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Scale 1401: "Pagian"

Scale 1401: Pagian, 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
Pagian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,4,5,6,8,10}
Forte Number7-24
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 981
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 687
Deep Scaleno
Interval Vector353442
Interval Spectrump4m4n3s5d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Modes

Modes are the rotational transformation of this scale. Scale 1401 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 687
Scale 687: Aeolythian, Ian Ring Music TheoryAeolythianThis is the prime mode
3rd mode:
Scale 2391
Scale 2391: Molian, Ian Ring Music TheoryMolian
4th mode:
Scale 3243
Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
5th mode:
Scale 3669
Scale 3669: Mothian, Ian Ring Music TheoryMothian
6th mode:
Scale 1941
Scale 1941: Aeranian, Ian Ring Music TheoryAeranian
7th mode:
Scale 1509
Scale 1509: Ragian, Ian Ring Music TheoryRagian

Prime

The prime form of this scale is Scale 687

Scale 687Scale 687: Aeolythian, Ian Ring Music TheoryAeolythian

Complement

The heptatonic modal family [1401, 687, 2391, 3243, 3669, 1941, 1509] (Forte: 7-24) is the complement of the pentatonic modal family [171, 1377, 1413, 1557, 2133] (Forte: 5-24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1401 is 981

Scale 981Scale 981: Mela Kantamani, Ian Ring Music TheoryMela Kantamani

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1401 is chiral, and its enantiomorph is scale 981

Scale 981Scale 981: Mela Kantamani, Ian Ring Music TheoryMela Kantamani

Transformations:

T0 1401  T0I 981
T1 2802  T1I 1962
T2 1509  T2I 3924
T3 3018  T3I 3753
T4 1941  T4I 3411
T5 3882  T5I 2727
T6 3669  T6I 1359
T7 3243  T7I 2718
T8 2391  T8I 1341
T9 687  T9I 2682
T10 1374  T10I 1269
T11 2748  T11I 2538

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 1403Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale
Scale 1405Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic
Scale 1393Scale 1393: Mycrimic, Ian Ring Music TheoryMycrimic
Scale 1397Scale 1397: Major Locrian, Ian Ring Music TheoryMajor Locrian
Scale 1385Scale 1385: Phracrimic, Ian Ring Music TheoryPhracrimic
Scale 1369Scale 1369: Boptimic, Ian Ring Music TheoryBoptimic
Scale 1337Scale 1337: Epogimic, Ian Ring Music TheoryEpogimic
Scale 1465Scale 1465: Mela Ragavardhani, Ian Ring Music TheoryMela Ragavardhani
Scale 1529Scale 1529: Kataryllic, Ian Ring Music TheoryKataryllic
Scale 1145Scale 1145: Zygimic, Ian Ring Music TheoryZygimic
Scale 1273Scale 1273: Ronian, Ian Ring Music TheoryRonian
Scale 1657Scale 1657: Ionothian, Ian Ring Music TheoryIonothian
Scale 1913Scale 1913, Ian Ring Music Theory
Scale 377Scale 377: Kathimic, Ian Ring Music TheoryKathimic
Scale 889Scale 889: Borian, Ian Ring Music TheoryBorian
Scale 2425Scale 2425: Rorian, Ian Ring Music TheoryRorian
Scale 3449Scale 3449: Bacryllic, Ian Ring Music TheoryBacryllic

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.