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Scale 1691: "Kathian"

Scale 1691: Kathian, 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

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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
Kathian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,7,9,10}
Forte Number7-31
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2861
Hemitonia3 (trihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes6
Prime?no
prime: 731
Deep Scaleno
Interval Vector336333
Interval Spectrump3m3n6s3d3t3
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9}
<6> = {9,10,11}
Spectra Variation1.714
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 1691 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2893
Scale 2893: Lylian, Ian Ring Music TheoryLylian
3rd mode:
Scale 1747
Scale 1747: Mela Ramapriya, Ian Ring Music TheoryMela Ramapriya
4th mode:
Scale 2921
Scale 2921: Pogian, Ian Ring Music TheoryPogian
5th mode:
Scale 877
Scale 877: Moravian Pistalkova, Ian Ring Music TheoryMoravian Pistalkova
6th mode:
Scale 1243
Scale 1243: Epylian, Ian Ring Music TheoryEpylian
7th mode:
Scale 2669
Scale 2669: Jeths' Mode, Ian Ring Music TheoryJeths' Mode

Prime

The prime form of this scale is Scale 731

Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian

Complement

The heptatonic modal family [1691, 2893, 1747, 2921, 877, 1243, 2669] (Forte: 7-31) is the complement of the pentatonic modal family [587, 601, 713, 1609, 2341] (Forte: 5-31)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1691 is 2861

Scale 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1691 is chiral, and its enantiomorph is scale 2861

Scale 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian

Transformations:

T0 1691  T0I 2861
T1 3382  T1I 1627
T2 2669  T2I 3254
T3 1243  T3I 2413
T4 2486  T4I 731
T5 877  T5I 1462
T6 1754  T6I 2924
T7 3508  T7I 1753
T8 2921  T8I 3506
T9 1747  T9I 2917
T10 3494  T10I 1739
T11 2893  T11I 3478

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 1689Scale 1689: Lorimic, Ian Ring Music TheoryLorimic
Scale 1693Scale 1693: Dogian, Ian Ring Music TheoryDogian
Scale 1695Scale 1695: Phrodyllic, Ian Ring Music TheoryPhrodyllic
Scale 1683Scale 1683: Raga Malayamarutam, Ian Ring Music TheoryRaga Malayamarutam
Scale 1687Scale 1687: Phralian, Ian Ring Music TheoryPhralian
Scale 1675Scale 1675: Raga Salagavarali, Ian Ring Music TheoryRaga Salagavarali
Scale 1707Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2
Scale 1723Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic
Scale 1755Scale 1755: Octatonic, Ian Ring Music TheoryOctatonic
Scale 1563Scale 1563, Ian Ring Music Theory
Scale 1627Scale 1627: Zyptian, Ian Ring Music TheoryZyptian
Scale 1819Scale 1819: Pydian, Ian Ring Music TheoryPydian
Scale 1947Scale 1947: Byptyllic, Ian Ring Music TheoryByptyllic
Scale 1179Scale 1179: Sonimic, Ian Ring Music TheorySonimic
Scale 1435Scale 1435: Makam Huzzam, Ian Ring Music TheoryMakam Huzzam
Scale 667Scale 667: Rodimic, Ian Ring Music TheoryRodimic
Scale 2715Scale 2715: Kynian, Ian Ring Music TheoryKynian
Scale 3739Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic

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.