The Exciting Universe Of Music Theory

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Scale 1859

Scale 1859, 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{0,1,6,8,9,10}
Forte Number6-Z10
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 2141
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
prime: 187
Deep Scaleno
Interval Vector333321
Interval Spectrump2m3n3s3d3t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6,7}
<3> = {4,8}
<4> = {5,6,9,10}
<5> = {7,10,11}
Spectra Variation3.667
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♯{6,10,1}121
Minor Triadsf♯m{6,9,1}210.67
Diminished Triadsf♯°{6,9,0}121
Parsimonious Voice Leading Between Common Triads of Scale 1859. Created by Ian Ring ©2019 f#° f#° f#m f#m f#°->f#m F# F# f#m->F#

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Central Verticesf♯m
Peripheral Verticesf♯°, F♯


Modes are the rotational transformation of this scale. Scale 1859 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2977
Scale 2977, Ian Ring Music Theory
3rd mode:
Scale 221
Scale 221, Ian Ring Music Theory
4th mode:
Scale 1079
Scale 1079, Ian Ring Music Theory
5th mode:
Scale 2587
Scale 2587, Ian Ring Music Theory
6th mode:
Scale 3341
Scale 3341, Ian Ring Music Theory


The prime form of this scale is Scale 187

Scale 187Scale 187, Ian Ring Music Theory


The hexatonic modal family [1859, 2977, 221, 1079, 2587, 3341] (Forte: 6-Z10) is the complement of the hexatonic modal family [317, 977, 1103, 2599, 3347, 3721] (Forte: 6-Z39)


The inverse of a scale is a reflection using the root as its axis. The inverse of 1859 is 2141

Scale 2141Scale 2141, Ian Ring Music Theory


Only scales that are chiral will have an enantiomorph. Scale 1859 is chiral, and its enantiomorph is scale 2141

Scale 2141Scale 2141, Ian Ring Music Theory


T0 1859  T0I 2141
T1 3718  T1I 187
T2 3341  T2I 374
T3 2587  T3I 748
T4 1079  T4I 1496
T5 2158  T5I 2992
T6 221  T6I 1889
T7 442  T7I 3778
T8 884  T8I 3461
T9 1768  T9I 2827
T10 3536  T10I 1559
T11 2977  T11I 3118

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 1857Scale 1857, Ian Ring Music Theory
Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
Scale 1863Scale 1863: Pycrian, Ian Ring Music TheoryPycrian
Scale 1867Scale 1867: Solian, Ian Ring Music TheorySolian
Scale 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale
Scale 1891Scale 1891: Thalian, Ian Ring Music TheoryThalian
Scale 1795Scale 1795, Ian Ring Music Theory
Scale 1827Scale 1827: Katygimic, Ian Ring Music TheoryKatygimic
Scale 1923Scale 1923, Ian Ring Music Theory
Scale 1987Scale 1987, Ian Ring Music Theory
Scale 1603Scale 1603, Ian Ring Music Theory
Scale 1731Scale 1731, Ian Ring Music Theory
Scale 1347Scale 1347, Ian Ring Music Theory
Scale 835Scale 835, Ian Ring Music Theory
Scale 2883Scale 2883, Ian Ring Music Theory
Scale 3907Scale 3907, 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.