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Scale 1831: "Pothian"

Scale 1831: Pothian, 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
Pothian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,5,8,9,10}
Forte Number7-Z17
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 631
Deep Scaleno
Interval Vector434541
Interval Spectrump4m5n4s3d4t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,6}
<3> = {4,5,7}
<4> = {5,7,8}
<5> = {6,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tones[10]
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 1831 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2963
Scale 2963: Bygian, Ian Ring Music TheoryBygian
3rd mode:
Scale 3529
Scale 3529: Stalian, Ian Ring Music TheoryStalian
4th mode:
Scale 953
Scale 953: Mela Yagapriya, Ian Ring Music TheoryMela Yagapriya
5th mode:
Scale 631
Scale 631: Zygian, Ian Ring Music TheoryZygianThis is the prime mode
6th mode:
Scale 2363
Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
7th mode:
Scale 3229
Scale 3229: Aeolaptian, Ian Ring Music TheoryAeolaptian

Prime

The prime form of this scale is Scale 631

Scale 631Scale 631: Zygian, Ian Ring Music TheoryZygian

Complement

The heptatonic modal family [1831, 2963, 3529, 953, 631, 2363, 3229] (Forte: 7-Z17) is the complement of the pentatonic modal family [283, 433, 1571, 2189, 2833] (Forte: 5-Z17)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1831 is 3229

Scale 3229Scale 3229: Aeolaptian, Ian Ring Music TheoryAeolaptian

Transformations:

T0 1831  T0I 3229
T1 3662  T1I 2363
T2 3229  T2I 631
T3 2363  T3I 1262
T4 631  T4I 2524
T5 1262  T5I 953
T6 2524  T6I 1906
T7 953  T7I 3812
T8 1906  T8I 3529
T9 3812  T9I 2963
T10 3529  T10I 1831
T11 2963  T11I 3662

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 1829Scale 1829: Pathimic, Ian Ring Music TheoryPathimic
Scale 1827Scale 1827: Katygimic, Ian Ring Music TheoryKatygimic
Scale 1835Scale 1835: Byptian, Ian Ring Music TheoryByptian
Scale 1839Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic
Scale 1847Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic
Scale 1799Scale 1799, Ian Ring Music Theory
Scale 1815Scale 1815: Godian, Ian Ring Music TheoryGodian
Scale 1863Scale 1863: Pycrian, Ian Ring Music TheoryPycrian
Scale 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
Scale 1959Scale 1959: Katolyllic, Ian Ring Music TheoryKatolyllic
Scale 1575Scale 1575: Zycrimic, Ian Ring Music TheoryZycrimic
Scale 1703Scale 1703: Mela Vanaspati, Ian Ring Music TheoryMela Vanaspati
Scale 1319Scale 1319: Phronimic, Ian Ring Music TheoryPhronimic
Scale 807Scale 807: Raga Suddha Mukhari, Ian Ring Music TheoryRaga Suddha Mukhari
Scale 2855Scale 2855: Epocrain, Ian Ring Music TheoryEpocrain
Scale 3879Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.