The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1807

Scale 1807, 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

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,8,9,10}
Forte Number7-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3613
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes6
Prime?no
prime: 239
Deep Scaleno
Interval Vector543342
Interval Spectrump4m3n3s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7}
<4> = {5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.429
Maximally Evenno
Maximal Area Setno
Interior Area1.933
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsG♯{8,0,3}110.5
Diminished Triads{9,0,3}110.5
Parsimonious Voice Leading Between Common Triads of Scale 1807. Created by Ian Ring ©2019 G# G# G#->a°

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1807 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2951
Scale 2951, Ian Ring Music Theory
3rd mode:
Scale 3523
Scale 3523, Ian Ring Music Theory
4th mode:
Scale 3809
Scale 3809, Ian Ring Music Theory
5th mode:
Scale 247
Scale 247, Ian Ring Music Theory
6th mode:
Scale 2171
Scale 2171, Ian Ring Music Theory
7th mode:
Scale 3133
Scale 3133, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 239

Scale 239Scale 239, Ian Ring Music Theory

Complement

The heptatonic modal family [1807, 2951, 3523, 3809, 247, 2171, 3133] (Forte: 7-5) is the complement of the pentatonic modal family [143, 481, 2119, 3107, 3601] (Forte: 5-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1807 is 3613

Scale 3613Scale 3613, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1807 is chiral, and its enantiomorph is scale 3613

Scale 3613Scale 3613, Ian Ring Music Theory

Transformations:

T0 1807  T0I 3613
T1 3614  T1I 3131
T2 3133  T2I 2167
T3 2171  T3I 239
T4 247  T4I 478
T5 494  T5I 956
T6 988  T6I 1912
T7 1976  T7I 3824
T8 3952  T8I 3553
T9 3809  T9I 3011
T10 3523  T10I 1927
T11 2951  T11I 3854

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 1805Scale 1805, Ian Ring Music Theory
Scale 1803Scale 1803, Ian Ring Music Theory
Scale 1799Scale 1799, Ian Ring Music Theory
Scale 1815Scale 1815: Godian, Ian Ring Music TheoryGodian
Scale 1823Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic
Scale 1839Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic
Scale 1871Scale 1871: Aeolyllic, Ian Ring Music TheoryAeolyllic
Scale 1935Scale 1935: Mycryllic, Ian Ring Music TheoryMycryllic
Scale 1551Scale 1551, Ian Ring Music Theory
Scale 1679Scale 1679: Kydian, Ian Ring Music TheoryKydian
Scale 1295Scale 1295, Ian Ring Music Theory
Scale 783Scale 783, Ian Ring Music Theory
Scale 2831Scale 2831, Ian Ring Music Theory
Scale 3855Scale 3855, 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.