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Scale 587: "Pathitonic"

Scale 587: Pathitonic, 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
Pathitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,1,3,6,9}
Forte Number5-31
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2633
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?yes
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 Triadsf♯m{6,9,1}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 587. Created by Ian Ring ©2019 d#° d#° c°->d#° c°->a° f#m f#m d#°->f#m f#° f#° f#°->f#m 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 587 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2341
Scale 2341: Raga Priyadharshini, Ian Ring Music TheoryRaga Priyadharshini
3rd mode:
Scale 1609
Scale 1609: Thyritonic, Ian Ring Music TheoryThyritonic
4th mode:
Scale 713
Scale 713: Thoptitonic, Ian Ring Music TheoryThoptitonic
5th mode:
Scale 601
Scale 601: Bycritonic, Ian Ring Music TheoryBycritonic

Prime

This is the prime form of this scale.

Complement

The pentatonic modal family [587, 2341, 1609, 713, 601] (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 587 is 2633

Scale 2633Scale 2633: Bartók Beta Chord, Ian Ring Music TheoryBartók Beta Chord

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 587 is chiral, and its enantiomorph is scale 2633

Scale 2633Scale 2633: Bartók Beta Chord, Ian Ring Music TheoryBartók Beta Chord

Transformations:

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

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 585Scale 585: Diminished Seventh, Ian Ring Music TheoryDiminished Seventh
Scale 589Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic
Scale 591Scale 591: Gaptimic, Ian Ring Music TheoryGaptimic
Scale 579Scale 579, Ian Ring Music Theory
Scale 583Scale 583: Aeritonic, Ian Ring Music TheoryAeritonic
Scale 595Scale 595: Sogitonic, Ian Ring Music TheorySogitonic
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 619Scale 619: Double-Phrygian Hexatonic, Ian Ring Music TheoryDouble-Phrygian Hexatonic
Scale 523Scale 523, Ian Ring Music Theory
Scale 555Scale 555: Aeolycritonic, Ian Ring Music TheoryAeolycritonic
Scale 651Scale 651: Golitonic, Ian Ring Music TheoryGolitonic
Scale 715Scale 715: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2
Scale 843Scale 843: Molimic, Ian Ring Music TheoryMolimic
Scale 75Scale 75, Ian Ring Music Theory
Scale 331Scale 331: Raga Chhaya Todi, Ian Ring Music TheoryRaga Chhaya Todi
Scale 1099Scale 1099: Dyritonic, Ian Ring Music TheoryDyritonic
Scale 1611Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic
Scale 2635Scale 2635: Gocrimic, Ian Ring Music TheoryGocrimic

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.