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Scale 3649

Scale 3649, 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

Cardinality5 (pentatonic)
Pitch Class Set{0,6,9,10,11}
Forte Number5-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 79
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes4
Prime?no
prime: 79
Deep Scaleno
Interval Vector322111
Interval Spectrumpmn2s2d3t
Distribution Spectra<1> = {1,3,6}
<2> = {2,4,7,9}
<3> = {3,5,8,10}
<4> = {6,9,11}
Spectra Variation4.8
Maximally Evenno
Maximal Area Setno
Interior Area1.25
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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
Diminished Triadsf♯°{6,9,0}000

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

Modes

Modes are the rotational transformation of this scale. Scale 3649 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 121
Scale 121, Ian Ring Music Theory
3rd mode:
Scale 527
Scale 527, Ian Ring Music Theory
4th mode:
Scale 2311
Scale 2311: Raga Kumarapriya, Ian Ring Music TheoryRaga Kumarapriya
5th mode:
Scale 3203
Scale 3203, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 79

Scale 79Scale 79, Ian Ring Music Theory

Complement

The pentatonic modal family [3649, 121, 527, 2311, 3203] (Forte: 5-4) is the complement of the heptatonic modal family [223, 1987, 2159, 3041, 3127, 3611, 3853] (Forte: 7-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3649 is 79

Scale 79Scale 79, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3649 is chiral, and its enantiomorph is scale 79

Scale 79Scale 79, Ian Ring Music Theory

Transformations:

T0 3649  T0I 79
T1 3203  T1I 158
T2 2311  T2I 316
T3 527  T3I 632
T4 1054  T4I 1264
T5 2108  T5I 2528
T6 121  T6I 961
T7 242  T7I 1922
T8 484  T8I 3844
T9 968  T9I 3593
T10 1936  T10I 3091
T11 3872  T11I 2087

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 3651Scale 3651, Ian Ring Music Theory
Scale 3653Scale 3653: Sathimic, Ian Ring Music TheorySathimic
Scale 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
Scale 3665Scale 3665: Stalimic, Ian Ring Music TheoryStalimic
Scale 3681Scale 3681, Ian Ring Music Theory
Scale 3585Scale 3585, Ian Ring Music Theory
Scale 3617Scale 3617, Ian Ring Music Theory
Scale 3713Scale 3713, Ian Ring Music Theory
Scale 3777Scale 3777, Ian Ring Music Theory
Scale 3905Scale 3905, Ian Ring Music Theory
Scale 3137Scale 3137, Ian Ring Music Theory
Scale 3393Scale 3393, Ian Ring Music Theory
Scale 2625Scale 2625, Ian Ring Music Theory
Scale 1601Scale 1601, 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.