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Scale 2025

Scale 2025, 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).

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,3,5,6,7,8,9,10}
Forte Number8-10
Rotational Symmetrynone
Reflection Axes1.5
Palindromicno
Chiralityno
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 765
Deep Scaleno
Interval Vector566452
Interval Spectrump5m4n6s6d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {7,9,10}
<7> = {9,10,11}
Spectra Variation2.75
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tones[3]
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 TriadsD♯{3,7,10}242.1
F{5,9,0}342.1
G♯{8,0,3}341.9
Minor Triadscm{0,3,7}341.9
d♯m{3,6,10}342.1
fm{5,8,0}242.1
Diminished Triads{0,3,6}242.1
d♯°{3,6,9}242.1
f♯°{6,9,0}242.1
{9,0,3}242.1
Parsimonious Voice Leading Between Common Triads of Scale 2025. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# G# G# cm->G# d#° d#° d#°->d#m f#° f#° d#°->f#° d#m->D# fm fm F F fm->F fm->G# F->f#° F->a° G#->a°

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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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2025 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 765
Scale 765, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 1215
Scale 1215, Ian Ring Music Theory
4th mode:
Scale 2655
Scale 2655, Ian Ring Music Theory
5th mode:
Scale 3375
Scale 3375, Ian Ring Music Theory
6th mode:
Scale 3735
Scale 3735, Ian Ring Music Theory
7th mode:
Scale 3915
Scale 3915, Ian Ring Music Theory
8th mode:
Scale 4005
Scale 4005, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 765

Scale 765Scale 765, Ian Ring Music Theory

Complement

The octatonic modal family [2025, 765, 1215, 2655, 3375, 3735, 3915, 4005] (Forte: 8-10) is the complement of the tetratonic modal family [45, 1035, 1665, 2565] (Forte: 4-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2025 is 765

Scale 765Scale 765, Ian Ring Music Theory

Transformations:

T0 2025  T0I 765
T1 4050  T1I 1530
T2 4005  T2I 3060
T3 3915  T3I 2025
T4 3735  T4I 4050
T5 3375  T5I 4005
T6 2655  T6I 3915
T7 1215  T7I 3735
T8 2430  T8I 3375
T9 765  T9I 2655
T10 1530  T10I 1215
T11 3060  T11I 2430

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 2027Scale 2027: Boptygic, Ian Ring Music TheoryBoptygic
Scale 2029Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
Scale 2017Scale 2017, Ian Ring Music Theory
Scale 2021Scale 2021: Katycryllic, Ian Ring Music TheoryKatycryllic
Scale 2033Scale 2033: Stolyllic, Ian Ring Music TheoryStolyllic
Scale 2041Scale 2041: Aeolacrygic, Ian Ring Music TheoryAeolacrygic
Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
Scale 1961Scale 1961: Soptian, Ian Ring Music TheorySoptian
Scale 1897Scale 1897: Ionopian, Ian Ring Music TheoryIonopian
Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
Scale 1513Scale 1513: Stathian, Ian Ring Music TheoryStathian
Scale 1001Scale 1001: Badian, Ian Ring Music TheoryBadian
Scale 3049Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
Scale 4073Scale 4073: Sathygic, Ian Ring Music TheorySathygic

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.