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Scale 421: "Han-kumoi"

Scale 421: Han-kumoi, 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

Unknown / Unsorted
Han-kumoi
Sutradhari
Carnatic Raga
Raga Shobhavari
Exoticisms
Japanese (b)
Zeitler
Ionitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,2,5,7,8}
Forte Number5-29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1201
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections2
Modes4
Prime?no
prime: 331
Deep Scaleno
Interval Vector122131
Interval Spectrump3mn2s2dt
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,5,6}
<3> = {6,7,9}
<4> = {8,9,10,11}
Spectra Variation2.4
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 421 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1129
Scale 1129: Raga Jayakauns, Ian Ring Music TheoryRaga Jayakauns
3rd mode:
Scale 653
Scale 653: Dorian Pentatonic, Ian Ring Music TheoryDorian Pentatonic
4th mode:
Scale 1187
Scale 1187: Kokin-joshi, Ian Ring Music TheoryKokin-joshi
5th mode:
Scale 2641
Scale 2641: Raga Hindol, Ian Ring Music TheoryRaga Hindol

Prime

The prime form of this scale is Scale 331

Scale 331Scale 331: Raga Chhaya Todi, Ian Ring Music TheoryRaga Chhaya Todi

Complement

The pentatonic modal family [421, 1129, 653, 1187, 2641] (Forte: 5-29) is the complement of the heptatonic modal family [727, 1483, 1721, 1837, 2411, 2789, 3253] (Forte: 7-29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 421 is 1201

Scale 1201Scale 1201: Mixolydian Pentatonic, Ian Ring Music TheoryMixolydian Pentatonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 421 is chiral, and its enantiomorph is scale 1201

Scale 1201Scale 1201: Mixolydian Pentatonic, Ian Ring Music TheoryMixolydian Pentatonic

Transformations:

T0 421  T0I 1201
T1 842  T1I 2402
T2 1684  T2I 709
T3 3368  T3I 1418
T4 2641  T4I 2836
T5 1187  T5I 1577
T6 2374  T6I 3154
T7 653  T7I 2213
T8 1306  T8I 331
T9 2612  T9I 662
T10 1129  T10I 1324
T11 2258  T11I 2648

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 423Scale 423: Sogimic, Ian Ring Music TheorySogimic
Scale 417Scale 417, Ian Ring Music Theory
Scale 419Scale 419: Hon-kumoi-joshi, Ian Ring Music TheoryHon-kumoi-joshi
Scale 425Scale 425: Raga Kokil Pancham, Ian Ring Music TheoryRaga Kokil Pancham
Scale 429Scale 429: Koptimic, Ian Ring Music TheoryKoptimic
Scale 437Scale 437: Ronimic, Ian Ring Music TheoryRonimic
Scale 389Scale 389, Ian Ring Music Theory
Scale 405Scale 405: Raga Bhupeshwari, Ian Ring Music TheoryRaga Bhupeshwari
Scale 453Scale 453: Raditonic, Ian Ring Music TheoryRaditonic
Scale 485Scale 485: Stoptimic, Ian Ring Music TheoryStoptimic
Scale 293Scale 293: Raga Haripriya, Ian Ring Music TheoryRaga Haripriya
Scale 357Scale 357: Banitonic, Ian Ring Music TheoryBanitonic
Scale 165Scale 165: Genus Primum, Ian Ring Music TheoryGenus Primum
Scale 677Scale 677: Scottish Pentatonic, Ian Ring Music TheoryScottish Pentatonic
Scale 933Scale 933: Dadimic, Ian Ring Music TheoryDadimic
Scale 1445Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari
Scale 2469Scale 2469: Raga Bhinna Pancama, Ian Ring Music TheoryRaga Bhinna Pancama

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.