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Scale 1845: "Lagian"

Scale 1845: Lagian, 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).

Common Names

Zeitler
Lagian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,4,5,8,9,10}
Forte Number7-30
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1437
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 855
Deep Scaleno
Interval Vector343542
Interval Spectrump4m5n3s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9,10}
<6> = {9,10,11}
Spectra Variation1.714
Maximally Evenno
Maximal Area Setno
Interior Area2.549
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 TriadsF{5,9,0}321.29
A♯{10,2,5}142.14
Minor Triadsdm{2,5,9}331.43
fm{5,8,0}331.43
am{9,0,4}231.71
Augmented TriadsC+{0,4,8}241.86
Diminished Triads{2,5,8}231.57
Parsimonious Voice Leading Between Common Triads of Scale 1845. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm am am C+->am dm dm d°->dm d°->fm F F dm->F A# A# dm->A# fm->F F->am

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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 VerticesF
Peripheral VerticesC+, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1845 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1485
Scale 1485: Minor Romani, Ian Ring Music TheoryMinor Romani
3rd mode:
Scale 1395
Scale 1395: Asian (a), Ian Ring Music TheoryAsian (a)
4th mode:
Scale 2745
Scale 2745: Mela Sulini, Ian Ring Music TheoryMela Sulini
5th mode:
Scale 855
Scale 855: Porian, Ian Ring Music TheoryPorianThis is the prime mode
6th mode:
Scale 2475
Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
7th mode:
Scale 3285
Scale 3285: Mela Citrambari, Ian Ring Music TheoryMela Citrambari

Prime

The prime form of this scale is Scale 855

Scale 855Scale 855: Porian, Ian Ring Music TheoryPorian

Complement

The heptatonic modal family [1845, 1485, 1395, 2745, 855, 2475, 3285] (Forte: 7-30) is the complement of the pentatonic modal family [339, 789, 1221, 1329, 2217] (Forte: 5-30)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1845 is 1437

Scale 1437Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1845 is chiral, and its enantiomorph is scale 1437

Scale 1437Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending

Transformations:

T0 1845  T0I 1437
T1 3690  T1I 2874
T2 3285  T2I 1653
T3 2475  T3I 3306
T4 855  T4I 2517
T5 1710  T5I 939
T6 3420  T6I 1878
T7 2745  T7I 3756
T8 1395  T8I 3417
T9 2790  T9I 2739
T10 1485  T10I 1383
T11 2970  T11I 2766

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 1847Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic
Scale 1841Scale 1841: Thogimic, Ian Ring Music TheoryThogimic
Scale 1843Scale 1843: Ionygian, Ian Ring Music TheoryIonygian
Scale 1849Scale 1849: Chromatic Hypodorian Inverse, Ian Ring Music TheoryChromatic Hypodorian Inverse
Scale 1853Scale 1853: Maryllic, Ian Ring Music TheoryMaryllic
Scale 1829Scale 1829: Pathimic, Ian Ring Music TheoryPathimic
Scale 1837Scale 1837: Dalian, Ian Ring Music TheoryDalian
Scale 1813Scale 1813: Katothimic, Ian Ring Music TheoryKatothimic
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1909Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
Scale 1589Scale 1589: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 1717Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
Scale 1333Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic
Scale 821Scale 821: Aeranimic, Ian Ring Music TheoryAeranimic
Scale 2869Scale 2869: Major Augmented, Ian Ring Music TheoryMajor Augmented
Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic

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.