The Exciting Universe Of Music Theory

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Scale 1665

Scale 1665, 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{0,7,9,10}
Forte Number4-10
Rotational Symmetrynone
Reflection Axes3.5
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
prime: 45
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[7]

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 1665 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 45
Scale 45, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 1035
Scale 1035, Ian Ring Music Theory
4th mode:
Scale 2565
Scale 2565, Ian Ring Music Theory


The prime form of this scale is Scale 45

Scale 45Scale 45, Ian Ring Music Theory


The tetratonic modal family [1665, 45, 1035, 2565] (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 1665 is 45

Scale 45Scale 45, Ian Ring Music Theory


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

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 1667Scale 1667, Ian Ring Music Theory
Scale 1669Scale 1669: Raga Matha Kokila, Ian Ring Music TheoryRaga Matha Kokila
Scale 1673Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic
Scale 1681Scale 1681: Raga Valaji, Ian Ring Music TheoryRaga Valaji
Scale 1697Scale 1697: Raga Kuntvarali, Ian Ring Music TheoryRaga Kuntvarali
Scale 1729Scale 1729, Ian Ring Music Theory
Scale 1537Scale 1537, Ian Ring Music Theory
Scale 1601Scale 1601, Ian Ring Music Theory
Scale 1793Scale 1793, Ian Ring Music Theory
Scale 1921Scale 1921, Ian Ring Music Theory
Scale 1153Scale 1153, Ian Ring Music Theory
Scale 1409Scale 1409, Ian Ring Music Theory
Scale 641Scale 641, Ian Ring Music Theory
Scale 2689Scale 2689, Ian Ring Music Theory
Scale 3713Scale 3713, 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.