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Scale 3127

Scale 3127, 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).

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,5,10,11}
Forte Number7-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3463
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 223
Deep Scaleno
Interval Vector544332
Interval Spectrump3m3n4s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7,8}
<4> = {4,5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.714
Maximally Evenno
Maximal Area Setno
Interior Area1.933
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsA♯{10,2,5}221
Minor Triadsa♯m{10,1,5}221
Diminished Triadsa♯°{10,1,4}131.5
{11,2,5}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3127. Created by Ian Ring ©2019 a#° a#° a#m a#m a#°->a#m A# A# a#m->A# A#->b°

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 Verticesa♯m, A♯
Peripheral Verticesa♯°, b°

Modes

Modes are the rotational transformation of this scale. Scale 3127 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3611
Scale 3611, Ian Ring Music Theory
3rd mode:
Scale 3853
Scale 3853, Ian Ring Music Theory
4th mode:
Scale 1987
Scale 1987, Ian Ring Music Theory
5th mode:
Scale 3041
Scale 3041, Ian Ring Music Theory
6th mode:
Scale 223
Scale 223, Ian Ring Music TheoryThis is the prime mode
7th mode:
Scale 2159
Scale 2159, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 223

Scale 223Scale 223, Ian Ring Music Theory

Complement

The heptatonic modal family [3127, 3611, 3853, 1987, 3041, 223, 2159] (Forte: 7-4) is the complement of the pentatonic modal family [79, 961, 2087, 3091, 3593] (Forte: 5-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3127 is 3463

Scale 3463Scale 3463, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3127 is chiral, and its enantiomorph is scale 3463

Scale 3463Scale 3463, Ian Ring Music Theory

Transformations:

T0 3127  T0I 3463
T1 2159  T1I 2831
T2 223  T2I 1567
T3 446  T3I 3134
T4 892  T4I 2173
T5 1784  T5I 251
T6 3568  T6I 502
T7 3041  T7I 1004
T8 1987  T8I 2008
T9 3974  T9I 4016
T10 3853  T10I 3937
T11 3611  T11I 3779

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 3125Scale 3125, Ian Ring Music Theory
Scale 3123Scale 3123, Ian Ring Music Theory
Scale 3131Scale 3131, Ian Ring Music Theory
Scale 3135Scale 3135, Ian Ring Music Theory
Scale 3111Scale 3111, Ian Ring Music Theory
Scale 3119Scale 3119, Ian Ring Music Theory
Scale 3095Scale 3095, Ian Ring Music Theory
Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
Scale 3191Scale 3191: Bynyllic, Ian Ring Music TheoryBynyllic
Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
Scale 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
Scale 3639Scale 3639: Paptyllic, Ian Ring Music TheoryPaptyllic
Scale 2103Scale 2103, Ian Ring Music Theory
Scale 2615Scale 2615: Thoptian, Ian Ring Music TheoryThoptian
Scale 1079Scale 1079, Ian Ring Music Theory

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.