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Scale 1865: "Thagimic"

Scale 1865: Thagimic, 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
Thagimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,6,8,9,10}
Forte Number6-Z45
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes5
Prime?no
prime: 605
Deep Scaleno
Interval Vector234222
Interval Spectrump2m2n4s3d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5,6}
<3> = {4,6,8}
<4> = {6,7,9,10}
<5> = {9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[6]
ProprietyImproper
Heliotonicno

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}231.5
Minor Triadsd♯m{3,6,10}231.5
Diminished Triads{0,3,6}231.5
d♯°{3,6,9}231.5
f♯°{6,9,0}231.5
{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 1865. Created by Ian Ring ©2019 d#m d#m c°->d#m G# G# c°->G# d#° d#° d#°->d#m f#° f#° d#°->f#° f#°->a° 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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1865 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 745
Scale 745: Kolimic, Ian Ring Music TheoryKolimic
3rd mode:
Scale 605
Scale 605: Dycrimic, Ian Ring Music TheoryDycrimicThis is the prime mode
4th mode:
Scale 1175
Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic
5th mode:
Scale 2635
Scale 2635: Gocrimic, Ian Ring Music TheoryGocrimic
6th mode:
Scale 3365
Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic

Prime

The prime form of this scale is Scale 605

Scale 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic

Complement

The hexatonic modal family [1865, 745, 605, 1175, 2635, 3365] (Forte: 6-Z45) is the complement of the hexatonic modal family [365, 1115, 1675, 1745, 2605, 2885] (Forte: 6-Z23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1865 is 605

Scale 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic

Transformations:

T0 1865  T0I 605
T1 3730  T1I 1210
T2 3365  T2I 2420
T3 2635  T3I 745
T4 1175  T4I 1490
T5 2350  T5I 2980
T6 605  T6I 1865
T7 1210  T7I 3730
T8 2420  T8I 3365
T9 745  T9I 2635
T10 1490  T10I 1175
T11 2980  T11I 2350

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 1867Scale 1867: Solian, Ian Ring Music TheorySolian
Scale 1869Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
Scale 1857Scale 1857, Ian Ring Music Theory
Scale 1861Scale 1861: Phrygimic, Ian Ring Music TheoryPhrygimic
Scale 1873Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
Scale 1881Scale 1881: Katorian, Ian Ring Music TheoryKatorian
Scale 1897Scale 1897: Ionopian, Ian Ring Music TheoryIonopian
Scale 1801Scale 1801, Ian Ring Music Theory
Scale 1833Scale 1833: Ionacrimic, Ian Ring Music TheoryIonacrimic
Scale 1929Scale 1929: Aeolycrimic, Ian Ring Music TheoryAeolycrimic
Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
Scale 1609Scale 1609: Thyritonic, Ian Ring Music TheoryThyritonic
Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns
Scale 1353Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
Scale 841Scale 841: Phrothitonic, Ian Ring Music TheoryPhrothitonic
Scale 2889Scale 2889: Thoptimic, Ian Ring Music TheoryThoptimic
Scale 3913Scale 3913: Bonian, Ian Ring Music TheoryBonian

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.