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Scale 1161: "Bi Yu"

Scale 1161: Bi Yu, 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

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
Bi Yu
Chord Names
Minor Seventh
Zeitler
Eporic

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

4 (tetratonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,3,7,10}

Forte Number

A code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

4-26

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

[5]

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

no

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

0 (anhemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

0 (ancohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

2

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

3

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 297

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[3, 4, 3, 2]

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<0, 1, 2, 1, 2, 0>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hanson.

p2mn2s

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<1> = {2,3,4}
<2> = {5,7}
<3> = {8,9,10}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

1.5

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

1.866

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

5.56

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

[10]

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Strictly Proper

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}110.5
Minor Triadscm{0,3,7}110.5
Parsimonious Voice Leading Between Common Triads of Scale 1161. Created by Ian Ring ©2019 cm cm D# D# cm->D#

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1161 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 657
Scale 657: Epathic, Ian Ring Music TheoryEpathic
3rd mode:
Scale 297
Scale 297: Mynic, Ian Ring Music TheoryMynicThis is the prime mode
4th mode:
Scale 549
Scale 549: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani

Prime

The prime form of this scale is Scale 297

Scale 297Scale 297: Mynic, Ian Ring Music TheoryMynic

Complement

The tetratonic modal family [1161, 657, 297, 549] (Forte: 4-26) is the complement of the octatonic modal family [1467, 1719, 1773, 1899, 2781, 2907, 2997, 3501] (Forte: 8-26)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1161 is 549

Scale 549Scale 549: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani

Transformations:

T0 1161  T0I 549
T1 2322  T1I 1098
T2 549  T2I 2196
T3 1098  T3I 297
T4 2196  T4I 594
T5 297  T5I 1188
T6 594  T6I 2376
T7 1188  T7I 657
T8 2376  T8I 1314
T9 657  T9I 2628
T10 1314  T10I 1161
T11 2628  T11I 2322

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 1163Scale 1163: Raga Rukmangi, Ian Ring Music TheoryRaga Rukmangi
Scale 1165Scale 1165: Gycritonic, Ian Ring Music TheoryGycritonic
Scale 1153Scale 1153, Ian Ring Music Theory
Scale 1157Scale 1157, Ian Ring Music Theory
Scale 1169Scale 1169: Raga Mahathi, Ian Ring Music TheoryRaga Mahathi
Scale 1177Scale 1177: Garitonic, Ian Ring Music TheoryGaritonic
Scale 1193Scale 1193: Minor Pentatonic, Ian Ring Music TheoryMinor Pentatonic
Scale 1225Scale 1225: Raga Samudhra Priya, Ian Ring Music TheoryRaga Samudhra Priya
Scale 1033Scale 1033, Ian Ring Music Theory
Scale 1097Scale 1097: Aeraphic, Ian Ring Music TheoryAeraphic
Scale 1289Scale 1289, Ian Ring Music Theory
Scale 1417Scale 1417: Raga Shailaja, Ian Ring Music TheoryRaga Shailaja
Scale 1673Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic
Scale 137Scale 137: Ute Tritonic, Ian Ring Music TheoryUte Tritonic
Scale 649Scale 649: Byptic, Ian Ring Music TheoryByptic
Scale 2185Scale 2185: Dygic, Ian Ring Music TheoryDygic
Scale 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. 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.