
Scale 1437Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending
Scale 1501Scale 1501: Stygyllic, Ian Ring Music TheoryStygyllic
Scale 1533Scale 1533: Katycrygic, Ian Ring Music TheoryKatycrygic
Scale 1341Scale 1341: Madian, Ian Ring Music TheoryMadian
Scale 1405Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic
Scale 1213Scale 1213: Gyrian, Ian Ring Music TheoryGyrian
Scale 1725Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop
Scale 1981Scale 1981: Houseini, Ian Ring Music TheoryHouseini
Scale 445Scale 445: Gocrian, Ian Ring Music TheoryGocrian
Scale 957Scale 957: Phronyllic, Ian Ring Music TheoryPhronyllic
Scale 2493Scale 2493: Manyllic, Ian Ring Music TheoryManyllic
Scale 3517Scale 3517: Epocrygic, Ian Ring Music TheoryEpocrygic

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.