The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1827: "Katygimic"

Scale 1827: Katygimic, 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
Katygimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,5,8,9,10}
Forte Number6-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2205
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 315
Deep Scaleno
Interval Vector323430
Interval Spectrump3m4n3s2d3
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5,7}
<3> = {4,5,7,8}
<4> = {5,7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation3.333
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1827 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2961
Scale 2961: Bygimic, Ian Ring Music TheoryBygimic
3rd mode:
Scale 441
Scale 441: Thycrimic, Ian Ring Music TheoryThycrimic
4th mode:
Scale 567
Scale 567: Aeoladimic, Ian Ring Music TheoryAeoladimic
5th mode:
Scale 2331
Scale 2331: Dylimic, Ian Ring Music TheoryDylimic
6th mode:
Scale 3213
Scale 3213: Eponimic, Ian Ring Music TheoryEponimic

Prime

The prime form of this scale is Scale 315

Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic

Complement

The hexatonic modal family [1827, 2961, 441, 567, 2331, 3213] (Forte: 6-14) is the complement of the hexatonic modal family [315, 945, 1575, 2205, 2835, 3465] (Forte: 6-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1827 is 2205

Scale 2205Scale 2205: Ionocrimic, Ian Ring Music TheoryIonocrimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1827 is chiral, and its enantiomorph is scale 2205

Scale 2205Scale 2205: Ionocrimic, Ian Ring Music TheoryIonocrimic

Transformations:

T0 1827  T0I 2205
T1 3654  T1I 315
T2 3213  T2I 630
T3 2331  T3I 1260
T4 567  T4I 2520
T5 1134  T5I 945
T6 2268  T6I 1890
T7 441  T7I 3780
T8 882  T8I 3465
T9 1764  T9I 2835
T10 3528  T10I 1575
T11 2961  T11I 3150

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 1825Scale 1825, Ian Ring Music Theory
Scale 1829Scale 1829: Pathimic, Ian Ring Music TheoryPathimic
Scale 1831Scale 1831: Pothian, Ian Ring Music TheoryPothian
Scale 1835Scale 1835: Byptian, Ian Ring Music TheoryByptian
Scale 1843Scale 1843: Ionygian, Ian Ring Music TheoryIonygian
Scale 1795Scale 1795, Ian Ring Music Theory
Scale 1811Scale 1811: Kyptimic, Ian Ring Music TheoryKyptimic
Scale 1859Scale 1859, Ian Ring Music Theory
Scale 1891Scale 1891: Thalian, Ian Ring Music TheoryThalian
Scale 1955Scale 1955: Sonian, Ian Ring Music TheorySonian
Scale 1571Scale 1571: Lagitonic, Ian Ring Music TheoryLagitonic
Scale 1699Scale 1699: Raga Rasavali, Ian Ring Music TheoryRaga Rasavali
Scale 1315Scale 1315: Pyritonic, Ian Ring Music TheoryPyritonic
Scale 803Scale 803: Loritonic, Ian Ring Music TheoryLoritonic
Scale 2851Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic
Scale 3875Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian

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.