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Scale 1317: "Chaio"

Scale 1317: Chaio, 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

Chinese
Chaio
Zeitler
Staditonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,2,5,8,10}
Forte Number5-34
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia0 (anhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes4
Prime?no
prime: 597
Deep Scaleno
Interval Vector032221
Interval Spectrump2m2n2s3t
Distribution Spectra<1> = {2,3}
<2> = {4,5,6}
<3> = {6,7,8}
<4> = {9,10}
Spectra Variation1.2
Maximally Evenno
Maximal Area Setyes
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tones[10]
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}121
Minor Triadsfm{5,8,0}121
Diminished Triads{2,5,8}210.67
Parsimonious Voice Leading Between Common Triads of Scale 1317. Created by Ian Ring ©2019 fm 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.

Diameter2
Radius1
Self-Centeredno
Central Vertices
Peripheral Verticesfm, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1317 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1353
Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
3rd mode:
Scale 681
Scale 681: Kyemyonjo, Ian Ring Music TheoryKyemyonjo
4th mode:
Scale 597
Scale 597: Kung, Ian Ring Music TheoryKungThis is the prime mode
5th mode:
Scale 1173
Scale 1173: Dominant Pentatonic, Ian Ring Music TheoryDominant Pentatonic

Prime

The prime form of this scale is Scale 597

Scale 597Scale 597: Kung, Ian Ring Music TheoryKung

Complement

The pentatonic modal family [1317, 1353, 681, 597, 1173] (Forte: 5-34) is the complement of the heptatonic modal family [1371, 1389, 1461, 1707, 1749, 2733, 2901] (Forte: 7-34)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1317 is 1173

Scale 1173Scale 1173: Dominant Pentatonic, Ian Ring Music TheoryDominant Pentatonic

Transformations:

T0 1317  T0I 1173
T1 2634  T1I 2346
T2 1173  T2I 597
T3 2346  T3I 1194
T4 597  T4I 2388
T5 1194  T5I 681
T6 2388  T6I 1362
T7 681  T7I 2724
T8 1362  T8I 1353
T9 2724  T9I 2706
T10 1353  T10I 1317
T11 2706  T11I 2634

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 1319Scale 1319: Phronimic, Ian Ring Music TheoryPhronimic
Scale 1313Scale 1313, Ian Ring Music Theory
Scale 1315Scale 1315: Pyritonic, Ian Ring Music TheoryPyritonic
Scale 1321Scale 1321: Blues Minor, Ian Ring Music TheoryBlues Minor
Scale 1325Scale 1325: Phradimic, Ian Ring Music TheoryPhradimic
Scale 1333Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic
Scale 1285Scale 1285, Ian Ring Music Theory
Scale 1301Scale 1301: Koditonic, Ian Ring Music TheoryKoditonic
Scale 1349Scale 1349: Tholitonic, Ian Ring Music TheoryTholitonic
Scale 1381Scale 1381: Padimic, Ian Ring Music TheoryPadimic
Scale 1445Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari
Scale 1061Scale 1061, Ian Ring Music Theory
Scale 1189Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic
Scale 1573Scale 1573: Raga Guhamanohari, Ian Ring Music TheoryRaga Guhamanohari
Scale 1829Scale 1829: Pathimic, Ian Ring Music TheoryPathimic
Scale 293Scale 293: Raga Haripriya, Ian Ring Music TheoryRaga Haripriya
Scale 805Scale 805: Rothitonic, Ian Ring Music TheoryRothitonic
Scale 2341Scale 2341: Raga Priyadharshini, Ian Ring Music TheoryRaga Priyadharshini
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic

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.