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Scale 1407: "Tharygic"

Scale 1407: Tharygic, 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
Tharygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,5,6,8,10}
Forte Number9-6
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?yes
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[6]
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 TriadsC♯{1,5,8}442
F♯{6,10,1}242.31
G♯{8,0,3}242.54
A♯{10,2,5}342.15
Minor Triadsc♯m{1,4,8}342.15
d♯m{3,6,10}242.54
fm{5,8,0}242.31
a♯m{10,1,5}442
Augmented TriadsC+{0,4,8}342.31
D+{2,6,10}342.31
Diminished Triads{0,3,6}242.62
{2,5,8}242.31
a♯°{10,1,4}242.31
Parsimonious Voice Leading Between Common Triads of Scale 1407. Created by Ian Ring ©2019 d#m d#m c°->d#m G# G# c°->G# C+ C+ c#m c#m C+->c#m fm fm C+->fm C+->G# C# C# c#m->C# a#° a#° c#m->a#° C#->d° C#->fm a#m a#m C#->a#m A# A# d°->A# D+ D+ D+->d#m F# F# D+->F# D+->A# F#->a#m a#°->a#m a#m->A#

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 1407 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2751
Scale 2751: Sylygic, Ian Ring Music TheorySylygic
3rd mode:
Scale 3423
Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
4th mode:
Scale 3759
Scale 3759: Darygic, Ian Ring Music TheoryDarygic
5th mode:
Scale 3927
Scale 3927: Monygic, Ian Ring Music TheoryMonygic
6th mode:
Scale 4011
Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
7th mode:
Scale 4053
Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
8th mode:
Scale 2037
Scale 2037: Sythygic, Ian Ring Music TheorySythygic
9th mode:
Scale 1533
Scale 1533: Katycrygic, Ian Ring Music TheoryKatycrygic

Prime

This is the prime form of this scale.

Complement

The nonatonic modal family [1407, 2751, 3423, 3759, 3927, 4011, 4053, 2037, 1533] (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 1407 is 4053

Scale 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic

Transformations:

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

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 1405Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic
Scale 1403Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale
Scale 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic
Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic
Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic
Scale 1343Scale 1343: Zalyllic, Ian Ring Music TheoryZalyllic
Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic
Scale 1535Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllian
Scale 1151Scale 1151: Mythyllic, Ian Ring Music TheoryMythyllic
Scale 1279Scale 1279: Sarygic, Ian Ring Music TheorySarygic
Scale 1663Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian
Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic
Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic
Scale 2431Scale 2431: Gythygic, Ian Ring Music TheoryGythygic
Scale 3455Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian

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.