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Scale 2227: "Raga Gaula"

Scale 2227: Raga Gaula, 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

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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

Carnatic Raga
Raga Gaula
Zeitler
Katadimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,4,5,7,11}
Forte Number6-Z43
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2467
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 359
Deep Scaleno
Interval Vector322332
Interval Spectrump3m3n2s2d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5,6}
<3> = {5,6,7}
<4> = {6,7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.116
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 TriadsC{0,4,7}210.67
Minor Triadsem{4,7,11}121
Diminished Triadsc♯°{1,4,7}121
Parsimonious Voice Leading Between Common Triads of Scale 2227. Created by Ian Ring ©2019 C C c#° c#° C->c#° em em C->em

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
Radius1
Self-Centeredno
Central VerticesC
Peripheral Verticesc♯°, em

Modes

Modes are the rotational transformation of this scale. Scale 2227 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3161
Scale 3161: Kodimic, Ian Ring Music TheoryKodimic
3rd mode:
Scale 907
Scale 907: Tholimic, Ian Ring Music TheoryTholimic
4th mode:
Scale 2501
Scale 2501: Ralimic, Ian Ring Music TheoryRalimic
5th mode:
Scale 1649
Scale 1649: Bolimic, Ian Ring Music TheoryBolimic
6th mode:
Scale 359
Scale 359: Bothimic, Ian Ring Music TheoryBothimicThis is the prime mode

Prime

The prime form of this scale is Scale 359

Scale 359Scale 359: Bothimic, Ian Ring Music TheoryBothimic

Complement

The hexatonic modal family [2227, 3161, 907, 2501, 1649, 359] (Forte: 6-Z43) is the complement of the hexatonic modal family [407, 739, 1817, 2251, 2417, 3173] (Forte: 6-Z17)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2227 is 2467

Scale 2467Scale 2467: Raga Padi, Ian Ring Music TheoryRaga Padi

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2227 is chiral, and its enantiomorph is scale 2467

Scale 2467Scale 2467: Raga Padi, Ian Ring Music TheoryRaga Padi

Transformations:

T0 2227  T0I 2467
T1 359  T1I 839
T2 718  T2I 1678
T3 1436  T3I 3356
T4 2872  T4I 2617
T5 1649  T5I 1139
T6 3298  T6I 2278
T7 2501  T7I 461
T8 907  T8I 922
T9 1814  T9I 1844
T10 3628  T10I 3688
T11 3161  T11I 3281

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 2225Scale 2225: Ionian Pentatonic, Ian Ring Music TheoryIonian Pentatonic
Scale 2229Scale 2229: Raga Nalinakanti, Ian Ring Music TheoryRaga Nalinakanti
Scale 2231Scale 2231: Macrian, Ian Ring Music TheoryMacrian
Scale 2235Scale 2235: Bathian, Ian Ring Music TheoryBathian
Scale 2211Scale 2211: Raga Gauri, Ian Ring Music TheoryRaga Gauri
Scale 2219Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic
Scale 2195Scale 2195: Zalitonic, Ian Ring Music TheoryZalitonic
Scale 2259Scale 2259: Raga Mandari, Ian Ring Music TheoryRaga Mandari
Scale 2291Scale 2291: Zydian, Ian Ring Music TheoryZydian
Scale 2099Scale 2099: Raga Megharanji, Ian Ring Music TheoryRaga Megharanji
Scale 2163Scale 2163, Ian Ring Music Theory
Scale 2355Scale 2355: Raga Lalita, Ian Ring Music TheoryRaga Lalita
Scale 2483Scale 2483: Double Harmonic, Ian Ring Music TheoryDouble Harmonic
Scale 2739Scale 2739: Mela Suryakanta, Ian Ring Music TheoryMela Suryakanta
Scale 3251Scale 3251: Mela Hatakambari, Ian Ring Music TheoryMela Hatakambari
Scale 179Scale 179, Ian Ring Music Theory
Scale 1203Scale 1203: Pagimic, Ian Ring Music TheoryPagimic

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.