The Exciting Universe Of Music Theory

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Scale 3745

Scale 3745, 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).


Cardinality6 (hexatonic)
Pitch Class Set{0,5,7,9,10,11}
Forte Number6-9
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 175
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
prime: 175
Deep Scaleno
Interval Vector342231
Interval Spectrump3m2n2s4d3t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,4,6,7}
<3> = {3,4,5,7,8,9}
<4> = {5,6,8,9,10}
<5> = {7,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.866
Myhill Propertyno
Ridge Tonesnone

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsF{5,9,0}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.


Modes are the rotational transformation of this scale. Scale 3745 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 245
Scale 245: Raga Dipak, Ian Ring Music TheoryRaga Dipak
3rd mode:
Scale 1085
Scale 1085, Ian Ring Music Theory
4th mode:
Scale 1295
Scale 1295, Ian Ring Music Theory
5th mode:
Scale 2695
Scale 2695, Ian Ring Music Theory
6th mode:
Scale 3395
Scale 3395, Ian Ring Music Theory


The prime form of this scale is Scale 175

Scale 175Scale 175, Ian Ring Music Theory


The hexatonic modal family [3745, 245, 1085, 1295, 2695, 3395] (Forte: 6-9) is the complement of the hexatonic modal family [175, 1505, 1925, 2135, 3115, 3605] (Forte: 6-9)


The inverse of a scale is a reflection using the root as its axis. The inverse of 3745 is 175

Scale 175Scale 175, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 3745 is chiral, and its enantiomorph is scale 175

Scale 175Scale 175, Ian Ring Music Theory


T0 3745  T0I 175
T1 3395  T1I 350
T2 2695  T2I 700
T3 1295  T3I 1400
T4 2590  T4I 2800
T5 1085  T5I 1505
T6 2170  T6I 3010
T7 245  T7I 1925
T8 490  T8I 3850
T9 980  T9I 3605
T10 1960  T10I 3115
T11 3920  T11I 2135

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 3747Scale 3747: Myrian, Ian Ring Music TheoryMyrian
Scale 3749Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
Scale 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian
Scale 3761Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri
Scale 3713Scale 3713, Ian Ring Music Theory
Scale 3729Scale 3729: Starimic, Ian Ring Music TheoryStarimic
Scale 3777Scale 3777, Ian Ring Music Theory
Scale 3809Scale 3809, Ian Ring Music Theory
Scale 3617Scale 3617, Ian Ring Music Theory
Scale 3681Scale 3681, Ian Ring Music Theory
Scale 3873Scale 3873, Ian Ring Music Theory
Scale 4001Scale 4001, Ian Ring Music Theory
Scale 3233Scale 3233, Ian Ring Music Theory
Scale 3489Scale 3489, Ian Ring Music Theory
Scale 2721Scale 2721: Raga Puruhutika, Ian Ring Music TheoryRaga Puruhutika
Scale 1697Scale 1697: Raga Kuntvarali, Ian Ring Music TheoryRaga Kuntvarali

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.