The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 649: "Byptic"

Scale 649: Byptic, 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
Byptic

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

{0,3,7,9}

Forte Number

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

4-27

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.

none

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.

yes
enantiomorph: 553

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.

3

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: 293

Deep Scale

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

no

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, 1, 1]

Interval Spectrum

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

pmn2st

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> = {5,6,7}
<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.

none

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
Minor Triadscm{0,3,7}110.5
Diminished Triads{9,0,3}110.5
Parsimonious Voice Leading Between Common Triads of Scale 649. Created by Ian Ring ©2019 cm cm 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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 649 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 593
Scale 593: Saric, Ian Ring Music TheorySaric
3rd mode:
Scale 293
Scale 293: Raga Haripriya, Ian Ring Music TheoryRaga HaripriyaThis is the prime mode
4th mode:
Scale 1097
Scale 1097: Aeraphic, Ian Ring Music TheoryAeraphic

Prime

The prime form of this scale is Scale 293

Scale 293Scale 293: Raga Haripriya, Ian Ring Music TheoryRaga Haripriya

Complement

The tetratonic modal family [649, 593, 293, 1097] (Forte: 4-27) is the complement of the octatonic modal family [1463, 1757, 1771, 1883, 2779, 2933, 2989, 3437] (Forte: 8-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 649 is 553

Scale 553Scale 553: Rothic 2, Ian Ring Music TheoryRothic 2

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 649 is chiral, and its enantiomorph is scale 553

Scale 553Scale 553: Rothic 2, Ian Ring Music TheoryRothic 2

Transformations:

T0 649  T0I 553
T1 1298  T1I 1106
T2 2596  T2I 2212
T3 1097  T3I 329
T4 2194  T4I 658
T5 293  T5I 1316
T6 586  T6I 2632
T7 1172  T7I 1169
T8 2344  T8I 2338
T9 593  T9I 581
T10 1186  T10I 1162
T11 2372  T11I 2324

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 651Scale 651: Golitonic, Ian Ring Music TheoryGolitonic
Scale 653Scale 653: Dorian Pentatonic, Ian Ring Music TheoryDorian Pentatonic
Scale 641Scale 641, Ian Ring Music Theory
Scale 645Scale 645, Ian Ring Music Theory
Scale 657Scale 657: Epathic, Ian Ring Music TheoryEpathic
Scale 665Scale 665: Raga Mohanangi, Ian Ring Music TheoryRaga Mohanangi
Scale 681Scale 681: Kyemyonjo, Ian Ring Music TheoryKyemyonjo
Scale 713Scale 713: Thoptitonic, Ian Ring Music TheoryThoptitonic
Scale 521Scale 521, Ian Ring Music Theory
Scale 585Scale 585: Diminished Seventh, Ian Ring Music TheoryDiminished Seventh
Scale 777Scale 777, Ian Ring Music Theory
Scale 905Scale 905: Bylitonic, Ian Ring Music TheoryBylitonic
Scale 137Scale 137: Ute Tritonic, Ian Ring Music TheoryUte Tritonic
Scale 393Scale 393: Lothic, Ian Ring Music TheoryLothic
Scale 1161Scale 1161: Bi Yu, Ian Ring Music TheoryBi Yu
Scale 1673Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic
Scale 2697Scale 2697: Katagitonic, Ian Ring Music TheoryKatagitonic

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.