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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

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

Exoticisms
Hawaiian
Zeitler
Epythimic

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

6 (hexatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,3,7,9,11}

Forte Number

A code assigned by theorist Alan Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

6-Z24

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 1579

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

2 (dihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

0 (ancohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

3

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

5

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 347

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

[2, 3, 3, 3, 3, 1]

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hansen.

p3m3n3s3d2t

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<1> = {1,2,4}
<2> = {3,4,5,6}
<3> = {4,5,7,8}
<4> = {6,7,8,9}
<5> = {8,10,11}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2.667

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.232

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

5.767

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

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 Flat 3, Ian Ring Music TheoryLydian Flat 3
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.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.