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Scale 1751: "Aeolyryllic"

Scale 1751: Aeolyryllic, 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

Zeitler
Aeolyryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,6,7,9,10}
Forte Number8-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3437
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes7
Prime?no
prime: 1463
Deep Scaleno
Interval Vector456553
Interval Spectrump5m5n6s5d4t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5}
<4> = {5,6,7}
<5> = {7,8}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.25
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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}342.23
D{2,6,9}242.23
F♯{6,10,1}441.92
A{9,1,4}441.92
Minor Triadsf♯m{6,9,1}441.85
gm{7,10,2}342.23
am{9,0,4}342.15
Augmented TriadsD+{2,6,10}342.15
Diminished Triadsc♯°{1,4,7}242.31
{4,7,10}242.31
f♯°{6,9,0}242.23
{7,10,1}242.31
a♯°{10,1,4}242.15
Parsimonious Voice Leading Between Common Triads of Scale 1751. Created by Ian Ring ©2019 C C c#° c#° C->c#° C->e° am am C->am A A c#°->A D D D+ D+ D->D+ f#m f#m D->f#m F# F# D+->F# gm gm D+->gm e°->gm f#° f#° f#°->f#m f#°->am f#m->F# f#m->A F#->g° a#° a#° F#->a#° g°->gm am->A A->a#°

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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 1751 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2923
Scale 2923: Baryllic, Ian Ring Music TheoryBaryllic
3rd mode:
Scale 3509
Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic
4th mode:
Scale 1901
Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic
5th mode:
Scale 1499
Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian
6th mode:
Scale 2797
Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic
7th mode:
Scale 1723
Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic
8th mode:
Scale 2909
Scale 2909: Mocryllic, Ian Ring Music TheoryMocryllic

Prime

The prime form of this scale is Scale 1463

Scale 1463Scale 1463, Ian Ring Music Theory

Complement

The octatonic modal family [1751, 2923, 3509, 1901, 1499, 2797, 1723, 2909] (Forte: 8-27) is the complement of the tetratonic modal family [293, 593, 649, 1097] (Forte: 4-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1751 is 3437

Scale 3437Scale 3437, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1751 is chiral, and its enantiomorph is scale 3437

Scale 3437Scale 3437, Ian Ring Music Theory

Transformations:

T0 1751  T0I 3437
T1 3502  T1I 2779
T2 2909  T2I 1463
T3 1723  T3I 2926
T4 3446  T4I 1757
T5 2797  T5I 3514
T6 1499  T6I 2933
T7 2998  T7I 1771
T8 1901  T8I 3542
T9 3802  T9I 2989
T10 3509  T10I 1883
T11 2923  T11I 3766

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 1749Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic
Scale 1747Scale 1747: Mela Ramapriya, Ian Ring Music TheoryMela Ramapriya
Scale 1755Scale 1755: Octatonic, Ian Ring Music TheoryOctatonic
Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic
Scale 1735Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam
Scale 1743Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic
Scale 1767Scale 1767: Dyryllic, Ian Ring Music TheoryDyryllic
Scale 1783Scale 1783: Youlan Scale, Ian Ring Music TheoryYoulan Scale
Scale 1687Scale 1687: Phralian, Ian Ring Music TheoryPhralian
Scale 1719Scale 1719: Lyryllic, Ian Ring Music TheoryLyryllic
Scale 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian
Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
Scale 2007Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
Scale 1239Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
Scale 1495Scale 1495: Messiaen Mode 6, Ian Ring Music TheoryMessiaen Mode 6
Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian
Scale 2775Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
Scale 3799Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic

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.