The Exciting Universe Of Music Theory

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Scale 45

Scale 45, 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

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).


Cardinality4 (tetratonic)
Pitch Class Set{0,2,3,5}
Forte Number4-10
Rotational Symmetrynone
Reflection Axes2.5
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Deep Scaleno
Interval Vector122010
Interval Spectrumpn2s2d
Distribution Spectra<1> = {1,2,7}
<2> = {3,9}
<3> = {5,10,11}
Spectra Variation4.5
Maximally Evenno
Maximal Area Setno
Interior Area0.866
Myhill Propertyno
Ridge Tones[5]

Common Triads

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


Modes are the rotational transformation of this scale. Scale 45 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 1035
Scale 1035, Ian Ring Music Theory
3rd mode:
Scale 2565
Scale 2565, Ian Ring Music Theory
4th mode:
Scale 1665
Scale 1665, Ian Ring Music Theory


This is the prime form of this scale.


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


The inverse of a scale is a reflection using the root as its axis. The inverse of 45 is 1665

Scale 1665Scale 1665, Ian Ring Music Theory


T0 45  T0I 1665
T1 90  T1I 3330
T2 180  T2I 2565
T3 360  T3I 1035
T4 720  T4I 2070
T5 1440  T5I 45
T6 2880  T6I 90
T7 1665  T7I 180
T8 3330  T8I 360
T9 2565  T9I 720
T10 1035  T10I 1440
T11 2070  T11I 2880

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 47Scale 47, Ian Ring Music Theory
Scale 41Scale 41: Vietnamese Tritonic, Ian Ring Music TheoryVietnamese Tritonic
Scale 43Scale 43, Ian Ring Music Theory
Scale 37Scale 37, Ian Ring Music Theory
Scale 53Scale 53, Ian Ring Music Theory
Scale 61Scale 61, Ian Ring Music Theory
Scale 13Scale 13, Ian Ring Music Theory
Scale 29Scale 29, Ian Ring Music Theory
Scale 77Scale 77, Ian Ring Music Theory
Scale 109Scale 109, Ian Ring Music Theory
Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita
Scale 301Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav Tukhari
Scale 557Scale 557: Raga Abhogi, Ian Ring Music TheoryRaga Abhogi
Scale 1069Scale 1069, Ian Ring Music Theory
Scale 2093Scale 2093, 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 ( 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.