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Scale 2701: "Hawaiian"

Scale 2701: Hawaiian, 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

Exoticisms
Hawaiian
Zeitler
Epythimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,7,9,11}
Forte Number6-Z24
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1579
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes5
Prime?no
prime: 347
Deep Scaleno
Interval Vector233331
Interval Spectrump3m3n3s3d2t
Distribution Spectra<1> = {1,2,4}
<2> = {3,4,5,6}
<3> = {4,5,7,8}
<4> = {6,7,8,9}
<5> = {8,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.232
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 TriadsG{7,11,2}131.5
Minor Triadscm{0,3,7}221
Augmented TriadsD♯+{3,7,11}221
Diminished Triads{9,0,3}131.5
Parsimonious Voice Leading Between Common Triads of Scale 2701. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ cm->a° Parsimonious Voice Leading Between Common Triads of Scale 2701. Created by Ian Ring ©2019 G D#+->G

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 Verticescm, D♯+
Peripheral VerticesG, a°

Modes

Modes are the rotational transformation of this scale. Scale 2701 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1699
Scale 1699: Raga Rasavali, Ian Ring Music TheoryRaga Rasavali
3rd mode:
Scale 2897
Scale 2897: Rycrimic, Ian Ring Music TheoryRycrimic
4th mode:
Scale 437
Scale 437: Ronimic, Ian Ring Music TheoryRonimic
5th mode:
Scale 1133
Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
6th mode:
Scale 1307
Scale 1307: Katorimic, Ian Ring Music TheoryKatorimic

Prime

The prime form of this scale is Scale 347

Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic

Complement

The hexatonic modal family [2701, 1699, 2897, 437, 1133, 1307] (Forte: 6-Z24) is the complement of the hexatonic modal family [599, 697, 1481, 1829, 2347, 3221] (Forte: 6-Z46)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2701 is 1579

Scale 1579Scale 1579: Sagimic, Ian Ring Music TheorySagimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2701 is chiral, and its enantiomorph is scale 1579

Scale 1579Scale 1579: Sagimic, Ian Ring Music TheorySagimic

Transformations:

T0 2701  T0I 1579
T1 1307  T1I 3158
T2 2614  T2I 2221
T3 1133  T3I 347
T4 2266  T4I 694
T5 437  T5I 1388
T6 874  T6I 2776
T7 1748  T7I 1457
T8 3496  T8I 2914
T9 2897  T9I 1733
T10 1699  T10I 3466
T11 3398  T11I 2837

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 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 2697Scale 2697: Katagitonic, Ian Ring Music TheoryKatagitonic
Scale 2699Scale 2699: Sythimic, Ian Ring Music TheorySythimic
Scale 2693Scale 2693, Ian Ring Music Theory
Scale 2709Scale 2709: Raga Kumud, Ian Ring Music TheoryRaga Kumud
Scale 2717Scale 2717: Epygian, Ian Ring Music TheoryEpygian
Scale 2733Scale 2733: Melodic Minor Ascending, Ian Ring Music TheoryMelodic Minor Ascending
Scale 2765Scale 2765: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 2573Scale 2573, Ian Ring Music Theory
Scale 2637Scale 2637: Raga Ranjani, Ian Ring Music TheoryRaga Ranjani
Scale 2829Scale 2829, Ian Ring Music Theory
Scale 2957Scale 2957: Thygian, Ian Ring Music TheoryThygian
Scale 2189Scale 2189: Zagitonic, Ian Ring Music TheoryZagitonic
Scale 2445Scale 2445: Zadimic, Ian Ring Music TheoryZadimic
Scale 3213Scale 3213: Eponimic, Ian Ring Music TheoryEponimic
Scale 3725Scale 3725: Kyrian, Ian Ring Music TheoryKyrian
Scale 653Scale 653: Dorian Pentatonic, Ian Ring Music TheoryDorian Pentatonic
Scale 1677Scale 1677: Raga Manavi, Ian Ring Music TheoryRaga Manavi

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.