The Exciting Universe Of Music Theory

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Scale 1729

Scale 1729, 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).


Cardinality5 (pentatonic)
Pitch Class Set{0,6,7,9,10}
Forte Number5-10
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 109
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
prime: 91
Deep Scaleno
Interval Vector223111
Interval Spectrumpmn3s2d2t
Distribution Spectra<1> = {1,2,6}
<2> = {3,7,8}
<3> = {4,5,9}
<4> = {6,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.366
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
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 are the rotational transformation of this scale. Scale 1729 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 91
Scale 91, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2093
Scale 2093, Ian Ring Music Theory
4th mode:
Scale 1547
Scale 1547, Ian Ring Music Theory
5th mode:
Scale 2821
Scale 2821, Ian Ring Music Theory


The prime form of this scale is Scale 91

Scale 91Scale 91, Ian Ring Music Theory


The pentatonic modal family [1729, 91, 2093, 1547, 2821] (Forte: 5-10) is the complement of the heptatonic modal family [607, 761, 1993, 2351, 3223, 3659, 3877] (Forte: 7-10)


The inverse of a scale is a reflection using the root as its axis. The inverse of 1729 is 109

Scale 109Scale 109, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 1729 is chiral, and its enantiomorph is scale 109

Scale 109Scale 109, Ian Ring Music Theory


T0 1729  T0I 109
T1 3458  T1I 218
T2 2821  T2I 436
T3 1547  T3I 872
T4 3094  T4I 1744
T5 2093  T5I 3488
T6 91  T6I 2881
T7 182  T7I 1667
T8 364  T8I 3334
T9 728  T9I 2573
T10 1456  T10I 1051
T11 2912  T11I 2102

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 1731Scale 1731, Ian Ring Music Theory
Scale 1733Scale 1733: Raga Sarasvati, Ian Ring Music TheoryRaga Sarasvati
Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns
Scale 1745Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
Scale 1761Scale 1761, Ian Ring Music Theory
Scale 1665Scale 1665, Ian Ring Music Theory
Scale 1697Scale 1697: Raga Kuntvarali, Ian Ring Music TheoryRaga Kuntvarali
Scale 1601Scale 1601, Ian Ring Music Theory
Scale 1857Scale 1857, Ian Ring Music Theory
Scale 1985Scale 1985, Ian Ring Music Theory
Scale 1217Scale 1217, Ian Ring Music Theory
Scale 1473Scale 1473, Ian Ring Music Theory
Scale 705Scale 705, Ian Ring Music Theory
Scale 2753Scale 2753, Ian Ring Music Theory
Scale 3777Scale 3777, 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.