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Scale 1609: "Thyritonic"

Scale 1609: Thyritonic, 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
Thyritonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,3,6,9,10}
Forte Number5-31
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 589
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?no
prime: 587
Deep Scaleno
Interval Vector114112
Interval Spectrumpmn4sdt2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5,6}
<3> = {6,7,8,9}
<4> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.183
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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}221.2
Diminished Triads{0,3,6}221.2
d♯°{3,6,9}221.2
f♯°{6,9,0}221.2
{9,0,3}221.2
Parsimonious Voice Leading Between Common Triads of Scale 1609. Created by Ian Ring ©2019 d#m d#m c°->d#m c°->a° d#° d#° d#°->d#m f#° f#° d#°->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.

Diameter2
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1609 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 713
Scale 713: Thoptitonic, Ian Ring Music TheoryThoptitonic
3rd mode:
Scale 601
Scale 601: Bycritonic, Ian Ring Music TheoryBycritonic
4th mode:
Scale 587
Scale 587: Pathitonic, Ian Ring Music TheoryPathitonicThis is the prime mode
5th mode:
Scale 2341
Scale 2341: Raga Priyadharshini, Ian Ring Music TheoryRaga Priyadharshini

Prime

The prime form of this scale is Scale 587

Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic

Complement

The pentatonic modal family [1609, 713, 601, 587, 2341] (Forte: 5-31) is the complement of the heptatonic modal family [731, 1627, 1739, 1753, 2413, 2861, 2917] (Forte: 7-31)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1609 is 589

Scale 589Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1609 is chiral, and its enantiomorph is scale 589

Scale 589Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic

Transformations:

T0 1609  T0I 589
T1 3218  T1I 1178
T2 2341  T2I 2356
T3 587  T3I 617
T4 1174  T4I 1234
T5 2348  T5I 2468
T6 601  T6I 841
T7 1202  T7I 1682
T8 2404  T8I 3364
T9 713  T9I 2633
T10 1426  T10I 1171
T11 2852  T11I 2342

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 1611Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic
Scale 1613Scale 1613: Thylimic, Ian Ring Music TheoryThylimic
Scale 1601Scale 1601, Ian Ring Music Theory
Scale 1605Scale 1605: Zanitonic, Ian Ring Music TheoryZanitonic
Scale 1617Scale 1617: Phronitonic, Ian Ring Music TheoryPhronitonic
Scale 1625Scale 1625: Lythimic, Ian Ring Music TheoryLythimic
Scale 1641Scale 1641: Bocrimic, Ian Ring Music TheoryBocrimic
Scale 1545Scale 1545, Ian Ring Music Theory
Scale 1577Scale 1577: Raga Chandrakauns (Kafi), Ian Ring Music TheoryRaga Chandrakauns (Kafi)
Scale 1673Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic
Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns
Scale 1865Scale 1865: Thagimic, Ian Ring Music TheoryThagimic
Scale 1097Scale 1097: Aeraphic, Ian Ring Music TheoryAeraphic
Scale 1353Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
Scale 585Scale 585: Diminished Seventh, Ian Ring Music TheoryDiminished Seventh
Scale 2633Scale 2633: Bartók Beta Chord, Ian Ring Music TheoryBartók Beta Chord
Scale 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic

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.