The Exciting Universe Of Music Theory

more than you ever wanted to know about...

Scale 1045

Scale 1045, 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{0,2,4,10}
Forte Number4-21
Rotational Symmetrynone
Reflection Axes1
Hemitonia0 (anhemitonic)
Cohemitonia0 (ancohemitonic)
prime: 85
Deep Scaleno
Interval Vector030201
Interval Spectrumm2s3t
Distribution Spectra<1> = {2,6}
<2> = {4,8}
<3> = {6,10}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area1.299
Myhill Propertyyes
Ridge Tones[2]

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 1045 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 1285
Scale 1285, Ian Ring Music Theory
3rd mode:
Scale 1345
Scale 1345, Ian Ring Music Theory
4th mode:
Scale 85
Scale 85, Ian Ring Music TheoryThis is the prime mode


The prime form of this scale is Scale 85

Scale 85Scale 85, Ian Ring Music Theory


The tetratonic modal family [1045, 1285, 1345, 85] (Forte: 4-21) is the complement of the octatonic modal family [1375, 1405, 1525, 2005, 2735, 3415, 3755, 3925] (Forte: 8-21)


The inverse of a scale is a reflection using the root as its axis. The inverse of 1045 is 1285

Scale 1285Scale 1285, Ian Ring Music Theory


T0 1045  T0I 1285
T1 2090  T1I 2570
T2 85  T2I 1045
T3 170  T3I 2090
T4 340  T4I 85
T5 680  T5I 170
T6 1360  T6I 340
T7 2720  T7I 680
T8 1345  T8I 1360
T9 2690  T9I 2720
T10 1285  T10I 1345
T11 2570  T11I 2690

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 1047Scale 1047, Ian Ring Music Theory
Scale 1041Scale 1041, Ian Ring Music Theory
Scale 1043Scale 1043, Ian Ring Music Theory
Scale 1049Scale 1049, Ian Ring Music Theory
Scale 1053Scale 1053, Ian Ring Music Theory
Scale 1029Scale 1029, Ian Ring Music Theory
Scale 1037Scale 1037: Warao Tetratonic, Ian Ring Music TheoryWarao Tetratonic
Scale 1061Scale 1061, Ian Ring Music Theory
Scale 1077Scale 1077, Ian Ring Music Theory
Scale 1109Scale 1109: Kataditonic, Ian Ring Music TheoryKataditonic
Scale 1173Scale 1173: Dominant Pentatonic, Ian Ring Music TheoryDominant Pentatonic
Scale 1301Scale 1301: Koditonic, Ian Ring Music TheoryKoditonic
Scale 1557Scale 1557, Ian Ring Music Theory
Scale 21Scale 21, Ian Ring Music Theory
Scale 533Scale 533, Ian Ring Music Theory
Scale 2069Scale 2069, Ian Ring Music Theory
Scale 3093Scale 3093, 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. Special thanks to Richard Repp for helping with technical accuracy.