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Scale 1673: "Thocritonic"

Scale 1673: Thocritonic, 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
Thocritonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,3,7,9,10}
Forte Number5-25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 557
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes4
Prime?no
prime: 301
Deep Scaleno
Interval Vector123121
Interval Spectrump2mn3s2dt
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,5,6,7}
<3> = {5,6,7,9}
<4> = {8,9,10,11}
Spectra Variation2.8
Maximally Evenno
Maximal Area Setno
Interior Area2.049
Myhill Propertyno
Balancedno
Ridge Tonesnone
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 TriadsD♯{3,7,10}121
Minor Triadscm{0,3,7}210.67
Diminished Triadsa°{9,0,3}121
Parsimonious Voice Leading Between Common Triads of Scale 1673. Created by Ian Ring ©2019 cm cm D# D# cm->D# a° a° cm->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.

Diameter2
Radius1
Self-Centeredno
Central Verticescm
Peripheral VerticesD♯, a°

Modes

Modes are the rotational transformation of this scale. Scale 1673 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 721		Scale 721: Raga Dhavalashri, Ian Ring Music TheoryRaga Dhavalashri
3rd mode:
Scale 301		Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav TukhariThis is the prime mode
4th mode:
Scale 1099		Scale 1099: Dyritonic, Ian Ring Music TheoryDyritonic
5th mode:
Scale 2597		Scale 2597: Raga Rasranjani, Ian Ring Music TheoryRaga Rasranjani

Prime

The prime form of this scale is Scale 301

Scale 301Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav Tukhari

Complement

The pentatonic modal family [1673, 721, 301, 1099, 2597] (Forte: 5-25) is the complement of the heptatonic modal family [733, 1207, 1769, 1867, 2651, 2981, 3373] (Forte: 7-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1673 is 557

Scale 557Scale 557: Raga Abhogi, Ian Ring Music TheoryRaga Abhogi

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1673 is chiral, and its enantiomorph is scale 557

Scale 557Scale 557: Raga Abhogi, Ian Ring Music TheoryRaga Abhogi

Transformations:

T0 1673  T0I 557
T1 3346  T1I 1114
T2 2597  T2I 2228
T3 1099  T3I 361
T4 2198  T4I 722
T5 301  T5I 1444
T6 602  T6I 2888
T7 1204  T7I 1681
T8 2408  T8I 3362
T9 721  T9I 2629
T10 1442  T10I 1163
T11 2884  T11I 2326

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 1675Scale 1675: Raga Salagavarali, Ian Ring Music TheoryRaga Salagavarali
Scale 1677Scale 1677: Raga Manavi, Ian Ring Music TheoryRaga Manavi
Scale 1665Scale 1665, Ian Ring Music Theory
Scale 1669Scale 1669: Raga Matha Kokila, Ian Ring Music TheoryRaga Matha Kokila
Scale 1681Scale 1681: Raga Valaji, Ian Ring Music TheoryRaga Valaji
Scale 1689Scale 1689: Lorimic, Ian Ring Music TheoryLorimic
Scale 1705Scale 1705: Raga Manohari, Ian Ring Music TheoryRaga Manohari
Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns
Scale 1545Scale 1545, Ian Ring Music Theory
Scale 1609Scale 1609: Thyritonic, Ian Ring Music TheoryThyritonic
Scale 1801Scale 1801, Ian Ring Music Theory
Scale 1929Scale 1929: Aeolycrimic, Ian Ring Music TheoryAeolycrimic
Scale 1161Scale 1161: Bi Yu, Ian Ring Music TheoryBi Yu
Scale 1417Scale 1417: Raga Shailaja, Ian Ring Music TheoryRaga Shailaja
Scale 649Scale 649: Byptic, Ian Ring Music TheoryByptic
Scale 2697Scale 2697: Katagitonic, Ian Ring Music TheoryKatagitonic
Scale 3721Scale 3721: Phragimic, Ian Ring Music TheoryPhragimic

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.