The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1145: "Zygimic"

Scale 1145: Zygimic, 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
Zygimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,4,5,6,10}
Forte Number6-Z41
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 965
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?no
prime: 335
Deep Scaleno
Interval Vector332232
Interval Spectrump3m2n2s3d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,4,5,6}
<3> = {3,5,6,7,9}
<4> = {6,7,8,10}
<5> = {8,9,10,11}
Spectra Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
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
Minor Triadsd♯m{3,6,10}110.5
Diminished Triads{0,3,6}110.5
Parsimonious Voice Leading Between Common Triads of Scale 1145. Created by Ian Ring ©2019 d#m d#m c°->d#m

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1145 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 655
Scale 655: Kataptimic, Ian Ring Music TheoryKataptimic
3rd mode:
Scale 2375
Scale 2375: Aeolaptimic, Ian Ring Music TheoryAeolaptimic
4th mode:
Scale 3235
Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
5th mode:
Scale 3665
Scale 3665: Stalimic, Ian Ring Music TheoryStalimic
6th mode:
Scale 485
Scale 485: Stoptimic, Ian Ring Music TheoryStoptimic

Prime

The prime form of this scale is Scale 335

Scale 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic

Complement

The hexatonic modal family [1145, 655, 2375, 3235, 3665, 485] (Forte: 6-Z41) is the complement of the hexatonic modal family [215, 1475, 1805, 2155, 2785, 3125] (Forte: 6-Z12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1145 is 965

Scale 965Scale 965: Ionothimic, Ian Ring Music TheoryIonothimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1145 is chiral, and its enantiomorph is scale 965

Scale 965Scale 965: Ionothimic, Ian Ring Music TheoryIonothimic

Transformations:

T0 1145  T0I 965
T1 2290  T1I 1930
T2 485  T2I 3860
T3 970  T3I 3625
T4 1940  T4I 3155
T5 3880  T5I 2215
T6 3665  T6I 335
T7 3235  T7I 670
T8 2375  T8I 1340
T9 655  T9I 2680
T10 1310  T10I 1265
T11 2620  T11I 2530

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 1147Scale 1147: Epynian, Ian Ring Music TheoryEpynian
Scale 1149Scale 1149: Bydian, Ian Ring Music TheoryBydian
Scale 1137Scale 1137: Stonitonic, Ian Ring Music TheoryStonitonic
Scale 1141Scale 1141: Rynimic, Ian Ring Music TheoryRynimic
Scale 1129Scale 1129: Raga Jayakauns, Ian Ring Music TheoryRaga Jayakauns
Scale 1113Scale 1113: Locrian Pentatonic 2, Ian Ring Music TheoryLocrian Pentatonic 2
Scale 1081Scale 1081, Ian Ring Music Theory
Scale 1209Scale 1209: Raga Bhanumanjari, Ian Ring Music TheoryRaga Bhanumanjari
Scale 1273Scale 1273: Ronian, Ian Ring Music TheoryRonian
Scale 1401Scale 1401: Pagian, Ian Ring Music TheoryPagian
Scale 1657Scale 1657: Ionothian, Ian Ring Music TheoryIonothian
Scale 121Scale 121, Ian Ring Music Theory
Scale 633Scale 633: Kydimic, Ian Ring Music TheoryKydimic
Scale 2169Scale 2169, Ian Ring Music Theory
Scale 3193Scale 3193: Zathian, Ian Ring Music TheoryZathian

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.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.