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Scale 2125

Scale 2125, 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

Cardinality5 (pentatonic)
Pitch Class Set{0,2,3,6,11}
Forte Number5-16
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1603
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?no
prime: 155
Deep Scaleno
Interval Vector213211
Interval Spectrumpm2n3sd2t
Distribution Spectra<1> = {1,2,3,5}
<2> = {3,4,6,8}
<3> = {4,6,8,9}
<4> = {7,9,10,11}
Spectra Variation3.6
Maximally Evenno
Maximal Area Setno
Interior Area1.683
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 TriadsB{11,3,6}210.67
Minor Triadsbm{11,2,6}121
Diminished Triads{0,3,6}121
Parsimonious Voice Leading Between Common Triads of Scale 2125. Created by Ian Ring ©2019 B B c°->B bm bm bm->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.

Diameter2
Radius1
Self-Centeredno
Central VerticesB
Peripheral Verticesc°, bm

Modes

Modes are the rotational transformation of this scale. Scale 2125 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1555
Scale 1555, Ian Ring Music Theory
3rd mode:
Scale 2825
Scale 2825, Ian Ring Music Theory
4th mode:
Scale 865
Scale 865, Ian Ring Music Theory
5th mode:
Scale 155
Scale 155, Ian Ring Music TheoryThis is the prime mode

Prime

The prime form of this scale is Scale 155

Scale 155Scale 155, Ian Ring Music Theory

Complement

The pentatonic modal family [2125, 1555, 2825, 865, 155] (Forte: 5-16) is the complement of the heptatonic modal family [623, 889, 1939, 2359, 3017, 3227, 3661] (Forte: 7-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2125 is 1603

Scale 1603Scale 1603, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2125 is chiral, and its enantiomorph is scale 1603

Scale 1603Scale 1603, Ian Ring Music Theory

Transformations:

T0 2125  T0I 1603
T1 155  T1I 3206
T2 310  T2I 2317
T3 620  T3I 539
T4 1240  T4I 1078
T5 2480  T5I 2156
T6 865  T6I 217
T7 1730  T7I 434
T8 3460  T8I 868
T9 2825  T9I 1736
T10 1555  T10I 3472
T11 3110  T11I 2849

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 2127Scale 2127, Ian Ring Music Theory
Scale 2121Scale 2121, Ian Ring Music Theory
Scale 2123Scale 2123, Ian Ring Music Theory
Scale 2117Scale 2117: Raga Sumukam, Ian Ring Music TheoryRaga Sumukam
Scale 2133Scale 2133: Raga Kumurdaki, Ian Ring Music TheoryRaga Kumurdaki
Scale 2141Scale 2141, Ian Ring Music Theory
Scale 2157Scale 2157, Ian Ring Music Theory
Scale 2061Scale 2061, Ian Ring Music Theory
Scale 2093Scale 2093, Ian Ring Music Theory
Scale 2189Scale 2189: Zagitonic, Ian Ring Music TheoryZagitonic
Scale 2253Scale 2253: Raga Amarasenapriya, Ian Ring Music TheoryRaga Amarasenapriya
Scale 2381Scale 2381: Takemitsu Linea Mode 1, Ian Ring Music TheoryTakemitsu Linea Mode 1
Scale 2637Scale 2637: Raga Ranjani, Ian Ring Music TheoryRaga Ranjani
Scale 3149Scale 3149: Phrycrimic, Ian Ring Music TheoryPhrycrimic
Scale 77Scale 77, Ian Ring Music Theory
Scale 1101Scale 1101: Stothitonic, Ian Ring Music TheoryStothitonic

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.