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Scale 1429: "Bythimic"

Scale 1429: Bythimic, 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
Bythimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,4,7,8,10}
Forte Number6-34
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1333
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 TriadsC{0,4,7}221
Minor Triadsgm{7,10,2}131.5
Augmented TriadsC+{0,4,8}131.5
Diminished Triads{4,7,10}221
Parsimonious Voice Leading Between Common Triads of Scale 1429. Created by Ian Ring ©2019 C C C+ C+ C->C+ C->e° gm gm e°->gm

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 VerticesC, e°
Peripheral VerticesC+, gm

Modes

Modes are the rotational transformation of this scale. Scale 1429 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1381
Scale 1381: Padimic, Ian Ring Music TheoryPadimic
3rd mode:
Scale 1369
Scale 1369: Boptimic, Ian Ring Music TheoryBoptimic
4th mode:
Scale 683
Scale 683: Stogimic, Ian Ring Music TheoryStogimicThis is the prime mode
5th mode:
Scale 2389
Scale 2389: Eskimo Hexatonic 2, Ian Ring Music TheoryEskimo Hexatonic 2
6th mode:
Scale 1621
Scale 1621: Scriabin's Prometheus, Ian Ring Music TheoryScriabin's Prometheus

Prime

The prime form of this scale is Scale 683

Scale 683Scale 683: Stogimic, Ian Ring Music TheoryStogimic

Complement

The hexatonic modal family [1429, 1381, 1369, 683, 2389, 1621] (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 1429 is 1333

Scale 1333Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic

Enantiomorph

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

Scale 1333Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic

Transformations:

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

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 1431Scale 1431: Phragian, Ian Ring Music TheoryPhragian
Scale 1425Scale 1425: Ryphitonic, Ian Ring Music TheoryRyphitonic
Scale 1427Scale 1427: Lolimic, Ian Ring Music TheoryLolimic
Scale 1433Scale 1433: Dynimic, Ian Ring Music TheoryDynimic
Scale 1437Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending
Scale 1413Scale 1413, Ian Ring Music Theory
Scale 1421Scale 1421: Raga Trimurti, Ian Ring Music TheoryRaga Trimurti
Scale 1445Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari
Scale 1461Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
Scale 1493Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor
Scale 1301Scale 1301: Koditonic, Ian Ring Music TheoryKoditonic
Scale 1365Scale 1365: Whole Tone, Ian Ring Music TheoryWhole Tone
Scale 1173Scale 1173: Dominant Pentatonic, Ian Ring Music TheoryDominant Pentatonic
Scale 1685Scale 1685: Zeracrimic, Ian Ring Music TheoryZeracrimic
Scale 1941Scale 1941: Aeranian, Ian Ring Music TheoryAeranian
Scale 405Scale 405: Raga Bhupeshwari, Ian Ring Music TheoryRaga Bhupeshwari
Scale 917Scale 917: Dygimic, Ian Ring Music TheoryDygimic
Scale 2453Scale 2453: Raga Latika, Ian Ring Music TheoryRaga Latika
Scale 3477Scale 3477: Kyptian, Ian Ring Music TheoryKyptian

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.