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Scale 1231: "Logian"

Scale 1231: Logian, 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
Logian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,6,7,10}
Forte Number7-Z18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3685
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 755
Deep Scaleno
Interval Vector434442
Interval Spectrump4m4n4s3d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 1231 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2663
Scale 2663: Lalian, Ian Ring Music TheoryLalian
3rd mode:
Scale 3379
Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending
4th mode:
Scale 3737
Scale 3737: Phrocrian, Ian Ring Music TheoryPhrocrian
5th mode:
Scale 979
Scale 979: Mela Dhavalambari, Ian Ring Music TheoryMela Dhavalambari
6th mode:
Scale 2537
Scale 2537: Laptian, Ian Ring Music TheoryLaptian
7th mode:
Scale 829
Scale 829: Lygian, Ian Ring Music TheoryLygian

Prime

The prime form of this scale is Scale 755

Scale 755Scale 755: Phrythian, Ian Ring Music TheoryPhrythian

Complement

The heptatonic modal family [1231, 2663, 3379, 3737, 979, 2537, 829] (Forte: 7-Z18) is the complement of the pentatonic modal family [179, 779, 1633, 2137, 2437] (Forte: 5-Z18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1231 is 3685

Scale 3685Scale 3685: Kodian, Ian Ring Music TheoryKodian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1231 is chiral, and its enantiomorph is scale 3685

Scale 3685Scale 3685: Kodian, Ian Ring Music TheoryKodian

Transformations:

T0 1231  T0I 3685
T1 2462  T1I 3275
T2 829  T2I 2455
T3 1658  T3I 815
T4 3316  T4I 1630
T5 2537  T5I 3260
T6 979  T6I 2425
T7 1958  T7I 755
T8 3916  T8I 1510
T9 3737  T9I 3020
T10 3379  T10I 1945
T11 2663  T11I 3890

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 1229Scale 1229: Raga Simharava, Ian Ring Music TheoryRaga Simharava
Scale 1227Scale 1227: Thacrimic, Ian Ring Music TheoryThacrimic
Scale 1223Scale 1223: Phryptimic, Ian Ring Music TheoryPhryptimic
Scale 1239Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
Scale 1247Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic
Scale 1263Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic
Scale 1167Scale 1167: Aerodimic, Ian Ring Music TheoryAerodimic
Scale 1199Scale 1199: Magian, Ian Ring Music TheoryMagian
Scale 1103Scale 1103: Lynimic, Ian Ring Music TheoryLynimic
Scale 1359Scale 1359: Aerygian, Ian Ring Music TheoryAerygian
Scale 1487Scale 1487: Mothyllic, Ian Ring Music TheoryMothyllic
Scale 1743Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic
Scale 207Scale 207, Ian Ring Music Theory
Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian
Scale 2255Scale 2255: Dylian, Ian Ring Music TheoryDylian
Scale 3279Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic

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.