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Scale 225

Scale 225, 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

Cardinality4 (tetratonic)
Pitch Class Set{0,5,6,7}
Forte Number4-6
Rotational Symmetrynone
Reflection Axes0
Palindromicyes
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections2
Modes3
Prime?no
prime: 135
Deep Scaleno
Interval Vector210021
Interval Spectrump2sd2t
Distribution Spectra<1> = {1,5}
<2> = {2,6,10}
<3> = {7,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1
Myhill Propertyno
Balancedno
Ridge Tones[0]
ProprietyImproper
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 225 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 135
Scale 135, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2115
Scale 2115, Ian Ring Music Theory
4th mode:
Scale 3105
Scale 3105, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 135

Scale 135Scale 135, Ian Ring Music Theory

Complement

The tetratonic modal family [225, 135, 2115, 3105] (Forte: 4-6) is the complement of the octatonic modal family [495, 1935, 2295, 3015, 3195, 3555, 3645, 3825] (Forte: 8-6)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 225 is itself, because it is a palindromic scale!

Scale 225Scale 225, Ian Ring Music Theory

Transformations:

T0 225  T0I 225
T1 450  T1I 450
T2 900  T2I 900
T3 1800  T3I 1800
T4 3600  T4I 3600
T5 3105  T5I 3105
T6 2115  T6I 2115
T7 135  T7I 135
T8 270  T8I 270
T9 540  T9I 540
T10 1080  T10I 1080
T11 2160  T11I 2160

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 227Scale 227, Ian Ring Music Theory
Scale 229Scale 229, Ian Ring Music Theory
Scale 233Scale 233, Ian Ring Music Theory
Scale 241Scale 241, Ian Ring Music Theory
Scale 193Scale 193: Raga Ongkari, Ian Ring Music TheoryRaga Ongkari
Scale 209Scale 209, Ian Ring Music Theory
Scale 161Scale 161: Raga Sarvasri, Ian Ring Music TheoryRaga Sarvasri
Scale 97Scale 97, Ian Ring Music Theory
Scale 353Scale 353, Ian Ring Music Theory
Scale 481Scale 481, Ian Ring Music Theory
Scale 737Scale 737, Ian Ring Music Theory
Scale 1249Scale 1249, Ian Ring Music Theory
Scale 2273Scale 2273, 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.