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Scale 745: "Kolimic"

Scale 745: Kolimic, 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
Kolimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,5,6,7,9}
Forte Number6-Z45
Rotational Symmetrynone
Reflection Axes0
Palindromicyes
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes5
Prime?no
prime: 605
Deep Scaleno
Interval Vector234222
Interval Spectrump2m2n4s3d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5,6}
<3> = {4,6,8}
<4> = {6,7,9,10}
<5> = {9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[0]
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsF{5,9,0}231.5
Minor Triadscm{0,3,7}231.5
Diminished Triads{0,3,6}231.5
d♯°{3,6,9}231.5
f♯°{6,9,0}231.5
{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 745. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° cm->a° f#° f#° d#°->f#° F F F->f#° F->a°

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 745 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 605
Scale 605: Dycrimic, Ian Ring Music TheoryDycrimicThis is the prime mode
3rd mode:
Scale 1175
Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic
4th mode:
Scale 2635
Scale 2635: Gocrimic, Ian Ring Music TheoryGocrimic
5th mode:
Scale 3365
Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
6th mode:
Scale 1865
Scale 1865: Thagimic, Ian Ring Music TheoryThagimic

Prime

The prime form of this scale is Scale 605

Scale 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic

Complement

The hexatonic modal family [745, 605, 1175, 2635, 3365, 1865] (Forte: 6-Z45) is the complement of the hexatonic modal family [365, 1115, 1675, 1745, 2605, 2885] (Forte: 6-Z23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 745 is itself, because it is a palindromic scale!

Scale 745Scale 745: Kolimic, Ian Ring Music TheoryKolimic

Transformations:

T0 745  T0I 745
T1 1490  T1I 1490
T2 2980  T2I 2980
T3 1865  T3I 1865
T4 3730  T4I 3730
T5 3365  T5I 3365
T6 2635  T6I 2635
T7 1175  T7I 1175
T8 2350  T8I 2350
T9 605  T9I 605
T10 1210  T10I 1210
T11 2420  T11I 2420

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 747Scale 747: Lynian, Ian Ring Music TheoryLynian
Scale 749Scale 749: Aeologian, Ian Ring Music TheoryAeologian
Scale 737Scale 737, Ian Ring Music Theory
Scale 741Scale 741: Gathimic, Ian Ring Music TheoryGathimic
Scale 753Scale 753: Aeronimic, Ian Ring Music TheoryAeronimic
Scale 761Scale 761: Ponian, Ian Ring Music TheoryPonian
Scale 713Scale 713: Thoptitonic, Ian Ring Music TheoryThoptitonic
Scale 729Scale 729: Stygimic, Ian Ring Music TheoryStygimic
Scale 681Scale 681: Kyemyonjo, Ian Ring Music TheoryKyemyonjo
Scale 617Scale 617: Katycritonic, Ian Ring Music TheoryKatycritonic
Scale 873Scale 873: Bagimic, Ian Ring Music TheoryBagimic
Scale 1001Scale 1001: Badian, Ian Ring Music TheoryBadian
Scale 233Scale 233, Ian Ring Music Theory
Scale 489Scale 489: Phrathimic, Ian Ring Music TheoryPhrathimic
Scale 1257Scale 1257: Blues Scale, Ian Ring Music TheoryBlues Scale
Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
Scale 2793Scale 2793: Eporian, Ian Ring Music TheoryEporian

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, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.