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Scale 1367: "Leading Whole-Tone Inverse"

Scale 1367: Leading Whole-Tone Inverse, 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

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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).

Common Names

Western Modern
Leading Whole-Tone Inverse
Zeitler
Pyptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,6,8,10}
Forte Number7-33
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections5
Modes6
Prime?yes
Deep Scaleno
Interval Vector262623
Interval Spectrump2m6n2s6d2t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9,10}
<6> = {10,11}
Spectra Variation1.429
Maximally Evenno
Maximal Area Setyes
Interior Area2.665
Myhill Propertyno
Balancedno
Ridge Tones[2]
ProprietyProper
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 TriadsF♯{6,10,1}231.4
Minor Triadsc♯m{1,4,8}231.4
Augmented TriadsC+{0,4,8}142
D+{2,6,10}142
Diminished Triadsa♯°{10,1,4}221.2
Parsimonious Voice Leading Between Common Triads of Scale 1367. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m a#° a#° c#m->a#° D+ D+ F# F# D+->F# F#->a#°

view full size

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.

Diameter4
Radius2
Self-Centeredno
Central Verticesa♯°
Peripheral VerticesC+, D+

Modes

Modes are the rotational transformation of this scale. Scale 1367 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2731
Scale 2731: Neapolitan Major, Ian Ring Music TheoryNeapolitan Major
3rd mode:
Scale 3413
Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
4th mode:
Scale 1877
Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
5th mode:
Scale 1493
Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor
6th mode:
Scale 1397
Scale 1397: Major Locrian, Ian Ring Music TheoryMajor Locrian
7th mode:
Scale 1373
Scale 1373: Storian, Ian Ring Music TheoryStorian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [1367, 2731, 3413, 1877, 1493, 1397, 1373] (Forte: 7-33) is the complement of the pentatonic modal family [341, 1109, 1301, 1349, 1361] (Forte: 5-33)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1367 is 3413

Scale 3413Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone

Transformations:

T0 1367  T0I 3413
T1 2734  T1I 2731
T2 1373  T2I 1367
T3 2746  T3I 2734
T4 1397  T4I 1373
T5 2794  T5I 2746
T6 1493  T6I 1397
T7 2986  T7I 2794
T8 1877  T8I 1493
T9 3754  T9I 2986
T10 3413  T10I 1877
T11 2731  T11I 3754

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 1365Scale 1365: Whole Tone, Ian Ring Music TheoryWhole Tone
Scale 1363Scale 1363: Gygimic, Ian Ring Music TheoryGygimic
Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian
Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic
Scale 1351Scale 1351: Aeraptimic, Ian Ring Music TheoryAeraptimic
Scale 1359Scale 1359: Aerygian, Ian Ring Music TheoryAerygian
Scale 1383Scale 1383: Pynian, Ian Ring Music TheoryPynian
Scale 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic
Scale 1303Scale 1303: Epolimic, Ian Ring Music TheoryEpolimic
Scale 1335Scale 1335: Elephant Scale, Ian Ring Music TheoryElephant Scale
Scale 1431Scale 1431: Phragian, Ian Ring Music TheoryPhragian
Scale 1495Scale 1495: Messiaen Mode 6, Ian Ring Music TheoryMessiaen Mode 6
Scale 1111Scale 1111: Sycrimic, Ian Ring Music TheorySycrimic
Scale 1239Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
Scale 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian
Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic
Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian
Scale 2391Scale 2391: Molian, Ian Ring Music TheoryMolian
Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.