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Scale 1829: "Pathimic"

Scale 1829: Pathimic, 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
Pathimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,5,8,9,10}
Forte Number6-Z46
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1181
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 599
Deep Scaleno
Interval Vector233331
Interval Spectrump3m3n3s3d2t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5,6}
<3> = {4,5,7,8}
<4> = {6,7,8,9,10}
<5> = {9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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
Major TriadsF{5,9,0}221.2
A♯{10,2,5}131.6
Minor Triadsdm{2,5,9}321
fm{5,8,0}231.4
Diminished Triads{2,5,8}221.2
Parsimonious Voice Leading Between Common Triads of Scale 1829. Created by Ian Ring ©2019 dm dm d°->dm fm fm d°->fm F F dm->F A# A# dm->A# fm->F

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.

Diameter3
Radius2
Self-Centeredno
Central Verticesd°, dm, F
Peripheral Verticesfm, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1829 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1481
Scale 1481: Zagimic, Ian Ring Music TheoryZagimic
3rd mode:
Scale 697
Scale 697: Lagimic, Ian Ring Music TheoryLagimic
4th mode:
Scale 599
Scale 599: Thyrimic, Ian Ring Music TheoryThyrimicThis is the prime mode
5th mode:
Scale 2347
Scale 2347: Raga Viyogavarali, Ian Ring Music TheoryRaga Viyogavarali
6th mode:
Scale 3221
Scale 3221: Bycrimic, Ian Ring Music TheoryBycrimic

Prime

The prime form of this scale is Scale 599

Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic

Complement

The hexatonic modal family [1829, 1481, 697, 599, 2347, 3221] (Forte: 6-Z46) is the complement of the hexatonic modal family [347, 1457, 1579, 1733, 2221, 2837] (Forte: 6-Z24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1829 is 1181

Scale 1181Scale 1181: Katagimic, Ian Ring Music TheoryKatagimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1829 is chiral, and its enantiomorph is scale 1181

Scale 1181Scale 1181: Katagimic, Ian Ring Music TheoryKatagimic

Transformations:

T0 1829  T0I 1181
T1 3658  T1I 2362
T2 3221  T2I 629
T3 2347  T3I 1258
T4 599  T4I 2516
T5 1198  T5I 937
T6 2396  T6I 1874
T7 697  T7I 3748
T8 1394  T8I 3401
T9 2788  T9I 2707
T10 1481  T10I 1319
T11 2962  T11I 2638

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 1831Scale 1831: Pothian, Ian Ring Music TheoryPothian
Scale 1825Scale 1825, Ian Ring Music Theory
Scale 1827Scale 1827: Katygimic, Ian Ring Music TheoryKatygimic
Scale 1833Scale 1833: Ionacrimic, Ian Ring Music TheoryIonacrimic
Scale 1837Scale 1837: Dalian, Ian Ring Music TheoryDalian
Scale 1845Scale 1845: Lagian, Ian Ring Music TheoryLagian
Scale 1797Scale 1797, Ian Ring Music Theory
Scale 1813Scale 1813: Katothimic, Ian Ring Music TheoryKatothimic
Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
Scale 1893Scale 1893: Ionylian, Ian Ring Music TheoryIonylian
Scale 1957Scale 1957: Pyrian, Ian Ring Music TheoryPyrian
Scale 1573Scale 1573: Raga Guhamanohari, Ian Ring Music TheoryRaga Guhamanohari
Scale 1701Scale 1701: Dominant Seventh, Ian Ring Music TheoryDominant Seventh
Scale 1317Scale 1317: Chaio, Ian Ring Music TheoryChaio
Scale 805Scale 805: Rothitonic, Ian Ring Music TheoryRothitonic
Scale 2853Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian

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.