The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3423: "Lothygic"

Scale 3423: Lothygic, 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
Lothygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,6,8,10,11}
Forte Number9-6
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1407
Deep Scaleno
Interval Vector686763
Interval Spectrump6m7n6s8d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tones[2]
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 TriadsE{4,8,11}242.31
F♯{6,10,1}242.54
G♯{8,0,3}342.15
B{11,3,6}442
Minor Triadsc♯m{1,4,8}242.54
d♯m{3,6,10}242.31
g♯m{8,11,3}442
bm{11,2,6}342.15
Augmented TriadsC+{0,4,8}342.31
D+{2,6,10}342.31
Diminished Triads{0,3,6}242.31
g♯°{8,11,2}242.31
a♯°{10,1,4}242.62
Parsimonious Voice Leading Between Common Triads of Scale 3423. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E C+->G# a#° a#° c#m->a#° D+ D+ d#m d#m D+->d#m F# F# D+->F# bm bm D+->bm d#m->B g#m g#m E->g#m F#->a#° g#° g#° g#°->g#m g#°->bm g#m->G# g#m->B bm->B

view full size

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3423 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3759
Scale 3759: Darygic, Ian Ring Music TheoryDarygic
3rd mode:
Scale 3927
Scale 3927: Monygic, Ian Ring Music TheoryMonygic
4th mode:
Scale 4011
Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
5th mode:
Scale 4053
Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
6th mode:
Scale 2037
Scale 2037: Sythygic, Ian Ring Music TheorySythygic
7th mode:
Scale 1533
Scale 1533: Katycrygic, Ian Ring Music TheoryKatycrygic
8th mode:
Scale 1407
Scale 1407: Tharygic, Ian Ring Music TheoryTharygicThis is the prime mode
9th mode:
Scale 2751
Scale 2751: Sylygic, Ian Ring Music TheorySylygic

Prime

The prime form of this scale is Scale 1407

Scale 1407Scale 1407: Tharygic, Ian Ring Music TheoryTharygic

Complement

The nonatonic modal family [3423, 3759, 3927, 4011, 4053, 2037, 1533, 1407, 2751] (Forte: 9-6) is the complement of the tritonic modal family [21, 1029, 1281] (Forte: 3-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3423 is 3927

Scale 3927Scale 3927: Monygic, Ian Ring Music TheoryMonygic

Transformations:

T0 3423  T0I 3927
T1 2751  T1I 3759
T2 1407  T2I 3423
T3 2814  T3I 2751
T4 1533  T4I 1407
T5 3066  T5I 2814
T6 2037  T6I 1533
T7 4074  T7I 3066
T8 4053  T8I 2037
T9 4011  T9I 4074
T10 3927  T10I 4053
T11 3759  T11I 4011

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 3421Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
Scale 3407Scale 3407: Katocryllic, Ian Ring Music TheoryKatocryllic
Scale 3439Scale 3439: Lythygic, Ian Ring Music TheoryLythygic
Scale 3455Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
Scale 3359Scale 3359: Bonyllic, Ian Ring Music TheoryBonyllic
Scale 3391Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic
Scale 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
Scale 3551Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian
Scale 3167Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
Scale 3679Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
Scale 3935Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 2911Scale 2911: Katygic, Ian Ring Music TheoryKatygic
Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic

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.