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Scale 1647: "Polyllic"

Scale 1647: Polyllic, 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.

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
Polyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,5,6,9,10}
Forte Number8-17
Rotational Symmetrynone
Reflection Axes1.5
Palindromicno
Chiralityno
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 891
Deep Scaleno
Interval Vector546652
Interval Spectrump5m6n6s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tones[3]
Coherenceno
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1647 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2871
Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
3rd mode:
Scale 3483
Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
4th mode:
Scale 3789
Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic
5th mode:
Scale 1971
Scale 1971: Aerynyllic, Ian Ring Music TheoryAerynyllic
6th mode:
Scale 3033
Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic
7th mode:
Scale 891
Scale 891: Ionilyllic, Ian Ring Music TheoryIonilyllicThis is the prime mode
8th mode:
Scale 2493
Scale 2493: Manyllic, Ian Ring Music TheoryManyllic

Prime

The prime form of this scale is Scale 891

Scale 891Scale 891: Ionilyllic, Ian Ring Music TheoryIonilyllic

Complement

The octatonic modal family [1647, 2871, 3483, 3789, 1971, 3033, 891, 2493] (Forte: 8-17) is the complement of the tetratonic modal family [153, 531, 801, 2313] (Forte: 4-17)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1647 is 3789

Scale 3789Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic

Transformations:

T0 1647  T0I 3789
T1 3294  T1I 3483
T2 2493  T2I 2871
T3 891  T3I 1647
T4 1782  T4I 3294
T5 3564  T5I 2493
T6 3033  T6I 891
T7 1971  T7I 1782
T8 3942  T8I 3564
T9 3789  T9I 3033
T10 3483  T10I 1971
T11 2871  T11I 3942

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 1645Scale 1645: Dorian Flat 5, Ian Ring Music TheoryDorian Flat 5
Scale 1643Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6
Scale 1639Scale 1639: Aeolothian, Ian Ring Music TheoryAeolothian
Scale 1655Scale 1655: Katygyllic, Ian Ring Music TheoryKatygyllic
Scale 1663Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
Scale 1615Scale 1615: Sydian, Ian Ring Music TheorySydian
Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
Scale 1583Scale 1583: Salian, Ian Ring Music TheorySalian
Scale 1711Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh
Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic
Scale 1903Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic
Scale 1135Scale 1135: Katolian, Ian Ring Music TheoryKatolian
Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic
Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 2671Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic
Scale 3695Scale 3695: Kodygic, Ian Ring Music TheoryKodygic

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. Bibliography