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Scale 1785: "Tharyllic"

Scale 1785: Tharyllic, 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
Tharyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,3,4,5,6,7,9,10}
Forte Number8-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1005
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 735
Deep Scaleno
Interval Vector556453
Interval Spectrump5m4n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
Coherenceno
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1785 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 735
Scale 735: Sylyllic, Ian Ring Music TheorySylyllicThis is the prime mode
3rd mode:
Scale 2415
Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
4th mode:
Scale 3255
Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
5th mode:
Scale 3675
Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic
6th mode:
Scale 3885
Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
7th mode:
Scale 1995
Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic
8th mode:
Scale 3045
Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic

Prime

The prime form of this scale is Scale 735

Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic

Complement

The octatonic modal family [1785, 735, 2415, 3255, 3675, 3885, 1995, 3045] (Forte: 8-13) is the complement of the tetratonic modal family [75, 705, 1545, 2085] (Forte: 4-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1785 is 1005

Scale 1005Scale 1005: Radyllic, Ian Ring Music TheoryRadyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1785 is chiral, and its enantiomorph is scale 1005

Scale 1005Scale 1005: Radyllic, Ian Ring Music TheoryRadyllic

Transformations:

T0 1785  T0I 1005
T1 3570  T1I 2010
T2 3045  T2I 4020
T3 1995  T3I 3945
T4 3990  T4I 3795
T5 3885  T5I 3495
T6 3675  T6I 2895
T7 3255  T7I 1695
T8 2415  T8I 3390
T9 735  T9I 2685
T10 1470  T10I 1275
T11 2940  T11I 2550

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 1787Scale 1787: Mycrygic, Ian Ring Music TheoryMycrygic
Scale 1789Scale 1789: Blues Enneatonic II, Ian Ring Music TheoryBlues Enneatonic II
Scale 1777Scale 1777: Saptian, Ian Ring Music TheorySaptian
Scale 1781Scale 1781: Gocryllic, Ian Ring Music TheoryGocryllic
Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 1721Scale 1721: Mela Vagadhisvari, Ian Ring Music TheoryMela Vagadhisvari
Scale 1657Scale 1657: Ionothian, Ian Ring Music TheoryIonothian
Scale 1913Scale 1913, Ian Ring Music Theory
Scale 2041Scale 2041: Aeolacrygic, Ian Ring Music TheoryAeolacrygic
Scale 1273Scale 1273: Ronian, Ian Ring Music TheoryRonian
Scale 1529Scale 1529: Kataryllic, Ian Ring Music TheoryKataryllic
Scale 761Scale 761: Ponian, Ian Ring Music TheoryPonian
Scale 2809Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
Scale 3833Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic

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