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Scale 1333: "Lyptimic"

Scale 1333: Lyptimic, 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
Lyptimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,4,5,8,10}
Forte Number6-34
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1429
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 683
Deep Scaleno
Interval Vector142422
Interval Spectrump2m4n2s4dt2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {5,6,7}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation1.667
Maximally Evenno
Maximal Area Setno
Interior Area2.482
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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 TriadsA♯{10,2,5}131.5
Minor Triadsfm{5,8,0}221
Augmented TriadsC+{0,4,8}131.5
Diminished Triads{2,5,8}221
Parsimonious Voice Leading Between Common Triads of Scale 1333. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm d°->fm A# A# d°->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
Radius2
Self-Centeredno
Central Verticesd°, fm
Peripheral VerticesC+, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1333 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1357
Scale 1357: Takemitsu Linea Mode 2, Ian Ring Music TheoryTakemitsu Linea Mode 2
3rd mode:
Scale 1363
Scale 1363: Gygimic, Ian Ring Music TheoryGygimic
4th mode:
Scale 2729
Scale 2729: Aeragimic, Ian Ring Music TheoryAeragimic
5th mode:
Scale 853
Scale 853: Epothimic, Ian Ring Music TheoryEpothimic
6th mode:
Scale 1237
Scale 1237: Salimic, Ian Ring Music TheorySalimic

Prime

The prime form of this scale is Scale 683

Scale 683Scale 683: Stogimic, Ian Ring Music TheoryStogimic

Complement

The hexatonic modal family [1333, 1357, 1363, 2729, 853, 1237] (Forte: 6-34) is the complement of the hexatonic modal family [683, 1369, 1381, 1429, 1621, 2389] (Forte: 6-34)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1333 is 1429

Scale 1429Scale 1429: Bythimic, Ian Ring Music TheoryBythimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1333 is chiral, and its enantiomorph is scale 1429

Scale 1429Scale 1429: Bythimic, Ian Ring Music TheoryBythimic

Transformations:

T0 1333  T0I 1429
T1 2666  T1I 2858
T2 1237  T2I 1621
T3 2474  T3I 3242
T4 853  T4I 2389
T5 1706  T5I 683
T6 3412  T6I 1366
T7 2729  T7I 2732
T8 1363  T8I 1369
T9 2726  T9I 2738
T10 1357  T10I 1381
T11 2714  T11I 2762

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 1335Scale 1335: Elephant Scale, Ian Ring Music TheoryElephant Scale
Scale 1329Scale 1329: Epygitonic, Ian Ring Music TheoryEpygitonic
Scale 1331Scale 1331: Raga Vasantabhairavi, Ian Ring Music TheoryRaga Vasantabhairavi
Scale 1337Scale 1337: Epogimic, Ian Ring Music TheoryEpogimic
Scale 1341Scale 1341: Madian, Ian Ring Music TheoryMadian
Scale 1317Scale 1317: Chaio, Ian Ring Music TheoryChaio
Scale 1325Scale 1325: Phradimic, Ian Ring Music TheoryPhradimic
Scale 1301Scale 1301: Koditonic, Ian Ring Music TheoryKoditonic
Scale 1365Scale 1365: Whole Tone, Ian Ring Music TheoryWhole Tone
Scale 1397Scale 1397: Major Locrian, Ian Ring Music TheoryMajor Locrian
Scale 1461Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
Scale 1077Scale 1077, Ian Ring Music Theory
Scale 1205Scale 1205: Raga Siva Kambhoji, Ian Ring Music TheoryRaga Siva Kambhoji
Scale 1589Scale 1589: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri
Scale 1845Scale 1845: Lagian, Ian Ring Music TheoryLagian
Scale 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic
Scale 821Scale 821: Aeranimic, Ian Ring Music TheoryAeranimic
Scale 2357Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana
Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian

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.