The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 261

Scale 261, 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

Cardinality3 (tritonic)
Pitch Class Set{0,2,8}
Forte Number3-8
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1041
Hemitonia0 (anhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes2
Prime?no
prime: 69
Deep Scaleno
Interval Vector010101
Interval Spectrummst
Distribution Spectra<1> = {2,4,6}
<2> = {6,8,10}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area0.866
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
Heliotonicno

Common Triads

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.

Modes

Modes are the rotational transformation of this scale. Scale 261 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 1089
Scale 1089, Ian Ring Music Theory
3rd mode:
Scale 81
Scale 81, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 69

Scale 69Scale 69, Ian Ring Music Theory

Complement

The tritonic modal family [261, 1089, 81] (Forte: 3-8) is the complement of the nonatonic modal family [1503, 1917, 2007, 2799, 3051, 3447, 3573, 3771, 3933] (Forte: 9-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 261 is 1041

Scale 1041Scale 1041, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 261 is chiral, and its enantiomorph is scale 1041

Scale 1041Scale 1041, Ian Ring Music Theory

Transformations:

T0 261  T0I 1041
T1 522  T1I 2082
T2 1044  T2I 69
T3 2088  T3I 138
T4 81  T4I 276
T5 162  T5I 552
T6 324  T6I 1104
T7 648  T7I 2208
T8 1296  T8I 321
T9 2592  T9I 642
T10 1089  T10I 1284
T11 2178  T11I 2568

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 263Scale 263, Ian Ring Music Theory
Scale 257Scale 257, Ian Ring Music Theory
Scale 259Scale 259, Ian Ring Music Theory
Scale 265Scale 265, Ian Ring Music Theory
Scale 269Scale 269, Ian Ring Music Theory
Scale 277Scale 277: Mixolyric, Ian Ring Music TheoryMixolyric
Scale 293Scale 293: Raga Haripriya, Ian Ring Music TheoryRaga Haripriya
Scale 325Scale 325: Messiaen Truncated Mode 6, Ian Ring Music TheoryMessiaen Truncated Mode 6
Scale 389Scale 389, Ian Ring Music Theory
Scale 5Scale 5: Vietnamese ditonic, Ian Ring Music TheoryVietnamese ditonic
Scale 133Scale 133, Ian Ring Music Theory
Scale 517Scale 517, Ian Ring Music Theory
Scale 773Scale 773, Ian Ring Music Theory
Scale 1285Scale 1285, Ian Ring Music Theory
Scale 2309Scale 2309, 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.

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.