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Scale 1871: "Aeolyllic"

Scale 1871: Aeolyllic, 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
Aeolyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,6,8,9,10}
Forte Number8-Z29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3677
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 751
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1871 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2983
Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
3rd mode:
Scale 3539
Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic
4th mode:
Scale 3817
Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
5th mode:
Scale 989
Scale 989: Phrolyllic, Ian Ring Music TheoryPhrolyllic
6th mode:
Scale 1271
Scale 1271: Kolyllic, Ian Ring Music TheoryKolyllic
7th mode:
Scale 2683
Scale 2683: Thodyllic, Ian Ring Music TheoryThodyllic
8th mode:
Scale 3389
Scale 3389: Socryllic, Ian Ring Music TheorySocryllic

Prime

The prime form of this scale is Scale 751

Scale 751Scale 751, Ian Ring Music Theory

Complement

The octatonic modal family [1871, 2983, 3539, 3817, 989, 1271, 2683, 3389] (Forte: 8-Z29) is the complement of the tetratonic modal family [139, 353, 1553, 2117] (Forte: 4-Z29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1871 is 3677

Scale 3677Scale 3677, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1871 is chiral, and its enantiomorph is scale 3677

Scale 3677Scale 3677, Ian Ring Music Theory

Transformations:

T0 1871  T0I 3677
T1 3742  T1I 3259
T2 3389  T2I 2423
T3 2683  T3I 751
T4 1271  T4I 1502
T5 2542  T5I 3004
T6 989  T6I 1913
T7 1978  T7I 3826
T8 3956  T8I 3557
T9 3817  T9I 3019
T10 3539  T10I 1943
T11 2983  T11I 3886

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 1869Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
Scale 1867Scale 1867: Solian, Ian Ring Music TheorySolian
Scale 1863Scale 1863: Pycrian, Ian Ring Music TheoryPycrian
Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
Scale 1887Scale 1887: Aerocrygic, Ian Ring Music TheoryAerocrygic
Scale 1903Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic
Scale 1807Scale 1807, Ian Ring Music Theory
Scale 1839Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic
Scale 1935Scale 1935: Mycryllic, Ian Ring Music TheoryMycryllic
Scale 1999Scale 1999: Zacrygic, Ian Ring Music TheoryZacrygic
Scale 1615Scale 1615: Sydian, Ian Ring Music TheorySydian
Scale 1743Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic
Scale 1359Scale 1359: Aerygian, Ian Ring Music TheoryAerygian
Scale 847Scale 847: Ganian, Ian Ring Music TheoryGanian
Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 3919Scale 3919: Lynygic, Ian Ring Music TheoryLynygic

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.